[
    {
        "image_filename": "designv11_11_0003198_s10846-004-7196-9-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003198_s10846-004-7196-9-Figure1-1.png",
        "caption": "Figure 1. A kinematic scheme of the mobile manipulator in the absolute coordinate system and the task to be accomplished.",
        "texts": [
            " Section 4 presents a computer example of solving the inverse kinematics problem for a mobile manipulator consisting of a nonholonomic wheel and a holonomic manipulator of two revolute kinematic pairs, operating in both a constraint-free task space and a task space including obstacles. Finally, some concluding remarks are made in Section 5. Consider a mobile manipulator composed of a nonholonomic platform whose wheels are not taken into account. It is described by the vector of generalized coordinates x \u2208 R l (i.e. platform center location (x1c, x2c) and orientation \u03b8 in an absolute coordinate system in Figure 1), where l 1 and a holonomic manipulator (mounted on the platform) with joint coordinates y \u2208 R n (coordinates y1 and y2 in Figure 1), where n is the number of its kinematic pairs. The platform motion is usually subject to 1 k < l nonholonomic constraints in the so-called Pfaffian form C(x)x\u0307 = 0, (1) where C(x) stands for the k \u00d7 l matrix of the full rank (that is, rank(C(x))= k) depending on x analytically. Suppose that Ker(C(x)) is spanned by vector fields c1(x), . . . , cl\u2212k(x). Then, the kinematic constraint (1) can be equivalently expressed by an analytic driftless dynamic system x\u0307 = N(x)v, (2) where N(x) = [c1(x), . ",
            " , cl\u2212k(x)]; rank(N(x)) = l\u2212k and the control v \u2208 R l\u2212k. The position and orientation of the end-effector with respect to an absolute coordinate system is described by a mobile manipulator kinematic equations p(x, y), where p: R l \u00d7 R n \u2192 R m denotes the m-dimensional (in general, nonlinear with respect to x and y) mapping; pair (x, y) represents the configuration of the mobile manipulator and m stands for the dimension of the task space (coordinates (p1, p2) in the absolute coordinate system in Figure 1 for the case of the end-effector position). A task accomplished by a mobile manipulator consists usually in shifting the end-effector to a desired position and orientation pf \u2208 R m in a finite time T , which may be given either explicitly or implicitly depending on a task specificity. Formally, the mobile manipulator task may be expressed by the following equations p(x, y) \u2212 pf = 0, (3) in which configuration (x, y) is to be determined. It is natural to assume, that at the initial moment t = 0, an initial, known (by assumption) configuration (x0, y0) = (x(0), y(0)) does not satisfy (3), that is, p(x0, y0) \u2212 pf = 0",
            " Hence, computation of \u2202A/\u2202q takes O((n+ l)n) operations. The number of arithmetic operations for computing \u2202B/\u2202q equals O((n + l)2N \u2032). Hence, computation of term F T(\u2202Vc/\u2202q) requires O((n + l)2N \u2032) operations. Finally, computational complexity of controller (40) is on the order of O((n+ l)2N \u2032). This section demonstrates on the three chosen mobile manipulator tasks, the performance of controllers given by Equations (15), (33) and (40). For this purpose, a mobile manipulator, schematically shown in Figure 1, is considered. In all numerical simulations, the SI units are used. The holonomic part (a SCARA type stationary manipulator) with two revolute kinematic pairs (n = 2) operating for simplicity of computations in two-dimensional task space (m = 2), is mounted on a wheel. The wheel is subject to the following nonholonomic constraint (k = 1) sin \u03b8 \u00b7 x\u03071,c \u2212 cos \u03b8 \u00b7 x\u03072,c = 0, (44) where \u03b8 is the angle measured in the task space; x1,c, x2,c mean coordinates of wheel center (l = 3); r = 0.4 denotes the radius of wheel needed in a collision avoidance task",
            "95 is chosen to keep a high holonomic manipulability which is a desirable property by efficient accomplishment of end-point (goal) tasks. Figures 6\u20139 show the results of computer simulations. As is seen from Figure 6, D(y(T )) 0.95 which significantly improves the manipulability measure at pf as compared to the first simulation. Third, the mobile manipulator considered in this section was used to solve the same inverse kinematics problem as in the second experiment, however, by the assumption that there are now two obstacles (circles), schematically presented in Figure 1, in the task space. The total number of collision avoidance constraints, which are assumed herein to be distance functions, equals N = 6. In order to calculate numerically the values of functions cj , each link of the holonomic part has been discretized into 20 points. The same discretization was carried out for the nonholonomic wheel. The threshold values \u03c1 \u2032\u2032 1 and \u03c1 \u2032\u2032 2 taken for computations are equal to \u03c1 \u2032\u2032 1 = 0.5 and \u03c1 \u2032\u2032 2 = 0.4. Gain parameter c\u2032\u2032 takes the following value c\u2032\u2032 = 100. A relatively large value for c\u2032\u2032 (as compared to c\u2032) is chosen to show the effect of straightening the holonomic manipulator links during the movement among obstacles (large c\u2032\u2032 does not permit a deep penetration into safety zones)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003406_j.surfcoat.2006.01.008-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003406_j.surfcoat.2006.01.008-Figure2-1.png",
        "caption": "Fig. 2. Set-up and geometry of (a) single-track and (b) mu",
        "texts": [
            " The experiment was performed with laser beam out of the focus plane, the chosen different substrate/lens distances give a laser spot size ranging from 3 to 6 mm. The energy distribution of the laser is \u201ctop-hat\u201d shape where the energy in the centre of beam is uniform. The injected powder was delivered by a Sulzer\u2013Metco powder feeder through a side injecting nozzle (2 mm in diameter) to the surface of the substrate. The nozzle was inclined 30\u00b0 from the laser beam axis and in front of the beam in the transverse direction (as shown in Fig. 2a). Mild steel with dimension of 300\u00d775\u00d710 mm3 was chosen as the substrate, and stellite 6 was used as the clad powder. PSF, PSI and W grade powders (supplied by Stoody Deloro Stellite, Industry, CA.) with particle size ranging from b44, 44\u201374 to 45\u2013140 \u03bcm respectively were used. A pattern of clad with dimension of 140\u00d710, 140\u00d720, 140\u00d725 and 140\u00d730 mm2 was performed on the substrate with increment of 0.5, 1.0, 1.5 and 2.0 mm respectively. The experiments were performed at different laser powers (1200\u20132000 W), scan rates (800\u20131600 mm/min) and powder mass flow rates (13",
            " In addition to heat build-up, the change in laser beam incident angle with track build-up is another feature of multi-track cladding, which leads to the increase in absorption and powder efficiency [18,19]. This results in the increase of clad area (Ai c) as shown in Fig. 4a. In the first track, the melt pool is normal to the laser beam axis in the transverse direction, the incident angle of laser beam axis with the normal of melt pool in transverse direction is \u03b8=0\u00b0.With increasing number of tracks, the incident angle (\u03b8) increases (as shown in Fig. 2b), therefore, the melt pool size increases, therefore, more powder can be captured. In addition, the clad angle (\u03b1, which is defined as the angle between substrate surface and the tangent of melt pool at the edge as shown in Fig. 2b) decreases with increasing track number until the steady clad height is achieved. The sharper corner works as a powder collector to stop particle flowing and rebounding away from the substrate surface which happens in single-track cladding, therefore, more particles were collected. Since only the powder collected by the melt pool is melted and forms a clad, the powder efficiency increases with the increasing melt pool size and clad angle, i.e., the clad area (Ac) increases in multi-track clad as: Ac \u00bc kcdA c 1 \u00f05\u00de where kc is the ratio of steady clad area in multi-track clad over the first single-track clad"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000910_20.877800-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000910_20.877800-Figure1-1.png",
        "caption": "Fig. 1. Magnetic field contour lines.",
        "texts": [
            " To have the possibility to measure it in practice, we try to correlate it with the temperature of a measurable point or with the mean temperature of the winding. The studied system is a 3 kW squirrel cage induction machine presented in Table I with 24 slots on the stator and 30 slots on Manuscript received October 25, 1999. E. Chauveau and D. Trichet are with E44-University of Nantes, BP 406, 44602 Saint-Nazaire Cedex, France. E. H. Za\u00efm and J. Fouladgar are with GE44-LARGE, BP 406, 44602 SaintNazaire Cedex, France. Publisher Item Identifier S 0018-9464(00)07143-0. the rotor. Fig. 1 shows the radial view of the stator. Windings are formed of 35 pairs of conductors per slot made of 0.8 mm diameter wires. Since a full three-dimensional model leads to a huge calculation time and memory costs, we use a two-dimensional model orthogonal to the shaft and nominally at the center of the machine. This choice is justified also by the measurement of the temperature along the axis of the machine, which is practically constant. 0018\u20139464/00$10.00 \u00a9 2000 IEEE We use the magnetic vector potential formulation of Maxwell\u2019s laws for the electromagnetic problem",
            " Due to the manufacturing process, the position of the conductors in the slots can\u2019t be known precisely. In addition, the distribution of conductors may change from one slot to another. Thus, we consider that the conductors are randomly distributed in the slots and impregnated in an insulating resin. We apply the inverse problem methodology to determine the equivalent homogenous electromagnetic properties to represent the bundle of conductors [4]. To do this, we calculate the properties which minimize the difference between the real field and the homogenized field. As the problem of Fig. 1 has a transverse magnetic configuration (i.e. the current source density is normal to the geometry plane) and due to the existence of the magnetic stator sheets, random distribution of the conductors has little influence on the magnetic field [5]. The electromagnetic problem is then solved with the homogenous slots using the finite element method. Fig. 1 shows the magnetic field with the equivalent homogenous material and equivalent current density. For a machine with an azimuthal periodicity, the solution of the thermal problem can be limited to only one slot as shown in Fig. 2. The boundary conditions in this case are: at the midline of two slots at the contact with free air (3) One can use the real distribution of the conductors to calculate the temperature field in the windings. But in the fabrication stage, the conductors are randomly distributed in the machine slots"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000132_bf02362831-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000132_bf02362831-Figure7-1.png",
        "caption": "Fig. 7a Fig. 7b",
        "texts": [
            " The first- or second-type admissible closed line is determined by a certain rule with regard for the lattice of asymptotic lines on S. This determination is such that every curve of the first type is at the same time a curve of the second type (it is necessary to note that any complete parallel on ,~ refers to curves of the first type). Let us now consider a domain S of a piecewise class C 1 on the surface S, such that in the case of a sphere its boundary 0S has one or two components of the admissible type (see Fig. 7a), any of which is non-homotopic to null on its own zone, but in the case of a torus, the boundary 0S is an admissible one 1014 of the first type and consists of a finite number of components arranged on one zone 5, and any of them is homotopic to null on S (see Fig. 7b). It turns out that the effect of a fixed parallel, determined in the Minagawa-Rado lemma, extends also to the domains S, in this case, any admissible line C' can be fixed instead of the parallel, but C must be non- homotopic to null on its zone (in particular, C may be a component of vo~'); moreover, if C is an admissible one of the second type, then it is sufficient to fix only a definite part of it; if any component of the boundary 05\" is free, it should be an admissible one of the first type"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000710_mech-34246-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000710_mech-34246-Figure2-1.png",
        "caption": "Figure 2a. The Left Six-Bar Linkage.",
        "texts": [
            " The first step in the graphical technique is to replace the ternary ground link 5 by two binary links, denoted as links +5 and *5 as shown in Figure 1b. The resulting nine-bar linkage has two degrees of freedom which means that the velocity of point B (i.e., the path tangent of point B) can be in any direction in the plane of the linkage. Therefore, disconnect links 3 and 7 at pin B and attach a slider, denoted as link +9 , to link 3 at pin 2 loaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/02/2016 Term +B (henceforth referred to as the instant center +39I ), see Figure 2a. Similarly, attach a slider, denoted as link *9 , to link 7 at pin *B (henceforth referred to as the instant center *79I ), see Figure 2b. The direction of the path tangents of links +9 and *9 are initially arbitrary, however, keep in mind that there is a unique direction of the path tangent of point B which will Copyright \u00a9 2002 by ASME s of Use: http://www.asme.org/about-asme/terms-of-use Down satisfy the constraint that links +5 and *5 have the same angular velocity as the original ternary link 5. To simplify the geometric construction we choose the path normal of point +B to be parallel to link 2 (i.e., the path tangent is perpendicular to link 2) and the path normal of point *B to be parallel to link 8 (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002319_tmag.2003.810511-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002319_tmag.2003.810511-Figure5-1.png",
        "caption": "Fig. 5. Distributions of eddy current density vectors. (a) x\u2013y plane (z = 0:24). (b) x\u2013z plane ( \u2013 section).",
        "texts": [
            " It is found that there are large flux density vectors in the stator teeth and in the rotation direction side of rotor core [cf. Fig. 3(a)] and those distributed in the surface of the silicon steel sheet due to the skin effects [cf. Fig. 3(b)]. Fig. 4 shows the flux density waveforms in the elements A and B as shown in Fig. 3(a) . It is found that the flux density waveforms in element A are similar to the sinusoidal waveforms, and those in element B have much more harmonic components, which are caused by the stator teeth. Fig. 5 shows the distributions of eddy current density vectors. It is found that there are large eddy current density vectors in the stator teeth and in the rotor core near the slots between the stator teeth [cf. Fig. 5(a)] and those distributed in the surface of the silicon steel sheet due to the skin effects [cf. Fig. 5(b)]. Fig. 6 shows the contours of eddy current loss. It is found that there is much more eddy current loss in the stator teeth and in the rotation direction side of rotor core. It is found that the eddy current loss in the stator yoke decreases, and that in the stator teeth increases, when the phase difference varies from 20 to 50 . It is also found that the eddy current loss in bridge of the rotor core increases as the phase difference increases. Fig. 7 shows the eddy current loss. It is found that the eddy current loss in the stator core has a minimum value when the phase difference is 35 and that in the rotor core decreases as the phase difference increases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003788_b511995b-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003788_b511995b-Figure3-1.png",
        "caption": "Fig. 3 Preparation of anisotropic filler loaded PDMS gels under uniform magnetic field. (a) Spherical gel beads, (b) cube-shaped gels.",
        "texts": [
            " If the polymerization reaction is performed under uniform external field, then due to the mutual interaction between particles, pearl chain structure develops. The chemical cross-linking locks in the chainlike structure, aligned along the direction of the field. The resulting sample becomes highly anisotropic. The mixture of the silicone prepolymers and magnetite particles, confined either in the spherical or cube-shaped mould was placed between the poles of a large electromagnet (JM\u2013PE\u2013I (JEOL, Japan) as it is seen in Fig. 3. The mixture 978 | Phys. Chem. Chem. Phys., 2006, 8, 977\u2013984 This journal is c the Owner Societies 2006 Pu bl is he d on 0 8 D ec em be r 20 05 . D ow nl oa de d by N or th ea st er n U ni ve rs ity o n 31 /1 0/ 20 14 0 9: 31 :1 7. was subjected to B=400 mT uniform magnetic field for 5 h. It took a few seconds to induce the pearl chain structuring of the filler particles before the reaction is completed. As a result, particles aggregates aligned parallel to the field direction and are built into the network"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003685_s00604-005-0407-7-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003685_s00604-005-0407-7-Figure1-1.png",
        "caption": "Fig. 1. Schematic illustration of the bi-layer bi-enzyme biosensor architecture",
        "texts": [
            " Moreover, it seems to be advantageous to apply a non-manual immobilization procedure at least for the second layer containing AOx aiming at improved reproducibility and the possibility to vary the polymer film thickness in a controlled manner. Thus, a bi-layer bi-enzyme sensor architecture is proposed involving a first layer containing either HRP or RPTP entrapped and crosslinked within an Os complex-modified redox hydrogel and a second layer created by non-manual, electrochemically induced deposition of a cathodic paint simultaneously entrapping AOx (Fig. 1). Hydrogel=Peroxidase Layer In a way similar to that reported previously [26], a redox polymer (PVI10-Os) crosslinked with a bifunctional crosslinker (PEG-DGE) was used to wire either HRP or RPTP to the underlying graphite surface. It is known that the operation properties of crosslinked redox hydrogel=enzyme layers are mainly governed by the redox hydrogel=enzyme ratio and the amount of crosslinker influencing the flexibility of the polymer chains. The polymer=enzyme ratio has to be kept at a sufficiently high value to wire all entrapped enzyme molecules, and the capacity of the network to carry current must equal or exceed the capacity of the entrapped enzyme molecules to deliver electrons"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.37-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.37-1.png",
        "caption": "Figure 3.37 Polar catenaries calculated from equation (3.141) with values of K spanning from \u20142 to 1. Results for an eight spokes configuration (0O = 22.5\u00b0) with very small width at the tip of the spokes {6l\u2014>0o)",
        "texts": [
            " It must be noted that the radius r(9) is normalized using the length R, which depends on the shape of the wire, i.e. on the value of K. It is, however, easy, once the value of K has been chosen, to calculate the value of r/R at the supporting points A or B simply by introducing 6 = 61 into equation (3.151). As the value of the radius R0 at which the points A and B are located is known, the value of R can be easily computed. The shapes corresponding to values of K spanning from \u20142 to 1, for wires supported on a hub with eight spokes with negligible thickness at the tip (0o = 0i =22.5\u00b0) are shown in Figure 3.37. If K = 1 the wire lies on a straight line, the chord connecting points A and B. This solution is, however, of no practical interest, as the stress in the wire goes to infinity when K approaches unity. The series of equation (3.151) cannot be used as its radius of convergence reduces when K\u2014*1. If K = 0 the arc of circumference is found. All values of K between 0 and 1 lead to sub-circular shapes and equation (3.151) holds for all cases of practical interest. If K is negative 'supercircular' shapes are found, and equation (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003800_ip-smt:20050073-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003800_ip-smt:20050073-Figure5-1.png",
        "caption": "Fig. 5 A sensor connected to a meter a The connecting wires are not twisted and create an unintended loop b The connecting wires are twisted in order to minimise the influence of the stray magnetic field",
        "texts": [
            " The value of that voltage is directly proportional to the rate of change of the flux and to the area enclosed. This phenomenon is the basis for many sensors since by measuring the voltage induced in a coil it is possible to derive the flux, flux density or magnetic field (depending on the application and configuration of the sensor). The voltage induced in such a sensor must be conveyed to a meter or other measuring device. Most commonly, the sensor is simply connected by means of conducting wires, as is schematically depicted in Fig. 5. If the connection is made as shown in Fig. 5a, then the unintended loop will pick up some stray magnetic field. Inevitably this contributes to the voltage measured by the metre. The simplest method to avoid this effect is to twist the connecting wires so that the IEE Proc.-Sci. Meas. Technol., Vol. 153, No. 4, July 2006 153 neighbouring loops induce voltages in opposite directions and thus they cancel one another (Fig. 5b). However, as can be seen in Fig. 5b, the neighbouring loops do not necessarily have exactly the same area and thus they might not completely cancel the voltages induced by the stray flux. Moreover, there is a stray field gradient, which may result in different levels penetrating neighbouring loops, hence inducing different voltages, which cannot entirely cancel one another. It is obvious that this effect will be more pronounced for a larger gradient of the magnetic field and larger and/or less uniform loops. Also, the phase of the voltage induced in the tiny loop depends on the direction of the stray field as well as on the positioning of the twisted wires"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003769_1.1859771-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003769_1.1859771-Figure2-1.png",
        "caption": "FIG. 2. Mechanical deformation in linear and nonlinear magnetic materials by using each different method is shown after the test body is enlarged 400 times of its original size. In linear and nonlinear magnetic materials, the physical shape of the mechanical deformation exhibited using the MX, KH, MC, and KV was essentially the same as shown in sad; whereas, using the CM it was different from others as shown in sbd. These four figures were obtained by using J1=2.53106 A/m2 and J2=253106 A/m2 in the KV and CM, respectively. Here, the nonlinear magnetic material ssilicon steel RM50d was employed in these four figures, and units are in the micron scale.",
        "texts": [
            " To calculate the mechanical deformation for small and large current densities, including B-H curve operating points in the linear and saturation regimes, the magnetic system containing a test body was tested, as shown in Fig. 1. The four vertices of the square test body were fixed along their length in the z direction as a mechanical constraint. The magnetic force density was calculated as a mechanical load at each FEM node. The MX, KH, MC, and KV yielded the same mechanical deformation, but the mechanical deformation using CM was different from the others, as shown in Fig. 2. In the nonlinear case, the KH was not used to calculate the mechanical deformation because of its complicated nature. The relative errors of the maximum mechanical deformation values fell within 1.7% in linear and nonlinear magnetic materials when the MX, KH, MC, and KV were used, as shown in Table I, for small and large current densities so that the operating point for maximum magnetic field is on the B-H curve shown in Fig. 1 in the linear sOP1d and highly saturated regimes sOP2d. The distinct five force density methods were compared to one another for incompressible linear and nonlinear mag- netic materials by utilizing the mechanical deformation obtained from FEM. The KV using total field was successfully applied to calculate the mechanical deformation for linear and nonlinear magnetic materials. Taking the given force density methods to be theoretically equivalent in incompressible magnetic materials, the numerical result of mechanical deformation found using the KV also yielded the same result as the KH and MC. From Fig. 2, we have verified that the CM produces an incorrect mechanical deformation when compared to other force density methods. When the current density was high, the magnetic material operated in the saturation region and the deformations were much smaller than when the magnetic material remained in the linear region. According to the numerical results of the mechanical deformation, the MC, KV, and KH are alternative ways of calculating the mechanical deformation in incompressible solid materials. For the future work utilizing the given force density expressions, the behavior of motion for compressible materials and magnetic fluids when subjected to magnetic fields must be evaluated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003163_robot.2003.1241578-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003163_robot.2003.1241578-Figure1-1.png",
        "caption": "Figure 1: Closeup of the salient Scout robot",
        "texts": [
            " Introduction Tasks such as Scout motion prediction and simula- tion require a mathematical formulation of the effects of the motion types on the Scout's pose. The models developed in this paper describe the configuration changes a Scout undergoes over time. The Scout robot (see Figure 1) is equipped with two kinds of actuators: two wheels and a winch. With these, three types of motion can he achieved. Rolling alters the Scout's location in the plane; tilting lets the robot rotate around its own main axis; and jumping opens up movement in three dimensional space. In order to better understand the effects of these three types of motion on the Scout's pose, it is necessary to investigate them in more detail. In the following sections, models for all three motion types are derived"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000184_70.631235-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000184_70.631235-Figure4-1.png",
        "caption": "Fig. 4. A spatial 3R Puma-type manipulator. (a) The manipulator with the singular configuration. (b) The trajectory of the end-effector. (c) Solution paths near the singularity. (d) Profiles of the joint velocities for r = 0.1. (e) Profiles of the joint velocities for different curvatures.",
        "texts": [
            " The 4-D joint space has been projected down to three dimensions by ignoring the first joint angle To further aid visualization of the 3-D figure, the projection of the path onto the plane is also shown. At each time step in the integration, was adjusted so as to have constant length, to satisfy the constraint and to point at a fixed angle away from the singularity. The error in this calculation (movement of the end effector) is less than 10 In this example we study a singularity of codimension 2. The manipulator is a generic three joint arm of Puma type [18]; the first joint rotates in azimuth and the second two joints rotate in elevation, and the workspace is a sphere in three dimensions [Fig. 4(a)]. The configurations in which the arm reaches straight up ( 0) are singular with codimension 2\u2014the range of the Jacobian matrix is 1-D. We consider a semicircular path with radius 0.1 and lying in a plane tipped by angle from horizontal, which passes through the singular point and is tangent there to the boundary of the workspace [Fig. 4(b)]. The speed is constant. To find the initial joint velocity, we begin with and solve for the parameters and in (9c). We find that one of these two quadratic equations is actually linear, so that there are only two initial velocities at the singularity that can be used in Theorem 1. There are two initial velocities for each initial condition since there are actually two initial conditions that cause (9b) to be satisfied, we find all four possible paths in space. Fig. 4(c) shows the portions near the singularities. The joint velocities are smooth as the arm passes through the singularity, and the total error is acceptably small [Fig. 4(d)]. By varying the radius of the circle, we can see how the joint velocities depend on the curvature of the path at the singular value, in accordance with (9c) [Fig. 4(e)]. In this section we discuss the significance and limitations of the three theorems proved in Section II, and then examine their relationship to previous research. Theorem 1 asserts the existence of initial joint rates that are tangent to a solution path, when second-order conditions are satisfied. This can be thought of as a \u201cdesingularization\u201d in two senses. First, the resolved motion rate control algorithm can be desingularized for this solution path, as demonstrated in (11): the matrix has full rank, while the matrix does not"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001700_1.1636193-Figure16-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001700_1.1636193-Figure16-1.png",
        "caption": "Fig. 16 Rolling and sliding down an incline",
        "texts": [
            " When the basketball slides on a surface, the friction force acts to decrease the basketball\u2019s velocity until the velocity of the contact point changes direction. Then, the friction force will change direction, so as to oppose the velocity of the contact point. Eventually, the object may begin to roll. Analytically, this situation is handled by drawing two free body diagrams, one for the case of roll and the other for the case of sliding. Numerically, however, it is sufficient to consider the sliding forces; roll occurs as a limiting case. To demonstrate this, consider Fig. 16. During sliding, the friction force is: F5H mN , vA.0 2mN , vA,0 During roll, the friction force is different. Summing forces in the x and y directions and summing moments ~positive counterclockwise! yields: ma5mg sin~b!2F , N5mg cos~b! Ia52FR , vA5v1Rv where I is the mass moment of inertia of the sphere, v is the velocity of the mass center C, vA is the velocity of the contact point A, a is the acceleration of C, v is the angular velocity and a rom: http://dynamicsystems.asmedigitalcollection.asme"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003479_elan.200403002-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003479_elan.200403002-Figure3-1.png",
        "caption": "Fig. 3. A) CV curves at a PG electrode of 30 mM D. norvegicum cytochrome c3 in 10 mM Tris-HCl buffer at pH 7.6: a) polished PG electrode; b) hydrogenase-modified PG electrode (after treatment for 2 min in 2.5 mM hydrogenase solution). Scan rate: 5 mVs 1. B) Scheme of reactions showing cytochrome c3 as electron shuttle between electrode and hydrogenase. (Reprinted from, K. Draoui et al., J. Electroanal. Chem. 1991, 313, 201, with permission from Elsevier).",
        "texts": [
            " Another immobilization procedure, which does not need premodification of the electrode surface, is based on the direct adsorption of the enzyme. This strategy may be informative for understanding the effect of immobilization on the catalytic efficiency of the enzyme. When working under hydrogen consumption condition, the modified pyrolytic graphite electrode resulting from the adsorption of hydrogenase from D. norvegicum on the carbon material was used initially to study the interaction between the enzyme and its physiological redox partner cytochrome c3 [18]. The catalytic current detected as illustrated in Figure 3, under hydrogen atmosphere condition, has been shown to be dependent upon several factors, especially the ionic strength and pH. By varying the cytochrome c3 concentration, a value of 3 mM has been obtained for theMichaelis-Menten constant. An interesting result was that hydrogenase, even in the adsorbed state, could continue to react productively with its redox partner, thus predicting favorably for future applications. Fig. 2. Cyclic voltammograms at a pyrolytic graphite electrode of 20 mM D. fructosovorans cytochrome c3 in 10 mM Tris chloride buffer pH 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001687_s0165-022x(01)00245-7-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001687_s0165-022x(01)00245-7-Figure1-1.png",
        "caption": "Fig. 1. Schematic of an experimental arrangement for imaging of isotope distribution on a protein microarray with a CCD as a quantum detector. The setup allows washing labeled metabolites without removing the microchip from a holder made of silicon rubber.",
        "texts": [
            " The latter was added in the amount necessary for obtaining equal volumes of fluorophor and dry BSA after solvent evaporation. Autoradiography and CCD detection with these samples were performed as with microarrays containing 14C compounds. The protective glass window was carefully detached from a CCD chip (ICX-055, Sony) without removing it from a B/W board camera. To facilitate this operation the edges of the protective window were cut with a small grinding diamond wheel. To protect the fine wires connecting the chip to pins a layer of epoxy glue was placed on the edge of microchip as shown schematically in Fig. 1. Different thin films [5\u20136 mm thick mica; 8 mm thick Mylar film and a layer of photopolymerizable glue (J91, Edmond Scientific, NJ, US)] were used to mechanically and electrically protect the sensitive CCD surface. In the case of glue protection, calculated amount of the glue (0.1 ml for 5-mm thick protection layer, 4 6 mm2 in size) was evenly spread over the whole sensitive area of the CCD and irradiated with UV. Attenuation of the counting efficiency due to the presence of such a protective layer estimated as described in Ref",
            " A 2 3-mm2 protein microarray was placed face down on a protective layer and gently pressed onto the sensitive surface of a CCD with a small piece of Styrofoam or soft rubber. The whole camera was placed then into a dark box. In another version of the device, the CCD chip was detached from the camera board and placed onto a Peltier cooler which allowed decreasing its operating temperature to 10 C. The CCD was thermally insulated and hermetically sealed into foam plastic to prevent water condensation. As shown schematically in Fig. 1, the microarray is placed at the rear end of a holder made of silicon plastic. Silicon allows firm and even pressure of the microchip against the CCD surface in the \u2018\u2018down\u2019\u2019 position. When turned into the \u2018\u2018up\u2019\u2019 position the holder with the microarray can be pressed into surface of a flow cell. The flow cell is designed as a groove cut in silicon rubber at the position where the protein microarray contacts the surface. The groove is connected to two holes, which allow pumping solutions though the groove"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002614_0301-679x(87)90094-6-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002614_0301-679x(87)90094-6-Figure7-1.png",
        "caption": "Fig 7 Actual con tact area of lip viewed from inside o f shaft",
        "texts": [
            " 1 2 3 4 Outer diameter, mm 108 108 108 108 Nominal diameter, mm 85 85 85 85 Interference, mm 1.3 1.4 1.5 1.5 Total contact load of lip, N 19.6 23.5 24.5 24.5 Test conditions The test conditions for observing asperity contact were: Diameter of hollow glass shaft: 85 mm Surface roughness of the hollow glass shaft: 0.02 #m R a Number of shaft revolutions: 0 - 1 0 r rain -1 in dry condition and 0 -700 r rain -z in lubricating condition Lubricating oil: motor oil (10W-30) Temperature of rubbing surface: 38 \u00b0C Shaft eccentricity: 0.005 ram. Experimental procedure Fig 7 shows the image of the contact surface of the test specimen, magnified 700 times by a microscope and observed through an industrial TV camera. This image is recorded by a VTR (video tape recorder) after projecting on the monitoring TV. The recorded VTR tape is the source of input data for image processing. Data analysis and parameter extraction are processed by the analysing and extracting processing unit with a microcomputer, an image store memory, colouring unit and colour monitor. The results of the analysis are obtained as output from the printer and the video graphic recorder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002730_tmag.1987.1065248-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002730_tmag.1987.1065248-Figure4-1.png",
        "caption": "Figure 4 Deterioration of iron loss in 3% Silicon non-oriented material due to the total",
        "texts": [
            "36T so the effect of the first harmonic in the waveform would be very different in each case. As the magnitude of the harmonic component increases, the fundamental must again be reduced but the loss attributable to the increasing 3rd harmonic has a far larger effect on the total loss. 100 9; OF drd. HARMONIC FLUX. Figure 2 Deterioration of iron loss due to third harmonic flux density in non-oriented steels magnetised at a peak flux density of 1.0~. The deterioration of iron loss due to 3rd harmonic distortion in the 3% silicon iron material is shown in Figure 4. The minor loop limit indicates the conditions under which minor loops would start to become present in the B-H loop of the material under test. This condition would cause some measuring problems so the region was avoided. The rapidly increasing effect of the 3rd harmonic flux is particularly noticeable when it was close to being in phase with the fundamental as would be expected from consideration of Figure 3. The effect of this phase angle on the total loss of a non-oriented sample magnetised at 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000507_027836499501400207-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000507_027836499501400207-Figure10-1.png",
        "caption": "Fig. 10. Acceleration cones for I = 2. (a) ~C = 2. (b) ~C = oc _",
        "texts": [
            " This is implied by the positive mass and squared radius of gyration of the slider. For a slider of unit mass, unit radius of gyration, and a rod angle of 45 degrees, we find the generalized acceleration of the slider center of mass (acx, acy, ce,): The rod endpoint acceleration as = (aSY\u2019 asy) is then Pulling is possible when the rod endpoint acceleration is away from the slider (a,, < 0); i.e., when Substituting p fy for fx and choosing 1 = 2, this condition becomes 3 f\u2019 - 2pJy < 0, which is satisfied for p > 1.5. Figure 10 shows the possible initial acceleration centers (found by the force-dual method of Brost and Mason [1989]) and the acceleration cones for I = 2 and two different values of the coefficient of friction, (a) ,~ = 2 and (b) p, = oc. The pusher and slider are initially at rest. In Figure 10A, pulling is a consistent solution if the pusher acceleration ap is inside the acceleration cone and at The University of Iowa Libraries on June 8, 2015ijr.sagepub.comDownloaded from 179 away from the slider (a.r,~ < 0). (This pulling example is equivalent to a well-known example of frictional ambiguity : a rod touching a nearly vertical wall in a gravity field; see L6tstedt [1981], Erdmann [1984, 1994], Rajan et al. [1987].) In Figure 1OB, slipping contact is the only solution if the pusher acceleration ap is outside the acceleration cone with apy > 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002288_bio.1170040171-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002288_bio.1170040171-Figure1-1.png",
        "caption": "Figure 1. Schematic representation of the luminescence fibre-optic biosensor. (a) septum; (b) needle guide; (c) thermostated reaction vessel; (d) fibre bundle; (e) enzymatic membrane; (f) screwed cap; (9) stirring bar; (h) reaction medium; (i) light-proof PVC jacket; (j) O-ring. Reproduced from Blum eta/ . (1988) p. 721. by courtesy of Marcel Dekker, Inc.",
        "texts": [],
        "surrounding_texts": [
            "546 L. J. BLUM, S. M. GAUTIER AND P. R. COULET\nmmol/l dithiothreitol was added in the reaction medium, a steady-state luminescent signal was obtained within 2min instead of the 8min necessary when the sulphydryl protective reagent was omitted. At 1 x lo-' mol/l NADH, the precision was 5%. 70% of the initial activity of these strips was retained after two weeks storage at 4\u00b0C in phosphate buffer, whereas a complete loss of activity was observed with the same enzymes in solution.\nLuminol chemiluminescence. Horseradish peroxidase (HRP) could also be immobilized on to preactivated polyamide membranes (Blum et af., 1987) prepared as previously described for the bioluminescent systems and used in a cuvette containing a final volume of 1 mi, stirred and thermostated (30\u00b0C). H202 could be detected in the range 1 x mol/l in the presence of 1 x mol/l luminol, by measuring the maximum intensity of the emitted light.\nThe possibility of coupling the peroxidasemediated luminol chemiluminescence reaction with H202-generating enzymes has been investigated. As an example of a metabolite luminescent assay, the determination of free cholesterol has been performed by adding soluble cholesterol oxidase (COD) which generates H202 according to the following reactions:\ncholesterol + o2 - cholest-4-en-3-one + H202\nmoVl to 1 x\n('OD\n(1)\nI I K P\n2 H202 + luminol + OH- __j (2) 3-aminophthalate + Nz + 3 H 2 0 + hv\nIn this case, a compromise between the optimum conditions for the expression of activity of both enzymes had to be found: for instance the pH of assays was fixed at 8.0 allowing both a sufficient light intensity and a low background luminescence. When using the maximum light intensity measurement as mode of detection, a linear calibration from 1 x lo-' mol/l to 2.5 x mol/ 1 with a response-time depending on the measured concentration was obtained whereas with the chemiluminescent signal integrated for 150 s, linearit was in the range 2.5 X 10-'mol/l to 2.5 x 10 mol/l. Free cholesterol in serum was assayed with this technique and a variation coefficient of 8% was then obtained. The operational stability was found fairly good since the -r\npolyamide-bound peroxidase still exhibited 65% of its initial activity after eight days and 50% after twenty days, the strips being stored overnight at 4 \"C between daily sets of assays.\nLuminescence biosensors\nA new approach in designing biosensors was proposed by Freeman and Seitz (1978) who immobilized peroxidase in a polyacrylamide gel and placed the enzyme phase at the end of a fibre-optic. With such a system, a concentration of 1 x 10-hmol/l peroxide could be measured with the enzymatically catalysed luminolhydrogen peroxide reaction. The related light emission was transmitted through the fibre-optic to a photomultiplier tube.\nThe design of a biophotodiode has been reported by Aizawa ef al. (1984) for the photovoltaic determination of hydrogen peroxide and glucose. A silicon photodiode was selected as a transducer associated to horseradish peroxidase entrapped in a polyacrylamide gel. The photocurrent was linearly related to hydro en eroxide\nmoI/I using Iuminol as luminescent reagent. The extension to glucose assay from 0.1 to 1.5 mol/l was also described with glucose oxidase co-immobilized with peroxidase.\nIn our group, we have recently developed a novel fibre-optic biosensor based on bioluminescence reactions for NADH or ATP and chemiluminescence for hydrogen peroxide (Blum ef al., 1988; Gautier et al. 1989a in press). Briefly, a bioactive membrane was maintained in close contact with one end of a glass fibre bundle by a screw-cap (Fig. l) , the other end being adequately connected to the photomultiplier window of a Berthold LB 9500 luminometer. The system was light tight and samples were introduced by a syringe through a septum into a stirred and thermostated vessel where the bioactive tip of the sensor was immersed.\nconcentration in the range 1 X lo-- F P mol/l to 1 x\nATP measurements. With the luciferase from Photinus pyralis immobilized on pre-activated Pall Immunodyne nylon membranes, ATP measurements could be performed over a quite large linear dynamic range, i.e. 2.8 x 10-lOmol/l to 1.6 X 10-6mol/l (Fig. 2(a)). ATP concentration strongly influences the time required for reaching a steady state which varies from 1 min at 2.8 x 1O-\"'mo\\/I to 6-7min at 3 x IO-'mol/I",
            "DESIGN OF LUMINESCENCE PHOTOBIOSENSORS 547\nafter which the light emission remains stable for several minutes.\nHydrogen peroxide measurements. The fibreoptic sensor was also used with the peroxidaseluminol reaction for H202 measurements in the range 2 X 10-8mol/l to 2 x 10-smol/l (Fig. 2(b)) but in this case if the maximum light intensity was obtained within 1 min, the signal was stable for only 20 to 30s and then decreased. The observed transition phase mainly depends here also on reagent concentration: hydrogen peroxide and luminol. For H z 0 2 concentrations higher or equal to 1 x 10-smol/l, the light intensity reaches a steady state whatever the luminol concentration. When the hydrogen peroxide concentration was lower than 1 x 10-6mol/l, the light intensity decreases after reaching a maximum value, and the lower the luminol concentration, the faster the light decrease. Similarly, with a fixed luminol concentration, the lower the H202 concentration, the faster the light decrease.\nNADH measurements. The luciferase and oxidoreductase luminescent system from V. fischeri was also co-immobilized on such membranes. The detection limit of the biosensor for NADH was as low as 3 x 1O-\"'rnoUI for a signahoise ratio of 2 and the calibration range was linear from 1 x 10-9mol/l to 3 x 10-6mol/l (Fig. 2(c)). The light emission is stable for several minutes and the time necessary to reach the plateau depends on NADH concentration and varies from 1 to 3 min. In addition, the shape of the bioluminescent signal depends on the relative activity of the two enzymes and we found that a longer steady light emission could be obtained by decreasing the oxidoreductase activity.",
            "548 L. J. BLUM, S. M. GAUTIER AND P. R. COULET\nWith the system presented here, cumulative or discrete assays could be performed with a relative standard deviation of 4.8% and 5.5% respectively at 4 X lo-' mol/l NADH. A recalibration must be carried out every ten assays when a better precision is required.\nOperational and storage stabilities. Both are important factors which primarily depend on the intrinsic properties of the enzyme itself when considering practical applications of biosensors. Furthermore, the fact that a two-enzyme system is required here made this goal even more difficult. In order to improve the performances of our biosensor, we first focused on the respective role of the luciferase and of the oxidoreductase on the stability. It appeared that when the two enzymes were stored in a dry state at 4\"C, only the luciferase was unstable. As an unexpected result, a three-fold increase in activity of the bacterial bienzymatic system was observed when stored at -20\u00b0C in the presence of 20% glycerol. This high level of activity was found constant for at least four months of storage.\nExtension to other anaiytes. The use of coupled reactions for determining various analytes with NADH-dependent enzymes has been investigated (Gautier et al . , 1989b). The microdetermination of D-sorbitol, ethanol and oxaloacetate has been successfully performed by coimmobilizing with the bacterial bioluminescent system on preactivated nylon membranes, sorbito1 dehydrogenase (SDH), alcohol dehydrogenase (ADH) and malate dehydrogenase (MDH) respectively. The auxiliary enzymatic reactions involved were the following:\nAD11\nethanol + NAD+ d acetaldehyde (3)\nu-sorbitol + NAD+ D-fructose (4) + NADH + H+\noxaloacetate + NADH + H+- L-malate (5) + NAD+\n+ NADH + H+ SDH\nMDH\nFor each analyte, the optimum conditions of assay with regard to substrate concentrations and pH were determined. Assays of ethanol and sorbitol were performed in a one-step procedure by injecting samples into a medium containing the appropriate compounds. Ethanol measurements\ncould be performed with a good precision (CV% = 5.4 for ten replicate assays at 5.7 x IOPmoI/I) in the linear range 4 X 10-7mol/l to 7 x lO-'mol/l with 5.5 mmol/l NAD+ at pH 7.5. For sorbitol, assays were performed with 1 mmolf NAD+ at pH 7.3. In these conditions, a linear calibration curve was obtained from 2 x lo-' mol/l to 2 X 10~srnol/l. The coefficient of variation was equal to 6% at 4.4 x lO-'mol/l (ten replicates). With ethanol, the steady state response-time varied from 1 min at 4 x lO-'mol/l to 8min at 7 x 10-'mol/l whereas it was about 7 min with sorbitol whatever the concentration measured. However, for ethanol and sorbitol, the rate of increase of light intensity could also be related to the analyte concentration with the same linear range. Then, the measurement could be done within 1 min. For oxaloacetate assays, two steps were necessary. First, NADH was injected and after the luminescent signal reached a steady state, the sample was introduced in the reaction medium. This resulted in a light decrease and either the absolute variation of light intensity or the rate of light decrease (ANAt) could be related to the oxaloacetate concentration. By the determination of ANAt, a linear calibration curve was obtained in the range 3 x 10-9mol/l to 2 x 10-\"mol/l. The detection limit was 1.4 X lop9 mol/l and the coefficient of variation was 5.1% for ten replicates at 5.5 ~ l O - ~ m o l / l .\nDISCUSSION-CONCLUSION\nThe field of biosensors is expanding rapidly with a constant search for new transducing systems associated to stable biosensing elements. The ultrasensitivity of bio- or chemiluminescence techniques together with the convenience of matrix-bound compounds constitute an attractive opportunity for designing novel analytical devices but so far, very few systems based on these principles have been reported in the literature.\nThe preparation of the bioactive support is important and we chose a pre-activated polyamide membrane because of its convenience for fast and reliable enzyme coupling. Compared to photometric or fluorimetric based fibre-optic sensors requiring a light source and monochromators, this novel type of biosensor requires a simpler signal processing system.\nUp to now, some reagents have to be supplied for each set of measurements but a luminescent"
        ]
    },
    {
        "image_filename": "designv11_11_0001516_iros.1997.649040-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001516_iros.1997.649040-Figure8-1.png",
        "caption": "Figure 8: The tension of link 2 When the manipulator swings with Bz=O and the swing amplitude is B i n , the motion of the manipulator",
        "texts": [
            " First, we choose the reference of joint 1 as the following equation: n c T, 12 T, 4 Btd = -sin(2z-) ( 0 5 E - ) After controlling joint 1 to obey the above equation until time T. /4, joint 1 is oscillated with small amplitude, hence it is expected that joint 2 will also oscillate with small amplitude. Therefore after time T,/4, it is easy to switch from the control of joint 1 to that of joint 2. The results of switching the control of the joints is shown in Figure 6, and the phase portrait for joint 1 is shown in Figure 7. Figure 8 shows the tension of link 2 in th is motion. Since we choose the amplitude of the reference of joint 1 to be small, the tension does not become negative. Figures 6, 7 and 8 show that an arbitrary swing motion is generated. Q.4r jc- switching -0.4L Figure 6: Switching control 4.4 Transition from one elliptic orbit to the other Before throwing the gripper, we can consider many ways of throwing the gripper corresponding to more target points if we can generate various amplitudes of the swing motion of the manipulator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003734_j.bioeng.2006.04.001-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003734_j.bioeng.2006.04.001-Figure10-1.png",
        "caption": "Fig. 10. Measuring setup. 1: Buffer reservoir; 2: HPLC pump; 3: injector; 4: thin-layer enzyme reactor; 5: sample in; 6: amperometric cell; 7: amperometric detector; 8: recorder. \u2018\u2018Reprinted from Adanyi and Varadi, 2004a, with permission from Springer-Verlaq\u2019\u2019.",
        "texts": [
            " There are some articles that describe the use of bioreactors for immobilizing enzymes and how to connect them into a flow injection analyzer (FIA) system with an amperometric detector. The following paragraphs related some articles that describe the use of enzyme reactors. Adanyi and Varadi (2004a) immobilized the catalase enzyme by glutaraldehyde on a natural protein membrane (pig\u2019s small intestine) in a thin-layer enzyme cell, connected to a stopped-flow injection analyser system (SFIA) with an amperometric detector (see Fig. 10), for the hydrogen peroxide determination in acetonitrile. They also developed a quick analytical method to monitor the water content (activator) in various butter and margarine samples by maintaining a fixed substrate concentration. The water content of samples obtained by this method was compared with that obtained by the gravimetric reference method and the correlation coefficient was 0.993 (Adanyi and Varadi, 2004a). With the aim to develop a flow-through measuring apparatus for glucose determination as model system in organic media, GOx was immobilized by Adanyi et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002157_s0734-743x(01)00153-1-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002157_s0734-743x(01)00153-1-Figure2-1.png",
        "caption": "Fig. 2. Geometry of the solid eroding-rod problem.",
        "texts": [
            " Upon assuming certain reasonable velocity fields in the tip of the rod and in the target crater, they proceed to solve the momentum equation in glorious detail, directly in the inertial XYZ laboratory frame of reference, to include noninertial effects. The analysis presented here is not intended to supplant the esteemed work of Walker and Anderson. Rather, it is intended to show that the concepts derived herein may be very simply applied to the same problem to a similar end. Furthermore, the manner in which an accelerating coordinate system, attached to the rod/target interface, affects the overall result should be apparent in a more direct way. In the eroding-rod problem (see Fig. 2), a solid rod, of density rR; instantaneous length L; and velocity V ; penetrates into a semi-infinite block of density rT: The rod is assumed to support a uniaxial-stress state in the longitudinal direction of the rod. The eroding interface is traveling into the target at velocity U : Furthermore, employing the assumed velocity profiles suggested by Walker and Anderson, there is a small plastically deforming region located at the eroding tip of the rod, of length s; where the velocity linearly transitions from the rigid-body rod velocity of V to the interface velocity of U : On the target side of the interface, the crater geometry (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000363_s0168-874x(99)00042-6-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000363_s0168-874x(99)00042-6-Figure10-1.png",
        "caption": "Fig. 10. Percentage increase in radial de#ection with an embedded load sensor.",
        "texts": [
            " 7, which shows that increasing the size of the module decreases the sti!ness of the bearing structure. For a module of a given size, Fig. 9 gives the relationship between q .!9 and the load sensor output, and Eq. (7) gives q .!9 as a function of the radial load F 3 . Thus, the radial load on the bearing can be determined by the output of the embedded load sensor. In addition to providing a direct measure of the dynamic load applied to the bearing, the embedded load sensor module provides structural support to the outer ring. As shown in Fig. 10, the sti!ness of the load sensor has greatly reduced the magnitude of the outer ring de#ections. For a bearing without any structural support to the modi\"ed ring, the largest slot analyzed caused the ring de#ections to increase by approximately 300%, as shown in Fig. 7. However, when an embedded load sensor was included in the analysis, the ring de#ections were drastically reduced by an order of magnitude to only 30% for the same size slot. Furthermore, Fig. 10 shows that a relatively small reduction in the size of the sensor module will signi\"cantly reduce the ring de#ections. The e!ect of various slot sizes on the ring de#ection, with and without an integrated sensor module, is further illustrated in Table 1. For comparison purpose, the width of both slots was assumed to be 34 mm. It can be seen that for the two representative slot sizes, substantial di!erence exists in outer ring de#ection (Q $ ) between the cases of with and without sensor module integration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002629_pime_proc_1987_201_156_02-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002629_pime_proc_1987_201_156_02-Figure2-1.png",
        "caption": "Fig. 2 The belt path round its pulley: (a) a general view and (b) entry region detail",
        "texts": [
            " In Proc Instn Mech Engrs Vol201 No D1 at WEST VIRGINA UNIV on July 21, 2015pid.sagepub.comDownloaded from 44 T H C CHILDS AND D COWBURN the next section, before presenting the experimental results of the present study, a simplified analysis of entry and exit is presented in which the natural dimensionless variables emerge as AT/(FR), (gEZ/R4)\"2 (where g is the radial compliance for y = 180\"), {g/(EZ)}'/2F and p. As torque loss varies little with torque transmission, the simplest case of zero torque transmission will be considered here, for which F, = F,. Figure 2a shows a belt in a pulley groove. It enters the groove at A and exits at B, both at the pitch circle radius R from the pulley centre 0. Between A and B there are angular extents (bA and 4B in which the belt sinks into and rises out of the groove, the radial displacement u varying with 4 to a maximum value, u F , given by equation (8) with p, = p. It is convenient to introduce the dimensionless displacement U = ufR: where g18,, denotes g for y = 180\". U 1 A and UlB, the angles between the pulley radius and belt normal at A and B, are given by dU/d4 at A and B. The torque on the pulley caused by the tensions F A and FB, shears Q A and QB and bending moments MA and MB, equal to the torque loss A T when F A = F B = F, is, after expanding sin U , as U , and cos U , as 1 - u:/2, L +MA-MB (1 1) The torque loss for power transmission between two equal pulleys is twice this. Values for Q, M and U , at A and B are obtained by consideration of the belt path at entry and exit. Figure 2b shows the entry region. The belt element subtending d$ at 0 has a radius p > R and subtends d$ at 0'. For small inclinations, U , of the belt in the groove and for u < R geometry determines that (12) p d$ N R d 4 and R p \" - 1 + u, where U 2 is d2U/d+2. Force equilibrium normal to the belt, assuming that the sliding between the belt and groove is radial and U , is small and using equation (12), gives - F - 2pH(tan p + p) - dQld4 = 0 P R where p , as in Fig. 1, is the belt contact pressure on the pulley groove"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003900_bfb0042539-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003900_bfb0042539-Figure2-1.png",
        "caption": "Figure 2",
        "texts": [],
        "surrounding_texts": [
            "The world fixed frame numbered - 1 can be defined arbitrary by the user, so frame 0 will be defined with respect to frame -1 by six parameters. Using Eq.4 the matrix -IT 0 can be def'med by the parameters: (Tz, bz, tZz, dz, 0z, rz). Since tg 1 = 0, d 1 = 0, the eompound transformation -1T 1 can be given as: -IT 1 = -1T 0 0 T I = Rot(z,Tz)Trans(z,bz)Rot(x,az)Trans(x,dz)Rot(z,0z)Trans(z,rz) Rot (z,01) Trans (z , r l ) which gives: \"IT 0 0T 1 = Rot(z,Tz)Trans(z,bz) Rot(x,~l , )Tran(x,dl , )Rot (z,el.) Trans(z\u00a2l , ) with: o~ 1, = o. z, d 1, = d z ,01, = 01 + 0 z, and r r = rl + rz (6) From Eq.6 we conclude that this change of variables on frame 1 parameters, will enable us to represent the fixed frame as we have done for the link frames. Such that: a0 = 0, do= 0, 00 = ~'z, r0-- bz (7) As a conclusion the calculation of \"lTn+ 1 will need 4(n+2)-2 independent parameters. 3-The identification model 3-1Position of the problem The tool frame location X can be calculated by the direct (forward) geometric model given as: X = \"lTn+ 1 = \"IT 0 0T 1 1'1\"2... n ' lT n nTn+ 1 (8) Owing to the errors on the geometric parameters, there will be a difference between the real location of the terminal frame and its location as calculated using the direct geometric model. The calibration problem is to adjust the geometric parameters such that this difference will be minimum. Xreal - Xmodel = minimum (9) As Xmodel is nonlinear function of the geometric parameters, this is a nonlinear problem. Assuming errors of first order, a linear differential model can be used [7,8,9]. If the errors cannot be considered as first order an iterative procedure based on the differential model also can be investigated using Newton-Gauss procedure. The differential vectors defining the deviation of the tool frame from the nominal value due to the differential error in the geometric parameters can be given by: I Dn+l I - - JBn+IAB 8n+l (lO) where: -Dn+I is the (3xl) translational differential vector of the tool frame, -Sn+l is the (3xl) rotational differential vector of the tool frame, - AB defines the error in the geometric parameters, - JBn+l is the extended jacobian matrix. 3-2- Definition of An From section 2, the calculation of -1Tn+ 1 will need 4(n+2)--2 independent parameters. So the elements of AB are the differential variation of the corresponding parameters, but we note that the representation of equation (4) on which this modeling is based, is singular when the z axes of two successive frames are parallel. Therefore ff zj.l is parallel to zj an additional differential parameter AI3 j must be taken into account [9,10,11], this additional parameter will represent a rotation around the axis Yi-1. On the other hand we remark that the change on rj will not be calculated because it is in ihe same direction of r j- i , thus the maximum number-of errors for each frame will remain equal to 4. On a case by case basis the errors of some other parameters may not be included in All see section 3-4 of this paper."
        ]
    },
    {
        "image_filename": "designv11_11_0003893_2006-01-3607-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003893_2006-01-3607-Figure1-1.png",
        "caption": "Figure 1. The tire coordinate system, definition of terms",
        "texts": [
            " Applications range from tire ride modeling, envelopment of road surface irregularities, tread shape analysis, rolling resistance calculations, tire dynamics, tire force & moment prediction and beyond. All tire models have their own strengths and weaknesses, and applications to which they are well-suited. The Radt/Milliken Nondimensional Tire Model is a semiempirical tire model used to predict net tire forces and moments. By semi-empirical, we mean that the model combines known operating conditions with assumptions about tire behavior to predict tire force and moment outputs [1]. This paper follows SAE naming and axis system conventions as defined in [2]. Figure 1, repeated from [2], defines the tire axis system and many of the terms used throughout this paper. Traditional inputs to the Nondimensional Model are: \u03b1 Slip Angle (deg, rad) \u03b3 Inclination Angle (deg, rad) \u03c3 Slip Ratio (unitless) zF Normal Load (lb, N) \u03bcS Surface Friction Coefficient (unitless) 2006-01-3607 Inflation Pressure Effects in the Nondimensional Tire Model Edward M. Kasprzak and Kemper E. Lewis University at Buffalo Douglas L. Milliken Milliken Research Associates, Inc. Copyright \u00a9 2006 SAE International Force and moment outputs are: yF Lateral Force (lb, N) xF Longitudinal Force (lb, N) zM Aligning Torque (lb-ft, N-m) xM Overturning Moment (lb-ft, N-m) The Nondimensional Tire Model takes a unique approach to modeling tire data"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000187_20.717713-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000187_20.717713-Figure8-1.png",
        "caption": "Fig. 8. B,H, and B,H, loops in point p",
        "texts": [
            " The material history has to be stored per axis and per triangle in the FE mesh, resulting in a large database. Equipotential lines at the same time point as in the nonhysteretic case are shown in Fig. 6. In the vicinity of point p , the intersection angle differs distinctly from go\u201d , indicating that B and I? are not parallel. In Fig. 7 the B-locus in point p (see Fig. 6), computed with either VP or SP formulation, and with either nonhysteretic and hysteretic material, is shown. The corresponding hysteresis loops are depicted in Fig. 8. The hysteresis losses (per m along the z-axis) have been calculated using two FE meshes, with 400 and 600 nodes respectively. The results are given in Table I. In this paper we have outlined a FE method for the evaluation of local field patterns in a 2D region applying two complementary formulations, viz the reduced scalar potential and the vector potential. In both formulations the vector Preisach model is introduced via the differential permeability tensor. The two formulations have been applied to a T-joint region problem with rotating flux excitation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000125_ma00128a059-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000125_ma00128a059-Figure2-1.png",
        "caption": "Figure 2. Relation between the director angles ($*, e*) and the Cartesian coordinate system of the shear flow geometry. Flow direction: x ; velocity gradient direction: y ; vorticity direction: z. When e* = 0 (e* # 01, the orientation is planar (nonplanar).",
        "texts": [
            " To compute the light transmission, a standard method for uniaxial crystals has been sed.^^>^^ The sample is discretized into a series of different homogeneous thin orientation layers normal to the light propagation direction (y-axis), with a thickness comparable to one wavelength of a given monochromatic light. For each homogeneous orientation layer, the amplitudes and orientations of the ordinary and extraordinary light vibration vector for a given three-dimensional orientation, as well as the phase lag between the ordinary and extraordinary light rays, are computed. Figure 2 shows the relation between the director orientation angles and the Cartesian coordinate system of the shear flow geometry used for the computation of the light transmission. The relations between the director components and the spherical angles are given by: n, = cos #* cos 8*, n, = sin 4*, n, = cos I$* sin 8\" (12) Here, the x-axis and z-axis are parallel to the polarizer and analyzer, respectively. In the light transmission simulation, we assume normal incidence and nonabsorbing rectilinear light propagation through a uniaxial nematic polymer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002350_taes.2003.1238732-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002350_taes.2003.1238732-Figure1-1.png",
        "caption": "Fig. 1. Collision geometry.",
        "texts": [
            " In Section V we present a game theoretic approach to guidance and demonstrate the superiority of canards. We consider a conflict between two players. The players dynamics is governed by the linear differential equations _x= A(t)x+B(t)u+C(t)v (1) u U, v V (2) where x is the state vector, A,B,C,D are the system matrices, and u and v are the two players controls. With dynamics (1) and constraints (2) we associate the terminal cost (like miss distance) J = Mx(T) (3) where T is a prescribed final time and M is a matrix defining J . To be more specific, consider a collision geometry as in Fig. 1 in which a missile and a target move each with a different constant speed towards a collision point. In this figure, \u00be is the line-of-sight (LOS) orientation in some inertial reference frame, \u00b0M is the missile path direction, and \u00c1M is the look angle. By geometry, this motion satisfies _\u00be = 0. Next consider a small deviation from collision course normal to the LOS. Let x1 be the deviation of the missile normal to the LOS. Then, x1(T) is the miss distance. By construction, _x1 = x2 _x2 = v u where u and v are the actual accelerations of the missile and the target, respectively, normal to the LOS",
            " Let the missile dynamics from command to actual acceleration (normal to LOS) have a realization A\u0302, b\u0302, c\u0302, d\u0302 with z as the state. That is, _z = A\u0302z+ b\u0302uc u= c\u0302z+ d\u0302uc where uc is the missile acceleration command. The augmented state equations now become _x1 = x2 (4a) _x2 = c\u0302z d\u0302uc+ v (4b) _z = A\u0302z+ b\u0302uc: (4c) Comparing (4) and (1), we observe that the augmented system matrices A,b,c appeared in (1) are A= 0 1 0 0 0 c\u0302 0 0 A\u0302 b = 0 d\u0302 b\u0302 c = 0 1 0 M = [1 0 : : : 0]: (5) For a small deviation from collision course, the state vector x is related to the angular variable of the collision triangle (Fig. 1) via _\u00be = d dt x1 Vc(T t) = 1 Vc\u00b5 2 (x1 + \u00b5x2) (6) where \u00b5 = (T t) is time-to-go and the closing speed Vc = _R where R is the range. As we will show in the sequel, optimal strategies can be found for a general missile dynamics. However, since the control loop (autopilot) stabilizes the missile with relatively small time constant, we approximate the missile by first-order dynamics. In this way we are able to sharpen the difference between nose control (minimum phase) and tail control (nonminimum phase)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001707_s0094-114x(03)00091-0-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001707_s0094-114x(03)00091-0-Figure1-1.png",
        "caption": "Fig. 1. The geared seven-bar mechanism.",
        "texts": [
            " The authors believe that this technique is an important and original contribution to the kinematics literature and can be extended to include all indeterminate mechanisms. They also believe it is the most direct technique requiring few geometric constructions. Section 4 presents the method of kinematic coefficients that will be used to check the graphical method. Section 5 presents a numerical example to illustrate the graphical technique and to compare the results with the analytical method. Finally, Section 6 presents some conclusions and suggestions for future research. A schematic drawing of the geared seven-bar mechanism is shown in Fig. 1. The ground is denoted as link 1 and the two gears, in rolling contact, are denoted as links 2 and 3. Link 2, pinned to the ground at O2, is regarded as the input link, and link 7, pinned to the ground at O7, is regarded as the output link. The revolute joints connecting the moving links are denoted as A, B, C, D, and E. Links 4, 5, and 7 are binary links and link 6 is a ternary link, henceforth referred to as the coupler link. For purposes of generality, pin A is not coincident with ground pin O2, pin B is not coincident with ground pin O3, and pins C, D, and E on the coupler link are separated by finite distances"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000383_10402009408983294-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000383_10402009408983294-Figure11-1.png",
        "caption": "Fig. 11-Holeentry hybrid bearing.",
        "texts": [
            " In comparing Curve 1 with Curves 2 and 3 at high eccentricity ratio, the stiffness and damping coefficients of a D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 2 0: 48 1 6 O ct ob er 2 01 4 Experimental Investigation of Hybrid Bearings 289 C O D E : m1 84 tI Fig. &Slotentry hybrid bearing. hybrid bearing are greater than those of the hydrostatic or the hydrodynamic bearings, so that the dynamic behavior of a hybrid bearing seems quite good because of its hydrostatic damping and hydrodynamic effects. Hole-Entry Hybrid Bearing The specifications of the hole-entry hybrid bearing shown in Fig. 11 are ;as follows: D = 50 mm, L = 50 mm, La = 7.5 mm, ho = 2.5*10- 2 mm, double rows and hole numbers No = 8 per row, uniform distribution of holes in circumference, diameter of hole 0.5 rnm, m = 5 Kg, -q = 3.4344*10-~ Pa . S, p, = 10*lo5 Pa. .,. I - .&= . 1 9 5 3 E + 8 2 CH= . !3687E+QQ The oil pressure distribution in circumferential direction A X = .QQBQE+QQ C' f=- .3125E-Q1 at the section of oil feed holes and at the central section are D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 2 0: 48 1 6 O ct ob er 2 01 4 - t h e o r e t i c a l e : ; p e r i m c n t ~ l I N=130er/min l , esperimentalIN:109Pr/min) 0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003927_s11665-006-9001-3-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003927_s11665-006-9001-3-Figure7-1.png",
        "caption": "Fig. 7 Effect of the protuberance shape on the fastened strength (50SX400)",
        "texts": [
            "2 mm thick) was o weakly fastened that it needed careful handling during core making or coil winding. For easy use and handling, 0.27 mm thick sheet is the thinnest gauge on the usual high-speed stamping for building a small-size motor. Kabasawa and Takahashi (Ref 7) reported that they applied the 0.27 mm thick non-oriented electrical steel sheet for hybrid electrical vehicles and mentioned that the 0.27 mm thickness sheet has the optimal balance between stacking strength and low core loss at high frequency. Figure 7 shows the effect of protuberance shape and fastened strength. We used four types of protuberances, two rectangular ones and two circular ones. The results of this test indicated that the rectangular type protuberances are fastened more strongly than circular types. This is an effect of hooked by corners on the rectangular protuberances. The deterioration of magnetic properties was caused by not only a simple obstacle of magnetic flux flow, but by flow from lamination to lamination through the interlocking protuberances and by compression or expansion stress between two fastened protuberances"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002801_nme.1620231107-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002801_nme.1620231107-Figure12-1.png",
        "caption": "Figure 12. Clamped conical shell: collapse mechanism for the shakedown or the limit analysis problem",
        "texts": [
            " Table 111 gives the comparison for the case h = t/4L = 0-01. In the case of shakedown analysis, Table IV shows the results obtained by the present and the lower bound\u2019 formulations. We can see that the bounds are brought closer to each other when increasing the number of degrees of freedom, which is the purpose of the present formulation. Number of finite elements p i c 11 0.578 lower bound 1 1 0.645 upper bound 41 0.591 lower bound 41 0.602 upper bound Approach -- ____________.- 2086 P. MORELLE Figure 12 shows the plastic displacements obtained in both cases of limit or shakedown analysis (less then 0.05 per cent difference). It can be seen that the limit loads and the deformed states are very similar in the two cases; on the contrary, Figure 13 shows that there is a larger difference between the two residual stress states (obtained by the lower bound formulation) and this is of great practical interest. CONCLUSIONS Equilibrium elastic finite elements and linear programming techniques are used to perform shakedown analyses of axisymmetric shells"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002590_3.20549-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002590_3.20549-Figure3-1.png",
        "caption": "Fig. 3 Geometry of the flexible arm model.",
        "texts": [
            " Numerical Results We present in this section two examples to illustrate the effectiveness of the design procedure. The first example treats a structural vibration model that arises in considering the rigid body and the first flexible mode of a lightweight flexible arm moving along a predefined path.11 The second example is a helicopter flight control problem using a tenth-order model for the fuselage and rotor dynamics.12 Example 1: Lightweight Flexible Arm The dynamic model of the flexible arm prototype in the Flexible Automation Laboratory at Georgia Institute of Technology is used in this example. Figure 3 illustrates the geometry from which the model was derived. The arm moves on the horizontal plane and is stiff with respect to torsional effects. This flexible beam can also be seen as the last member of an open kinematic structure whose previous links are rigid. The derivation of the dynamic model for the flexible beam of Fig. 3 directly follows from Ref. 11. For the example considered here, the model is reduced to include the rigid body and the first flexible mode through residualization of the second flexible mode with a frequency equal to 87.5 rad/s. This results in a direct feedthrough of the input to the output. However, the form of the model is representative of the general problem of controller design for rapid pointing of a flexible structure. The control is motor torque in foot pounds. The rigid body and the first flexible mode dynamics and outputs are defined by the following system matrices: A = 0 1 0 0 0 1 11"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002427_50009-5-Figure7.27-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002427_50009-5-Figure7.27-1.png",
        "caption": "FIGURE 7.27 (a) Equivalent AC circuit of the hysteresisgraph-wattmeter shown in Fig. 7.24. The magnetizing frequency is assumed to be sufficiently low as to permit one to neglect the effects of stray capacitances and leakage inductances of the primary and secondary windings. Rwl is the resistance of the magnetizing winding. The resistance of the secondary winding is negligible with respect to the input resistance R 2 of the secondary instrument. The e.m.f, u2(t) appearing across the secondary winding is related to the voltage uc(t) by the equation u2(t)= -(N2/N 1)uc(t ). (b) Corresponding vector diagram (linear approximation) for nonnegligible load current i2(t) and imposed flux. The total magnetizing current im(t) (i.e. the field H(t)), phase shifted with respect to the flux ~(t) because of iron loss, is imposed and, consequently an extra-current i2~(t)= -(N2/N1)i2(t) must flow in the primary winding to counter the effect of i2(t) in the secondary winding. The total current ill(t) = ira(t) + i21(t) to be supplied in the primary winding accounts then for the additional power consumption in the load. The vector diagram is drawn here for N2/N1 = I and the proportions of i 2 are somewhat exaggerated for the sake of clarity.",
        "texts": [
            " With a closed magnetic configuration, H(t) coincides with the applied field and under AC excitation it is the field existing at the specimen surface, where the eddy-current counterfield is zero. H(t) is then equal to the sum of the field required by the DC constitutive equation of the hysteresis loop and the additional field that must be applied at any instant of time in order to antagonize the eddy 368 CHAPTER 7 Characterization of Soft Magnetic Materials current counterfield and preserve the same value J(t) of the polarization, averaged across the specimen cross-section. Let us consider the equivalent circuit in Fig. 7.27, where we have assumed, for the time being, that there are no leakage inductances and stray capacitances and that the resistance of the secondary winding is negligible with respect to the input resistance R 2 of the measuring instrument (either voltmeter, pre-amplifier, or acquisition device). We also assume that R 2 is so high that i 2 ~ 0. The average power delivered by the generator into the magnetizing winding, purged of the ohmic losses in the winding resistance Rwl, is given, per unit of effective sample mass, by Pw- 11f~UL(t)iH(t)dt\" (7",
            " However, when old-fashioned electrodynamic wattmeters, especially if connected in parallel with an average value voltmeter and an r.m.s, value voltmeter, are employed, we might have to account for the additional power consumption in the instruments brought about by the circulatha.g current i2(t). Loading by the secondary circuit results, under rated flux, in an additional current i2/(t)--(N2/N1)i2(t) in the primary winding, as defined by the condition that the total magnetizing current ira(t)i l l ( t ) - i2/(t) is imposed (see the vector diagram in Fig. 7.27b). The generated field, resulting from the currents circulating in the primary and secondary circuits, is then N1 N2 H(t) - ~m ill(t) + -~m i2(t)\" (7.27) By introducing it, together with the expression for the induction derivative dB u2(t) d t N 2 A ' in Eq. (7.25), one obtains for the specific power loss P = H ( t ) - d t d t = - ,, u2(t) iH(t) d t - u2(t)ia(t) d t ma - ~ 2 0 \" (7.28) The second term within square brackets is the power consumed in the secondary circuit, which must then be subtracted from the indication of the wattmeter in order to obtain the magnetic power loss",
            " The basic question we pose here is how we can estimate the error introduced by the distributed parameters on the measured values of the power loss P and apparent power S. Both these quantities are experimentally determined, according to the base equations (7.20) and (7.24), starting from the current ill(t) supplied to the primary winding and the voltage u2(t ) appearing at the input of the acquisition device. In the presence of stray parameters, the quantities to be considered will be, instead, the magnetizing current im(t), resulting from the composition of ill(t) with the current i2~(t) (see Fig. 7.27b), and the voltage Uc2(t ) (see Fig. 7.47). The current ira(t) = (Im/N1)H(t) is then the current that flowing in the magnetizing winding in the absence of any secondary load, would 418 CHAPTER 7 Characterization of Soft Magnetic Materials provide the field H(t) ensuring the rated induction B(t). If as is often the case, we disregard, the effect of the capacitance Co, we write for the current i m(t) N2 im(t) - i l l ( t ) - icl(t)+ ~-~i2(t), (7.51) where icl(t) is the current leaking through the self-capacitance C1",
            " It is an acceptable approach because, on the one hand, we are often only interested in order of magnitude estimates of the errors deriving from the interference of the distributed parameters with field application and signal detection. On the other hand, a linear-like response of the material at increasing test frequencies is observed, due both to the prevalence of the classical eddy current loss contribution with respect to the domain-wall dependent loss contributions and the natural limitation on the achievable peak induction values. We have already introduced in Section 7.3.1 (Eqs. (7.27) and (7.28)) and illustrated with the equivalent circuit and the vector diagram in Fig. 7.27b the case where current is drained in the secondary circuit by the measuring instrument of input resistance R2. The correspondingly dissipated power AP must be subtracted from the measured loss Pmeas in order to obtain the actual power loss P in the material. With reference to Fig. 7.27a and b, no stray parameters being considered, we re-formulate Eq. (7.28) for the specific power loss under the assumption of sinusoidal time-dependent quantities. P = H(t) dt is thus calculated by posing and thereby obtaining p ~ ~ ~ H(t)-- Nlim(t)/lm dB(t) u2(t) dt N2A ' 1 N1 ~ ~_~3H p ma N2 imU2 cos qo -- Bp sin ~H 1 Xl~ ~ ma N2 IHU 2 COS q012 -- -- Pmeas - hP, (7.52) ma R2 7.3 AC MEASUREMENTS 419 where ~12 is the phase shift between ill(t) and u2(t)~ the measured power loss 1 X l ~ ~ Pmeas - - ma N2 ZHU 2 COS q~12 and the power dissipated in the load is 1 522 & p - ma R 2 \" Also, the measured and actual values of the specific apparent power (Smeas and S, respectively) differ because of the current circulating in the resistive load. We define them, based on Eq. (7.20), as ~ ~ N1 1 N1 1 Smeas - - I H U 2 ~ ~ ~ S - - l'mR2 ~ ~ (7.53) N 2 m a N 2 m a and, being in this case N2 im(t) -- ill(t) + ~ / 2 ( t ) , we obtain, under the general assumption i 2 <K Z~m, S --- Smeas - AS ~ Smeas -{- ~ c o s (7.54) ma R22 qo~ where ~ is the phase shift between/m(t) and u2(t ) (see Fig. 7.27b). Notice that ~o12 and ~ are both larger than vr/2, so that the terms cos ~012 and cos ~ in Eqs. (7.52) and (7.54), respectively, are always negative. The terms AP and AS are relevant only when using relatively low impedance r.m.s, voltmeters for the reading of 52 or somewhat obsolete electrodynamic wattmeters for the measurement of P. With R 2 - -1 Mf~, no significant corrections are expected. For example, a sample made of 12 strips of 0.10 mm thick grain-oriented strips tested by means of an Epstein frame, modified according to the Standard IEC 60404-10, will display, at 10 kHz and Jp = 1 T, a power loss figure of the order of apparent power Smeas ~ 1.2 X 103 V A/kg. The relative deviations AP/p and AS/S turn out to be, according to Eqs. (7.52) and (7.54), lower than 10 - 3. The equivalent circuit in Fig. 7.27a is of limited validity at medium and high frequencies and we should try to make our evaluation of AP/P and AS/S having in mind the complete circuit shown in Fig. 7.47. We start by assuming that either an electrostatic screen is used or the windings are 420 C H A P T E R 7 Charac te r iza t ion of Soft Magnet ic Mater ials laid upon the specimen in such a way that the interwinding capacitance Co is negligible. We equally neglect the leakage inductances and the winding resistances, so that the equivalent circuit and the associated vector diagram become as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002371_s0043-1648(03)00371-5-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002371_s0043-1648(03)00371-5-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of the stage driving principle with ultrasonic motor.",
        "texts": [
            " In this paper, we propose the selecting method of the optimum preload of USM and the optimum gains of PID controller to control wear mode of Al2O3 drive tip into mild wear mode for stable precision positioning. Fig. 1 shows schematic diagram of the configuration of the precision stage positioning system used in this investigation. The stage system consists of one tip type USM (Naomotion Ltd.) [9], a linear stage with cross roller guide, a PID controller, a motor driver, a glass scale and a linear encoder. The curvature radius of drive tip is 7 mm. Al2O3 is selected for drive tip and driven rail. Material properties of Al2O3 used in this investigation are shown in Table 1. Fig. 2 shows schematic diagram of the stage driving principle with ultrasonic motor. The longitudinal and bending resonance vibration modes are coupled by asymmetry of a piezoelectric actuator realized by cross-connection of feeding electrodes 1\u20134 and 2\u20133. The traveling direction of the drive can be changed by switching the one pair cross connected electrodes to another pair. This changes the bending mode phase by \u03c0 and results in reversing the direction of surface oval motion. This oval vibration frequency is 40 kHz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003493_robot.1986.1087719-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003493_robot.1986.1087719-Figure1-1.png",
        "caption": "Figure 1.",
        "texts": [
            " frame dx,dy,d, Deformational dlsplacements of the distal frame along the axes of the ( X l Y, Z1 ) frame @x,$y,$z Angular deformations of the distal frame about the axes ofthe - (Xl Y1 Z1 ) i frame b Absolute Angular Velocity of the - (XIYl Z1 ) frame ab Absolute Angular Acceleration of - the (XIYIZl)i frame Relative Angular Velocity of the differential segment with respect Relative Angular Acceleration of the differential seament with Density of the link material Area of cross section of the link 'b - - - w wd - to the (XIYIZl)i frame 'd - ( 1 ) Kinematic & Kinetic Relations: I respect to the (XIYIZl )i frame For thepurpose f derivjng the kinematic and differential segment kinetic expressions, let us consider the ith link of a serial manipulator shown in figure 1. The ith I the differential segment link will have joint 'it at its proximal end (proximal to the base ofthe manipulator) andf the (XIYIZl)i frame. joint 'i+l ' at its distal end. Three reference frames are associated with each link of the If [Ail is the commanded gross motion manipulator as shown in figure 2. Frames (XIYIZ,)i transformation at joint 'if, then we have, and (X2Y2Z2)i will be located at the proximal and distal ends of the link. The 'Z' axes of these [Ail = [L1 1-l [Hi] [Llil CL2.1 ( 1 1 frames will be parallel to a reference line on the i-1 link",
            " In such cases, the procedure is easily automated without having to require the user p ovide the compatibility matrices. These global, elemental matrices should then be assembled using asuitable assembly procedure to yield the final set of system equations as below: CJ(qs)ls + CC(qs,(is)ls { ( i s ] + CK(qS,os,qs)lstqs} = {F(qs9~s,bs)}s (25) An iterative procedure was then used to solve the above set of coupled, non-linear, ordinary differential equations. CASE STUDIES In order to demonstrate the capabilities of the methodology developed in this paper, a 3-R manipulator (figure 1 ) was chosen. The performance of the algorithm was investigated for a wide range of aspect ratios and the stability and convergence were monitored. The analysis was run in two different modes through a soft switch in the computer code. In the first mode, the contributions of the elastic deformations of the proximal links to the accelerations (hence, the inertial loads) of the distal links were ignored. This approach will then yield a set of linear, but coupled ordinary differential equations. The results of this linearized problem were compared with those of the non-linear problem (equation 251, in order to study the effects of interactions of the elastic deformations and the gross motions of the manipulator links"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001384_epjap:2002122-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001384_epjap:2002122-Figure3-1.png",
        "caption": "Fig. 3. Stator deformation and orientations of the external forces at the contact point.",
        "texts": [
            " These modal forces are calculated in the next section. When a precise modelization of the contact mechanism is done to describe the rotor-stator interface, for example using friction Coulomb\u2019s laws, the modal forcing vectors are non linear, and the calculation is quite difficult to achieve [2,6]. But introducing the ideal rotor, and the assumption of a punctual contact, the calculation of the effect of the external forces FN and FT on the wave becomes much easier, as it can be seen along this section. Figure 3 depicts the forces which act on the stator and their orientation, in the \u03b8 reference frame. According to the Hamilton\u2019s principle, the variational power \u03b4p due to the forces FN and FT at the stator-rotor interface must be equal to the one dissipated by the modal forces. So, we write [7]: \u03b4p = \u2212fr\u03b1\u03b4w\u0307\u03b1 \u2212 fr\u03b2\u03b4w\u0307\u03b2 . (12) By definition, the power dissipated by the external forces at the stator-rotor interface, is simply expressed when the contact is punctual (see Fig. 3 for orientations): \u03b4p = FT \u03b4VTid \u2212 FN\u03b4VNid = \u2212k h b FT (\u2212\u03b4w\u0307\u03b1(t) sin(k\u03b8c) + \u03b4w\u0307\u03b2(t) cos(k\u03b8c)) \u2212 FN (\u03b4w\u0307\u03b1(t) cos(k\u03b8c) + \u03b4w\u0307\u03b2(t) sin(k\u03b8c)) = \u2212 ( cos(k\u03b8c))FN \u2212 k h b sin(k\u03b8c)FT ) \u03b4w\u0307\u03b1 \u2212 ( sin(k\u03b8c)FN + k h b cos(k\u03b8c)FT ) \u02d9\u03b4w\u03b2 . (13) Let F \u2032 T = k h b FT . When identifying (12) and (13), the expression for fr\u03b1 and fr\u03b2 appears:( fr\u03b1 fr\u03b2 ) = ( cos(k\u03b8c)FN \u2212 sin(k\u03b8c)F \u2032 T sin(k\u03b8c)FN + cos(k\u03b8c)F \u2032 T ) . (14) Once again, it is possible to introduce R(k\u03b8c), and a simplification occurs:( fr\u03b1 fr\u03b2 ) = R(k\u03b8c) ( FN F \u2032 T ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003259_095440604322900435-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003259_095440604322900435-Figure8-1.png",
        "caption": "Fig. 8 A mesh of 320 null elements in a user-de ned uid lm element for ABAQU S. The mesh is in contact with the rail",
        "texts": [
            " In the FLUENT analyses, uid was assumed to be incompressible and Newtonian. Five different cases have been studied and the results are summarized in Table 2. For cases 4 and 5 the pad is tilted in the length and width directions such that the maximum variations in the lm thickness became +20 mm. The coordinate frame for the de nitions of tilt angles yy (longitudinal tilt) and yx (tilt in the width direction) are shown in Fig. 7. Two grades of mesh with 122 and 320 null elements were used in conjunction with a userde ned element. Figure 8 shows a mesh of 320 null elements. In spite of differences in the numbers of null elements, the pressure distributions shown in F ig. 9 are very similar. The major sources of error are believed to be simpli cations of the corner radius in the models. In the quasi-static analyses, a mesh of 122 null elements was used. The inertial effect of uid and structures was neglected. The relative velocity of the pad normal to the rail was given such that the uid lm thickness decreases from 30 to 29.9mm in 1 ms and the pressure distribution was calculated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003559_0471497398.mm334-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003559_0471497398.mm334-Figure2-1.png",
        "caption": "Figure 2. A controlled mercury capillary electrode. Mercury is held under nitrogen in the reservoir and drops are released at strictly controlled times as required. Skoog, Holler and Nieman (1998). (Reproduced by permission of Harcourt Brace College Publishers.)",
        "texts": [
            " The current magnitude relates to how much is present, and the current direction tells whether oxidation or reduction is occurring. Voltammetric techniques are dominated by polarography and its variants. This is the measurement of the diffusionlimited current between a dropping mercury electrode (DME) (or working electrode) and a second or counter electrode. The applied potential is controlled against a reference (see Table 1), with no current drawn through the reference. The dropping mercury electrode (Figure 2) has major advantages over alternatives despite efforts to replace it as the working electrode because of environmental concerns. The mercury microdrop is renewed at a set time (a value within the range 0.5\u20132 s being commonly selected) at the end of a 100-\u00b5m glass capillary. Both depleted solution and the \u2018contaminated\u2019 electrode surface are renewed by the microdrop process. Secondly, mercury has a large hydrogen overpotential, which means that a wide range of cathode potentials is available without the danger of solution electrolysis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000909_tsmc.1995.7102305-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000909_tsmc.1995.7102305-Figure5-1.png",
        "caption": "Fig. 5. Contour map for /NEC (solid) and /SUF (dashed) for m's typical of those determined from numerical method.",
        "texts": [
            " These trials show that the 0-value level curves of both functions either thread through the nodes vertically as does case b', or horizontally as does case a', or diagonally as does case c'. Except when the results are those of (27), in no case do /NEC and /SUF thread the nodes in a consistent way. For example, in Fig. 4 the two functions have a common 0-value level curve over an appreciable range, yet because one function threads the nodes vertically and the other horizontally, they cannot be further perturbed into a conservative case. Fig. 5 shows a case where both curves thread the nodes vertically but the curves are tangent where the one curve is reversed, so again the curves cannot be adjusted to a conservative case. In all cases examined these types of mismatches in pattern occur. The conclusion of our numerical search is that there are no conservative solutions except for the very limited form of M that generates the same locked joint configurations as shown by Shamir and Yomdin. Between analytical and numerical results, it has been seen that for a 3 link, planar, revolute manipulator that, in addition to the conservative cases shown by Shamir and Yomdin, there is another set of cases that are conservative"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000082_s0003-2670(98)00522-4-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000082_s0003-2670(98)00522-4-Figure1-1.png",
        "caption": "Fig. 1. Cyclic voltammograms of the oxidation of 1-AA in acetonitrile solution with 0.1 M TBAP; potential sweep rate: 0.1 V/s.",
        "texts": [
            "13 M NaCl was used as the supporting electrolyte. For the analysis of the in\u00afuence of interfering ions, KCl and LiCl were used to replace NaCl. The solution pH was changed by the addition of 1 M HCl solution under stirring. The temperature during the potentiometric measurement was maintained constant at 25.0 0.18C using a Polyscience model 900 thermostat. All potentiometric data are an average of three measurements of fresh solutions. A cyclic voltammogram during the electropolymerization of a PAA \u00aelm is shown in Fig. 1. During the \u00aerst cycle to a more positive potential the dominant process is monomer oxidation, followed by chemical coupling reactions and electrochemical oxidation reactions, leading to the polymer formation on the platinum surface. In the subsequent cycles the anodic peak (A1) gradually decreases, whereas an increase in the anodic current associated with the process in A2 and an increase in the cathodic current are observed. The cathodic processes in C1 and C2 are related to the anodic processes in A1 and A2, respectively. The mechanism for \u00aelm growth is similar to that reported for poly-1-naphthylamine [22]. The in\u00afuence of the electrolytic solution on the resulting polymeric \u00aelm was analyzed. The in\u00afuence of pyridine on the solution is shown in Fig. 2, where the shape of the cyclic voltammogram is similar to that presented in Fig. 1. However, the current associated with the redox process is twice that observed in the absence of pyridine. Different from what is proposed in the literature [23], the pyridine acts as a proton scavenger and the protons liberated during the dimer formation are consumed by the pyridine, a stronger base than the monomer in acetonitrile [24]. In the absence of pyridine, the monomer is protonated and becomes electroinactive, decreasing the electroactive interfacial monomer concentration, consequently decreasing the electrical current associated with monomer oxidation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000534_s1474-6670(17)47309-5-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000534_s1474-6670(17)47309-5-Figure7-1.png",
        "caption": "Fig. 7. A sketch of the fire truck system showing the virtual extension that is added in front of the rear steering wheel. The extra steering wheel at the rear of the trailer is used for improved maneuverability on narrow city streets.",
        "texts": [
            " In this case, finding the input parameters will re quire solving nonlinear algebraic equations. More details on this algorithm can be found in (Tilbury et al., 1993a) . Two examples will be briefly presented to illus trate the conversion procedure. In (Bushnell et al. , 1993), it was shown that the fire truck system could be converted into a multi input chained form . The bottoms of the chains in the chained form (or equivalently the flat out pu ts of the system) were chosen to to be the (x, y) position of the passive axle along with the angle of the trailer (see Figure 7) , and because of the relative simplicity of the three-axle system, that choice allowed the kinematic equations to be put into multi-input chained form without using dy namic state feedback . Since the fire truck fits into the class of multi-steering trailer systems, it can also be converted into multi-input chained form using the (x, y) position of the last axle and the trailer angle as the bottoms of the chains. One virtual trailer will then need to be added, showing that although virtual extension is not always nec essary, the procedure outlined in this paper will always result in a chained form "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002781_iros.2004.1389341-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002781_iros.2004.1389341-Figure4-1.png",
        "caption": "Fig. 4. Distances from the fool io hip & bee",
        "texts": [
            " The robot moves its hip backward as much as possible to position p', with highest hip position and maintaining the balance (i.e., xeom 2 -d2, where xcom i s the X coordinate of the robot CoM), and then swings forwards the thigh with the shank to reach hip joint limit, swapping an arc. arc l is the trajectory of the point in the leg fastest away from the hip joint, with the radius raTC1 = moz{il + T n , maz(dp ,h , dpff; + e , dp, t ) l , where rn is the radius of the knee, dprh and dp,t are the distances from the heel and the toe to the hip when the ankle joint is at its two limits, respectively (refer to Fig. 4(1)), and can he calculated easily according to 11, l z , d,, d z and e, and the limits of the knee and ankle joint angles. The robot then moves its hip forward by rotating the supporting leg about its ankle joint, under the condition of xcom 5 d l . The lifted leg swap another arc ( a r c 3 during this motion. The radius rarcz of arc2 is the maximum distance from the ankle joint f l to the lifted sole, which can he computed according to the distance dhp,from f l to p'. 11, 12, and the limits of hip joint and knee joint. Finally the robot swings the shank forward, forming the third arc. The radius of arc3 should he rarc3 = maz(d,,h, 12 + e , dn,t), where the distances dnzh and dnXt from the heel and the toe to the knee joint can he gotten according to 1 2 , d l , dz, e and the Limits of the ankle joint (refer to Fig. 4(2)). Ohviously, to avoid the collision in this phase, the obstacle vertices ~ ( x . h) and ~ ( x + w, h) should he out of arc l and arc3, and within arc2, where x is the distance of the obstacle with respect to the supporting foot, w and h are the width and height of the obstacle, respectively. To maintain the stability, the project of CoM to the Xaxis should be within the segment of the foot, that is, 4 2 5 5 4. Now to get the maximum height of the obstacle in tbis phase, we have the following GO model: nmx h d i 5 x i smor - (dz + W) (1) (z - xP"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002464_bf03258690-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002464_bf03258690-Figure2-1.png",
        "caption": "Figure 2. Reactive alloy induction melting unit. Its vacuum chamber includes a melting cham ber and a mold loading chamber separated by a flapper valve. This feature allows molds to be loaded into the unit while metal is being melted above. In addition, a vibratory feeding system, isolated by a vacuum interlock, al lows metal to be charged in vacuum or inert atmosphere. After a mold is filled, it is al lowed to cool in an inert atmosphere in the loading chamber while a new heat is being melted. In this way, melt cycle time is minimized.",
        "texts": [
            " A schematic of a unit, installed at Duriron in late JOURNAL OF METALS\u00b7 September 1986 Along with discussing the develop ment history of the induction-slag pro cess for melting titanium, zirconium, and other reactive alloys, this paper examines a recent modification to the process which eliminates calcium fluo ride slag, producing inclusion-free metal. Also considered are the applica tion and commercialization of this technology. In addition, some of the me chanical properties and structure of in duction skull melted Ti-6Al-4V, includ ing very good fatigue strengths, are reported. \u00b7Formerly referred to as \"Inductoslag.\" 51 52 1982, is shown in Figure 2. Currently, it is the world's only production induction melter designed to both melt and pour reactive alloys. Inert atmospheres or vacuum conditions may be used in this unit. Dur ing initial pumping with the furnace off, the chamber can be evacuated to 8-9 microns pressure. The vacuum level during melting is dependent on the quality of the melt stock. Clean, low interstitial titanium melt stock can be easily held at 15-20 microns pressure in this unit. As in the original USBM furnace, the crucible is a slotted, water-cooled copper design"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001625_robot.1994.351105-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001625_robot.1994.351105-Figure12-1.png",
        "caption": "Fig. 12: Motion from the find configuration",
        "texts": [],
        "surrounding_texts": [
            "from Eq.(17). Therefore, the total equations can be solved by substituting the solution of Eq.(18) to Eq.(19). That is, we can have the desired curve in the configuration space by solving the quadratic equations with three variables because the number of variables in Eq.(18) can be reduced to three in each cube Ci. The end point of the curve is determined by\n(20) 1 Z~~(&(VA' - V A ~ ) @ N B ~ ) = 0,\nwhich is the condition that VA,VA' is parallel to the face FB, whose normal vector is represented by NB, . We computed the solution for the example, but it is too long to be written down here. So it is illustrated in Fig.7. The equations are algebraic but nonlinear,\nso several solutions can be found in general. We used the applicability conditions presented in Sec.2 to select the proper solution.\nNext we move the edge V A ~ V A ~ to be in contact with the face F B ~ while keeping the position of V A ~ . This motion can be given by Eqs.(l7), (20) and\n1 - t r ( N ~ , (Viz - Vil )Q(VA~ - V i )Qt) = 0, 2i (21)\nwhich determines the axis of rotation. The motion terminates when\nThese equations can also be solved in three variables, and the planned motion is shown in Fig.8. If we con-\nsider the edge contact as the conjunction of two point contacts, the obtained algebraic equations may include\n1 1 - ~ ~ ( - - B , Q Q ~ 2 + N B ~ ( Q V A ~ Q ~ + Q Q ~ X ) ) = 0, (23) - t r ( -dB1~Qt 2 + N B ~ ( Q V A ~ Q ~ + QQ+W = 0, (24)\ninstead of Eqs.(l7) and (22), which consider the edge contact as the conjunction of one point contact and the orientation of the edge being parallel to the face. Then we must solve the equations with six variables, which should be much more difficult than our equations. Though Eqs.(23) and (24) have the linear forms in X as pointed out in [6], but they can not be solved only in variables z,y,z. Because the coefficients of these variables come from the same N B ~ , so Eqs.(23) and (24) are linearly dependent with respect to z, y, z .\nThough the edge can be in contact with the face by a single motion from the initial configuration, instead of the above motions. But we use two motions because the first motion makes the polyhedron be a robuster configuration. and the second motion can be used for the transition which is intermediate in the topological path as well as initial.\nNow the edge V A ~ V A ~ is in contact with the face Fsl, and must be moved to the edge VB~VB~ in the next according to the planned topological path. This sliding motion can be specified by Eqs.(20), (22) and\n1 2 -Q(VA~ + V A ~ ) Q ~ + X\nwhere Viz is the current position of VA~. The midpoint of the edge V A ~ V A ~ is at the initial position if t = 0, and at the midpoint of the edge VB, Vg2 if t = 1. Besides, the final orientation of the edge VA,VA~ can be determined by",
            "at which the edge V A ~ V A ~ becomes perpendicular to the edge VB~V\u2019~. The planned motion is shown in Fig.9.\nThe next motion is the rotation along the edge VB,V,, while keeping the contact point with VA,VA~. This motion can be determined by Eqs.(20), (26) and\n1 1 ~ Q ( V A , + VA~)Q+ X = -(Vi, 2 + Viz), (27)\nwhich keeps the contact point where Vil and Viz are the position of V A ~ and V A ~ at the final configuration in Fig.9. The planned motion is shown in Fig.10.\nNow A is at the C4face-type-B which is the fourth element on the topological path whose length is five. In this case, we first plan the motion reversely on the C5face-Type-C which is the last one on the path. The final motion can be determined by\nQ ( V A , ( ~ - U ) + V A ~ U ) Q \u2019 + X = ( V j 1 ( 1 - u ) + V j 2 ~ ) , (28) (29) Q(VA~ - VA, )Qt = Vi2 - Vi1, where Vi, (1 - U) + ViZ U is the contact point between the edges VA,V,, and VB~VB, at the A\u2019s final configuration(See Fig.11). The start configuration of the motion is given by\n1 ~ ~ T ( Q ( V A * - V A ~ ) Q + N B ~ ) = 0, (30)\nwhere N B ~ is shown in Fig.11. The diagonal line VA~VA, becomes parallel to the face F B ~ at the start configuration. The planned motion is shown in Fig.lZ(a). We can move the edge VA~ V A ~ to be in contact with the face F B ~ in the same way as Fig.8. The planned motion is shown in Fig.l2(b).\nFinally, the sliding motion from the final configuration in Fig.10 to the start one in Fig.l2(b) can be planned by Eqs.(30), (22) with N B ~ and\nQ V ~ ~ Q + + x = v:,(i - t ) +vi), (31)\nin the same way as Eq.(25), where Vi: is the position of VA, a t the start configuration in Fig.l2(b). The planned motion is shown in Fig.13.\nThe planned overall motion is illustrated in Fig.14. Though we presented the equations only for three combinations of the adjacent Cfaces within twelve ones due to the limit of the space, but it is not difficult to imagine the other equations from them. Our algorithm is complete, that is, it is guaranteed to find a solution.",
            "4.2 Implement at ion\nThe geometrical part of the proposed algorithm is implemented in Euslisp, which is the subset of the CommonLisp with object oriented primitives and has been developed by one of the authors[l2]. Its algebraic part is implemented in Mathematics[ 131.\n4.3 Complexity of the algorithm\nThe asymptotic time complexity of the algorithm to solve the algebraic equations increases single exponentially according to the number of variables when we use the multivariate resultant and doubly exponentially when we use the Groebner basis[l4]. We implemented the proposed algorithm in Mathematica, which uses the Groebner basis computation.\nIn spite of such difficulties, the proposed algorithm is able to be computed in the practical time, because our algorithm need to solve the quadratic equations only in three variables. In fact, we can compute the above example within several minutes using a Sparc Station 10/40 whose performance is about 75MIPS.\n5 Conclusions\nThis paper studied the motion planning of convex polyhedra in contact under translation and rotation, and proposed an implemented algorithm.\nWe presented an algorithm to determine a sequence of the contact states with the optimal asymptotic time complexity. We also proposed an algorithm to plan the motion between the contact states. In our algorithm, the roadmap can be determined by solving quadratic equations symbolically only in rotational variables, and by substituting the solution to the other equations with the translational and rotational ones.\nThis study is the first step to more general problem. Our next interest includes the motion planning of nonconvex polyhedra in contact, where the geometry of the C-Obstacle boundary faces is essential to determine the topology between the faces.\nReferences\nJ.Hopcroft and G.Wilfong, \"Motion of objects in contact\", Int J. Robotics Research, Vo1.4, No.4, 32/46, 1986.\nA.Koutsou, \"A geometric reasoning system for moving an object while maintaining contact with others\", Proc. ACM Symp. Computational Geometry, 67/74, June, 1985. F.Avnaim and J.D.Boissonnat, \"Polygon Placement under Translation and Rotation\", INRIA TR-No.889, 1988. R.C.Brost, \"Computing Metric and Topological Properties of Configuration-Space Obstacle\", IEEE Conf. Robotics and Automation, 170/176, 1989. R.C.Brost, \"Analysis and Planning of Planar Manipulation Tasks\", Doctoral thesis at Carnegie Mellon Univ., 1991. B.R.Donald, \"A search algorithm for motion planning with six degrees of freedom\", Artificial Intelligence, vo1.31,\nJ.Canny, The Complexity of Robot Motion Planning, The MIT Press, 1987. H.Hirukawa, T.Matsui and K.Takase, \"A general algorithm for derivation and analysis of constraint for motion of polyhedra in contact\", IEEE IROS'91, 38/43, 1991. R.H.Wilson and T.Matsui, \"Partitioning an assembly for infinitesimal motions in translation and rotation\", IEEE IROS'92, 1311/1318, 1992. P.McMullen, \"The Maximum Numbers of Faces of a Convex Polytope\", Mathematika,Vol.l7,No.34,179/184,1970. J.C.Latombe, Robot Motion Planning, Kluwer A.P., 1991. T.Matsui and M.Inaba, \"Euslisp: An object-baaed implementation of lisp\", J. Info. Processing, Vo1.13, No.3, 1990. %Wolfram, Mathematica, Addison- Wesley Pub., 1991. D.Kapur and Y.N.Lakshman, \"Elimination methods: an introduction\", in B.R.Donald et al. (Eds.), Symbolic and Numerical Computation for Artificial Intelligence, Academic Press, 1992.\npp.295-353, 1987."
        ]
    },
    {
        "image_filename": "designv11_11_0001699_1.1538619-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001699_1.1538619-Figure3-1.png",
        "caption": "Fig. 3 Finite element model for elastic analysis, with loads and boundary conditions",
        "texts": [
            " The loading for the non-linear thermoelastic analysis consists of the thermal loads applied as nodal temperatures and the radial force acting on the journal. The time dependent thermal load is obtained from the results of the transient thermal analysis. The static load, W is applied to act in the negative y-direction on the shaft. As the model utilizes half-symmetry, a load of W/2 is applied. Boundary Conditions. Symmetry boundary conditions are used to model the one-half symmetry as shown in Fig. 3. The constraint of the bearing on its outer surface is modeled by fixing the bearing at the node under the shaft on the outer edge of the bearing on the symmetry plane. This constraint approximates the boundary conditions of the bottom surface of the bearing support structure as shown in Figs. 1 and 3. rom: http://tribology.asmedigitalcollection.asme.org/ on 08/30/2017 Term 2.3 Seizure Criterion. Frictional torque is the torque resisting the driving torque exerted by the motor. When the frictional torque increases beyond the extent of the driving torque capability, it can be concluded that the journal has seized in the bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002767_978-3-642-71015-5-Figure2.4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002767_978-3-642-71015-5-Figure2.4-1.png",
        "caption": "Fig. 2.4. Streamline pattern for sheet of finite width. Ratio of stator length to pole pitch: 21h:= 8",
        "texts": [],
        "surrounding_texts": [
            "The complex representation of the exciting (\"primary\") traveling flux density B~), residing in the z = 0 plane even in the absence of the conducting sheet, is formulated by means of the ph as or Eo. This exciting field, characterized by a pole pitch r, advances in the + x-direction and its mathematical formulation is taken to be represented by z=o (2.2.8) B(p) = 0 Z ' [x[>l, [y[>h. Further, along with the complex amplitude Eo pertaining to the imposed magnetic flux density, we also define the complex amplitude of the magnetic flux iJo == (Eox2h x21). We now choose to satisfy the boundary conditions of vanishing normal current flow at the sheet boundaries y = \u00b1 a by an image procedure (Fig. 2.3); hence, the exciting magnetic flux density is taken to alternate (in space) in the y-direction and its analytic representation is given in terms of the continuous wave number m and the discrete, odd wave number k ( = 1,3,5,7 ... ), by B(p) = iJo ~e-iwt J dm Z 7[2 2a -00 z=o. (2.2.9) The amplitude p(p) of the primary z-directed Fitzgerald vector superpotential, F(p), from which this field is \"derived\", satisfies the Laplace equation; this potential is coherent in x and y with B~P) as per (2.2.9) and can be expressed in integral form through the (still unknown) weighting functions Kk(m): (2.2.10) For the z-component of the magnetic flux density in the z = 0 plane, see (2.2.7), we therefore obtain \" III +- \" III t-\" III +--~- I \" III t\" III L rl ..L. __ LI r-, III I .L . rl [I Z= 0 . 2.2 Linear Induction Devices 49 y Fig. 2.3. Series of images 8. 1 8. j , 8. I -8. 1 fIoB. 1 (2.2.11) Comparing (2.2.9 and 11), we have (2.2.12) and therefore 50 2. Principles of Magneto-Electric Interactions p(p) = _~e-iwt J dm L 2na -00 k (2.2.13) The primary phasor in the primed system of reference p(p)', as obtained now through the Galilean transformation 4, reads piP)' = _~e-iwt J dm L 2na -00 k sin (kT~) (k ; ~) sin (~-m) I eim(x' + vt') cos (kT~) X (: ~+ (k 2n.)'+m2 (2.2.14) Using (2.2.6) adapted to the primed coordinates, we obtain the \"primary\" electric field components E~)', ECj,l' in the sheet plane z = z' = 0 as follows: E (p)' - x' - . (kn h) sm -- - 00 2 a _~e-iwt'i J dm L ----- 2na -00 k (k; ~) 4 In Sect. 2.1.2 it has been proved that F(P) is invariant for velocities which are negligible with respect to c, see (2.1.27); henceforth, even though Galilean relativity is resorted to, we denote for clarity the time parameter by (' in the primed frame; thus only a kinematic transformation is required here. 2.2 Linear Induction Devices 51 sin (:-m) I n x k-(w-mv) ( n ) 2a --m I r sin (kf~) (k ; ;) sin (:-+ e;m(x\"\"CO+ ; :') x (: _ m ) I m( w - m V)--(-k-2-:-)-o2~+-m-2-- We now turn our attention to the reaction field. 2.2.4 Reaction Field (2.2.15) . (2.2.16) The electric field in the sheet plane is linked to an electric current density j'. Let A~, A; be the components of the surface current A ' = j 'LI. The continuity equation aA~, + aA;, = 0 ox' ay' (2.2.17) is satisfied identically by a stream function D' = D'(x', y', t') defined through aD' --= +A;, ox' On account of the streamline equation dy' = A;, dx' A~, (2.2.18) 52 2. Principles of Magneto-Electric Interactions the family of curves D' = const represents the current flow pattern at the instant (' = (~. By means of the still undetermined spectral amplitudes f~(m), we now introduce the stream function D 1 D' = e- iwt' J dm L~(m)eim(x'+vt')cos (k!!....t...) , -00 k 2 a which in turn yields, via (2.2.18), the surface current distributions A~,= +~ e- iwt' J dm I h-(m) keim(x'+ vt) sin (k!!....t...) , 2a -00 k 2 a A;,= +ie- iwt' J dmm Ih-(m)eim(X'+vt')cos (k!!....t...) . -00 k 2 a (2.2.19) (2.2.20) (2.2.21) As noted, the original stator has been replaced by iron of infinite horizontal dimensions, but comprising windings so distributed that the exciting magnetic field is confined to the region I x I < /; I y I < h. This procedure enables us to formulate in the air gap a \"secondary\" Fitzgerald vector superpotential F(s) (due to the sheet current) comprising again a z-component p(s) only, adapted, in turn, to the boundary conditions of the problem, for which the Laplace equation is solvable by separation of variables. Now by our assumptions, the stator winding is supplied - in technical terms - by a known imposed voltage totally \"compensated\" by the primary field; hence the tangential components of the secondary electric field must vanish on the stator at z = \u00b1 b. Subject to this boundary condition, the primed superpotential p(s)', expressed in the primed system of reference through the still unknown spectral function Lk(m), reads p(s)' = e- iwt' J dm I Lk(m)eim(X'+vt')cos (k!!....t...) -00 k 2 a x sinh [V (k ;a)' +m2(bH1l z'''O. (2.2.22) The secondary horizontal magnetic field components are therefore given in the sheet plane, via the primed version of (2.2.7), by Hls), = \u00b1_1_ ie- iwt' J dm m I Lk(m)eim(X'+vt') Po -00 k Z'= \u00b1o , (2.2.23) 2.2 Linear Induction Devices 53 H~~)' = +_1_ ~e-iwt' r dm ~ Lk(m)keim(x'+vt') fJo 2a -00 k Z'= \u00b1O . (2.2.24) The integral form of Maxwell's law V XH' = j I at the interface Z' = 0 reads (2.2.25) H~,( +O)-H~,( -0) = +A;, (2.2.26) and hence (2.2.27) The secondary Fitzgerald potential component pI (s) may now be expressed by the spectral coefficientsh(m): p(s)' = !!:!!...e- iwt' J dm 2 -00 h(m)eim(x'+vt,cos (k ~ :') x L -----,::::.==:::;;:==-- k V h;;-)' +m' sinh [V (k-f;)' +m'(b+zl] x cosh [V (k 2'.)' +m'b] z:::::O, (2.2.28) and therefore the secondary electric field components in the sheet plane read 54 2. Principles of Magneto-Electric Interactions E1S)' = +~ ~ie-iwt' r dm L kh(m)(w-mv) 2 2a -00 k For the conducting sheet, we now apply Ohm's law aL1 (E}f?)' + E1s),) = A~, , a L1 (E~)' + E~>'> = A;, , and obtain, see (2.2.15 and 16; 20 and 21; 29 and 30), h(m) = i+ aL1,uo (w-mv) 2 tanh [V h~ )'+m2h] V (k 2:)'+m2 (2.2.31) (2.2.32) (2.2.33) Returning to (2.2.19) and formulating the stream function D(x, y, t) in the unprimed system (Sect. 2.2.8B) we have 2.2 Linear Induction Devices 55 D(x, y, t) = 2iJo _l_ e- iwt T dm f.lo 2na -00 (2.2.34) Relevant patterns of streamlines are reproduced in Figs. 2.4 to 6. Increasing the ratio 211 r reduces the influence of the end effects on the overall shape of the streamlines, and flow patterns resembling those of Fig. 2.7 are obtained. It should be borne in mind, however, that the plotted results are obviously affected by the somewhat arbitrary model chosen for analysis. 56 2. Principles of Magneto-Electric Interactions 211r=12 211r=40 2.2.5 Two Special Cases A) Rotor of \"Infinite\" Extension If the sheet width 2 a is much larger than the dimensions 2/, 2 h, we may use the limit a-----HX>. Passing in this case from Fourier series expansion to Fourier integral representation, we obtain for the stream function -1.6 58 2. Principles of Magneto-Electric Interactions 2\":;;0 1 . D(x, y, t) = _'1' ____ e -lwt f.1,0 (2 n)2 O'Llf.1,o sinnh w-(nlr)v i[(rrlr)x+ny] 2 2 2 e X r 2 n h n + n Ir dn \u2022 (2.2.37) -00. O'Llf.1,o ( n) tanh [Vn 2+(nlr)2b] 1+-- w--v 2 r Vn 2+(nlr)2 A streamline pattern for this case is shown in Fig. 2.7. B) Rotor of \"Infinite\" Conductivity (0'-+ 00; LI = finite) The case of a rotor of superconducting material involves the concept of \"frozen-in fields\". For 0'-+ 00, (2.2.37) becomes 2\":;;0 1 . D(x, y, t) = _'I' ____ e- lwt f.1,0 (2 n)2 00 sinnh ei[(rrlr)x+nY]dn x J ----;:::::;;==~--------;~=~- -00 nh V n 2+ (nlr) 2 tanh [V n 2+ (nlr)2b] (2.2.38) Calculating the fields and currents in the sheet plane by the procedure outlined in Sects. 2.2.3 and 4, we obtain for the components of the primary electric field: E (p)' - B- -iwt' ( n) 2h x' - - 0 e w- - v - r 2n E (p)' - B- - iwt' ( n) n 2 h y' - + oe w--v-r r 2n z'= 0 , The secondary field components are now given by: E (Sl' _ B- -iwt' ( n) 2h x( - + 0 e w - - v - r 2n z'= 0 , (2.2.39) (2.2.40) (2.2.41) 2.2 Linear Induction Devices 59 E (s)' _ B- -iwt' ( n) n 2h y' - - oe w-- V -- r r 2n (2.2.42) evidently leading towards E(P)' + E(s)' = 0, as required by the condition a ...... 00; LI = finite. The surface currents are expressed by the integrals A _ . Eo - iwt 4 h x- -l-e - 110 2n A . Eo -iwt 4h y= +l-e - 110 2n (2.2.43) (2.2.44) and it is seen that their magnitude depends neither on the velocity of motion v nor on the angular frequency w of the exciting field. The current flow in the present case is governed not by Ohm's law, but by Maxwell's law j = V' xH; an infinitesimal displacement of the superconducting strip must generate a field such as to compensate entirely for the exciting magnetic field: the discontinuity in the tangential components of this secondary reaction field fully determines, see (2.2.25,26), the current distribution in the sheet."
        ]
    },
    {
        "image_filename": "designv11_11_0000969_iros.2001.976369-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000969_iros.2001.976369-Figure1-1.png",
        "caption": "Figure 1: System overview.",
        "texts": [
            " They may change their movements depending on the situation perceived by their sensor systems. Thus our object avoidance method first judges whether or not the moving object is a human. If so, it continues watching his/her face and determines how to avoid him/her based on the observation result. This can realize the friendly collision avoidance among humans mentioned above. 67803-6612-3/0l/$10.0@2001 IEEE 201 8 2 Overview of the Intelligent Wheelchair System This section briefly describes the overview of our intelligent wheelchair system. Fig. 1 shows a photograph of the system. It has a PC (AMD K6-111 400 MHz), a video camera (SONY EVI-DSO), and sixteen ultrasonic sensors ( Polaroid ). The PC contains a real-time image processing board consisting of 256 processors developed by NEC [6]. The camera is installed on the front of the wheelchair to take the front scene. The ultrasonic sensors are installed around the wheelchair to cover 360 degrees. The ultrasonic sensors are continuously obtaining the range data around the wheelchair. Thus the wheelchair can avoid static obstacles entering the dangerous zone"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002327_s11044-004-2516-1-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002327_s11044-004-2516-1-Figure2-1.png",
        "caption": "Figure 2. Full multibody model.",
        "texts": [
            " OF THE SUSPENSION After the torsion beam was implemented as a flexible body, the other elements of the suspension model were created: shock absorbers, springs, bumpstops, reboundstops, wheel bearings and chassis attachment bushings. At first, the bushings were assimilated to uni-ball joints with very high translational stiffness (K = 50,000 N/mm) and zero rotational stiffness in all directions. This choice was operated in order to evaluate the effect of torsion beam deformation on suspension parameters since the bushing deformations are negligible. The bumpstops have also constant stiffness. In a second time, the bushings were modelled considering feasible non-linear force-deformation curves with increasing stiffness (Figure 2) and constant rotational stiffness in all directions [8, 9]. The bumpstops have also non-linear force\u2013 deformation curves. At the end, the testrig for elasto-kinematic analysis was generated. It includes parts, joints and numerical functions to assign the vertical displacements to the wheels or to apply wheel loads. The vertical motion can be assigned to the wheel centres directly or to the tyre contact patch, including the tyre vertical static stiffness. The full model is shown in Figure 2. Two kinds of simulation were submitted: wheel travel analysis and static load analysis. Wheel travel analyses are described below (+= bump travel, \u2212= rebound travel): \u2022 parallel wheel travel analysis, z0 = 0 mm: equal vertical displacements are assigned to both wheel centres in the range \u00b180 mm from the initial nominal position; \u2022 opposite wheel travel analysis, z0 = 0 mm: opposite vertical displacements are assigned to both wheel centres in the range \u00b180 mm from the initial nominal position; \u2022 opposite wheel travel analysis, z0 = \u221240 mm: opposite vertical displacements are assigned to both wheel centres in the range \u00b140 mm from \u221240 mm initial position; \u2022 opposite wheel travel analysis, z0 = +40 mm: opposite vertical displacements are assigned to both wheel centres in the range \u00b140 mm from +40 mm initial position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001003_s1474-6670(17)37970-3-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001003_s1474-6670(17)37970-3-Figure2-1.png",
        "caption": "Fig. 2. The unicycle mobile platform (left), the kinematic car (right) .",
        "texts": [
            " Controllers developed for robot manipulators and mobile platforms can be applied to steer mobile manipulators if only they are equipped with a component able to annihilate the correction term in Eq. (27) determined by the matrices in Eq. (34). Now, a simple example is given to show that the correction matrix in Eq. (27) is a sparse matrix. Thus, controllers for mobile manipulators should be slightly modified versions of controllers devel oped for manipulators or mobile platforms. For the unicycle-type mobile platform (for instance, for the three wheel mobile platform Ulisses de picted in Fig. 2, (Tchon and et. al , 2000), with a free wheel having negligible mass and inertia), nonholonomic constraints result in the matrix GT = [-Sine cose 000] (35) o 0 100 ' where coordinates q = (x, y, e, qWI, qW2 f are de fined in Fig. 2. The vector 'f] appearing in the control system q = G'f] and resulting from non holonomic constraints , is composed of the linear and angular velocities of the mobile platform. The [0 (;TQPWM] correction matrix - 0 0 is a sparse matrix, and taking derivative of GT introduces even more zeroes. The correction term aT QPW M will be examined once more. Eq. (19) shows that QPWM = [Q~M], so only first np columns of the matrix eT, corresponding to coordinates qP (= (x,y,e) for the unicycle nad the kine matic car mobile platform), influence the value of eT QPW M, but not coordinates of wheels",
            " Proof: For the unicycle mobile platform the ma trix C, resulting from nonholonomic constraints, does not depend explicitly on position coordinates ~,y but depends on the orientation angle e. Thus, C is a linear function with respect to the deriva tive of the orientation angle e. Consequently, when the mobile platform is moved along a straight line on the x - y plane then iJ = 0 and the thesis of Proposition 3.2 holds. The proof for a kinematic car follows . The non holonomic constraints of the kinematic car, with coordinates of the platform depicted in Fig. 2 and coordinates of wheels omitted, are trans formed into the following matrix, (Murray and Sastry, 1993) eT = [cos e sin e 0 1/1 tan IP] (36) o 0 1 0 ' where I is the distance between front and rear wheels. When the kinematic car moves along a straight line on the x - y plane, then IP = 0 and ~ = iJ = O. Consequently, e = 0 and the correction term vanishes for that motion. In this paper it has been shown that the dynamics of mobile manipulators do not obey properties displayed by the mobile platform and the manip ulator considered separately"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002266_ijmee.31.2.5-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002266_ijmee.31.2.5-Figure3-1.png",
        "caption": "Fig. 3 A beam in deflection.",
        "texts": [
            " A clamped\u2013free beam In this section, based on the Euler\u2013Bernoulli theory, the analytical expressions of the elastic deflections of a beam will be derived using the mathematical and physical curvatures, and linear theory for comparison purposes. Assuming that the beam is clamped at one end and free at the other, then the beam is subjected to a single moment at its free end. The reason for choosing such a basic example is to have a simple deflection curve with a constant radius of curvature as (13) Since a planar curve with a constant radius of curvature is known to be a circle, the deflection curve of the beam will be a circular arc. Then, with the help of Fig. 3, the following relationships can be written: (14) (15) (16)u X x R x R x= - = \u00ca \u00cb \u02c6 \u00af -sin X R R x R = = \u00ca \u00cb \u02c6 \u00afsin sinj OA OA x R\u00a2 = = = j R M EI = = 1 k at HEC Montreal on July 10, 2015ijj.sagepub.comDownloaded from International Journal of Mechanical Engineering Education 31/2 and (17) Eqns (16 and 17) give the horizontal and vertical deflections of a point of the beam. Furthermore, note that the u deflections are due to transversal deflections because the median line is inextensional for this kind of loading"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003817_rsta.2006.1897-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003817_rsta.2006.1897-Figure4-1.png",
        "caption": "Figure 4. Polar and non-polar clusters interacting with polar filaments. Assuming that clusters always bind to the smallest angle, polar clusters (g/N) bind only to filaments in configuration (a), while non-polar clusters (gZ0) bind to both configurations (a) and (b) equally.",
        "texts": [
            " We describe the system by a concentration of polar filaments f \u00f0r; n\u0302; t\u00de in two dimensions (dZ2), modelled as hard rods of fixed length [ and diameter b ([[b) at position r with filament polarity characterized by a unit vector n\u0302, and a density of motor clusters m(r,t). The filament and motor concentrations satisfy the equations vtf ZKV$J fKR$J ; \u00f06:1\u00de vtm ZKV$Jm; \u00f06:2\u00de where RZ n\u0302!vn\u0302 and the translational (Jf,Jm) and rotational (J ) currents have diffusive, excluded volume and active contributions. The active contributions to the currents are obtained from relative velocities (and angular velocities) of interacting filaments owing to the motors. Rotations are parametrized by g0,g1, corresponding to two classes of motor clusters (figure 4): polar clusters, which tend to bind to filaments with similar polarity Phil. Trans. R. Soc. A (2006) (g0/g1[1; Ne\u0301de\u0301lec et al. 1997; Surrey et al. 2001; Ahmadi et al. 2005) and nonpolar clusters, which bind to filament pairs of any orientation (g0/g1/1; Humphrey et al. 2002). Translations are parametrized by a, b and l, and all having dimensions of velocity and depending on the angle between the filaments. The term proportional to b drives the separation of filaments of opposite polarity, while the contribution arises from the net velocity of the filament pair (see \u00a77)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002365_robot.1994.350994-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002365_robot.1994.350994-Figure5-1.png",
        "caption": "Figure 5: The relative position of the camera and Puma 3-DOF Arm",
        "texts": [
            " 4 shows the variation of the combined manipulability and observability measure we against a variation of the camera parameter 8 (hm 0 to r / 3 , with fixed R = 100) and a circular trajectory of the end effector of the robot as traced by changing 82 @om 0 to T ) , with O1 h e d . As discussed in the previous section, an effective trajectory planning strategy using a cost function that uses w, would be one along the m e a of surface in Fig. 4. 7 3-DOF PUMA-type Arm In this section we consider a Puma-type robot with three degrees of freedom (Fig. 5). The task space is described by P(X, Y, Z), the position of a point in the end effector, while the joint space is described by (81,02,0s) the three joint angles. Unlike the previous case here we consider a more complicated motion of the cam- era, where its orientation changes but the optical axis passes through the origin of the common coordinate system, as shown in Fig. 5. This constraint on the camera helps us to describe its motion with the help of only three parameters-the spherical coordinates of its position (R, e,$) even though the actual orientation of the camera is also changed. For achieving the necessary servo control we need to track three image features. We consider two points on its end effector (PI and P2 of Fig. 5), and describe the feature space in terms of the z and y image coordinates of the first point and the z coordinates of the second point. To compute the manipulability and observability measures, we first compute the manipulator Jacobian J, and the image Jacobian J, and then compute their determinants to compute w, by a simple product because both J, and J, are square matrices. We omit the details of the derivation due to lack of space. Instead we show the plot of the variation of we with parame- terized variation of the camera postion in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003409_s0737-0806(84)80050-7-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003409_s0737-0806(84)80050-7-Figure6-1.png",
        "caption": "Figure 6. Decreasing hoof angle by cutting down the heelquarters, a., and the change of pastern attitude as a result, b. The increase of 1 as the hoof rotates is apparent.",
        "texts": [
            " The theo ry holds fo r increasing as well as decreasing hoof-ground angulation. I N T R O D U C T I O N The angular relationships of the horse's hoof with the ground and with the several joints of the digit have long been recognized as important determinants in the gait of the horse and suspected to be of importance in.the cause and treatment of several types of lameness? It has been shown that decreasing the angle of the hoof, measured at the toe, (Figure 1), causes the angle of the pastern with the ground to increase, while the pastern elevates (Figure 6) 12 The change in hoof angle may be accomplished by rasping the bearing surface of the hoof wall or by wedges. Elevation of the pastern is accompanied by an increase of the dorsal angle of the fetlock joint. These observations contradict earlier, apparently untested opinions) It has also been shown that the forces experienced by the leg are related to hoof angulation. 2 7 This fact has been ignored in other recent studies of the forces in the foreleg of the moving horse. Author's address: Department of Veterinary Science, College of Agriculture, University of Kentucky, Lexington, KY 40546-0076 The investigation reported in this paper (No",
            " The experimental test was carried out with an Instron 1122 testing machine, a A foreleg was cut off above the carpus and placed in the machine with four 5 \u00b0 wedges beneath the heels. The fetlock dorsal angle was measured with a protractor. The wedges were removed one by one and the angle measured as the vertical force exerted on the foot was held constant. a'The author thanks Dr. I.J. Ross, Agricultural Engineering Department, University of Kentucky, for making the machine available and helping with its operation. EQUINE VETERINARY SCIENCE A usual, normal orientation of the foreleg in the standing horse (the static case) is shown in Figure 6a for a hoof angle of about 50 \u00b0 . The equations describing the static equilibrium of moments for the leg overall and for the joints of the digit are given and justified below, Figure 2. Leg Overall Mmh-Mh+Rh'=0 Coffin Joint DFb-FI-EBa=0 Pastern Joint DFc+SL(c-s~q-SF(c-s)-Fp-EBa'=0 Fetlock Joint DF(d-r)+SL(d-2r)+SFr-Ff-EBa\"=0 O) (4) The general equation for the equilibrium of static linear forces in the digit, Figure 3, is: R E S U L T S A N D D I S C U S S I O N Theoretical . The proposal is that the angular changes of the pastern and fetlock joint are passively, automatically, determined by changing tensile forces in the tendinous structures of the metacarpus and digit",
            " With the coffin joint as an example, with F removed, DFb>EBa , and DF must be reduced in order to regain equilibrium, DFb=EBa. DF, then, is \"T\" in equation (7). Since 1, E, and A are constants, or nearly so in the static case, Al must decrease if DF is to decrease; the deep flexor tendon must shorten. Decreas ing the H o o f Angle When the angle of the hoof is changed, decreased, by rasping the bearing edge of the hoof wall toward the quarters and heels, the foot rotates clockwise around a center of rotation at the toe, (Figure 6). If the same angular change is accomplished by elevating the toe with wedges, the center of rotation is at the heel, but the rotation is still clockwise. There is, then, rotation of the Volume 4, Number 3 DFb+FI:EBa coffin joint, so that the deep flexor tendon tightens (lengthens, DF increases), and the extensor branches loosen (shorten, EB decreases). Equation (1) is no longer in equilibrium, and it would appear that either F must increase (a scalar change) or 1 must increase. It is apparent that 1 does increase, (Figure 6), as the hoof rotates, hoof angle decreasing. There is, however, no vector or scalar change of F, as can be shown on theoretical grounds alone. Thus, Figure 7, F=V+*-H t' (8) and H, a frictional force, is H=V~ (9) where ~1 is the coefficient of static friction, therefore, Since V is a cons tan t and la is a cons tan t for a given surface, F mus t be a constant , bo th in the scalar and vector sense since equa t ion (8) is a vec tor equat ion. This holds for the s tat ic case under d iscuss ion here"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003825_j.finel.2005.08.001-Figure13-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003825_j.finel.2005.08.001-Figure13-1.png",
        "caption": "Fig. 13. Representative model of ball bearing study.",
        "texts": [
            " The model is made up of the outer bearing ring sector associated to one bolt and the bolt providing clamp against the mounting. As for the 2D model, the mounting will act as an infinite rigid structure. The unilateral contact between the ring and the mounting is provided by specific contact elements \u201cnode-to-ground gap\u201d (I-DEAS MS 8.1). Kinematic restraints are specified on the border planes of the bearing sector to simulate the cyclic symmetry. The model of the ball bearing in respect of the geometrical particularities is presented in Fig. 13. The preload is introduced as an imposed displacement on the bolt, while the equivalent axisymmetric force is installed as a point load on the raceway. A two step simulation procedure is performed to establish the desired preload followed by the variation of the external loading of the bearing sector. The procedure is similar for all three types of bearings. The particularity of the three row roller bearing is the presence of two contact planes: between the ring and the mounting and between the two parts which compose the outer ring (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001559_b978-0-08-092509-7.50008-7-Figure4.6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001559_b978-0-08-092509-7.50008-7-Figure4.6-1.png",
        "caption": "FIGURE 4.6. Workspaceof 3R planarmanipulator:The workspaceof thekinematicmapfor theredundant3R planarmanipulatorwith l1 = 5, l2 = 4, le = 3. The four annularregionsare separatedby the Jacobiansurfaceswhichare the imagesof thesingularitiesof theforwardkinematicfunction.",
        "texts": [
            "4 Example:The 3R PlanarManipulator We canapplythetopologicalinsightsdevelopedin theprevious ubsection to theredundantplanarpositioningmanipulatorconsistingof threeunlimitedrotationaljoints(a 3Rmanipulator),withno link largerthanthesum of theothertwo links.The forwardkinematicfunctionfor the3R redundantplanarpositioningmanipulatormapsa vectorof threejointanglesto an end-effectorlocationinadiskin }R2 of radiusequalto thesumof the link lengths: (4.3) The correspondingJacobiansurfacesin theworkspacearecircles,asillustratedin Figure4.6, andpartitionthe workspaceintofour w-sheets,Wi. Thepartitionof theconfigurationspaceintosolutionbranchesis shownin Figure4.7. Lemma4.3 [11] Forthe 3R planar manipulator,thefiberbundle (Bf, flBj,t\u00bb:\u00bb.Wi) is a trivial fiber bundle. '/, Proof:Recallthatr:' (Wi) will consistofoneor moresolutionbranches 8f, whicharealsofiber bundlesasa consequenceof Lemma4.1.Afiberin 8i is homeomorphicto Sl, whichhastwo possibleorientations:Clockwise or counterclockwise.Any nontrivialfiber bundlewith Sl asthefiber must constrainasmooth\",closedpathoffibers whichreversesthe orientation of the fiber",
            " Theparametersisan elementof Sl == F, thecanonicalfiberfor thefiber bundle8{, and() == \u00a2ij1 (s) ison theactual fiber j-1(X) C 8i for x E Wi. For the3Rplanarmanipulator,therearethreedifferent opologicalclass offibers.Thereareactuallysevenpossibledistinctclassesfor thegeneral3R manipulator,dependingon thespecificlinklengths.\"Thethreetopological classesfor the 3R manipulatorconsideredin this chapterare shownin Figure4.5. Theseareallclosedloopshomeomorphicto thecircle,s'.One ison the \"surface\"of the 3-torus,andthusdoesnot wraparoundin any dimension.Thisisthefiberfor end-effectorlocationslocatedin thew-sheets W 1 andW3 of Figure4.6.For end-effectorlocationsin W2, thefiber wraps aroundthetorusalongthe()3 dimension.Thismeansthattraversalof the self-motionmanifoldresultsina 21r rotationof joint angle(}3o Forendeffectorlocationsin W4, the fiber wrapsaroundthe torusalongthe ()1 direction.In thiscase,traversalof theself-motionmanifoldresultsina 21r rotationof jointangle()1. Figure4.8 illustratesthefiber bundlestructure of B1 == j-1(W1). Exploitingwhatisnow qualitativelyknownaboutthetopologicalstructureof themanipulator,wecancrafteffectivelearningalgorithmsto determinethespecifictopologicalstructureandpropertiesofa particularmanipulator",
            " Thisisa data-drivenmethod of querypointselection,guaranteeingthatquerypointswillbein areasof theworkspaceforwhich datasamplesexist,andthatquerypointXq+l is nearquerypointxq\u2022 In the limit thatM, N ~ 00, thesequenceof query pointswillfollowa space-fillingcurvethroughthedata[12]. Thisyieldsan approximatespace-fillingcurvethroughtheworkspace,alongwhichwecan doa one-dimensionalsearchfor thebifurcationphenomenawhichindicate thepresenceofa Jacobiansurface.For the3-linkplanarmanipulator,this methodeasilyidentifiestheworkspaceregionsshownin Figure4.6. 4.4.2 SeparatingSolutionBranches We learnedfromthetopologicalanalysisof Section4.2 thatgenericallythe preimageofa neighborhoodin the workspaceconsistsofafinite number of disjointneighborhoodsin theconfigurationspace.Therefore,generically thepreimageof querypointxq will consistof disjointfibers.Forany particularquerypoint,thefibers(oneineach solutionbranch)canbe identified byany patternrecognitiontechniqueusefulforseparatingdisjointdata.In particular,wehaveused hierarchicalclusteringwith greatsuccess"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003443_isie.2006.295962-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003443_isie.2006.295962-Figure5-1.png",
        "caption": "Fig. 5 Flux sectors",
        "texts": [
            "5(l /AI + /B + Vfc |) (hexagonal trajectory) (3d) In (1)-(3), 0 is the angle by which stator flux -'5 leads rotor flux q'/, p is number of poles, Rs is the stator resistance, A is the dummy variable of integration, and vSa V,8A isa and isp are obtained through ABC-to- a,/ transformation of the stator voltage and current. VA, B and ic are the stator fluxes of phases A, B and C, respectively. In DTC, the torque Te and flux magnitude Vs are kept within the small hysteresis bands around the In order to select the proper voltage space vector, the trajectory of flux should be divided into six sectors, as shown in Fig. 5. In typical DTC, the outputs of hysteresis comparators of stator flux and torque are used to select directly one of the six active or the two zero voltage vectors generated by the VSI (Fig. 4), in order to maintain the estimated stator flux and torque within the hysteresis bands. Fig. 6 shows the schematic diagram ofDTC based on VSI. The rule for the selection of voltage vector in each sampling period is described in Table 1. one of the six active voltage vectors through DTC. Moreover, the input current should be modulated according to the input voltage so that near sinusoidal input current and adjustable input displacement angle can be achieved"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003653_hxh083-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003653_hxh083-Figure2-1.png",
        "caption": "FIG. 2. Two point masses M and m connected by a straight mass-less tether. M moves on a circular Keplerian orbit.",
        "texts": [
            " It is shown in Goldstein (1980) that, although the system of two masses, moving in planar motion in the orbital plane, has four degrees of freedom, its equations of motion can be reduced to a system of two degrees of freedom under the assumption that the mass center of the whole system follows a circular Keplerian orbit. These two degrees of freedom are the distance between the two masses and the angular orientation with respect to the local vertical direction as it is used for the optimal control in Section 3.3. However, for the targeting calculations it is more convenient to choose to prescribe the motion by cartesian coordinates located in the main satellite and directed parallel to the orbital frame (Fig. 2). Analogous assumptions are also made for the model of the space billiard in Beletsky & Levin (1993) and Steiner (1998), where two point masses connected by a mass-less tether move in a gravity field and behave like a mathematical billiard. Having in mind the deployment of a subsatellite from a space shuttle another simplification can be made, namely that for the phases of stretched tether the tether force has only an effect on the motion of the subsatellite (mass m), but does not disturb the Keplerian motion of the shuttle (mass M)",
            " for slack tether, we have the same equations of motion of the space billiard as in Beletsky & Levin (1993) and Steiner (1998), we improve the model of the impact used in Beletsky & Levin (1993), where only elastic impacts are considered, and in Steiner (1998), where impacts with a restitution factor smaller than one are considered. We stipulate for the impact phase the mechanical model of viscoelastic stretching of the tether, which is what actually happens for the real system. That the tether is properly modelled as a viscoelastic string, i.e. neglecting any bending stiffness, is supported by experiments reported in Angrilli et al. (1988). Details on the effects of viscoelasticity can be found in Barkow (2002) and Barkow et al. (2003). 2.1.1 Derivation of the equations of motion (Chobotov, 1991, p. 175). According to Fig. 2 we have r = rM + q. (2) The acceleration r\u0308 expressed in the moving frame is given by the well-known expression r\u0308 = r\u0308M + q\u0308 + 2(\u03c9c \u00d7 q\u0307) + \u03c9\u0307c \u00d7 q + \u03c9c \u00d7 (\u03c9c \u00d7 q), (3) where \u2022 r\u0308 is the inertial acceleration of the subsatellite, \u2022 r\u0308M is the inertial acceleration of the main satellite, \u2022 q\u0308 is the acceleration of the subsatellite relative to the moving orbital frame, \u2022 2(\u03c9c \u00d7 q\u0307) is the Coriolis acceleration, \u2022 \u03c9\u0307c \u00d7 q is the Euler acceleration and \u2022 \u03c9c \u00d7 (\u03c9c \u00d7 q) is the centripetal acceleration",
            " However, to be close to the radial relative equilibrium configuration does not mean that the system remains there, because still large radial velocity components of the motion will be present, which must be extinguished by proper manipulations of the tether tension. This creates the essential task to act on the tether tension in such a way that this radial speed is reduced and that the system also remains close to this configuration. It is most effective to perform a tether relaxation when the system moves radially near the local vertical configuration q = (t), \u03d1 \u2248 0, \u03d1\u0307 \u2248 0, where q is given by (12) and \u03d1 = \u03c0 \u2212 \u03d5 denotes the angle from the local vertical (see Fig. 2). Therefore, the targeting strategy aims towards directing the system to a trajectory leading it as close as possible to such a configuration. In each phase of stretched tether a large number of different trajectories is computed, which can be obtained by a small variation of the tension force pulling on the tether in the stretched configuration. For the control action the most promising trajectory is then selected. This procedure is repeated the next time the tether gets stretched. By computing not only one but a whole sequence of control actions, the efficiency of the strategy can be further improved"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001344_ma9911997-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001344_ma9911997-Figure1-1.png",
        "caption": "Figure 1. Sketch of the scattering geometries for bend mode detection (a) and splay mode detection (b): n director; qi, qf wavevectors of incident and scattered rays; i, f polarizations of incident and scattered rays; q scattering vector with components q||, q\u22a5 parallel and perpendicular to the director. In the bend mode geometry, due to the optical anisotropy the scattered ray\u2019s wavevector and electric field are not perpendicular (\u03b4 * \u03c0/2).",
        "texts": [
            " Photon correlation analysis yields the relaxation rates \u03c4\u03bd -1 of the two deformation modes with effective viscosities where the Ri values denote the Leslie viscosity coefficients, \u03b31 denotes the rotational viscosity and \u03b7a, \u03b7b, and \u03b7c denote the Miesowicz viscosities. In our experiment, the sample was centered as a homogeneously orientated film in the light-scattering setup. We analyzed the depolarized scattering using two different scattering geometries. 1. Alignment of the director in the scattering plane and approximately parallel to the scattering vector (Figure 1a): In this case (q|| . q\u22a5 and p1(q) ) 0), mode 1 in eq 1 vanishes, and mode 2 reduces to pure bend The bend mode relaxation rate \u03c4bend -1 is determined by the ratio of the elastic constant K33 and the effective bend viscosity \u03b7bend: 2. Alignment of the director perpendicular to the scattering plane (Figure 1b): In this case (q|| ) 0) the bend contributions in eqs 1-5 vanish and a superposition of splay and twist mode fluctuations is detected, weighed by the angular dependent factors p\u03bd ) f\u03bd 2. In the investigated q range, the splay contribution is predominant. The differential cross section then ap- R ) 1 V d\u03c3 d\u2126 ) (\u03c0\u2206\u03b5 \u03bb2 )2 kBT \u2211 \u03bd)1,2 p\u03bd(q) K\u03bd\u03bdq\u22a5 2 + K33q|| 2 (1) p\u03bd ) (i\u03bdf0 + i0f\u03bd) 2 (2) \u03c4\u03bd -1(q) ) K33q|| 2 + K\u03bd\u03bdq\u22a5 2 \u03b7\u03bd(q) (3) \u03b71(q) ) \u03b31 - (q\u22a5 2R3 - q| 2R2) 2 q\u22a5 4\u03b7b + q\u22a5 2q|| 2(R1 + R3 + R4 + R5) + q|| 4\u03b7c (4) \u03b72(q) ) \u03b31 - R2 2q|| 2 q\u22a5 2\u03b7a + q|| 2\u03b7c (5) 1 V d\u03c3 d\u2126 ) (\u03c0\u2206\u03b5 \u03bb2 )2 kBT f0 2(q) K33q 2 (6) \u03c4bend -1 ) K33 \u03b7bend q2 (7) \u03b7bend ) \u03b31 - R2 2 \u03b7c (8) 10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001563_a:1008185917537-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001563_a:1008185917537-Figure3-1.png",
        "caption": "Figure 3. One-wheel caster and dual-wheel caster.",
        "texts": [
            " This mechanism can generate not only the forward velocity Vx in the center of steering axis, but also the side velocity Vy caused by the angular velocity difference of the left- and right-wheels, because the passive steering axis is arranged in the front of the axle. It is clear that this mechanism has two-degrees of freedom motion ability. Now, we consider the difference between the single-wheel caster mechanism proposed by Wada et al. [12] and the active dual-wheel caster mechanism proposed here. The both mechanisms are shown in Figure 3. For the single-wheel caster depicted in the left-hand side of the figure, the forward velocity Vx is generated directly by the wheel rotation and the side velocity Vy is induced directly by the rotational torque caused by the driving motor arranged on the steering axis. On the other hand, for the dual-wheel caster, the forward velocity Vx is generated by an averaged translational velocity of the left- and right-wheels and the side velocity Vy is induced by the rotational torque caused by the angular velocity difference of the left- and right-wheels"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003746_1.2159036-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003746_1.2159036-Figure6-1.png",
        "caption": "Fig. 6 Auxiliary support system",
        "texts": [
            " Using a self-expandable flywheel hub, an energy-storage flywheel and a motor/generator are attached to a vertical rotor suspended on AMBs as shown in Fig. 5 top: radial AMB, bottom: combo AMB . Since the hub and the auxiliary support stiffness are designed to be very flexible compared to rigidity of the rotor, the flywheel, rotor, and motor are modeled as a rigid multibody system, including cross-coupled stiffness and gyroscopic moments. The flywheel and the motor have unbalanced masses with 90 deg phase difference each other and the rotor is assumed to be well balanced. The inner and outer races of the top CB in Fig. 6 have two translational motions in the radial direction, each and only the inner race has one rotational motion. A squeeze film damper SFD 9 with a parallel to O-rings provides viscous damping force. The bottom CB is modeled as a 7-DOF system, including the axial transverse motions of the inner and outer races. Both the CBs are modeled as back-toback duplex pairs, which are matched pairs of bearings with built-in means of preloading to greatly increase radial and axial rigidity with easy assembly and minimum runout. In Fig. 6, the frame of reference O ,X ,Y is fixed to the machinery frame. The geometric centers of the rotor and the bearing inner race are Or and Ob, respectively. x ,y is the location of Or in the reference frame, while xb ,yb is the location of Ob. Normal Fn and tangential Ft, friction contact forces are determined using the Hertzian contact stiffness Kc. The bearing stiffness and damping Kb and Cb represent the Hertzian contact force applied to each ball and races, while the terms Ks and Cs represent the O-ring stiffness and SFD viscous damping force. The rotational speed of the bottom CB is accelerated by the axial and radial contacts with the rotor, while that of the top CB only by the radial contact. The angle at contact between the rotor and the CB in Fig. 6 is APRIL 2006, Vol. 128 / 205 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F j = tan\u22121 yj \u2212 ybj xj \u2212 xbj , j = 1,2 21 where subscripts 1 and 2 represent the top and bottom bearings, respectively. When the rotor has a contact with the CB, the modified Hertzian 11 contact normal force Fn is applied as Fnj = Kcsj n \u00b7 1.5 s\u0307 j + 1 if sj 0 0 if sj 0 , j = 1,2, 22 where sj = xj \u2212xbj 2+ yj \u2212ybj 2\u2212c and the contact stiffness Kc depends on material property and contact geometry, n=10/9 for a line contact, c is the CB radial clearance, and the constant has a Table 1 Specifications of CB and damper 206 / Vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001096_305-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001096_305-Figure1-1.png",
        "caption": "Figure 1. The coordinate system in the bearing clearance.",
        "texts": [
            " The longchain hyaluronic acid molecules are found as additives in synovial fluid; this suggests to us modelling synovial fluid as a couple-stress fluid in human joints. On the basis of Stokes\u2019s couple-stress-fluid model, the present paper considers the effects of couple stress on the characteristics of fluid film behaviour in thrust curvilinear bearings with reference to synovial joints. It is hoped that such an analysis will be useful in understanding the mechanism of human joint lubrication and the role of the long-chain hyaluronic acid molecules in synovial fluids behaving like couple-stress fluids. The bearing flow configuration is shown in figure 1. The fixed surface is described by a function R(x) which represents the radius of this surface. The fluid film thickness in the bearing clearance is described by the function h(x, t) which denotes the distance between the fixed lower surface and the rotating surface, measured along a normal to the fixed surface. An intrinsic curvilinear orthogonal coordinate system x, \u03d1, y linked with the fixed surface is presented in figure 1. The field equations for the motion of an incompressible fluid with couple stresses are (Stokes 1966) div V\u0304 = 0 (1) \u03c1 dV\u0304 dt = \u2212grad p + \u00b5\u22072V\u0304 \u2212 \u03b7\u22074V\u0304 (2) where V\u0304 is the velocity vector, p is the hydrodynamic pressure, \u03c1 is the density, \u00b5 is the shear viscosity and \u03b7 is a new material constant responsible for the couple-stress property. The physical parameters of the flow are the velocity components vx, vy, vz and pressure p. After the reduction allowed by assuming axial symmetry and that h(x, t) R(x) the governing differential equations are (Walicka 1989, 1994) 1 R (Rvx) \u2202x + \u2202vy \u2202y = 0 (3) \u00b5 \u22022vx \u2202y2 \u2212 \u03b7 \u22024vx \u2202y4 = \u2202p \u2202x \u2212 j\u03c1v2 \u03d1 R\u2032 R (4) \u00b5 \u22022v\u03d1 \u2202y2 \u2212 \u03b7 \u22024v\u03d1 \u2202y4 = 0 (5) \u2202p \u2202y = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002767_978-3-642-71015-5-Figure2.8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002767_978-3-642-71015-5-Figure2.8-1.png",
        "caption": "Fig. 2.8. System under investigation",
        "texts": [
            "3 Unipolar Induction - Basic Principles 69 moving magnetization M' to the stationary laboratory. Reverting to (2.3.1), we finally obtain V \u00b7E= V\u00b7 [,uo(vxM)] , (2.3.12) or, for p2 <II: 1 V \u00b7E= V\u00b7 [,uo(vxM)] (2.3.13) Insight into the occurrence of unipolar induction has thus been provided 6, and we are now able to consider specific configurations. 2.3.2 Formulation of Problem and Approach to Solution The first system to be investigated resembles in many respects that described in Sect. 2.1.3 and reproduced in Fig. 2.1. There are, however, also some differences (Fig. 2.8). The poles are now excited, not by alternating current, but by a direct current carrying coil (alternatively, they may be regarded as permanent magnetic poles); further, they are not rectangular but circular-cylindrical of diameter 2R. The strip - of width 2h > 2R and gliding with regulated constant speed v - exhibits an electric conductivity a; we therefore ascribe to it a finite surface resistance (Sect. 2.2.1) defined by the fictitious limiting process lim (aLi) = finite (2.3.14) Nevertheless, even though the strip is conducting, we shall waive considera tions concerning the secondary magnetic field due to the induced current flow; 6 An even more formal approach might be based on (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002143_bf00374763-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002143_bf00374763-Figure5-1.png",
        "caption": "Fig. 5. [After TAIT].",
        "texts": [
            " However, to apply equilibrium equations to the finite element, one must either postulate that equilibrium equations hold for a deformable body (which KELVIN & TAIT refused to do) or one must invoke the physical axiom (A) as one does in method (3). 88 It is in connection with his treatment of the equilibrium of a chain that TAIT introduces Statement (A') in [13]. The Principle of Rigidification KELVIN & TAI3: begin the derivation by applying Statement (A): 89 357 The ehain being in equilibrium, any arc of it may be supposed to become rigid without disturbing the equilibrium. The only forces acting on this rigid body are the tensions at its ends, and its weight. (KT 3) Thus, referring to Fig. 5, 90 on an arbitrary finite rigidified segment PQ of the chain the tensions 7\"1 and T2 act tangentially 91 and the weight W acts through the center of gravity of PQ. Being three in number, these forces must, in accordance with the result derived in w 564, 92 lie in one plane. Since the weight is vertical, it follows that the segment PQ lies in a vertical plane. TAIT observes that since the tensions are not parallel to one another, the lines of action of all three forces must meet in a single point, 93 a result which we have met previously in PARDIES"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001505_1.1401015-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001505_1.1401015-Figure2-1.png",
        "caption": "Fig. 2 Relative position between stator and rotor",
        "texts": [
            " Since gsi is fixed in space and gr is rotating at the shaft speed v, the resultant vector gs will possess a time-varying precession ~whirl! speed, c\u0307 . Green and Etsion @10#, expressed the vector gs as follows: gW s5gW sl1gW sr , (1) where gW sl is the response to gW si alone and it is fixed in space, while gW sr is the response to gW r alone and thus is whirling at the shaft speed. The relative misalignment between the stator and rotor, g, is also a rotating vector, given by the vector subtraction and its magnitude gW 5gW s2gW r ; ugu5@gs 21gr 222gsgr cos~c2vt !#1/2. (2) Figure 2 shows the relative position between the seal components. The tilt vector go is the relative misalignment g in the special case when gsl50, so using Eqs. ~1\u20132! gives 152 \u00d5 Vol. 124, JANUARY 2002 rom: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Term gW o5gW sr2gW r . (3) The equations of motion of the flexibly mounted stator are ~see Green and Etsion @9,10#!: I~ g\u0308s2c\u03072gs!5M x (4) I~ c\u0308gs12c\u0307g\u0307s!5M y (5) mZ\u03085FZ , (6) where M x and M y are, respectively, the moments acting on the stator about axes x and y of a coordinate system xyz which whirls at a rate c\u0307 within an inertial system XYZ ~see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001929_robot.1994.351401-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001929_robot.1994.351401-Figure3-1.png",
        "caption": "Figure 3: Imaging mechanism for acquiring omnidirectional range information",
        "texts": [
            " The sensing along a path provides a 2(1/2)-D representation which consists of a route panoramic view and its range information. Outline structure of environment estimated from omnidirectional visual information The outline structure of the environment is estimated by examining the distribution of directions of horizontal lines in the 3D space. Let us assume that many horizontal and vertical lines exist in an indoor environment. A simple and straightforward method to estimate the distribution is to examine all images taken while the camera rotates. While the camera rotates as shown in Fig. 3, we can find camera directions at which some of horizontal 3-D lines are projected onto the image plane as horizontal. The camera directions are perpendicular to the horizontal 3-D lines, and they indicate the environment structure. If the robot is in a rectangular room, we find images with a significant number of horizontal lines at four camera directions with an interval The above-mentioned method, however, has a disadvantage of a very long image processing time. By using an omnidirectional view, we can save the imaging processing time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003587_bfb0035226-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003587_bfb0035226-Figure1-1.png",
        "caption": "Figure 1. Schematic view of 4 wheeled vehicle Figure 2. Contact flame",
        "texts": [
            " The assumptions are: \u2022 the bodies system composed by (1 axle, 2 wheels) can be considered as a gyrostat since its inertia properties (mass center, inertia momentum) are constant in this system of bodies [11] \u2022 the links between axles and plate-form (fig.l) or between modules (fig.7) are considered massless. By substitution of forces exerted at internal links and by including contact forces (function of the relatives velocities and displacements), the motion equations system can be written as follows: Ai2 = B(& U, P,...) (S) where U is the vector of kinematic parameters, A is mass matrix and P is the torque vector at internal links. For the example of the 4 wheeled vehicle given in figure 1, /~r = (u, v, to, p, q, r, col, c~2,0,3, co4, ~}1, 02, q3, 04) where (u, v, w, p, q, r) are the kinematic parameters of the reference body (plate-form). Tile direct dynamic problem concerns the prediction of the behavior of the mechanical system under the effect of a given actuator torque. Some examples, illustrating this problem, will be discussed in the next section. The inverse dynamic problem is not studied because vehicle motion with slipping and skidding is instantaneously uncontrollable and then there is often no solution of actuator torques which produce a given accelerations on the plate-form"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002101_ac0259459-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002101_ac0259459-Figure1-1.png",
        "caption": "Figure 1. Diagram of the channel flow cell (cell 1) constructed for application to the ITIES. (A) Channel (aqueous) half of the flow cell: (1) compression block to apply pressure to the gasket, (2) glass channel cover plate, (3) aqueous electrodes, (4) aqueous inlet and outlet, (5) channel, (6) ITIES, and (7) Viton gasket. The coordinate scheme adopted is shown. (B) Schematic representation of the laminar flow profile in the mobile (aqueous) phase. (C) Stationary (organic) cell half: (1) PET membrane (supporting the interface when assembled with the channel), (2) Luggin capillary, (3) organic solution inlet (connected to a gastight syringe), (4) silver/silver tetraphenylborate reference electrode (sealed directly into the cell), and (5) platinum counter electrode (sealed directly into the cell). (D) Gravity-fed flow system: (1) constant head reservoir, (2) feed reservoir (for the constant head), (3) constant head overflow, (4) control capillaries, and (5) system waste outlet.",
        "texts": [
            "40 In parallel, recent preliminary reports from our laboratories have described liquid/liquid measurements within a channel cell.41,42 The present report extends the latter work to the quantitative analysis of the ion transfer currents in the channel flow cell, using polyester tracketched membranes to stabilize the ITIES. The membrane employed at the ITIES has been investigated under stationary conditions and been shown to have a \u201cpassive\u201d influence on the interfacial transfer of the ion investigated here. Apparatus The cell was constructed from two main parts (see Figure 1): the channel, containing the mobile aqueous phase, and a glass cell half containing the stationary phase (the organic electrolyte solution). The channel (Figure 1A) was milled into a PTFE block with dimensions of 40 (length), 7 (width) and 1.1 mm (depth). Flow in the channel was induced as shown schematically in Figure 1B. A 6-mm-diameter hole within the channel floor enabled the stationary cell half (Figure 1C) to be incorporated flush to the floor of the channel. A track-etched membrane, as employed by Martin and co-workers to modify the metal/ electrolyte interface,28-30 was used to stabilize the stationary organic phase against the mobile aqueous phase. The membrane was manufactured from PET (by Osmonics Inc., Livermore CA), the material used in the earlier laser ablation study by Girault and co-workers.16-18 PET is chemically resistant to the organic solvents required for liquid/liquid voltammetry43 and does not swell appreciably in such media",
            " The wire was then oxidized in a solution of 3 M sodium tetraphenylborate (Lancaster) in acetone (Prolabo) for 24 h in the dark, using a 9-V battery with a 5.1-k\u2126 resistor attached in series. The stationary cell half was attached to a 5-cm3 gastight syringe (Hamilton) using PTFE tubing. The combined cell was placed within a homemade Faraday cage and attached to an EG&G model 273 potentiostat, converted for 4-electrode use, which was controlled by a personal computer. The overall gravity-fed flow system is depicted schematically in Figure 1D. The head reservoir was designed to maintain a constant head level at the height of the overflow. The waste outlet allowed the overall system height to be adjusted, enabling volume flow rates in the range of 1.4 \u00d7 10-4 to 0.2 cm3 s-1 to be obtained. The three parallel control capillaries incorporated into the flow system allowed three different volume flow rates to be accessed at a given system height. The stationary cells used for comparative purposes, with and without the PET track-etched membrane, are shown schematically in Figure 2",
            " Hence, analysis of the voltammetry can only be performed by consideration of the coupled diffusion fields in the adjacent phases.55 Membrane-Stabilized Interface under Flowing Conditions. The PET membrane-stabilized ITIES was combined with the channel flow cell to induce laminar flow on the aqueous side of the ITIES. Mass transport can reach a steady state under these conditions, with convection along the length of the cell (x coordinate) balanced by diffusion of the ion in the coordinate normal to the ITIES (y coordinate; see Figure 1). Hence, where vx is the velocity of the solution. Under laminar flow conditions, a parabolic flow profile is established with respect to the y coordinate, with the velocity reaching a maximum, v0, in the center of the channel,39 where h is the half-height of the channel. Figure 5 shows typical voltammograms observed for TEA transfer across the liquid/liquid interface at various volume flow rates. The sigmoidal forward sweep, representing the transfer of the TEA from the aqueous phase to the organic phase, is characteristic of a steady-state response, whereas the reverse sweep displays a diffusioncontrolled peak-shaped response"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002427_50009-5-Figure7.49-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002427_50009-5-Figure7.49-1.png",
        "caption": "FIGURE 7.49 If the equivalent circuit in Fig. 7.48a is modified with the addition of the leakage inductance Lwl and the resistance Rwl of the magnetizing winding, the vector diagram in Fig. 7.48b is accordingly changed, by adding the corresponding contributions URw 1 = Rwlil and ULw I - - j r a L w l i l .",
        "texts": [
            "47, that the reactance jcoCw2 and the resistance Rw2 provide a negligible voltage drop on the secondary circuit because of the high value of the input impedance of the measuring instrument (typically 1 Mf~ with 10 pF in parallel). If, under practical circumstances, it is suspected that this is not the case, we might add a second instrument in parallel with the first one using similar connecting cables and look for a possible change of the reading. We will then consider a simplified equivalent circuit, similar to the circuit in Fig. 7.48a, but for the addition of the leakage inductance Lwl and the resistance Rwl in the primary circuit. The vector diagram in Fig. 7.48b is correspondingly modified in the diagram shown in Fig. 7.49. Again, we wish to relate Prneas and P, Smeas and S, which calls for determination of the relationship between the magnetizing current im(t), the supply current ill(t), and the secondary current i2(t). Based on the vector diagram of Fig. 7.49 and the equivalent circuit, we write im --- iH + jcoC1 N1 N2 ~ U 2 -}- ~ 1 1 i 2 - jtoCl(Rwl +jwLwl)il, (7.58) where the current il = im + i2 / -- im -- (N1/N2)i2. If we substitute il in Eq. (7.58), we obtain the desired relationship between the quantities appearing in the definition of Pmeas and P. The calculations and the due approximations i 2 KK i ra , co2LwlC1 << 1, ~oRwlC1 << 1 (7.59) done, we eventually obtain that measured and actual specific power loss are related by the equation Pmeas -- P + AP ~ P(1 - co2C1nwl) -}- ~ 1 NI_ _ + ~oC1Rwl ~ma N22 zmu2 sin ~"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002319_tmag.2003.810511-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002319_tmag.2003.810511-Figure6-1.png",
        "caption": "Fig. 6. Contours of eddy current loss (z-direction average). (a) Phase difference 20 . (b) Phase difference 30 . (c) Phase difference 40 . (d) Phase difference 50 .",
        "texts": [
            " It is found that the flux density waveforms in element A are similar to the sinusoidal waveforms, and those in element B have much more harmonic components, which are caused by the stator teeth. Fig. 5 shows the distributions of eddy current density vectors. It is found that there are large eddy current density vectors in the stator teeth and in the rotor core near the slots between the stator teeth [cf. Fig. 5(a)] and those distributed in the surface of the silicon steel sheet due to the skin effects [cf. Fig. 5(b)]. Fig. 6 shows the contours of eddy current loss. It is found that there is much more eddy current loss in the stator teeth and in the rotation direction side of rotor core. It is found that the eddy current loss in the stator yoke decreases, and that in the stator teeth increases, when the phase difference varies from 20 to 50 . It is also found that the eddy current loss in bridge of the rotor core increases as the phase difference increases. Fig. 7 shows the eddy current loss. It is found that the eddy current loss in the stator core has a minimum value when the phase difference is 35 and that in the rotor core decreases as the phase difference increases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003784_1.1829070-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003784_1.1829070-Figure5-1.png",
        "caption": "Fig. 5 \u201ea\u2026 The single flier eight-bar linkage. \u201eb\u2026 A two-degree-of-freedom nine-bar linkage. \u201ec\u2026 The first arbitrary choice of the instant center I27 . \u201ed\u2026 The second arbitrary choice of the instant center I27 . \u201ee\u2026 The secondary instant center I28 .",
        "texts": [
            "org/about-asme/terms-of-use 254 \u00d5 Vol. 127, Downloaded From: http://mechan theorem can now be used to determine the unique location of the instant center I19 . In other words, the instant center of the coupler link 9 is the point of intersection of the two lines I16I69 and I14I49 , as shown in the figure. The remaining secondary instant centers can now be obtained directly from the Aronhold\u2013Kennedy theorem. Example 2. The Single Flier Eight-Bar Linkage. Consider the single flier eight-bar linkage shown in Fig. 5~a!. Note that the secondary instant centers I13 and I24 can be located from the Aronhold\u2013Kennedy Theorem. The second method presented in Sec. 3 will be used to locate the instant center I28 . The procedure is to replace link 8 by two links, denoted as 8 and 88, which will result in a two-degree-of-freedom linkage with nine links, see Fig. MARCH 2005 icaldesign.asmedigitalcollection.asme.org/ on 02/26/20 5~b!. Note that the two instant centers I688 and I888 are coincident with the instant center I68 of the original single flier eight-bar linkage",
            " The secondary instant center I13 is not required in the solution and is, therefore, not shown on the figure for the purpose of clarity. The goal is to find the two lines on which the instant centers I28 and I288 must lie for this two-degree-of-freedom linkage. The procedure is to find one point on each line as follows. It is known that the instant center I27 must lie on the line I24I47 . Therefore, the two-degree-of-freedom linkage can be reduced to a single-degreeof-freedom linkage by choosing I27 ~denoted here as I27 1 ) arbitrarily on this line, see Fig. 5~c!. The location of the instant centers Transactions of the ASME 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F I28 1 and I288 1 can be obtained by: ~i! locate I37 1 at the intersection of the two lines I23I27 1 and I34I47 ; ~ii! locate I388 1 at the intersection of the two lines I36I688 and I37 1 I788 ; ~iii! locate I288 1 at the intersection of the two lines I27 1 I788 and I23I388 1 ; and finally ~iv! locate I28 1 at the intersection of the two lines I288 1 I888 and I25I58 . Now choose a second arbitrary location of I27 ~denoted here as I27 2 ), as shown on Fig. 5~d!. The location of the two instant centers I28 2 and I288 2 can be obtained by following a procedure similar to steps ~i!\u2013~iv!. The location of the two instant centers are shown on this figure. Therefore, the instant center I28 for the original indeterminate linkage is the point of intersection of the two lines I28 1 I28 2 and I288 1 I288 2 , as shown in Fig. 5~e!. The justification for this final step is as follows. If links and 8 and 88, of the two-degree-offreedom linkage, have the same relative velocity with respect to link 2 then the instant centers I28 and I288 must be coincident. In order for these two instant centers to be coincident, they must lie at the intersection of the two lines I28 1 I28 2 and I288 1 I288 2 . Therefore, links 8 and 88 must act as a single link, instantaneously, and can be replaced by the single link 8, resulting in the original singledegree-of-freedom indeterminate linkage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000158_s002211209700760x-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000158_s002211209700760x-Figure4-1.png",
        "caption": "Figure 4. Streamlines describing the flow around a cylinder in the fluid frame of reference. The cylinder is moving perpendicularly to the density gradient and the density gradient is characterized by \u03b5 = 1. A large density gradient is taken so that the perturbation to the streamlines is large and can be see. The direction of the force on the cylinder, F, is shown.",
        "texts": [
            "5) The strength of the line vortex, \u0393 , is indeterminate even though the flow it induces satisfies the kinematic condition on the surface of the cylinder and in the far field. However, an infinite amount of kinetic energy must be introduced to generate the flow induced by a line vortex; this is an unphysical assumption, so that \u0393 = 0. This could also be derived from the initial value problem for t > 0. Therefore, the streamfunction for the velocity field, v, around the cylinder is \u03c8 = \u2212Ur ( 1\u2212 a2 r2 ) sin \u03b8 + Ua2 4\u03c1B d\u03c10 dy {( 1\u2212 a2 r2 ) cos 2\u03b8 + a2 2r2 } . (4.6) The last term gives the effective circulation around the body which induces the lift force. Figure 4 shows the streamlines for the full velocity field (i.e. v+U ) around the cylinder in a fixed frame of reference when d\u03c10/dy > 0. Note that the streamfunction describing the flow past a cylinder (4.6) is only valid in the region r a/\u03b5, where \u03b5 = a|d\u03c10/dy|/\u03c10 1. However, for the specific case when the unperturbed density field has a quadratic dependence on y, so that \u03c10(1+\u03b5y/2a)2 (where \u03b5 is not necessarily small), the streamfunc- tion can be derived for the flow everywhere, namely \u03c8 = \u22122(Ua/\u03b5) ( 1\u2212 \u03c8s\u03b5/Ua )1/2 , where \u03c8s is the streamfunction describing the inviscid flow around a two-dimensional body fixed in a constant shear \u03b5U/2a"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000925_20.917621-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000925_20.917621-Figure1-1.png",
        "caption": "Fig. 1. Technical position of application of HDD.",
        "texts": [
            " Since then, there has been increasing demand for higher speed and longer life, making the application of higher technology necessary for the HDBs of HDDs. This problem is solved in the camcorder, so this is not a new subject [1] although rotor gyro issues remain. An oil seal design, which has higher reliability than conventional designs, is required for HDD hydrodynamic bearings. Fluid seal design is achieved through the use of oil surface tension and hydrodynamic pumping forces provided by grooves. Fig. 1 shows how we have advanced the commercialization of hydrodynamic bearing units from ordinary products in the lower-left of the figure (low speed, normal lifespan), to bearing units for HDDs in the upper-right or upper-middle of the Figure. These units require higher technology than seen in conventional products. There are three important design criteria for HDD bearings: 1) Optimization of groove angles and suction height of oil to prevent bubble ingestion, 2) Optimization of pump power combined with oil outflow prevention, and 3) Structural considerations with respect to high-speed rotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002758_jahs.49.109-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002758_jahs.49.109-Figure2-1.png",
        "caption": "Fig. 2. Spur gear fatigue rig gearbox with cover removed.",
        "texts": [
            " When damage was found, the damage was documented and correlated to the test data based on a reading number. Reading number refers to the once per minute data collection rate. Reading number is equivalent to minutes and can also be interpreted as mesh cycles equal to reading number times 104. In order to document tooth damage, reference marks are made on the driver and driven gears during installation to identify tooth 1. The mating teeth numbers on the driver and driven gears are then numbered from this reference. Figure 2 identifies the driver and driven gear with the gearbox cover removed. The principal focus of this research is the detection of pitting damage on spur gears. Pitting is a fatigue failure caused by exceeding the surface fatigue limit of the gear material. Pitting occurs when small pieces of material break off from the gear surface, producing pits on the contacting surfaces (Ref. 7). Gears are run until pitting occurs on one or more teeth. Two levels of pitting were monitored, initial (pits less than 0",
            "0397 cm diameter and cover less than 25 percent of tooth contact area) and destructive pitting (pits greater than 0.0397 cm diameter and cover greater than 25 percent of tooth contact area). If not detected in time, destructive pitting can lead to a catastrophic transmission failure if the gear teeth crack. Data were collected using vibration, oil debris, speed and pressure sensors installed on the test rig. Vibration was measured on the gear housing and at a support bearing location using miniature, lightweight, piezoelectric accelerometers. Location of both sensors is shown in Fig. 2. These locations were chosen based on an analysis of optimum accelerometer locations for this test rig (Ref. 8). Oil debris data were collected using a commercially available oil debris sensor that measures the change in a magnetic field caused by passage of a metal particle where the amplitude of the sensor output signal is proportional to the particle mass. The sensor measures the number of particles, their approximate size (125 to 1000 microns) and calculates an accumulated mass (Ref. 9). Shaft speed was measured by an optical sensor once per revolution of the shaft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003878_0301-679x(82)90074-3-FigureI-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003878_0301-679x(82)90074-3-FigureI-1.png",
        "caption": "Fig I Oil circulation through a porous bearing in which all the pores and the bearing gap are completely filled with oil",
        "texts": [],
        "surrounding_texts": [
            "Porous bearings A. L. Braun*\nMuch equipment in everyday use, such as small domestic appliances and audio equipment, has porous bearings to support a rotating shaft. The bearings in this type of equipment can only be supplied with lubricant once, during manufacture, so the use of porous bearings is an obvious solution. The porous wall of these bearings functions as a reservoir from which the bearing gap is filled with lubricant. With these bearings, problems are regularly encountered, such as noise, loss of lubricant, premature failure, irregular friction and inaccurate shaft position. In a practical investigation, attempts were made to obtain a better understanding of the causes of these problems and, where possible, to lay down guidelines for restricting or avoiding them. The investigation was concerned exclusively with cylindrical porous bearings, between 2.5 and 5 mm diameter, impregnated with oil having a relatively low viscosity and operating in the mixed lubrication regime\nKeywords. lubrication, porous bearings, lubricant loss\nIf a load is applied to a rotating shaft in a solid journal bearing, a pressure caused by the wedge effect will be generated in the lubricant in the bearing gap. This pressure is such that the shaft and the bearing bush are completely separated from each other by the lubricant film, ie hydrodynamic lubrication. Besides the load, the following parameters entirely determine the pressure generated in the bearing:\nb Bearing width hmin Minimum lubricant film thickness in the bearing R Shaft radius AR Shaft radial clearance in the bearing r/ Dynamic viscosity of the lubricant 6o Relative angular speed of the shaft with respect to\nthe bearing\nThe advantages of this type of bearing are the low wear of shaft and bearing bush and the low bearing friction. Also, the friction remains absolutely constant during a revolution so that, theoretically, the behaviour of this type of bearing can be predicted precisely.\nA disadvantage is that lubricant has to be pumped constantly into the bearing gap. This makes the solid journal bearing less suitable for use in consumer products.\nFor this very reason, the porous journal bearing is often found in consumer articles. 10 to 35% of the volume of porous bearings consists of interconnected pores which are impregnated once with lubricant, usually an oil with a low viscosity. The porous bearing material functions as a reservoir from which the bearing gap is filled with lubricant during operation and in which the lubricant is stored during standstill. This method should ensure that a porous bearing continues to function well throughout its life, usually without any further maintenance.\nWhen the shaft in the porous bearing is stationary, capillary action causes some of the oil to enter the bearing gap. The amount of oil which enters the bearing gap is determined\n*NF Philips' Gloeilampenfabrieken, Videq Lab, Building SFJ 7, 5600 MD Eindhoven, The Netherlands\nby the size of the bearing gap, the diameter of the pores and also, as we found, by the length of time that the shaft remains stationary. When the shaft begins to rotate, a pressure will be generated in the oil film, as is the case with the solid journal bearing (Fig 1). This pressure build-up causes oil in the loaded part of the bearing to disappear into the pores. A deficiency ofoit in the bearing gap is produced. According to current theory, this will bring about a lower pressure in the unloaded part, so that oil is sucked into the bearing gap. It is reasonable to assume, though, that the capillary action of the bearing gap also contributes to this oil transport.\n0301--679X/82/050235-08 $03.00 \u00a9 1982 Butterworth & Co (Publishers) Ltd 235",
            "I-\nA constant flow of oil from the loaded part to the unloaded part via the porous bearing therefore exists x . It should be noted, however, that this only applies when the bearing and the bearing gap are completely filled with oil.\nBesides the parameters which determine the pressure buildup in a solid journal bearing, the following may be added for a porous bearing:\nH Thickness of the bearing wall q~ Permeability of the bearing. This material property\ndetermines the flow resistance to which the oil is subjected in the porous bearing wall\nBearing materials with the same porosity may have an entirely different permeability. It has also been found that the spread in the permeability of a number of bearings of the same type is sometimes quite large 2 . These material properties will have an effect, albeit difficult to determine, on the pressure generated.\nThe literature provides various approximate calculations of the hydrodynamic load-carrying capacity of porous bearings, usually using shafts and porous bearings immersed in an oil bath. As far as normal porous bearing practice is concerned, neither these calculations nor the tests done to check them are valid.\nA look into the bearing gap\nAn experiment was carried out using a set-up which allows the bearing gap of a porous bearing to be viewed via a hollow glass shaft. In the set-up, a mirror-smooth polished\nhollow glass shaft rotates in a self-adjusting porous bronze bearing: R = 4 mm;AR = 13/am;speed = 500 r/min; oil viscosity: 0.043 N s m -2 at 20 \u00b0C and 0.015 N s m -2 at 70 \u00b0C; and radial load: 5 N. With the aid of a small mirror in the hollow glass shaft and a microscope with a large focal length, every point in the bearing gap can be observed (Fig 2).\nThe porous bearing was impregnated with oil just before the start of the test. After starting the glass shaft in the statically loaded porous bearing, it was observed that the oil became darker due to the bronze particles which were worn off from the bearing bush and scratches developed in the loaded part of the bearing. Shortly after the shaft started up, small air-bubbles appeared in the unloaded part of the bearing gap at the pores which had the largest crosssection. These air-bubbles increased in size and collected to form elongated air fingers. The porous bearing wall was then clearly no longer completely filled with oil: in some of the pores the oil had been replaced by air. Since the pores with the largest cross-section exert the smallest capillary force on the oil, the oil in these pores will be sucked out the easiest into the bearing gap. The air in the bearing wall can then penetrate into the bearing gap via these larger pores.\nFig 3 shows the bearing gap photographed in the test set-up, several hours after the start of the experiment. The bearing gap in the middle of the bearing was photographed in ten positions of a complete circle, by rotating the mirror through 36 \u00b0 each time. By joining the photos together we obtained a picture of the bearing gap in the middle of the\nbearing. It can be seen that the air which was sucked into the bearing has collected to form elongated air fingers. The oil in the region of the air fingers will not contribute to the load-carrying capacity of tile porous bearing. The loaded part of the bearing, in which there are no inclusions of air in the oil, so that here the oil can contribute to the loadcarrying capacity, occupies only one-seventh of the total circumference of the porous bearing in Fig 3. (In a solid bearing, the pressure-generating part of the oil film occupies virtually half of the bearing circumference.)\nShaft position in the porous bearing\nOne of the experiments done to see how porous bearings work under practical circumstances was an investigation into the shaft position in porous bearings operating in various types of small electric motors. A test set-up was used which displayed on an oscilloscope screen the\n-tr d = 25.1 _1\n0 \u00b0 L i ...... \u2022 270 \u00b0 IdO \u00b0 9 0 \u00b0 0 o\nDirection of rotation of the shaft"
        ]
    },
    {
        "image_filename": "designv11_11_0001224_1.2801113-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001224_1.2801113-Figure1-1.png",
        "caption": "Fig. 1 Robot SMART 3S",
        "texts": [
            " The role of the motor damping is also emphasized and it is shown how a feedback on motor velocity can greatly widen the range of the stabilizing integral gains, as well as the achievable bandwidth. Finally, some experimental results, obtained on the fifth joint of the robot SMART 3S, are reported in Section 4, to confirm the theoretical analysis. The experimental setup consists of a robot SMART 3S: a 6 d.o.f., 6 Kg payload industrial manipulator manufactured by COMAU, equipped with the open version of the COMAU C3G 9000 controller, linked to a DELL 486 50 MHz PC, and an ATI 6-axes force/torque sensor (Fig. 1). In the open version, the VME bus of the standard C3G con troller is linked to the AT bus of the PC through a VME-AT Journal of Dynamic Systems, Measurement, and Control DECEMBER 1995, Vol. 1 1 7 / 5 4 7 Copyright \u00a9 1995 by ASME Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jdsmaa/26219/ on 06/16/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use bus-to-bus communicator adapter (BIT3). The PC can read basic controller internal variables (e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002767_978-3-642-71015-5-Figure4.1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002767_978-3-642-71015-5-Figure4.1-1.png",
        "caption": "Fig. 4.1. Assumed configuration with image",
        "texts": [
            " Experiment has shown that equipment insulation is frequently punctured and transformer and/or circuit breaker bushings tend to flash over under current surges; it is therefore evident that resistances under surge conditions are high compared with their static counterparts. In the present section, an estimate of the surge resistance of ground rods is sought for the case of a lightning stroke. The outlined approach is of interest also for more complicated ground systems as well as for arbitrarily imposed transient current inputs. The circular ground rod (or pipe) is assumed to have a radius Qo and to be buried at a depth h ;p Qo beneath the soil surface (Fig. 4.1). The soil is model- 4.1 Surge Impedance of Extended Grounding Rods 165 led by an isotropic, homogeneous semi-infinite region, exhibiting an electric conductivity Us, vacuum magnetic permeability J.lo and vanishingly small dielectric coefficient Sr [4.1,2]: this implies a fictitious configuration in which the magnetic diffusion time constant Td outweighs its electric relaxation counterpart Tr , i.e. (4.1.1) Hence, according to this point of view, we regard the system - immediately after the stroke - as described by a magneto-quasistatic approximation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002614_0301-679x(87)90094-6-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002614_0301-679x(87)90094-6-Figure4-1.png",
        "caption": "Fig 4 Effect o f the crevice coefficient B/b, o f the rubbing contact, on K, the leakage coefficient",
        "texts": [],
        "surrounding_texts": [
            "existence of microasperities on contact surfaces of oil seals and their relationship to sealing performance. In their studies, it was shown that there was a significant correlation between sealing performance and wear configuration on the oil side of contact surfaces of oil seals. Tabor 4 indicated that peaks and valleys of the contact surfaces would generate the suction, although he did not mention the relationship between the sealing performance and the sucking action directly.\nSince these findings have agreed with empirical knowledge obtained through experience of oil seal designing, it was thought that the analysis of the sealing mechanism would be completed by understanding quantitatively the dynamic behaviour of the microasperities of contact surfaces and relating this to sealing phenomena s'6.\nThe sealing mechanism was analysed as follows:\n(1) Dynamic behaviour of microasperities on sealing surfaces and triple interlines between air, oil and solid surfaces was observed through a hollow glass shaft with the aid of a microscope, a video camera and a video-tape recorder (VTR). The original recorded pictures of the microasperity contacts were analysed statistically after digital image processing. As a result, some parameters (M1, N1/No, n/No, 71,7z ) relevant to the microgeometries of sealing surfaces which affect the sealing mechanism were obtained. (2) Next, the relation between the above parameters and the sealing condition was clarified. (3) By giving a physical meaning to each parameter value, models of sealing surfaces were proposed to characterize actual microgeometries for non-leaking and leaking oil seals. (4) In order to confirm the adequacy of the model of the dynamic behaviour of contact surfaces, model seals were made in order to try to reproduce a non-leaking oil seal.\nThrough a series of such analysis, the quality of sealing was able to be explained by differences in the form of the contact surface.\nIn this paper, fundamental matters which have been used during the study are briefly explained, and the points which require attention are clarified. The research procedure and the experimental results are then explained. Further-\nNakamura - sealing mechanism o f rotary shaft l ip-type seals\nmore, thetheoretical sealing mechanism obtained from the experimental results is compared with the simulative experiment, and the adequacy of the theory is discussed.\nP r e v i o u s i n v e s t i g a t i o n s\nThe frictional behaviour of oil seals is shown in Fig 1 and expressed by the following equation:\nf = ~ G x/a (1)\nwhere f i s the coefficient of friction and G is a nondimensional duty parameter. According to Fig 1, qb is a characteristic number expressing the lubricating condition of the lip, is closely related to the non-leaking and the leaking phenomenon, and there exists the following relations:\n> ~c : non-leaking q5 < q5 c : leaking\nwhere ~c is a critical value of ~ between the non-leaking and the leaking condition. Further, through theoretical investigation, q5 has been expressed, from the schematic representation in Fig 2, in the following equation:\nqb = 2C (hmax/X) a/3 (D/2hmax) 1/3 exp (/3P a ~J'/hmax)\n(2)\nand has been discussed in relation to the shaft surface roughness and the visco-elasticity of lip materials 7. However, in that investigation, peaks and valleys of contact surfaces of oil seals were not discussed.\nT R I B O L O G Y i n t e r n a t i o n a l 91",
            "Nakamura - sealing mechanism o f ro tary shaft l ip - type seals\nbeen reported 2'3. In these studies, the authors have paid attention to the phenomena where oil leaks with converse installation of the oil seals and air is generally sucked into the oil side with normal installation. They tried to grasp the sealing phenomena by quantitative evaluation of the oil transferred through the gap between contact surfaces with converse installation of oil seals, instead of quantitative evaluation of the air sucked through the gap with normal installation.\nFrom these previous experimental and theoretical investigations, it was considered that the course of investigation should be directed to the dynamic behaviour of the rubbing portion between the shaft and the lip edge.\nExperiment Apparatus Apparatus for observation of sealing surfaces of oil seals is shown schematically in Fig 5. The observation apparatus is constructed with a lighting system (a light source, a condenser lens, an optical fibre, and a mirror, a seal specimen which is installed into a housing and the measuring system (a hollow glass shaft, a mirror, a microscope, a TV camera for industrial use, a monitoring TV and a video tape recorder). The hollow glass shaft is rotated by a variable speed changer through a spindle.\n92 April 87 Vol 20 No 2",
            "Fig 6. It consists of the input unit (a video tape recorder), the analysing and extracting-processing unit (a microcomputer, an image store memory, a colouring unit and a colour monitor) and the output unit (a printer and a video graphic recorder).\nTable 1 shows seal lip configurations and classification symbols of test specimens. Based on differences in finishing method, there are two groups of oil seals: the group with trimmed lips (1 and 2) and the group with non-trimmed lips (3 and 4). These oil seals are also classified into two groups in Table 1 by wear configuration; the group which has the wear at the atmospheric side of the lip leading edge (1 and 3), and the group which has the wear at the oil side of the lip leading edge (2 and 4).\n1 2 3 4\nOuter diameter, mm 108 108 108 108 Nominal diameter, mm 85 85 85 85 Interference, mm 1.3 1.4 1.5 1.5 Total contact load of lip, N 19.6 23.5 24.5 24.5\nTest conditions The test conditions for observing asperity contact were:\nDiameter of hollow glass shaft: 85 mm Surface roughness of the hollow glass shaft: 0.02 #m R a Number of shaft revolutions: 0 - 1 0 r rain -1 in dry\ncondition and 0 -700 r rain -z in lubricating condition\nLubricating oil: motor oil (10W-30) Temperature of rubbing surface: 38 \u00b0C\nShaft eccentricity: 0.005 ram.\nExperimental procedure Fig 7 shows the image of the contact surface of the test specimen, magnified 700 times by a microscope and observed through an industrial TV camera. This image is recorded by a VTR (video tape recorder) after projecting on the monitoring TV. The recorded VTR tape is the source of input data for image processing. Data analysis and parameter extraction are processed by the analysing and extracting processing unit with a microcomputer, an image store memory, colouring unit and colour monitor. The results of the analysis are obtained as output from the printer and the video graphic recorder. This procedure is shown in Fig 8.\nT h e o r y\nDefinition of microgeometry oil seat contact surfaces\nAs the numbers, sizes, distributions, cross-sectional areas, configurations, orientations, neighbouring relations etc of microasperities existing at contact surfaces of oil seals express totally the features of the contact surfaces, a quantified expression of these factors is first necessary. Reference is therefore made to the following three experimental results:\nOil seals with the peak of contact pressure distribution on the oil side tend to seal 7.\nWhen the contact surfaces of oil seals become smooth, they tend to have difficulty sealing 2'3 \u2022\nTRIE~OLOGY international 93"
        ]
    },
    {
        "image_filename": "designv11_11_0000932_cdc.1991.261862-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000932_cdc.1991.261862-Figure1-1.png",
        "caption": "Fig. 1. ~~IIU d c v of f d o m Robot",
        "texts": [
            " In the present problem of eliminating small insignificant parameten of well conditioned models, this reduction method is less efficient than the stepwise regression method. The latter is more adapted in keeping the model-error as small as possible and in reducing the model complexity. It will be used to determine and identify the essential parameters Xr which are parameters of important contribution to the model (IIWrXrll is important). This section presents an application of the above results to a serial rigid link robot. The first 3 d.0.f. of the PUMA 560 robot is considered (see Fig. 1.). The standard parameters are given by Armstrong [12] and modified so that zeto value inertial parameters are supposed to be 1.E4 The base parameters are then calculated f\" methods presented in [3,113. We get nb= 15 base parameters. The energy difference equation (2) and the exciting trajectory obtained by Gautier [10,113 are used to compute W. The condition number is: Condo= 1.1158WO1 All the identification simulations are realized using an additive noise as described in section 3.2. with: where the perturbation coefficient PertCoef represents the importance of the simulated noises"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001532_s0022-460x(03)00283-9-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001532_s0022-460x(03)00283-9-Figure5-1.png",
        "caption": "Fig. 5. Spring\u2013damper model of cable.",
        "texts": [
            " For the ith actuator, the general driven force vector acted on the base and stabilized platforms can be partitioned as Fai n0ai \" # \u00bc u\u00f0t\u00dei dUiLi dUiLi 2GT a *s 0 aiA T a dUiLi \" # ; Fbi n0bi \" # \u00bc u\u00f0t\u00dei dUiLi dUiLi 2GT b *s 0 biA T b dUiLi \" # ; \u00f07\u00de where dUiLi is the length of vector dUiLi: Ai represents the transformation matrix of the ith rigid body with respect to the global reference frame defined in Eq. (A.6) (see Appendix A). The top operator \u2018\u2018B\u2019\u2019 gives the skew matrix of a vectors. Thus in Eq. (7), *s is defined as *s \u00bc 0 sz sy sz 0 sx sy sx 0 2 64 3 75: \u00f08\u00de In the analysis of the plant, the supporting cables are modelled with springs and dampers. Consider the spring-damper model, shown in Fig. 5, which connects point Pi \u00f0i \u00bc 1;y; 12\u00de on the base platform and Pj \u00f0j \u00bc 1;y; 12\u00de on the fixed reference frame (in the radio telescope, Pj is on the stabilized tower or on the ground). The vector from Pi to Pj is dij \u00bc rj ra Aas 0 ai: \u00f09\u00de Thus, the square of the length of the cable is given by l2ij \u00bc dT ijdij \u00f010\u00de and the time rate of the change of the length is \u2019lij \u00bc dij lij T \u00f0\u2019rj \u2019raAa*s 0 aix 0 a\u00de; \u00f011\u00de where x0 represents the relative angular velocity of the rigid body defined as x0 \u00bc 2G\u2019p: \u00f012\u00de The magnitude of force acting on the base platform by the jth cable, with tension taken as positive, is fj \u00bc k\u00f0lij lij0\u00de \u00fe c\u2019lij; \u00f013\u00de where k is the spring coefficient, c is the damping coefficient, and lij0 is the initial length of the jth cable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000466_s0039-9140(00)00551-8-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000466_s0039-9140(00)00551-8-Figure1-1.png",
        "caption": "Fig. 1. Construction of the flow through cell. (A) Perspex block; (B) stainless steel fitting; (C) inlet fitting; (D) lead to the working electrode; (E) carbon felt working electrode; (F) millipore membrance filter; (G) rubber washer; (H) nylon mesh; (I) platinum reference electrode; (J) outlet fitting.",
        "texts": [
            " Construction of electrode and cell The working electrode was made of porous carbon felt which was originally designed for use as high-temperature insulation in inert-atmosphere or higher-vacuum electric furnaces made of carbon fibers. This flexible material has low density, which results in a large surface area combined with small volumes, and it is chemically resistant to acids and bases. Therefore, the porous carbon felt is a kind of ideal material for the working electrode in a coulometric detector. The flow-through cell (see Fig. 1) was constructed from a perspex block (A). The perspex block was drilled and tapped to accepted a stainless steel fitting (B), which served as the counter electrode. One end of the stainless steel fitting was sealed with an inlet fitting (C) joined with a stainless steel tube (D), which served as the lead to the carbon felt working electrode (E). A piece of millipore membrane filter (F) was adjusted in the stainless steel fitting to isolate the working electrode from the counter one. A rubber washer (G) was gently pushed down, in order to mantain the millipore membrane filter stick in the inner wall of the stainless steel fitting"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003733_j.engstruct.2006.03.018-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003733_j.engstruct.2006.03.018-Figure2-1.png",
        "caption": "Fig. 2. (a) Pile whose end at the first regions is semi-rigid connected and simply supported and the end at the second region is simply supported. (b) Pile whose end at the first region is semi-rigid connected and not restricted for horizontal displacement and the end at the second region is free.",
        "texts": [
            " Bending moment at the semi-rigid connected end is written as: M1 = C\u03b8 \u00b7 \u03c6\u2032 1 ( L1 L ) (40) where M1 and \u03c6\u2032 1( L1 L ) are the bending moment of the pile end at the first region and the rotation, respectively. The position vectors at the simply supported and the free ends are transferred to the position vectors at the semi-rigid connected end by Eqs. (41) and (42) using Eq. (38) in the cases that the pile ends at the first region is restricted for horizontal displacement and semi-rigid connected against rotation as in Fig. 2(a), and is not restricted for horizontal displacement and semi-rigid connected against rotation as in Fig. 2(b): 0 \u03c6\u2032 1 ( L1 L ) \u03c6\u2032 1 ( L1 L ) \u00b7 C\u03b8 T 1 ( L1 L )  =  F11 F12 F13 F14 F21 F22 F23 F24 F31 F32 F33 F34 F41 F42 F43 F44   0 \u03c6\u2032 2(0) 0 T 2(0)  (41) \u03c61 ( L1 L ) \u03c6\u2032 1 ( L1 L ) \u03c6\u2032 1 ( L1 L ) \u00b7 C\u03b8 0  =  F11 F12 F13 F14 F21 F22 F23 F24 F31 F32 F33 F34 F41 F42 F43 F44   \u03c62(0) \u03c6\u2032 2(0) 0 0  (42) where the terms Fi j are the terms of the transfer matrix [F(L1+ L2)]; \u03c62(0) and \u03c6\u2032 2(0) are the displacement and the rotation of the pile end at the second region, respectively; and T 1( L1 L ) and T 2(0) are the shear forces of the pile ends at the first and the second regions, respectively",
            " (43a)\u2013(43d) and (44a)\u2013(44d) are written in matrix form as:  F12 F14 0 0 F22 F24 0 \u22121 F32 F34 0 \u2212C\u03b8 F42 F44 \u22121 0   \u03c6\u2032 2(0) T 2(0) T 1 ( L1 L ) \u03c6\u2032 1 ( L1 L )  = 0 (45)  F11 F12 0 \u22121 F21 F22 \u22121 0 F31 F32 \u2212C\u03b8 0 F41 F42 0 0   \u03c62(0) \u03c6\u2032 2(0) \u03c6\u2032 1 ( L1 L ) \u03c61 ( L1 L )  = 0. (46) The following conditions are written for non-trivial solutions of relations (45) and (46):\u2223\u2223\u2223\u2223\u2223\u2223\u2223\u2223 F12 F14 0 0 F22 F24 0 \u22121 F32 F34 0 \u2212C\u03b8 F42 F44 \u22121 0 \u2223\u2223\u2223\u2223\u2223\u2223\u2223\u2223 = 0 (47) \u2223\u2223\u2223\u2223\u2223\u2223\u2223\u2223 F11 F12 0 \u22121 F21 F22 \u22121 0 F31 F32 \u2212C\u03b8 0 F41 F42 0 0 \u2223\u2223\u2223\u2223\u2223\u2223\u2223\u2223 = 0. (48) Thus, frequency equations of piles that are semi-rigid connected at the first region end and that the support type of both ends is given in Fig. 2(a) and (b) is obtained using Eqs. (47) and (48) respectively as: F12 F34 \u2212 F32 F14 + (F22 F14 \u2212 F12 F24)C\u03b8 = 0 (49) F41 F32 \u2212 F31 F42 + (F21 F42 \u2212 F41 F22)C\u03b8 = 0. (50) Two models for piles that are partially embedded in the soil and whose ends above the soil are semi-rigid connected by elastic rotational springs having the stiffnesses of the rotational springs of C\u03b8 are considered for numerical analysis. In the first pile model, the end of the pile at the first region is restricted for horizontal displacement and the end of the pile at the second region is simply supported"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000534_s1474-6670(17)47309-5-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000534_s1474-6670(17)47309-5-Figure8-1.png",
        "caption": "Fig. 8. The five-axle, two-steering system showing the virtual extension which is added in front of the second steering wheel. Such a system is en visioned as being used where maneuverability around narrow passageways in danger zones is of utmost importance.",
        "texts": [
            " The bottoms of the chains in the chained form (or equivalently the flat out pu ts of the system) were chosen to to be the (x, y) position of the passive axle along with the angle of the trailer (see Figure 7) , and because of the relative simplicity of the three-axle system, that choice allowed the kinematic equations to be put into multi-input chained form without using dy namic state feedback . Since the fire truck fits into the class of multi-steering trailer systems, it can also be converted into multi-input chained form using the (x, y) position of the last axle and the trailer angle as the bottoms of the chains. One virtual trailer will then need to be added, showing that although virtual extension is not always nec essary, the procedure outlined in this paper will always result in a chained form . Consider now a five-axle system with two steering wheels, as depicted in Figure 8. In effect, this is a fire truck with two passive trailers . Using the pro cedure outlined in Section 3, choosing the bottoms of the chains as the (x, y) position of the last axle and the hitch angle ifil, this system can be con verted into multi-input chained form and steered using one of the methods outlined in Section 4. In fact , as has been recently proven in (Tilbury and Sastry, 1994), there does not exist a transforma tion into chained form for this particular five-axle system without using dynamic feedback "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003154_3-540-28247-5_19-Figure19.7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003154_3-540-28247-5_19-Figure19.7-1.png",
        "caption": "Fig. 19.7. A robot arm of six joints",
        "texts": [
            " Spherical, cylindrical, and planar joints, which have more than one degree of freedom, may be represented by combinations of the simple joints above; for example, a spherical joint is represented by three revolute joints with axes all intersecting in one point but not all three axes coplanar. See Hunt [12], Table 1.1, for details and figures. Suppose a three-dimensional robot arm has six simple joints (after replacing joints of more than one degree of freedom by combinations of simple joints), say A1, A2, . . . , A6. Some of the Ai are allowed to be indecomposable. Then the robot arm has full mobility if A1 \u2228 A2 \u2228 . . . \u2228 A6 = V (2), in other words, A1, A2, . . . , A6 span all of V (2). A critical configuration is any configuration in which A1 \u2228 A2 \u2228 . . . \u2228 A6 = 0. Figure 19.7 shows a robot arm with full mobility in the illustrated position. Since it has six simple joints, full mobility means the six joints have Pl\u00fccker coordinate vectors that are linearly independent, and hence are NOT in a critical configuration. Much of the theory of screw systems and of line geometry (see Hunt [12]) can be expressed in terms of the Grassmann\u2013Cayley Algebra of V (2). For example, a cylindroid may be defined by a 2-system of screws, which may be represented as an general two-dimensional subspace of V (2), and thus as the support of A1 \u2228 A2 for some 2-tensors A1 and A2",
            " Thus the twist space of the parallel connection of C and D is the support of AC \u2227 AD if the super meet is not zero, and the wrench space of the parallel connection of C and D is the support of BC \u2228 BD if the superjoin is not zero. Similar considerations apply to series\u2013parallel robots, by applying the above ideas to one step of the construction at a time. There is also the possibility of computing the twist and wrench spaces of complicated robots which are not constructable by successive series and parallel constructions. This is done by Delta\u2013Wye transformations; see [8] or [21]. Consider the example of a robot arm with six revolute joints, as shown in Fig. 19.7. This is modified from a robot considered for the US space shuttle. The large cylinders represent revolute joints, and the thin cylinders represent links. We wish to find the critical configurations of the arm. We choose two points on each joint axis, and consider the six joint centers a1a2, b1b2, c1c2, d1d2, e1e2, f1f2. Notice that where possible we have chosen the points determining the axes to coincide, namely a2 = b1, e2 = f1, and c2 = d1, where the last of these is a point at infinity. Since the robot arm consists of the six joints in series, the twist space is a1a2 \u2228 a2b2 \u2228 c1c2 \u2228 c2d2 \u2228 e1e2 \u2228 e2f2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000609_s0957-4158(98)00031-2-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000609_s0957-4158(98)00031-2-Figure2-1.png",
        "caption": "Fig[ 2[ A car!pole inverted pendulum[",
        "texts": [],
        "surrounding_texts": [
            "In this section\\ the proposed chattering elimination algorithm is applied to the following non!linear system \u00f07\u0141] y\u00be $ 9 0 \u2212a \u22121\u00a6x\u00be%y\u00a6$ 9 0%u\\y $ x x\u00be% \"14# where the parameter a is uncertain[ The estimated value of a is 1 but the actual value of a in the simulation is 4[ Therefore we have feq\"y# $ 9 0 \u22121 \u22121\u00a6x\u00be%y \"15# A sliding plane is de_ned as s \u00f00 0\u0141e 9\\ where e $ e e\u00be% $ xd\u2212x \u2212x\u00be % and xd is the reference input[ Obviously this sliding plane is stable since e will exponentially decrease to zero once the sliding plane is hit[ The parameters td\\ ked\\ ks and kmax are selected as 0\\ 1\\ 09 and 09 respectively[ The system is put to simulation[ The discontinuous switching is assumed to have a time!delay of 0 ms[ Figures 0 and 1 show the closed!loop transient responses of the system with respect to a unit step reference input in xd without and with the application of the chattering elimination algorithm respectively[ The value of k without applying our algorithm is set at kmax 09[ It can be seen that the transient responses are similar[ So\\ the proposed algorithm does not a}ect the transient behavior very much[ However\\ due to the time! delay of the switch\\ a chattering in the output and a steady!state error of 9[91 in x are seen in Fig[ 0[ On applying the proposed chattering elimination algorithm\\ it can be seen from Fig[ 1 that both the chattering and the steady!state error are eliminated[ In fact\\ since the discontinuous control ud is completely replaced by ux in the steady! state\\ the control power is much reduced[ As an application example\\ the proposed chattering elimination algorithm is also applied to a car!pole inverted pendulum \u00f08\u0141 as shown in Fig[ 2[ The equation of motion is as follows] x\u00be0 x1 x\u00be1 `sin\"x0#\u2212amlx1 1sin\"1x0#:1\u2212acos\"x0#u 3l:2\u2212amlcos1\"x0# \"16# where x0 denoted the angle \"in rad# of the pendulum from the vertical axis\\ x1 is the angular velocity \"in rad s\u22120#\\ ` 8[7 ms\u22121 is the acceleration due to gravity\\ m 1[9 kg is the mass of the pendulum\\ a \"m\u00a6M#\u22120\\ M 7[9 kg is the mass of the cart\\ 1l 0[9 m is the length of the pendulum\\ and u is the force applied to the cart \"in Newtons#[ A sliding plane is de_ned as s \u00f00 9[0\u0141 x 9\\ where x \u00f0x0 x1\u0141T is the system state vector[ This sliding plane is stable because x0 will exponentially decrease to zero once the sliding plane is hit[ The discontinuous switching has a time!delay of 0 ms[ Figure 3 shows the zero!input responses of x under the initial condition x9 \u00f01 9\u0141T when k 09[ It can be seen that chattering in x1 occurs[ On applying the proposed chattering elimination algorithm with td\\ ked\\ ks and kmax selected as 0\\ 09\\ 09 and 09 respectively\\ the zero!input responses are shown in Fig[ 4[ Although chattering exists during the transient response \"before 3 s#\\ it is successfully eliminated at steady state[ Moreover\\ the transient responses in Figs 3 and 4 are similar\\ showing that the proposed algorithm does not signi_cantly a}ect the transient responses["
        ]
    },
    {
        "image_filename": "designv11_11_0003146_1-84628-214-4-Figure2.4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003146_1-84628-214-4-Figure2.4-1.png",
        "caption": "Fig. 2.4. Basic receptors (equilibrium, touch, smell) and effectors (muscles) in Framsticks.",
        "texts": [
            " The two basic Framsticks effectors are muscles: bending and rotating. Positive and negative changes of muscle control signal make the sticks move in either direction, which is analogous to the natural systems of muscles, with flexors and extensors. The strength of a muscle determines its effective ability of movement and speed (acceleration). If energetic issues are considered in an experiment, then a stronger muscle consumes more energy during its work. A sample framstick equipped with basic receptors and effectors is shown in Fig. 2.4. Other examples of receptors and effectors are energy level tester, water detector, vector eye, length muscle, and thrust. 2 Framsticks 43 The world can be flat or built of smooth slopes, or blocks. It is possible to adjust the water level, so that not only walking/running/jumping creatures, but also the swimming ones, are simulated. The boundaries of the virtual world can be one of three types: \u2022 hard (surrounding wall: it is impossible to cross the boundary); \u2022 wrap (crossing the boundary means teleportation to the other world edge); \u2022 no boundaries (the world is infinite)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000698_1.1326030-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000698_1.1326030-Figure6-1.png",
        "caption": "FIGURE 6. A right humeral rotation involving 90\u00b0 flexion and 90\u00b0 external rotation can be performed in two sequences. In sequence 1, the first rotation is 90\u00b0 external rotation from attitude \u201eu0,v0,w0 \u2026 in \u201ea\u2026 to attitude \u201euf,vf,wf \u2026 in \u201ef\u2026, then followed by 90\u00b0 flexion to attitude \u201eug,vg,wg \u2026 in \u201eg\u2026. In sequence 2, the first rotation is 90\u00b0 flexion from attitude \u201eu0,v0,w0 \u2026 in \u201ea\u2026 to attitude \u201euh,vh,wh \u2026 in \u201eh\u2026, then followed by 90\u00b0 external rotation to attitude \u201eui,vi,wi \u2026 in \u201ei\u2026. As shown in the figure the two sequences are equivalent, since final attitude \u201eug,vg,wg \u2026 of sequence 1 equals to final attitude \u201eui,vi,wi \u2026 of sequence 2. XYZ is a reference coordinate system fixed on the trunk.",
        "texts": [
            " The sign of the angles a and g can also be determined using Eqs. ~5!, ~6!, ~12!, and ~13!. Therefore, the three spherical rotation angles a590\u00b0, b590\u00b0, and g590\u00b0 are fully determined. Example 2 In this example, we investigate another pattern of humeral rotation involving 90\u00b0 flexion and 90\u00b0 external rotation, which is described as a 90\u00b0 elevation at zero elevation plane and a 90\u00b0 axial rotation in the spherical rotation coordinate system. The three angles are b 590\u00b0, a50\u00b0, and g590\u00b0. Graphical presentation of this pattern of rotation ~Fig. 6! shows that the unique final attitude is u25ug5ui5F u1 2 u2 2 u3 2 G5F 0 1 0 G , v25vg5vi5F v1 2 v2 2 v3 2 G5F 0 0 1 G , w25wg5wi5F w1 2 w2 2 w3 2 G5F 1 0 0 G . ~38! Forward Solution of Example 2. The three known rotation angles are b590\u00b0, a50\u00b0, and g590\u00b0. Knowing the three rotation angles, the integrated rotation matrix can be found from Eq. ~26! as R5U0 0 1 1 0 0 0 1 0 U . ~39! Therefore, the attitude following the rotation can be obtained using Eq. ~28! as u95Ru05U0 0 1 1 0 0 0 1 0 UU1 0 0 U5U0 1 0 U , v95Rv05U0 0 1 1 0 0 0 1 0 UU0 1 0 U5U0 0 1 U , w95Rw05U0 0 1 1 0 0 0 1 0 UU0 0 1 U5U1 0 0 U "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000965_iros.2001.976407-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000965_iros.2001.976407-Figure1-1.png",
        "caption": "Fig. 1 Mobile manipulator",
        "texts": [
            " First we derive the dynamics of the mobile manipulator considering it as the combined system of the manipulator and the nonholonomic mobile platform. Then the trajectory planning problem is formulated as the optimal control problem with some constraints. To solve the problem numerically, we use the concept of the order of priority and the gradient function which are synthesized in the hierarchical manner [14]. Simulation results are given to show the effectiveness of the proposed algorithm. 2 Modeling of Dynamic Equation We consider a mobile manipulator shown by Fig.1. 2264 Dynamic equation of the mobile manipulator is given by the following equation. B r ( q r ) = Mrn ( 4 ) i + C(4, 4) = F (1) where M,(q) is the inertia matrix and C(q,q) represents the Coriolis and centrifugal forces. Their details are omitted. q and F are the following vectors. Q = (2,Y,4,~1,w2,@l,Q2)T (2) - - ;cos$ $cos$ 0 0 21, 2fw 0 0 - 0 0 0 1 - ;sin4 $sin$ 0 0 0 0 1 0 (17) -- (3) F = (O,O, 0, r,, , 7w2, 761 , 7 e 2 ) Pc(z,y) is the coordinates of the center of gravity of the mobile platform, 4 is the heading angle of the mobile platform, w1 and w2 are angular positions of two driving wheels, 81 and 62 are joint angles of the manipulator and T ~ , and rw2 are input torques of the platform and 78, and re2 are joint torques of the manipulator",
            " Next, the constraint equation to which the platform is subjected is given T where r ( 5 ) 1 1 0 0 -$cos@ -;cos@ 0 0 0 -$sin@ -;sin$ 0 0 0 0 1 -k 0 0 - 21, where T is the radius of the driving wheel and 21, is the distance of two wheels. Using the B(q) matrix which satisfies q can be expressed as follows where kc = (7iI1,2i)2,e&)T One choice of B(q) is as follows. ' $cos@ $cos4 0 0 $sin@ $sin@ 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 . o 0 0 1 r -- - 21, 21, 3 End-Effector\u2019s Specified Path Constraint From Fig.1 the position of the end-effector, P, (z,, 9,) is given by Se = 2 + COS $ + 11 COS($ + 01) +z2 COS(^ + el + e,) Ye = y + d sin $ + 11 sin($ + 61) +Z2 sin($ + O1 + 0,) (19) (20) Let the path which the end-effector must follow be given as follows g(pe) E g(Ze ,Ye) = 0 (21) Here x, and ye are functions of qr. rewrite eq. (21) as Therefore we Differentiating the above equation we have where Jr (qr ) = agl (qr ) /aqr . Differentiating eq. (23) once more, we have Substituting Q r = Br(qr)ic and qr = B,",
            " If the following conditions llr;+l(( < \u20ac1, ((T;+l(( < \u20ac 2 , IIr;+lll < \u20ac 3 , ( ( P + l - P k ) / P k ( < \u20ac4 are satisfied simultaneously, stop calculation. If not, then set k = k + 1 and return to Step 3. 7 Example In this section, the proposed algorithm is applied to plan the sub-optimal trajectory of the 2-link planar nonholonomic mobile manipulator. Parameter values are as follows; mass of the platform : rn, = 50.0 [kg], mass of the wheel : m, = 15.0 [kg], mass of the link : ml = m2 = 10.0 [kg], length of the link : l1 = 12 = 2.0 [m], I , and 1, in Fig. 1 are 1.7 [m] and 1.5[m] respectively., End-effector's psth is assumed to be the straight line connecting (z,y) = (0,O) and (z,y) = (15.0,15.0). zo and xd are assumed as follows. ICO = (-3.323, -3.323,45.0,0,0,0,0,0,0)T ~ , j = (11.677,11.677,45.0,0,0,0, O , O , O ) T t f is set to 5.0. Perfomance index is given by t f P = l u T W u d t Where W is the weighting matrix and set to W = diag.[l.O, 1.0, 1.0, 1.01. Two obstacles which.are circles of radii r , = 2.0 [ m ] ' ~ centerd at Pt(x,y) = (5.0,l"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002848_0020-7462(84)90034-9-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002848_0020-7462(84)90034-9-Figure1-1.png",
        "caption": "Fig. 1. Definition of coordinate system, loading and stress state.",
        "texts": [
            " The well-known equations of membrane equilibrium of axi-symmetric shells of revolution for a deformed \"'mean\" surface of such a membrane are written as d N ,\u00a2, ~ (Ro sin(/~ N,/,) = O: R~ q (la, b) which after simple transformations are rearranged into 2~rsin0 - Req\" Q = 27r q R j cos(/~d(/~ (2a, b) in which the unknown meridional membrane force, N e, was replaced by (2 representing the total vertical force exerted on the membrane by the internal pressure\" R~ and R0 denote the meridional and circumferential radii of curvatures: q signifies internal pressure and 4) designates the meridional angle as defined in Fig. 1. For an axi-symmetrical membrane r = R0sin0 and the single (non-trivial) 1 dr Gauss Codazzi equation takes the form R,~- . Substituting this result into cosO dq5 equations (2), one obtains dr Q f \" d 0 - 2 r r r - q ' t a n 4 ' ( 2 = 2 ~ ~qrdr (3a, b) the second of which may also be written as dO = 27zrq. (4) dl' If the internal pressure q is given as a function oft', equat ions (3) can be solved for the shape of the wrinkled region in the polar coordinate system r, qS. To determine the shape in terms of the o r thogona l coordinates (r, h), a further equat ion relating t7 to r and qS, and given by dh - - = tan ~b (5) d r has to be solved, assuming that the internal pressure is also expressed in terms of h as q = q(h) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003504_apec.2004.1295998-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003504_apec.2004.1295998-Figure5-1.png",
        "caption": "Fig. 5 Mechanical plant for experiment",
        "texts": [
            " 4 shows the system block diagram for the closed loop operation. All controllers, notch filters, and the position estimator are implemented in the digital domain. Notch filters are implemented to decouple the high frequency signals at the injection frequency from the signals used in controllers. If high frequency signals are not properly decoupled, it may cause divergence in the position controller, because the position controller has the derivative term (D controller) for the stability issue. III. EXPERIMENT Fig. 5 shows the mechanical plant of the AMB. The maximum rotating speed of the rotor is 60,000r/min. Fig. 6 shows the power amplifier and the controller using the TMS320VC33 DSP. It has 7 three-phase inverters (Fairchild Semiconductor Smart Power Module; FSBS10SH60), which means 21 arms are available, and thus it can derive 10 coils by 10 full-bridge inverters. Table I shows the major parameters of the experimental system. Fig. 7 shows the step response of the proposed sensorless position control. The position reference changes by 10\u00b5m"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003146_1-84628-214-4-Figure2.2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003146_1-84628-214-4-Figure2.2-1.png",
        "caption": "Fig. 2.2. Forces involved in the native Framsticks simulation.",
        "texts": [
            " Parts and joints have some fundamental properties, like position, orientation, weight, and friction, but there may also be other (custom) properties, like the ability to assimilate energy, durability of joints in collisions, etc. Articulations The power of contemporary computers suffices to use very accurate simulation engines for evolutionary optimization processes [18]. The integration of such an engine is planned for Framsticks version 3.0. 2 Framsticks 41 exist between sticks where they share an endpoint; the articulations are unrestricted in all three degrees of freedom (bending in two planes plus twisting). Figure 2.2 shows forces considered in the native Framsticks simulator. Brain (the control system) is made of neurons and their connections. A neuron may be a signal processing unit, but it may also interact with body as a receptor (sensor) or effector (actuator). There are some predefined types of neurons, for example: \u2022 \u201cN\u201d \u2014 the standard Framsticks neuron, which is a generalized version of the popular weighted-sum sigmoid transfer function neuron used commonly in AI. The three additionally introduced parameters influence speed and tendency of changes of the inner neuron state, and the steepness of the sigmoid transfer function"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003507_jsen.2006.881421-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003507_jsen.2006.881421-Figure4-1.png",
        "caption": "Fig. 4. FE model of the bearing with support structure.",
        "texts": [
            " 3), which also provided a physical platform for placing accelerometers for bearing vibration measurement. Three pockets were machined on the housing plate to accommodate the sensors. The inner raceway rotates with the shaft driven by a dc motor. A static preload was applied to the bearing through a hydraulic cylinder. Using the FE software package ANSYS, a geometry-true FE model of the bearing with surrounding support structure (e.g., housing plate, shaft, and two supporting pillow blocks) was constructed, as shown in Fig. 4. To reduce computational load, coupling between the dc motor and the shaft through a universal joint as well as between the hydraulic cylinder and the bearing housing was not included in the FE model. To reflect upon their effects on the bearing structure being modeled, these couplings were modeled by a noise load and a static load, respectively. Bearing defect-induced vibration was modeled using a transient dynamic force of 2860 N with a 1-ms duration. Such a dynamic force impulse represents 10% of the bearing\u2019s dynamic load rating [15] and simulates the impact generated by the rolling element-defect interactions. Through a spectral analysis, the generated impulsive vibration was determined to be closely resembling what was measured in realistic experiments. The noise load, which is denoted as Fa in Fig. 4, was chosen to be 1/10 in magnitude of the transient dynamic force. The static load, which is denoted by the symbol Ps, represents the preload applied to the bearing when the hydraulic cylinder pulls the bearing housing. Given that the major function of the two pillow blocks was to support the driving shaft, they were modeled as solid cylinders without considering the relative degrees of freedom of the rolling elements within the pillow blocks. The pillow blocks were retained in the model since they present a source of structural noise for the bearing system being monitored"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000415_a904925h-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000415_a904925h-Figure1-1.png",
        "caption": "Fig. 1 Schematic diagram of the flow-through cell packed with sol\u2013gel powder and an oxygen optode membrane. (1) Stainless steel cell body; (2) sol\u2013gel powder; (3) oxygen optode membrane; (4) transparent glass plate; (5) sample inlet; (6) sample outlet; (7) excitation light beam; and (8) emission light beam.",
        "texts": [
            "250 cm3 of 20 mmol dm23 sodium 4-(2-hydroxyethyl)-1-piperazineethanesulfonate buffer solution (pH 7.5) were mixed, then solution A was added. A vacuum was applied to the stirred mixture until a gel was formed. The gel was rinsed with 2 cm3 of water three times. The gel was allowed to dry at 4 \u00b0C for 6 d. The dried gel was collected and ground to a powder form. Unless stated otherwise, this gel was used for most studies. The laboratory-made flow-through cell used in this work was machined from stainless steel and had a chamber volume of approximately 0.45 cm3 (Fig. 1). An oxygen sensing film plus a blank glass plate were positioned as the window of the flow cell. The enzyme-doped silica gel powder was subsequently packed into the flow cell to form a small packed flow bed resulting in a minireactor or biosensor ready for glucose sensing. This minireactor was situated in a spectrofluorimeter in conjunction with a continuous sample flow system. When the glucose biosensor was not in use, it was stored at 4 \u00b0C. Fluorescence intensity was measured on a Perkin-Elmer (Beaconsfield, Bucks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003493_robot.1986.1087719-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003493_robot.1986.1087719-Figure2-1.png",
        "caption": "Figure 2 . Link Reference Frames distal frame with respect to the proximal frame of the link when the link undergoes deformation due to elastic effects. For small perturbations of the distal frame from its rigid body position, one may want to model the shape-deformation transformation",
        "texts": [
            " frame dx,dy,d, Deformational dlsplacements of the distal frame along the axes of the ( X l Y, Z1 ) frame @x,$y,$z Angular deformations of the distal frame about the axes ofthe - (Xl Y1 Z1 ) i frame b Absolute Angular Velocity of the - (XIYl Z1 ) frame ab Absolute Angular Acceleration of - the (XIYIZl)i frame Relative Angular Velocity of the differential segment with respect Relative Angular Acceleration of the differential seament with Density of the link material Area of cross section of the link 'b - - - w wd - to the (XIYIZl)i frame 'd - ( 1 ) Kinematic & Kinetic Relations: I respect to the (XIYIZl )i frame For thepurpose f derivjng the kinematic and differential segment kinetic expressions, let us consider the ith link of a serial manipulator shown in figure 1. The ith I the differential segment link will have joint 'it at its proximal end (proximal to the base ofthe manipulator) andf the (XIYIZl)i frame. joint 'i+l ' at its distal end. Three reference frames are associated with each link of the If [Ail is the commanded gross motion manipulator as shown in figure 2. Frames (XIYIZ,)i transformation at joint 'if, then we have, and (X2Y2Z2)i will be located at the proximal and distal ends of the link. The 'Z' axes of these [Ail = [L1 1-l [Hi] [Llil CL2.1 ( 1 1 frames will be parallel to a reference line on the i-1 link. Let another frame of reference (HxH H,Ii be where, [L, 1 is a constant transformation at the attached rigidly at he distal tip of txe link. distal e& of the ith link relating the This frame of reference will be oriented from a Hartenberg-Denavit Frame (HxHyH,)i, and the distal description of the Hartenberg-Denavit parameters frame (X,Y,Z2)i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002315_robot.1993.291875-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002315_robot.1993.291875-Figure1-1.png",
        "caption": "Figure 1: The ith joint twist in a serial chain. (ui is the an ular velocity of the ith link relative to the (i-I)th linf; and p, is the linear velocity of the ith link relative to that of the (i-11th link at Pi)",
        "texts": [
            " A family of global solutions obtained by specifying global compliance functions is described in Section 4. Applications to mobile (wheeled) manipulators are presented in Section 5. Results from computer simulations and our experimental wheeled manipulator are described in Section 6. Section 7 concludes the paper. modeling the joint compliance in serial c I ain manipu- 2 Kinematic of Serial Chains Consider a n-jointed, serial-chain robot linkage whose end-effector is instantaneously twisting about a screw axis SE. We represent the instantaneous unit twist a t the ith joint (shown in Figure 1) by a 6 x 1 vector of screw coordinates, Sip, given in ray coordinates by: 713 1050-4729/93 $3.00 0 1993 IEEE where A is a vector of Lagran e multipliers. By setting the partial derivatives wit% respect to Aq and A respectively to zero, we obtain: (7) X = (JW-' JT)-'SEAt (8) Aq = W-' J T X The physical interpretation of these results is as follows. W is a n x n matrix that represents the stiffness of the mechanical system. This stiffness may be due to the inherent properties of the actuator, transmission and the structure or may be acquired from the steady state characteristics of the controller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003356_1.15680-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003356_1.15680-Figure2-1.png",
        "caption": "Fig. 2 Differential thrust at vertical fin loss.",
        "texts": [
            " Therefore, for serious failures, the functions of the aircraft that are lost should be compensated for by the remaining control devices. Those functions will be considered in numerical simulations described in section VI. For example, when the rudder effectiveness is seriously hampered, the yawing cannot be controlled. In that case, differential thrust can be used.13 That is, the desired yawing moment N\u0304e is generated by the thrust difference between the left and the right engines, expressed as N\u0304e = (TL \u2212 TR)\u03b4Thle (23) where le is the moment arm as shown in Fig. 2. The effect on the rolling and pitching moments is neglected. The equations of motion are modified as[ p\u0307 r\u0307 ] = [ f p(x) fr (x) ] + [ gpa(x) gpt (x) gra(x) grt (x) ][ \u03b4a \u03b4\u0303Th ] (24) where \u03b4\u0303Th is the ratio of \u03b4Th to qt S. Thus, the desired aileron deflection and the thrust difference are calculated as follows:[ \u03b4a \u03b4\u0303Th ] = [ gpa(x) gpt (x) gra(x) grt (x) ]\u22121 ([ Up Ur ] \u2212 [ f p(x) fr (x) ]) (25) Similarly, when the function of the elevator is lost, the longitudinal motion is compensated using the flaps, which function as the horizontal stabilizer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002334_robot.2001.932993-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002334_robot.2001.932993-Figure3-1.png",
        "caption": "Figure 3: 3D grasp system",
        "texts": [
            " The frictionless contact force in 3D is explicitly forniulated. And grasp stability is determined by the potential cnergy method. From numerical examples, it is shown that there exists a region of contact force for stable grasp and an optimum contact force. Moreover, frictional grasp stability is also investigated by using contact kinematics of pure rolling. By comparing frictional grasp stability with frictionless one, we prove that friction enhances stability of grasp. 2 Formulation Suppose that an object is grasped by a multifingered hand as shown in Fig.3. We explore stability of the grasp. 2.1 Assumptions In this paper. the following assumptions are considered. ( A l ) The geometries of the fingertips and the object are known and rigid. Finger is shaped a sphere with curvature fit,. Local geometry of the object at the contact point is shaped a second-order model with primary curvatures f i a L and f ib% whose principal axes are denoted by rzz and ryir respectively. (A2) Initial configuration is known and is in equilibrium. (A3) Infinitesimal displacement is occurred in the object due to external disturbances"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002078_s00604-003-0177-z-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002078_s00604-003-0177-z-Figure4-1.png",
        "caption": "Fig. 4. Cyclic voltammograms of DA (1 mM) at the PGCE in the presence of different concentrations of AA. [AA]: (a) 0, (b) 2 mM, (c) 4 mM, (d) 6 mM, (e) 8 mM",
        "texts": [
            " Figure 3(a) shows the cyclic voltammograms obtained at a non-treated GCE for 1 mM DA solution containing 5 mM AA. It can be observed that the oxidation peaks of DA and AA overlap completely with a single oxidation peak at around 352 mV. Consequently, it is impossible to distinguish the voltammetric signals of DA and AA at a non-treated GCE. However, as is shown in Fig. 3(b), the oxidation peak potential of DA at a PGCE is 449 mV, while the oxidation peak potential of AA is 158 mV. The peak separation is as large as 291 mV. This is good enough for the simultaneous determination of both AA and DA. Figure 4 shows that with the increase in AA concentration, the oxidation peak potentials of DA and AA will shift positively. Under the same experimental conditions, we checked the cyclic voltammograms of DA (1 mM, 0.5 mM, 0.1 mM) at the PGCE, but no peak shift can be observed. We also checked the cyclic voltammograms of AA (8 mM, 6 mM, 4 mM, 2 mM) at the PGCE, and a peak shift can be observed due to the electrocatalytic oxidation of AA at the PGCE [23]. Because the anodic peak of AA at the PGCE follows a typical electrocatalytic mechanism [23] and the based line current of the anodic curve in the cyclic voltammogram is downward, the peak shifts of DA and AA will take place in the cyclic voltammograms of a mixture of DA and AA, and the peak shift of AA will be larger than that of DA"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002365_robot.1994.350994-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002365_robot.1994.350994-Figure1-1.png",
        "caption": "Figure 1: The observability ellipsoid in the visual fe& ture space.",
        "texts": [
            " We introduce such a measure, wv which is motivated by the manipulability measure first presented in [91, and (4) wv = Jd.t(J,JT,. ( 5 ) We now study the physical meaning of the observability measure. Consider the set of all robot end-effector velocities i such that It can be shown that the corresponding set of visual feature velocities is given by the set of all i such that 11i11 = ( i l + +' + . . . i ,)l/' 5 1 (6) +T(~:)T~.+ 1, (7) where JvP is an appropriate pseudoinverse of J,. Equation (7) defines a hyper-ellipsoid in the visual feature E= [ u2 - . space (Fig. 1), which we shall refer to as the observability ellipsoid. The dimensions of the observability ellipsoid provide a quantitative evaluation of the observability of the robot motion given by :. The volume of the observability ellipsoid is given by K d q , or Kw, , where K is a scaling constant that depends on the dimension of the ellipsoid. This volume provides a concise and intuitively pleasing measure of observability. Additional insights can be gained by examining the principal axes of the observability ellipsoid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002996_j.dyepig.2004.11.001-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002996_j.dyepig.2004.11.001-Figure4-1.png",
        "caption": "Fig. 4. Plot of normalized emission intensity (I0/I ) vs. glucose concentration for monolayer configuration, M-1.",
        "texts": [
            " Absorption and emission characteristics of the two-layer composition M-2 were very similar to the M-1 in terms of absorption/emission maximum and signal intensity (see Fig. 3). From the results of the emission based measurements, the dynamic working range of the sensor slides were found between 1.0e15.0 mM and 1.0e12.0 mM glucose in 10 3 M BES buffered solutions for M-1 and M-2, respectively. The drop in the dynamic working range of M-2 can be attributed to the accessibility difficulties of two-layer configuration. The glucose induced emission spectra of M-1 and M-2 are given in Fig. 3. Fig. 4 shows the plot of normalized emission intensity (I0/I ) vs. glucose concentration for monolayer configuration within the dynamic working range. Data presented are mean of four sets of measurements all with different fresh sensor slides. The linearized calibration plot of sensor can be described by yZ 0.0754xC 1.0564 and the correlation coefficient R2Z 0.9759. As expected, the monolayer configuration has the fastest response time (t90Z 20 s) but suffers from leaching upon prolonged use. Response time of the cross-linking agent containing two-layer configuration was approximately twofold of the M-1, 47 s"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001541_ias.1997.643017-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001541_ias.1997.643017-Figure10-1.png",
        "caption": "Fig. 10. Self Inductance seen by the rotor current distributions, saturated motor",
        "texts": [
            " However, there is no such variation due to stator slotting present in the self inductance seen by a rotor current distribution. The stator slotting produces a current distribution in the rotor which has a different spatial variation from that of the fundamental The self inductances seen by the a-axis and p-axis current of a stator winding was examined a periodic variation due a-axis and @-axis current distributions and so has no effect on the self inductance seen by these distributions. The effect of saturation on the self inductance seen by a rotor current distribution is clearly visible in Fig. 10. There is a periodic variation in inductance at a frequency of 2 Hz about a mean value. This variation at twice slipfrequency is due to the rotation of the axis of saturation in the rotor. There is a 180\" phase difference between the variation of La and Lp because the a-axis and ,&axis current distributions are orthogonal. Iv. THE EFFECT OF SKEW ON INDUCTANCES Now that the effect of saturation on the inductances L1, M,, MsT and L, is understood the effect of skew on these inductances will be examined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003942_0166-2236(79)90101-2-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003942_0166-2236(79)90101-2-Figure2-1.png",
        "caption": "Fig. 2. Diagram o f a hypothetical PCM implant ]br chronic recordinglstimulating in mammalian brain. P: primary unit; S: secondary unit; T: tertiary unit: ~l: amplifwrs or pulse shapers,\" c: conductor, i; insulator,\" m: multiplexor,\" su: substrate; t: telemeter,\" ti: tissue terminal",
        "texts": [
            " With greater knowledge of the electronic capabilities of small neuronal matrices it is possible that cultured cells in life-support units could be placed inside conventional computers and interfaced with them through PCMs in and around the culture medium. Probing tissue terminals have been fabricated on the edges of primary unit substrates with various degrees of substrate support for the conducting channels ~.\",~7. Recording tips of less than 0.2/zm in width have been produced with u.v. mask exposures, but recent techniques using electron beams for improved definition have realized line widths of <0.5/xm 7. The end-product envisaged in the development of probing PCMs for intra- and extracellular work is illustrated in Fig. 2. The conducting channels of the primary unit could consist of electrolytes, as in glass capillary microelectrodes, or non-polarizing interface compounds if required for the measurement of DC potential changes H. Secondary unit developments By using junction field-effect transistors (JFETs) as on-site buffer amplifiers in secondary units, Wise and Angell TM were able to reduce output impedance levels of their PCM to <500 11 but retained tissue terminal input impedances of > 100 Mfl at I kHz (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000203_s1474-6670(17)51648-1-Figure1.1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000203_s1474-6670(17)51648-1-Figure1.1-1.png",
        "caption": "Figure 1.1: The vehicle MARIUS",
        "texts": [
            " The paper is organized as follows: Section 2 intro duces the model of the AUV MARIUS and derives its linearized equations of motion about trimming trajectories. Section 3 describes the structure of a gain scheduled trajectory tracking controller for the vehicle. Section 4 describes the AUV's multi rate navigation system. Finally, Section 5 assesses the performance of combined navigation, guidance and control in simulation. 2 Vehicle Dynamics. This section describes the dynamic model of the AUV MARIUS, depicted in figure 1.1. A com plete study of the AUV dynamics based on hydro dynamic tank tests with a Planar Motion Mech anism (PMM) can be found in \"Fryxell (1994)\" . In what follows, {I} denotes a universal reference frame, and {B} denotes a body-fixed coordinate frame that moves with the AUV. The following no tation is required: p = [x, y, z]' - position of the origin of {B} expressed in {I}; v = [u, v, w]' -linear velocity of the origin of {B} relative to {I}, expressed in {BL ,x = (t/J, fJ, t/J)' - vector of Euler angles which describe the orientation of frame {B} with re spect to {I} w =(p, q, r]' - angular velocity of {B} relative to {I}, expressed in {B}; R = R(,x) - rotation matrix from {B} to {I}"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001344_ma9911997-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001344_ma9911997-Figure2-1.png",
        "caption": "Figure 2. Schematic representation of the light-scattering setup.",
        "texts": [
            " The polymer under investigation has the structural unit It has a broad molecular weight distribution with an average degree of polymerization Pw \u2248 100. The glass transition and nematic-isotropic transition temperatures are Tg \u2248 15 \u00b0C and TNI \u2248 99 \u00b0C, respectively. The samples were prepared as homogeneously oriented films between two polyimide-coated and subsequently rubbed glass slides separated by Kapton spacers (thickness 25 \u00b5m). Uniform director orientation was supported by annealing the sample in a magnetic field of about 1.2 T at 75 \u00b0C for about 20 h. Figure 2 shows a sketch of the light-scattering setup. The sample cell was centered in a refractive index matching bath (silicone oil WACKER AK50). Temperature was controlled with accuracy better than 0.1 K. A commercial goniometer (ALV-Langen) with an argon-ion laser operating at a wavelength of 488 nm was used. For selection of the VH scattering component, the experiment was equipped with appropriately adjusted polarizers in front of the scattering cell and in front of the detector. The photon correlation analysis was performed using an ALV-5000/E Multiple Tau Digital Correlator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000698_1.1326030-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000698_1.1326030-Figure5-1.png",
        "caption": "FIGURE 5. A right humeral rotation involving 90\u00b0 abduction and 90\u00b0 external rotation can be performed in two sequences. In sequence 1, the first rotation is 90\u00b0 external rotation from attitude \u201eu0,v0,w0 \u2026 in \u201ea\u2026 to attitude \u201eub,vb,wb \u2026 in \u201eb\u2026, then followed by 90\u00b0 abduction to attitude \u201euc,vc,wc \u2026 in \u201ec\u2026. In sequence 2, the first rotation is 90\u00b0 abduction from attitude \u201eu0,v0,w0 \u2026 in \u201ea\u2026 to attitude \u201eud,vd,wd \u2026 in \u201ed\u2026 followed by 90\u00b0 external rotation to attitude\u201eue,ve,we \u2026 in \u201ee\u2026. As shown in the figure the two sequences are equivalent, since final attitude \u201euc,vc,wc \u2026 of sequence 1 equals to final attitude \u201eue,ve,we \u2026 of sequence 2. XYZ is a reference coordinate system fixed on the trunk.",
        "texts": [
            " Example 1 In this example, a pattern of humeral rotation involves a 90\u00b0 abduction and a 90\u00b0 external rotation. In the spherical rotation coordinate system this pattern of rotation is described as a 90\u00b0 elevation in the coronal plane, and a 90\u00b0 axial rotation. The three spherical rotation angles are a590\u00b0, b590\u00b0, and g590\u00b0. There are two possible sequences for a combination of the abduction and axial rotation; the first is 90\u00b0 external rotation followed by 90\u00b0 abduction; and the second is 90\u00b0 abduction followed by 90\u00b0 external rotation. Graphical representation of the pattern of rotation in Fig. 5 shows that final attitudes (uc,vc,wc) and (ue,ve,we) of the two possible sequences of rotation are the same, which demonstrates the sequence independence of the long axis rotation and the axial rotation. As shown in Fig. 5, the final attitude (u1,v1,w1) can be expressed in the reference coordinate system as u15uc5ue5F u1 1 u2 1 u3 1 G5F 0 0 1 G , v15vc5ve5F v1 1 v2 1 v3 1 G5F21 0 0 G , w15wc5we5Fw1 1 w2 1 w3 1 G5F 0 21 0 G . ~30! Forward Solution of Example 1. The objective of forward kinematics is to find a final attitude from a set of given rotation angles. By substituting the three angles ~a 590\u00b0, b590\u00b0, and g590\u00b0! into Eq. ~26!, the integrated rotation matrix can be found as R5U0 21 0 0 0 21 1 0 0 U . ~31! Therefore, the attitude following the rotation can be calculated from Eq. ~28! and presented as unit vectors of the body-fixed coordinate system u85Ru05U0 21 0 0 0 21 1 0 0 UU1 0 0 U5U0 0 1 U , v85Rv05U0 21 0 0 0 21 1 0 0 UU0 1 0 U5U21 0 0 U , w85Rw05U0 21 0 0 0 21 1 0 0 UU0 0 1 U5U 0 21 0 U . ~32! Comparing the results with graphic presentation in Fig. 5, and mathematical expressions in Eq. ~30!, it can be found u85u15uc5ue, v85v15vc5ve, w85w15wc5we. ~33! Therefore, the attitude of the humerus for the given rotation pattern is successfully determined. Since attitudes (uc,vc,wc) and (ue,ve,we) were obtained from different sequences of rotation, the results demonstrate that the final attitude can be determined quantitatively in the spherical rotation coordinate system without considering the rotation sequences. Inverse Solution of Example 1. The objective of inverse kinematics of human movement analysis is to find a set of rotation angles from recorded attitudes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000118_0022-0728(94)03818-n-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000118_0022-0728(94)03818-n-Figure3-1.png",
        "caption": "Fig. 3. Voltammograms showing the complete detachment of the reduced thionine SAM from the S-modified gold in a single sweep experiment. After the first negative-going sweep (curve 1) the electrode was lifted above the test solution at the negative potential limit ( - 4 5 0 mV). The solution was then stirred with argon bubbles, and the electrode was reimmersed with the potential set to the positive limit ( - 110 mV). A second cycle (curve 2) was applied to check the remaining amount of the surface thionine. Curve 0 is the cyclic voltammogram of S-adlayer before immersion into the thionine solution.",
        "texts": [
            " This process is not clearly put in evidence when continuous cycling voltammetry is used [11]. concentration is 2.8 \u00d7 10 -1() mol cm 2. The average surface area for the thionine molecule would be 0.58 nm 2. This value is in a good agreement with the surface area computed from a molecular model for the edge-on orientation (0.61 nm z) [14]. It was proved that at the positive potentials, before the onset of reduction, the SAM is perfectly stable for a longer period even when the solution is stirred. Fig. 3 shows two reductive half-cycles where the first vol tammogram corresponds to the reduction of the initial thionine SAM (curve 1). The second voltammogram (curve 2) was recorded after the electrode was removed from the solution and reimmersed at the initial potential after stirring to prevent reoxidation of leucothionine detached during the first reduction. This experiment proves unambiguously that the thionine Thionine SAMs on free gold surface wcre prepared by the same procedure as on the S-modified gold",
            " Thus the electrode reactions involved could be presented by the following scheme (individuality of redox centers was preserved in polymeric thionine films [16,17]): LTH s.l,.ion + L', LTH First reduction \", 2e t I \" //'//A:; 9\"/\u00a2/ (TH z) (Au-TH I) (Au-LTH) (3) TH E~ LTH Second reduction ~ 2e H* (Au-TH II) (Au-LTH) (4) The behavior of methylene blue, which lacks the primary amino groups possessed by thionine, is quite different on gold, i.e. under the same experimental conditions we could not detect formation of electroactive SAMs of methylene blue (Fig. 3(a) in Ref. [8]). Hence, it seems reasonable to conclude that the pri- mary amino groups a re respons ib le for the chemiso rp - t ion of th ion ine molecu les on gold. A c c o r d i n g to the surface concen t r a t i on of th ion ine in the ini t ial SAM, F = 4 . 5 9 \u00d7 1 0 -1\u00b0 tool cm -2 in Tab le 2, the a p p a r e n t a r ea pe r molecu le is 0.36 nm 2. T h e mo lecu l a r mode l gives 0.34 nm 2 for end -on or ienta t ion (with p r imary amino groups) . This would suggest tha t the p r e d o m i n a n t o r i en t a t i on be fo re the redox change is end on"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001756_jsvi.2001.4016-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001756_jsvi.2001.4016-Figure1-1.png",
        "caption": "Figure 1. Schematic diagram of a bevel gear pair.",
        "texts": [
            " For example, in a bevel geared rotor system, the axial displacement of one rotor may give rise to the lateral displacement and torsional angle of the other rotor through bevel gears. Namely, the axial, lateral and torsional vibrations of the system may couple with each other. The present paper, therefore, is mainly concerned with the coupling among the axial, torsional and lateral vibrations due to the bevel gear transmission. 2. KINETIC CONSTRAINT FOR A PAIR OF SPUR BEVEL GEARS The tooth surface of a pair of spur bevel gears is the envelope of a family of spherical involute curves. Figure 1 shows a pair of bevel gears, whose transmission can be simpli\"ed as a pair of virtual cylindrical gears shown in Figure 2. In this study, the following assumptions upon the system of concern will be used hereinafter: and the torsional angles and can be simpli\"ed to x sin #y cos #r \"x sin #y cos #r , (1) where is the pressure angle of gear, r and r are the radii of base circles of the two virtual cylindrical gears. As shown in Figure 3, the motion described in the co-ordinate frame ox y z can be determined from x y z \" cos 0 sin 0 1 0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001659_s0094-114x(02)00003-4-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001659_s0094-114x(02)00003-4-Figure2-1.png",
        "caption": "Fig. 2. Drive ratio calculation.",
        "texts": [
            " The moveable coordinate systems S1\u00f0O1 X1Y1Z1\u00de and S2\u00f0O2 X2Y2Z2\u00de are rigidly connected to the gear and the TI worm, while the fixed coordinate systems S\u00f0O XYZ\u00de and Sp\u00f0Op XpYpZp\u00de are attached to the machine housing and are the original position of S1 and S2, respectively. The gear and the TI worm rotate about axes Z1 and Z2 with the angular velocities x1 and x2, respectively. The rotating angles are u1 and u2 at some instant. Between axes of Z1 and Z2, the shortest distance is a. The directions of rotation correspond to the right-hand worm-gear drive are shown in Fig. 1. For the gear and the TI worm (Fig. 2), the helical angles are b1 and b2, the rotating velocities are v1 and v2, respectively. The drive ratio i21 may be determined by considering that the velocity v1 equals to v2 on the direction perpendicular to the helical line. Then, we obtain i21 \u00bc x2 x1 \u00bc r1 \u00f0a r1\u00de tan b1 ; \u00f01\u00de a \u00bc mnz2 2 cos b2 \u00fe mnz1 2 cos b1 ; \u00f02\u00de where mn is the normal module, z1 and z2 are the tooth numbers of the gear and the TI worm, respectively, and r1 is the gear pitch radius. To perform TCA on the worm-gear set, the following analyses are based on the hypothesis: the gear tooth surface RI is known, while the TI worm tooth surface RII is to be derived"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003507_jsen.2006.881421-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003507_jsen.2006.881421-Figure2-1.png",
        "caption": "Fig. 2. Position of an inner raceway defect varying with the bearing rotation.",
        "texts": [
            " To retain a maximal energy content in the defect-induced signal, sensors for machine condition monitoring shall be placed in general, as closely as possible, to the source of vibration where the defect is located. However, in many real-world applications, the exact position of the defect may be unknown or time variant due to the nature of rotating machines. Furthermore, preferred locations for placing a sensor may be inaccessible or subject to structural constraints, e.g., due to the proximity to the bearing load zone. An example of the time-variant position of a localized defect on the inner raceway of a bearing is shown in Fig. 2. When the defect is located at the top position of the bearing and interacts with ball #1 (as shown in the left part of Fig. 2), the intensity of the signal measured by the sensor on top of the bearing (sensor location 1) will be generally higher than that measured by the sensor placed to the left of the bearing (sensor location 2). As the defect rotates away from the top to the left side of the bearing (as shown in the right part of Fig. 2), the strength of the vibration signal picked up by sensor location 2 will become stronger. This example illustrates that the two sensor locations specified here would have theoretically the same weight or effectiveness in detecting vibrations induced by such a localized defect. In reality, the strength of the signal will further be affected by the structural specifics (e.g., stiffness, damping, material interface, etc.) where the bearing is located, the preload conditions, structure-borne vibration cause by other components, etc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002399_ias.2001.955985-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002399_ias.2001.955985-Figure7-1.png",
        "caption": "Fig. 7. Voltage vectors used in the third process.",
        "texts": [
            " In this study, the value determined in advance is 0.03 A and it is determined by considering the accuracy of the current sensor. The estimated angle is obtained by similar way to the first process. Next, vectors 13 and 14 shown in Fig. 6 are provided after the vector 4 or 10 is provided once again to remove the effect of the residual magnetism [7]. This process is omitted in Fig. 5. 3) Third process: Three kinds of voltage vectors whose angles are \u03b8M \u2212 7.5, \u03b8M, and \u03b8M + 7.5 elec.deg. as shown in Fig. 7(a) are provided to the motor based on the result of the second process. The angle \u03b8M in Fig. 7(a) represents the angle estimated by the second process. The estimated angle is updated by similar way to the second process. In this stage, the estimation accuracy is \u00b13.75 elec.deg. Furthermore, the process mentioned above is repeated twice as shown in Fig. 7(b) and Fig. 7(c). Since the initial rotor position is estimated by using the current response for the voltage vector, this method is not affected by the set errors and the variation of the motor parameters. The theoretical maximum accuracy of the rotor position estimated by this method is \u00b10.9375 elec.deg. III. DECISION METHOD OF OPTIMUM VOLTAGE VECTOR The amplitude and output time of the voltage vector are important because the estimation is implemented based on the variation of current response caused by the magnetic saturation for the voltage vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002591_0094-114x(85)90040-0-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002591_0094-114x(85)90040-0-Figure5-1.png",
        "caption": "Fig. 5. Rack tip cutting geometry.",
        "texts": [
            " For a pressure angle of 20 \u00b0, the maximum dedendum possible is 2.158/Pd. For dedenda less than this, one has a choice of three rack form tip shapes. The basic shape is shown in Fig. 4(b) with two rounded corners and a small bot tom land. The two limits of this shape are shown in Fig. 4(a) with a full radius tip, which has the maximum possible tip radius for the given dedendum, and in Fig. 4(c) with the maximum tip bottom land. For this family of rack form tips the cutter tip radius, rack form addendum and gear dedendum are related as shown in Fig. 5. Note that the rack form addendum is not normally the same as the gear addendum. It should be equal to or greater than the gear addendum to produce a truly interchangeable gear with a full active involute. This cutter addendum is ac = d - rc(l - sin (b). (9) For standard AGMA 20 ~ full-depth teeth, d = 1.25/ Pd, rc = 0.3/Pd and ac = 1.053/Pdma value slightly higher than the gear addendum of 1.0/Pd. A further limit on the cutter tip geometry is given by the bottom land, 5. This distance cannot be negative",
            " Thus, an arc of radius r : = R - d (12) If there is involute interference, the trochoid traced out by Q will cross the involute of P before the surface normal direction, angle 13, drops to the value of the pitch line pressure angle, 4. The determination of the fillet trochoid for values of 0: between pc/4R and that given by eqn (16) will complete the information required to describe the tooth (13) fillet. For this trochoid the surface normal is is cut at the center of the tooth root by the rack tip n = - s i n 13il + cos 13jj. (17) land, as shown in Fig. 5. For plotting purposes the tooth is constructed from the center of its right side As shown in Fig. 6, the angle 13, which causes n to root to the center of its left side root. Thus, the gear pa_._~ss through the pitch point, is defined by line blank rotation angle, 02, has the limits OC. The equation for the slope of this line is pfl4 - hi2 < 02 < p--~ (14) tan 13 = ac - rc s in ~ (18) R 4R ' R02 - ac tan ~ - r, cos \u00a2b 356 B. HEFENG el al, as a direct function of the gear blank rotation angle 0:"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000393_s0003-2670(99)00805-3-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000393_s0003-2670(99)00805-3-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the flow biosensor for urea determination: (a) sample; (b) H2O; (c) NaOH; (P1) pump1; (P2) pump2; (C) ion-exchange resin column; (A) anion-exchange column with immobilized permanganate; (T) plant tissue column as sample loop; (L) anion-exchange column with immobilized luminol; (V) valve; (F) flow cell; (W) waste; (D) detector; (R) recorder.",
        "texts": [
            " D201 \u00d7 7 strongly basic chloride-form anion-exchange resin purchased from Nankai University were used for the immobilization of luminol and permanganate. 732 strongly acid sodium-form cation-exchange resin and 717 strongly basic chloride-form anion-exchange resin were obtained from Shanghai Resin for ion-interference separation. These are styrenic resins (20\u201350 mesh) with quaternary ammonium and sulfonic acid functional groups. The soybean used throughout this study was purchased from a local grocery store and stored at 4\u25e6C in the refrigerator until use. The flow system employed in this work (Fig. 1) consisted of two peristaltic pumps. One delivered a water carrier stream at a flow rate of 2.0 ml min\u22121, and a CL reaction medium stream of 0.10 M sodium hydroxide passing through the anion-exchange column with immobilized permanganate at a flow rate of 3.5 ml min\u22121; the other delivered a sample stream at a relatively low flow rate of 1.0 ml min\u22121 for an efficient removal of interfering ions in an ion exchanger. PTFE tubing (0.8 mm i.d.) was used to connect all components in the flow system. After an appropriate time for the enzyme-catalyzed hydrolysis of urea in the plant tissue reactor, which was used as the sample loop, the HCO3 \u2212 produced was injected by a six-way injection valve into the water carrier stream to release luminol from the anion-exchange column, which then merged with the medium stream containing eluted permanganate just prior to reaching a spiral flow cell (200 ml)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002138_j.triboint.2004.05.008-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002138_j.triboint.2004.05.008-Figure1-1.png",
        "caption": "Fig. 1. Misaligned bearing geometry.",
        "texts": [
            " The present work is an effort to assess the combined effect of the shaft misalignment and pad distortion on the tilting-pad journal bearing performance. Therefore, a three-shoe tilting-pad journal bearing with elastic pads subjected to unbalance load having misaligned journal have been studied. This section describes the governing equations for the lubrication of tilting-pad journal bearing assuming elastic and thermal deformation of the pad. The geometry of the misaligned bearing is given in Fig. 1. The problem is solved under both isothermal and thermo-hydrodynamic boundary conditions and the lubricant viscosity is assumed to be a function of film pressure and temperature. Moreover, the pivot is assumed to be rigid. The governing equations are as follows. On the basis of conventional assumptions of lubrication theory, the equation governing the pressure distribution in the lubricant film in its nondimensional form is written as follows [14]: @ @h H3G @P @h \u00fe g2 @ @Z H3G @P @Z \u00bc @ @h H 1 I2 J2 \u00fe @H @ t \u00f01\u00de where I2 \u00bc \u00f01 0 Y l dY ; J2 \u00bc \u00f01 0 dY U and G \u00bc \u00f01 0 Y l Y I2 J2 dY The above Reynolds equation is normalized by using the following nondimensional parameters: P \u00bc pc2 l0xR2 ; H \u00bc h c ; Y \u00bc y c ; Z \u00bc z c ; g \u00bc R L ; l \u00bc l l0 ; and t \u00bc xt Taking shaft misalignment and pad elastic and thermal distortion into consideration, the lubricant oil film thickness at any position can be calculated using the following formula [6], h\u00f0h\u00de \u00bc c \u00f0c cb\u00decos\u00f0h ui\u00de \u00f0R\u00fe d\u00de/isin\u00f0h ui\u00de \u00fe xcos\u00f0h\u00de \u00fe ysin\u00f0h\u00de \u00fe am z L cos\u00f0h bm\u00de \u00fe dtotal\u00f0h\u00de \u00f02\u00de where bm is the misalignment angle and dtotal\u00f0h\u00de is the total internal surface displacement of the pad due to elastic and thermal distortion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003861_iros.2006.281944-Figure14-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003861_iros.2006.281944-Figure14-1.png",
        "caption": "Fig. 14. Task plan",
        "texts": [
            " The proposed algorithm was used to confirm whether the rope is deformed. The system configuration is as shown in Fig. 13. The task flow is as follows: 1) Image of rope caught by manipulator is obtained by cameras set on the right side of manipulator. 2) The catching point of rope is measured by PC connected to cameras. 3) Orders of manipulation are given by PC to control system based on RT-Linux through the Ethernet. 4) Manipulator system deforms rope. The procedure for knotting a rope is as follows: 1) A rope is caught by the left hand (see Fig. 14(a)). 2) The downside of the rope is caught by the right hand and the part of the rope between both hands is put on the gripper of the left hand to make a loop (see Fig. 14(b)). 3) The tip of rope is put through the loop by the right hand (see Fig. 14(c)). The appearance of the experiment is shown in Fig. 15. Confirmation of the task plan using the proposed algorithm is made at points in the experiment corresponding to Figs. 15(b), (f) and (h). At those times, the manipulator that does not hold the rope moves away from the rope in order to avoid occlusion. One of the cameras is used to recognize the graph structure and the anteroposterior relation, while the other two cameras are used to detect the catching point. The procedure for confirming that the manipulator has deformed the rope correctly is described below for the time shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002037_1.1510879-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002037_1.1510879-Figure6-1.png",
        "caption": "Fig. 6 \u201ea\u2026 Equilibrium position of bristle tip on rotor surface at point A in absence of friction, and \u201eb\u2026 inclusion of friction gives rise to shear force Fs\u00c4mFn, and revised equilibrium position of bristle tip toward point C on rotor.",
        "texts": [
            " 5, contact forces that arise in the presence of friction at the rotor-bristle interface are shown. The results are intriguing, and indicate that an increasing level of moderate friction ~i.e., m <0.8) successively reduces the resultant contact force F res . This finding is somewhat unexpected and merits further discussion. To this end, the normal force exerted on a bristle tip in frictionless Transactions of the ASME s of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F contact with the rotor is shown in Fig. 6~a!. Here, the equilibrium position of the filament tip corresponds to point A on the shaft, and is independent of the direction of shaft rotation. In the presence of friction, however, a counterclockwise shaft rotation gives rise to the transverse ~shear! force Fs which, in turn, generates a rom: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Term ~virtual! displacement of the bristle tip toward position B as depicted in Fig. 6~b!. Since this virtual displacement is directed away from the shafts surface, it is accompanied by a reduction in the normal reaction force. Thus, the actual equilibrium position of the fiber tip on the rotor surface is directed along the shaft away from point A, toward the point C, and gives rise to the condition AFn 21(mFn)2uC,FnuA . Further studies carried out by the authors have shown that this phenomena does not occur in the presence of larger friction coefficients, which are not considered relevant to the current problem"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002360_pat.401-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002360_pat.401-Figure1-1.png",
        "caption": "FIGURE 1. Schematic representation of the synthesis of a polypyrrolecoated, PNVP-stabilized polystyrene latex.",
        "texts": [
            " PS particles were syntheiszed by dispersion polymerization using poly(N-vinylpyrrolidone) (PNVP) as a steric stabilizer. The \u2018\u2018as-prepared\u2019\u2019 PNVP-stabilized PS latexes had a narrow size distribution. The use of a polymeric stabilizer (PNVP or poly(ethylene glycol) (PEG)) is critical for producing stable colloidal dispersions. The ICP shell was formed by oxidative chemical polymerization of pyrrole in the presence of the PS latex which acted as a colloidal substrate for the deposition of PPy (see Figure 1). If the ICP overlayer is continuous, relatively high conductivities can be obtained even at very low ICP loadings. Moreover, the latex particles have a much wider size range compared to the rather limited size range of sterically stabilized conducting polymer colloids (30\u2013300 nm) or ICP\u2013silica nanocomposites (100\u2013500 nm). It was suggested that the conducting polymer was formed as an ultrathin layer at the surfaces of the latex particles. Latex particles are suitable carriers for the immobilization of proteins in various diagnostic systems [9]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003520_12.7973908-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003520_12.7973908-Figure1-1.png",
        "caption": "Fig. 1. Schematic showing restraint of plates and placement of cameras.",
        "texts": [
            " The Inframetrics instrument also came equipped with a color enhancement system with isothermal line scan and a 3x telescope system. All experiments were conducted using 12 in. x 12 in. plain carbon steel plates (AISI 1040) ranging in thickness from 0.275 in. to 0.325 in. The edges to be joined were milled for a precise fit. A Miller model 330A /BP -AC /DC inert gas welder with water -cooled torch and a 3/16 in. tungsten electrode was used to produce the welds. The torch was mounted to a precision positioning table allowing movement in three orthogonal directions (see Fig. 1). Movements were controllable to within \u00b1 0.01 in. After the initial stationary arc experiments, penetration was maintained between 80% and 95% to assure that no burn -through occurred that might have damaged monitoring equipment placed on the opposite side of the plates. 3. STATIONARY ARC MEASUREMENTS Initial measurements were made using a stationary arc positioned on the seam of two plates. The plates were clamped tightly together, as shown in Fig. 1, to restrain motion due to thermal expansion. Backside measurements were investigated first to avoid molten metal splatter, frontside positioning, and arc reflection problems. Figure 2(a), here reproduced in black- and -white, is the resulting two - dimensional thermal scan with the arc positioned within \u00b1 0.01 in. of the seam center. The color bar at the bottom of the photograph shows the color assignment to regions of temperature ranging from blue (coolest temperature) to white (hottest temperature)",
            " off the seam is seen by comparing Figs. 2 and 3. The results obtained tend to indicate that seam tracking may be based on the difference in radii of isothermal curves to the left and right of the seam. A simple linear control could be used to move the arc until both radii were equal. 4. MOVING ARC MEASUREMENTS The next group of experiments that was conducted involved the measurement of temperature distributions produced by a moving arc. The camera was positioned for frontside measurements as in Fig. 1, and the arc moved at a speed of 2.0 in. /min down the seam of two matched and fully restrained plates. Monitoring thermal distributions at a distance in front of the molten metal pool allows one to \"preview\" upcoming plate geometry variations, contaminants, and seam position. Using this technique of previewing, Figs. 4 and 5, here reproduced in black- and -white, show the ability to identify seam position and contaminants. Sequential photographs 4(a) and 4(b) show the effect of a zig -zag seam on the thermal distribution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001003_s1474-6670(17)37970-3-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001003_s1474-6670(17)37970-3-Figure1-1.png",
        "caption": "Fig. 1. Coordinate frames of a mobile manipu lator: I - the inertial frame, 0 - the ma nipulator's base coordinate frame; Wj - the coordinate frame of the j-th wheel, i denotes the i-th (local) coordinate frame.",
        "texts": [
            " \u2022 Et denotes an item concerned with the j th body and expressed in the i-th coordinate frame, while Ei denotes an item characteris tic to the i-th body, \u2022 Transformation matrices between coordinate frames belong to the special Euclidean group and they are denoted by the symbol T E 5E(3). The composition of transformations T/ = T? Toi is used frequently. \u2022 no, n is the number of degrees of freedom of the mobile platform and manipulator, respec- tively, nw is the number of driven wheels. To simplify notations, it is assumed that each wheel has only one degree of freedom, \u2022 the time differentiation of matrices from 5E(3) is given by the expression . dimq 8T T= L ~q;, ;=1 q, (6) Characteristic coordinate frames and useful vec tors and transformations are visualized in Fig. 1. Modeling of a free mobile manipulator based on Euler-Lagrange equations will be d 8L 8L F dt 8q - 8q = U , (7) where the Lagrange function L = K - V is the difference of the kinetic and potential energy of the mobile manipulator. At first , the kinetic and potential energy of the free mobile manipulator should be calculated and substituted into Eq. (7) to form equations of dynamics of the free mobile manipulator . Then, nonholonomic constraints will be posed on the model to form dynamics of the mobile manipulator "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002801_nme.1620231107-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002801_nme.1620231107-Figure11-1.png",
        "caption": "Figure 11. Clamped conical shell submitted to variable external pressure",
        "texts": [],
        "surrounding_texts": [
            "NUMERICAL SHAKEDOWN ANALYSIS 2083\nCylindrical shell\nchoose We consider a clamped cylindrical shell subject to internal uniform pressure (Figure 8). We\n-=LJ(;IZ;)=2 (93)\nand are looking for the limit analysis solution. We can compare our results with a bound obtained analytically by HodgeI2 using the Tresca sandwich plastic condition and neglecting the stress resultant n. He obtains\nx'P = 1.257 = 201'~ (94) Figure 9 shows the convergence curve when using an increasing number of equal size finite elements.\nComparison with the lower bound computation' is also given. The plastic displacements ( qp) are illustrated in Figure 10 for three discretizations.\nConical shell\nIn the case of the clamped conical shell illustrated in Figure 10, we consider two problems:\n(i) shakedown analysis: p a [0,1] (ii) limit analysis: P E C I [ ~ , 11 Exact solutions are not known for these problems. Nevertheless, for what concerns limit analysis, we can compare with several results coming from References 11 and 13, all obtained with",
            "NUMERICAL SHAKEDOWN ANALYSIS 2085\nthe use of a von Mises sandwich yield condition, which leads to results a little higher then the Tresca yield condition. Table 111 gives the comparison for the case h = t/4L = 0-01.\nIn the case of shakedown analysis, Table IV shows the results obtained by the present and the lower bound\u2019 formulations.\nWe can see that the bounds are brought closer to each other when increasing the number of degrees of freedom, which is the purpose of the present formulation.\nNumber of finite elements p i c\n11 0.578 lower bound 1 1 0.645 upper bound 41 0.591 lower bound 41 0.602 upper bound\nApproach -- ____________.-"
        ]
    },
    {
        "image_filename": "designv11_11_0001479_19.245656-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001479_19.245656-Figure1-1.png",
        "caption": "Fig. 1 . VR motor typical structure.",
        "texts": [
            " Starting from an original digital method for the experimental determination of the saturation curves presented in a previous paper [4], this work proposes a method for the determination of the coenergy curves and the static and dynamic torque characteristics based on appropriate digital processing procedures of the saturation curves and of the flux-linkage values. 11. ANALYTICAL APPROACH The role played by the saturation curves in the determination of the VR motor performances can be outlined rapidly if the mathematical model of the VR motor is taken into account. The typical structure of a VR motor is indicated in Fig. 1. Voltage and current of the generic phase k are related by the equation: where 1) u k ( t ) = supply voltage of winding k, 2) ik(t) = current in winding k, 3) R, = resistance of winding k, and 4) hk(t) = flux-linkage with the winding. Since VR motors are built so that the magnetic coupling between phases can be neglected, flux-linkage h k can be assumed to be unaffected by currents in the other phases. 0018-9456/93$03.00 0 1993 IEEE In this respect, it can be considered as a function of the only current ik and of the reluctance assumed by the magnetic paths during the rotor displacement from the unaligned to aligned pole positions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000387_jtbi.2001.2332-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000387_jtbi.2001.2332-Figure1-1.png",
        "caption": "FIG. 1. A two-degree-of-freedom link-segment model of",
        "texts": [
            " The model is essentially the same as the model of Chowdhary & Challis (1999), but is used here to examine di!erent tasks, which are outlined in the section on the model controller. The details of the model are presented under the following subheadings: model equations of motion, model of muscles, model controller, and model parameters. The model is described in more detail in Chowdhary & Challis (1999). The model consisted of two segments, the forearm and hand, with two joints, the elbow and wrist (see Fig. 1). The hand was considered to hold the ball until the instant of release. For this system the equations of motion represent a coupled set of second-order ordinary di!erential equations, which can be written as qK\"M(q)~1 (M J !v (q, qR )!G (q)), (1) where qK is the vector of angular accelerations, M(q) the inertia matrix, which is a function of the masses, moments of inertia, lengths (\u00b81, \u00b82), and center of mass locations (r1, r2) of the segments, the arm. Center of mass location ( ); projectile ( ); q 1 is the orientation of the forearm, q 2 is the orientation of the hand, g is the gravitational \"eld vector, \u00b81 is the length of the forearm, \u00b82 is the length of the hand, r1 is the distance from the elbow joint center to the forearm's center of mass, and r2 is the distance from wrist joint center to the hand's center of mass",
            " The outputs from the simulations are either the distance thrown or the kinetic energy of the ball, and the timings of the MTM activations. For some of the simulations the net positive work performed by the MTMs was computed from =\"PM elb.ext dq 1 #PM wrist.flx d(q 2 !q 1 #n), (6) where = the total positive work done by the elbow extensors and wrist #exors, M elb.ext the moment produced by elbow extensors, M wrist.flx the moment produced by wrist #exors and q 1 , q 2 are the orientation of the segments (see Fig. 1) To evaluate the model the kinematics of the subjects throwing a tennis ball (mass 0.05 kg) for maximum possible distance were compared with the kinematics of the models simulations of these throws. For subject 1 the model predicted a maximum throw of 8.42 m, the actual maximum distance thrown by this subject was 8.38 m. For subject 2 the model predicted a maximum throw of 6.42 m, and the actual maximum distance thrown by the subject was 6.31 m. Therefore, although the model was a simpli\"cation of the complex human musculo-skeletal system, it accurately represents movements of the type to be simulated in this study"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003825_j.finel.2005.08.001-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003825_j.finel.2005.08.001-Figure11-1.png",
        "caption": "Fig. 11. Area cross-sections of hybrid elements.",
        "texts": [
            " Calculate the lower part flexibility Sp2 = Sp \u2212 Sp1. (9) 4. Calculate Ap2 obtained from Sp2, as equivalent cross-section of the lower segment. The lower part can be partitioned into as many segments as necessary, without repeating the algorithm since it is sufficient to preserve constant the sum of the elements flexibilities (Sp2). This approach is possible since they act in the same way during loading. Thus, our bearing ring model is made up of three segments corresponding to the hybrid elements (Fig. 11). The length L1 of the first segment is directly related to the location where the external force is applied, accordingly to the bearing geometry. In order to refine the flexibility distribution, an adjustment factor has been introduced. It multiplies the calculated cross-section Ap1, in order to obtain the adjusted equivalent cross-section Ap1a = \u2217 Ap1. (10) Obviously, the introduction of this factor will also affect the value of the second equivalent section Ap2, while the sum of the Sp flexibilities must remain constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001928_iros.2001.977178-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001928_iros.2001.977178-Figure7-1.png",
        "caption": "Figure 7. Sonar transducer and video camera layout.",
        "texts": [
            "2 The Behavior-based Architecture To accomplish this mission a Behavior-based architecture with three behaviors was designed. Each behavior has its own input from sensors and generates a 3D-speed vector defined by (U, w, r). In association with this response, the behavior generates the activation level which determines the final robot movement. Figure 6 shows the schema of the architecture. The three behaviors are: Obstacle avoidance. The goal is to avoid any obstacles perceived by means of 7 sonar sensors, see figure 7. The behavior is learnt using a continuous Q-learning algorithm for each DOF (x,y,z). A reinforcement function gives negative rewards depending on the distance at which obstacles are detected. The activation level is also proportional to the proximity of obstacles. Target folZowing. The behavior follows the target using a video camera pointed towards X-axis, see figure 7. A real-time tracking board based on chromatic characteristics gives the relative position of the target. The behavior is learnt using a continuous Q-learning algorithm for each DOF (x,y,z). The reinforcement function gives negative rewards when the target moves away from the position X=5, Y=O and Z=O, relative to the on-board coordinate system. The activation level is 1 when the target is detected, alternatively, it is 0. Target recovery. The goal of this behavior is to recover the target when it disappears from the camera view"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001922_2002-01-1003-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001922_2002-01-1003-Figure2-1.png",
        "caption": "Figure 2. Schematic drawing of the modified Brugger fatigue specimens. Dimensions are in millimeters.",
        "texts": [
            " The processing histories included an asgas-carburized set as a baseline, a set shot-peened after gas carburizing, a reheated set to refine the case grain size, and a set processed by vacuum carburizing to minimize intergranular oxidation at the surface. EXPERIMENTAL PROCEDURE SAE 8620 steel, with the composition shown in Table 1, was commercially produced into pinion gear forgings. The pinion forgings were upset from 38.1 mm (1.5\u201d) diameter bar stock. Then, the forgings were machined to the final pinion dimensions. Modified Brugger samples were machined from the stems of some of the pinions. A schematic drawing of the location of the modified Brugger samples is shown in Figure 1 and the sample geometry is shown in Figure 2. The remaining pinion blanks were commercially processed into pinion gears and matched with a set of ring gears for testing on a dynamometer. In this study, only the pinions were analyzed and the ring gears were used to facilitate dynamometer testing. CARBURIZING/PROCESSING - Four processing histories, designated baseline, shot-peened, reheated, and vacuum carburized and summarized in Table 2, were used in this study. Each processing history was simultaneously applied to groups of modified Brugger samples and commercial gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003859_iros.1989.637921-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003859_iros.1989.637921-Figure1-1.png",
        "caption": "Figure 1: Application of CEBOT inside a tank.",
        "texts": [],
        "surrounding_texts": [
            "Thc Dynamically Rcconflgurahlc Robotic Systcm (1)IllCS) I s a n c w kind ol' robot l r system whlch Is a b l r to reconrlguratc I Lscl f to optimal structure dcpending on purpose and environment. To rea l ize t h i s concept, we h a s p r o p o s e d CEBOT ( C e l l u l a r R o b o t i c s ) . Communication is needed in CEBOT system as follows: When cells are separated , communication master cell needs t o know o t h e r cell's function, position and determine t h e target cell f o r docking. A mobile cells should be ab le t o coordinate with o t h e r mobile cells. When cells are docked, forming cell structure/module, a master cell should c o n t r o l bending j o i n t cell and know of which cells t h e construct ion is composed. In th i s paper, w e propose a communication protocol f o r both cases with opt ica l sensor applicable t o CEBOT. Some experimental r e s u l t s are shown by realizing t h e proposed communication method between cells.\nKEYWORDS: Applicat ion of C o n t r o l , Dynamical ly Reconfigurable Robotic System, C e l l Structure , SelfOrganizing System, Communication, Protocol , SelfRepairing Robot, Faul t Tolerance,\n1. Introduct ion\nR e c e n t l y \"Advanced r o b o t i c s i n h o s t i l e environments\" has been studied intensively nation and p r i v a t e e n t e r p r i s e s . Ins tead of humans t h e r o b o t performs many tasks under many environments e.g. space, nuclear reactors , underwater and plants on f i r e where man can not d o tasks. Hardware and software needs t o be appl icable t o various tasks under many environments. In order to rea l ize t h e concept, we have proposed and s t u d i e d Dynamically R e c o n f i g u r a b l e Robotic Systcm(DRRS) cal led Cel lular Robotic System \"CEBOT\" which consis ts of separable autonomous uni ts cal led cel ls . [ l , 2, 31 Now most of developed and s t u - died reconfigurable systems can not change t h e i r t o t a l form, only t h e i r p a r t i a l form and can not connect f o r themselves but depend on other 's help. In shor t CEBOT Is i i r i r i i r l o r i o m o i r s r t r c . r n 1 rnl Izcd c * o o r d l 1 1 1 1 1 c'tl sysl VJJI which is ab le t o c a r r y out tasks by creat ing t h e optimal s t r u c t u r e and construct ing i t by i tself . The autonomous approach, connecting, detaching and the theory of \"Optimal s t ruc ture\" have already been studied.[4] In order t o cons t ruc t optimal s t r u c t u r e automatically, the CEBOT communication system i s necessary. Thc reasons are as follows, (1) When undocked , a communication master cell has t o\n(2) Should t h e r e be such ce l l s , t h e master cell must\n(3) After construct ing optimal s t ruc ture , t h e cell\nknow if t h e r e are cells with t h e desired functions.\nchoose one t a r g e t cell from those available.\nneeds to cont ro l t h e s t ruc ture .\nThus, t h l s paper shows t h e CI.:BOT rrcognition and rommunicritlon syslcm w l i i r h Is riccy'ssury L o b p i l r t autonomous. dcrcntral izcd and coortiinntcti system. Communication protocols in docked and undocked states and experimental results of t h e communication a r e shown. The communication between cells based on t h e protocols , is realized by using opt ical sensors, whiclh do not d i s turb o t h e r systems, and by communication bus in cells.\n2. Outline of CEBOT\nCEBOT is t h e system which i s constructed by autonomous components cal led cells o r modules : C e l l : a cell is an in te l lec tua l function uni t which\nhas one funct ion and more than one connectable face.\nModule: A module is an in te l lec tua l function component which is constructed of cells and has more than one connectable face. The c e l l l i t e r a l l y corresponds t o a biological ce l l , t h r m o c l i i l r cwrrcsponds l o n hlolofcicnl ccllulntion O P\norgan which Is group of' cells. ?'he cell type Is shown in t a b l e 1 and a example of cel ls(ser ies 11) w e made are shown in Fig.2. 3. Figure 2 shows t h e cells in iln undocked state and Fig.3 shows a constructed module of docked cells . Every cell has e ight LEDs and three photodiodes(PD I, 2, 3)for autonomous approach arid docking and three ultrasonic sensors(one transmitter, two receivers) f o r obs tac le avoidance.(see Fig.4) The efficiency of t h e sensor arrangement and experimental results of automatic approach, docking, detaching and obstacle avoidance have already been reported. Every cell has two communication systems. One is an opt ical ro ta t ing sensor on t h e f r o n t connectable face f o r\n-291-",
            "and a t t i t u d e detection. and photodiodes.\nIn o r d e r to be an autonomous, decentral ized and coordinated system, it is necessary t o communicate between cells. The necessi ty of communication under both states i s shown as follows.\n3.1 The necessity of communication in t h e undocked state.\nWhen CEBOT creates an optimal s t r u c t u r e f o r a given t a s k , CEBOT needs t o communicate f o r t h e following reasons. (1) A moving master cell has to know if cells with t h e\nThere are various cell types(see Table 1). Therefore a mobile cell/module must be able t o recognize if t h e cell with desired funct ion is there . (2) Thc master ccll has t o choose one t a r g e t cell from\nIf t h e r e are many cells which h a v e t h e d e s i r e d func.1 i o n :I mob1 I(\u2019 c*cI 1 Itas 1 o c.hoosc. wliic*h c.cl 1 1 o couple with. (3) The master has to measure re la t ive angle and\ndistance. After t h e master cell chooses t h e t a r g e t ce l l , t h e da ta of re la t ive angle and dis tance between cells help autonomous approach and docking.\ndesired funct ion are there .\nt h e su i tab le function cells.\n-292-"
        ]
    },
    {
        "image_filename": "designv11_11_0003026_0191-8141(83)90020-2-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003026_0191-8141(83)90020-2-Figure5-1.png",
        "caption": "Fig. 5. (a) Strain field resulting from a doublet near a rigid boundary (method of images, see Johnson 1970, pp. 267,417). (b) A1 trajectories in a centrifuged diapir model after Dixon (1975). Viscosity contrast between overburden and source layer: 1/10. IP, isotropic point; IL, isotropic line.",
        "texts": [
            " It is especially interesting to look at the strain pat tern produced by a doublet (Fig. 3). We note the existence of an isotropic line and two isotropic points well defined by the principal A 1 trajectories. ASSOCIATIONS OF I S O T R O P I C POINTS AND LINES RESULTING FROM DOUBLET-TYPE F L O W Diapirs Numerical and experimental models of diapirism show that the velocity field during a diapir growth may be simulated by eccentric flow cells (Elder 1977) (Fig. 4). Such a pat tern is close to that of a doublet near a rigid boundary (Fig. 5a), and the resulting strain fields (Figs. 5a & b) are comparable , if we exclude some peculiarities due to viscosity contrasts in the experimental models (Dixon 1975). During the evolution of the diapir, the isotropic line migrates towards the centre of the diapir core and is progressively reduced to a point (Fig. 6). A consequence of this change in the isotropic line configuration is that subvertically stretched areas become progressively horizontally stretched. In rocks, such a kinematic evolution can produce superposed fabric (crenulation of an early piano-linear fabric) giving a material trace of the migration of the isotropic line (Dixon 1975, Schwerdtner 1977, Brun & Choukroune 1981)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000507_027836499501400207-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000507_027836499501400207-Figure5-1.png",
        "caption": "Fig. 5. Coordinate conventions.",
        "texts": [
            " This at The University of Iowa Libraries on June 8, 2015ijr.sagepub.comDownloaded from 176 problem is ambiguous. In fact, there is a third solution involving pulling with slip at the contact point, but we will concentrate on pulling with sticking contact. To show that the solutions shown in Figures 3 and 4 really are solutions, we integrate the support frictional forces around the ring and show that the total frictional force the slider applies to the support equals the pushing force f. We use two coordinate systems (Figure 5), one system .x-y aligned with the pusher, and a primed system x\u2019-y\u2019 aligned with the applied force but centered on the ring of the slider. With some modifications, Goyal (1989) gives the following expressions for frictional force and torque applied by the ring to the support surface in the primed system: where T~TI is the slider weight multiplied by the support friction coefficient, c,~ is the slider angular velocity, and v is the velocity of the slider center along the y\u2019-axis. (The velocity of the slider center along the 3/-axis is zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002804_j.mechmachtheory.2005.07.008-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002804_j.mechmachtheory.2005.07.008-Figure3-1.png",
        "caption": "Fig. 3. Aerospace pinion modelled.",
        "texts": [
            " (58), (60) allow us to determine ~f ;n and ~f ;h, which become ~f ;n\u00f0n; h;/\u00de \u00bc ffiffiffi E p k\u00f0n; h;/\u00de \u00bc R1k\u00f0n; h;/\u00de \u00f0133\u00de ~f ;h\u00f0n; h;/\u00de \u00bc ffiffiffiffiffiffiffiffiffiffi G\u00f0n\u00de p k\u00f0n; h;/\u00de \u00bc \u00f0Xp \u00fe R1 cos n\u00del\u00f0n; h;/\u00de \u00f0134\u00de while derivative ~f ;/ is evaluated by employing (62) as follows ~f ;/\u00f0n; h;/\u00de \u00bc mu e\u00f0n; h\u00de he;/\u00f0n; h;/\u00de \u00f0135\u00de The last step is the evaluation of the function of singular points in the strict sense ~g. This scalar function specializes now in ~g\u00f0n; h;/\u00de \u00bc 1 R2 1\u00f0Xp \u00fe R1 cos n\u00de2 R2 1 0 ffiffiffi E p he ge1 0 \u00f0Xp \u00fe R1 cos n\u00de2 ffiffiffiffi G p he ge2 ~f ;n ~f ;h ~f ;/ 2 64 3 75 \u00f0136\u00de The proposed approach is employed to perform a curvature analysis of a spiral bevel pinion for aerospace application shown in Fig. 3. The main data of the transmission, the geometric parameters of the convex side (inside blade) of the grinding wheel and the machine settings employed, are given in Tables 1\u20133. As a result of the proposed approach, the principal radii of curvature Rg 1 \u00bc 1=kg1 and Rg 2 \u00bc 1=kg2 along the profile, computed employing Eqs. (113), are plotted in Figs. 4 and 5. In particular, Fig. 4 shows that the minimum radius of curvature Rg 1 increases in absolute value both travelling from the fillet to the top of the tooth and from the front cone to the back cone"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003206_j.mechmachtheory.2003.12.003-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003206_j.mechmachtheory.2003.12.003-Figure6-1.png",
        "caption": "Fig. 6. Two positions of the driving slider to correspond to the coupler point.",
        "texts": [
            " Directions of rotation of the driven link of six-link mechanisms whose link-chain configurations hold in common a limit position are different mutually. These directions are discriminated by using the sign of the determinant d\u00f0s\u00de or d\u00f0h6\u00de. In the case of the Stephenson-3 six-link mechanism of the slider drive, a link-chain configuration of the constituent four-link mechanism corresponds to two positions of the driving slider, which are symmetry with respect to the perpendicular from the coupler point E to the pairing straight line on the stationary link as shown in Fig. 6. These positions can be discriminated by the sign of the sine of the relative angle hT (\u00bc h5 a2 \u00fe p=2) between the slider and the link EF of the external dyad. When the driving slider moves in a direction, the pairing point E of the coupler link BC of the constituent four-link mechanism and the second link EF of the external dyad, moves on the coupler curve and it turns back at such positions that the link EF becomes perpendicular to the pairing straight line on the stationary link, that is, the condition sin hT \u00bc 0 holds"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001626_robot.1990.126316-Figure13-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001626_robot.1990.126316-Figure13-1.png",
        "caption": "Figure 13. Assignment of joint angles for path find example 2.",
        "texts": [
            " Obstacles as discovered by the range finding system The first path was 1326 units long. It took 19.6 seconds to find and 340,000 kBytes of memory were used for 3380 C-space blocks. After 615 seconds the path length had droppped to 846 units, 67745 blocks were explored taking 22 MBytes. Times and memory usage do not include the time taken to distance transform the free space and the memory it occupied (9 seconds, 100'1 00'100 voxels, 2 MBytes). In figure 11 the joint angles belonging to the first path are shown (see figure 13 for the notation). The robot lifts his arm (joints 2 & 3), pulls it in (joints 2 & 3) and rotates around his base (joint 1). The freedom left for a trajectory planner is defined by the space between the upper and lower contours which represents the size of blocks in C-space. Wrist action (joint 4 and 5) is less constrained than arm action because of the low spatial impact of gripper movements. Figure 12 shows the path after 615 seconds of calculation time. The path is shorter because the arm is less lifted and less pulled in"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002847_b:tril.0000044500.75134.70-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002847_b:tril.0000044500.75134.70-Figure1-1.png",
        "caption": "Figure 1. Two-beam optical EHL interferometry.",
        "texts": [
            " 0 electric vector of light waves h film thickness h0 film thickness of the zero order I, I1, I2, Iin intensity of light Im measured intensity in grey levels I; Im normalized intensity k1, 3 attenuation coefficient n, n0,1,2,3 real refractive index s spectrum of the light source, ue entrainment speed w sensitivity of the CCD ; 1; 2 bright fringe order range d, d1, d2 dark fringe order range wavelength of lights initial phase shift < Reflectance < relative reflectance Elastohydrodynamic lubrication (EHL) is a key feature of highly loaded machine elements, such as rolling bearings, gears and cams and followers. Optical interferometry has proven to be a very useful tool in the thickness measurement of EHL film. In the 1960s, Cameron and his group [1,2] at Imperial Col- lege were the first to successfully demonstrate the well-known, horseshoe-shaped EHL film in optical interference images. This technique makes use of a loaded contact of a partially chromium-coated glass disc and a steel ball in conjunction with a lubricant layer in-between, as schematically shown in figure 1. In conventional optical EHL experiments, the interferogram is interpreted by the two-beam interference theory, in which the fringe is from the interference of the two coherent beams rays I and II reflected from the partially coated chromium and the steel surface, and is utilized to infer the film profile. The interference intensity I versus the film thickness h follows a cosine relationship, I \u00bc I1 \u00fe I2 \u00fe 2 ffiffiffiffiffiffiffiffi I1I2 p cos 4nhp k \u00fe U ; \u00f01\u00de where I1 and I2 are the intensities of rays I and II, n is the refractive index of lubricants, k is the wavelength of the light and F is the initial phase shift of the system, which is equivalent to an optical thickness difference of U 2p k2, and can be obtained experimentally",
            " In the early 1970s, Roberts and Tabor [22] already proposed to use the variation in interference intensity to measure much thinner film thickness and to obtain higher resolution. This idea was adopted by Luo et al. [23] and Muraki and Sano [24] to measure the interference intensity of monochromatic light, which is reflected from a typical optical EHL contact, and to calculate film thickness from this intensity based on two-beam interference theory in the 1990s. However, the optical EHL contact is a combination of four optical media, including metals and glass, as can be seen in figure 1. Multi-beam interference occurs within the chromium layer and lubricant film, and there is light absorption in both chromium and steel. It has recently been shown by the authors [25,26] that significant errors are induced by using the two-beam interference theory on optical EHL contacts when ultra thin lubricant film thickness and local tiny film thickness variation are detected. Based on a full theoretical analysis of optical EHL contact, a multi-beam intensity-based (MBI) scheme was proposed for accurate thin-lubricating-film measurement [25]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002122_s0921-5093(01)01722-1-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002122_s0921-5093(01)01722-1-Figure6-1.png",
        "caption": "Fig. 6. Experimental device for crossing magnetic measurements (a); samples and secondary windings (b); estimation of the airgap between sample and ferrimagnetic yoke by microscopic observation (c).",
        "texts": [
            " (3) is applied with X representative of the multiaxial internal stress level which appears during strengthening (in this equation, , p, X and I denote the stress, plastic strain, kinematic back stress and identity tensors, respectively). These internal stresses could induce an anisotropic effect on the magnetic behaviour [26,27], for instance in the crossed direction of the tensile one. For this purpose, an appropriate experimental device was elaborated in order to carry out complementary transverse measurements. 3.1. Experimental frame and samples The experimental frame is composed of two ferrimagnetic \u2018E\u2019 yokes positioned vertically and face to face (Fig. 6a), and surrounded with the field coils. Two samples (20\u00d720 mm) were carefully taken from the same tensile test specimen (Fig. 6b). They were set between the yokes in order to create an appropriate circulation of the field lines. The ferrimagnetic material of the yoke was chosen to keep a constant initial relative permeability over the range of driving field H used in the experiments. Its reluctance is very small compared with that of the samples, its section being 100 times bigger. The secondary induction coils were wounded directly around each sample. 3.2. Electromagnetic calculations and numerical simulations The frame is supplied with an applied sinusoidal current i(t)",
            " The frequency range is 0.1\u2013400 Hz, the lower value corresponding to quasistatic magnetisation. Ampere\u2019s law is applied along the medium magnetic closed circuit representative of a quarter of the experimental device in order to compute the magnetic field strength H(t). Hy(t)Ly+2Ha(t)La+H(t)L=Ni(t) (4) L is the effective length of the sample crossed by the flux lines. Ly and La are, respectively, the medium length of the ferrimagnetic yoke and the airgap length evaluated to about 6 m by means of optical mi- croscopy (Fig. 6c). N is the number of turns of the primary field coil. Hy, Ha and H are the magnetic field strengths inside the yoke, the airgap and the sample, respectively. The magnetic flux is supposed to be invariant along the magnetic closed circuit (no leakage of flux). Its value is one half of the total flux inside each sample, which can be computed using Faraday\u2019s law. e(t)= \u2212n d (t) dt (t)= \u2212 1 n t 0 e(t)dt+C (5) where n is the number of turns of the secondary winding, e(t) the induced electromotive force inside this winding and C an appropriate integration constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002414_027836403128965277-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002414_027836403128965277-Figure2-1.png",
        "caption": "Fig. 2. Obstacle avoidance motivation. The robot must avoid the obstacle while staying on the road. Given the length of the arcs being evaluated (which reflects the stopping distance at this speed), there is no curvature which does not hit either the obstacle or the road edge. Yet, a compound curve easily avoids both.",
        "texts": [
            " In our application, a vision system determines where the fork holes are, so the goal posture may not be known until limited space requires an aggressive maneuver to address the load correctly. In the event that the fork holes are located after traveling past the point where a feasible capture motion exists, it still may be valuable to optimize the terminal posture error based on the fact that the holes are often much larger than the forks. Obstacle avoidance also requires precise models of mobility. In Figure 2, for example, the space of constant curvature arc trajectories does not contain a solution to the problem of both staying on the road and avoiding the obstacle. However, the space of all feasible vehicle motions does contain a solution. Simplistic approaches can quickly lead to unnecessary problems. In the fork truck example, simply steering toward the pallet is exactly the wrong thing to do. The only way to achieve the goal is to turn away from the pallet in order to lengthen the path enough to achieve the required heading change"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002284_analsci.19.289-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002284_analsci.19.289-Figure2-1.png",
        "caption": "Fig. 2 Experimental set-up of sequential injection renewable surface system. B, microbead suspension; C, H2O carrier; F, chipbased flow-through cell; H, holding coil (0.7 mm i.d. \u00d7 200 cm); M, multistrand bifurcated optical fiber; P, syringe pump; R, mixed NaOH and K3Fe(CN)6 oxidizing solution; S, spectrofluorometer; V1, six-position valve; V2, two-position valve; W, waste; CR, chart recorder.",
        "texts": [
            " With this modification, the flow-through cell was coupled to the fiber-optical probe via the optical glass window, resulting in less stray light and background fluorescence. A multistrand bifurcated optical fiber (Chunhui High Tech. Co., Nanjing, China), composed of 32 fibers (core diameter of 80 \u00b5m) for incident light and 32 fibers for emission light, was used to couple the chip-based flow-through cell to a spectrofluorometer, as described in detail in the section of Method development. Flow manifold is shown in Fig. 2; PTFE tubing with 0.7 mm i.d. was used to fabricate the holding coil and to make connections. Thiamine hydrochloride stock solution (1000 mg l\u20131) was prepared by dissolving 0.1 g of thiamine hydrochloride (Sigma) in 100 ml of 0.01 mol l\u20131 HCl; it was stored in a refrigerator. Working standard solutions were prepared daily by appropriate dilution of the stock solution with water. Alkaline oxidizing solution {0.003% (w/v) in K3Fe(CN)6 and 4% (w/v) in NaOH} was daily prepared by mixing 1 ml of 0.15% (w/v) K3Fe(CN)6 solution with 50 ml of 4% (w/v) NaOH solution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001624_robot.1996.506582-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001624_robot.1996.506582-Figure6-1.png",
        "caption": "Figure 6: Region for A",
        "texts": [
            " In general, however, the displacement of the fingertip of the third finger due to the grasping fingers becomes small because of their limited joint motions as a result of the grasping configuration. Hence we neglect it in this example. Fig.4 (1) shows W1, and (2) shows the workspace W(60\"). Fig.5 shows RA(W(Q, ,~) , e2(a, ,k)) for a hexagon when Ps = 0\" and p, = 360\". The orientation is divided into Mp = 24 angles. RA(W(CY, ,~) , e,(a, k)) is shown for the three edges which are indicated by arrows. Fig.6 (1) shows U(&, 1) for the digitized orientations k = 1,. . . , 24 and (2) shows their intersection W ) . 3 First Planning the sequence of primitives we describe the following assumptions. finger 3 h cone % \u2019 (1) Wl Figure 4: Workspaces Figure 5: Region for A for each edge 1. Although three fingered hand can perform the regrasping, a four fingered hand is more likely to be applied. So that three fingers can maintain stable grasp, when the fourth one is spared for repositioning during rotation primitive"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002334_robot.2001.932993-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002334_robot.2001.932993-Figure4-1.png",
        "caption": "Figure 4: Coordinate frame",
        "texts": [
            " Local geometry of the object at the contact point is shaped a second-order model with primary curvatures f i a L and f ib% whose principal axes are denoted by rzz and ryir respectively. (A2) Initial configuration is known and is in equilibrium. (A3) Infinitesimal displacement is occurred in the object due to external disturbances. The displacement is denoted by E = [x, y, z , E , 7, (1\". (A4) Finger's displacement is infinitesimal, and the relationship between finger's displacement and reaction force is replaced with 3D linear spring model which is fixed at center of the fingertip as shown in Fig.4. Stiffness of the spring is programmable. One spring k,i(> 0) is set along the normal and the others k,i(> 0) and k,i(> 0) are parallel to the tangent. k,i and k,i are parallel to the primary curvatures ~ b i and frail respectively. 2.2 Notations Reference coordinate and the i-th finger's coordinate are denoted by and Cf i , respectively. Cfi is aligned with the 3D spring model. 5 axis of C f i is aligned with the inward normal of the finger. Position and orientation of Cfi with respect to Cb are denoted by x f i and Rji := [rZi, ryi, rzi]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000737_s0890-6955(01)00101-8-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000737_s0890-6955(01)00101-8-Figure2-1.png",
        "caption": "Fig. 2. Showing the co-ordinate systems connected to both gear and cutting tool.",
        "texts": [
            " The normal sections of the cutters show straight lines for the imaginary rack-cutter flanks, with zero pressure angle as shown in the figures. During the rolling motion, the generating point M describes the involute of the tooth flank. This generating process provides an involute tooth flank at all positions around the curved gear face width. However, unlike spur and helical gears, the base circle varies around the face width. The gear tooth surface generation is modeled using the methods proposed by Oancea [6\u20138] and Litvin [9]. We consider the following coordinate systems (see Fig. 2), where: Oxyz is the fixed coordinate system whose axis Oz in the plane of the paper coincides with gear rotational axis, O1X1Y1Z1 is a movable coordinate system rigidly connected to the tool, where the axis O1X1 coincides with tool rotational axis, OXYZ is a movable coordinate system rigidly connected to the gear being generated, and O2\u03be\u03b7\u03b6 is a movable coordinate system rigidly connected to the imaginary rack cutter. The generating circle shown by the curve MO2 and onwards is represented in the coordinate system O1X1Y1Z1 by the equations: X1=0 Y1=\u2212Rcosv Z1=Rsinv (1) where R (O1M) is the radius of the generating circle and v is the variable parameter of the tool rotational motion about its axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001499_20.877692-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001499_20.877692-Figure5-1.png",
        "caption": "Fig. 5. Noise pressure caused by the 5th harmonic (1250 Hz) of the magnetic forces and velocity boundary conditions.",
        "texts": [
            " (14) where is a weighted average of the velocity in the th acoustic node, is the velocity in the th structural node and is the distance from the th structural node to the th acoustic node; is the number of structural nodes. The interpolation between the acoustic mesh and the structural mesh is illustrated in Fig. 3. The acoustic parameters as radiation efficiency, sound power and sound pressures are calculated by the methodology shown in Fig. 4. As examples of acoustic calculations applying BEM, Fig. 5 shows the noise pressure and velocity boundary conditions caused by the 5 harmonic (1250 Hz) of magnetic forces (this result was calculated considering a distance of 0.3 m from the source for illustration purposes). Fig. 6 shows the radiation efficiency as a function of the excitation frequencies, obtained applying the numerically calculated sound power radiated values in (2) and solving for . These radiation efficiency values are much more precise than the ones calculated using (3) because the electric motor is not a monopole source"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000943_physreve.66.045102-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000943_physreve.66.045102-Figure1-1.png",
        "caption": "FIG. 1. Geometry of spinning disk. X8,Y 8, and Z8 are bodyfixed axes, and a is the angle between the normal (Z8) to the plane of the disk and the vertical direction Z. The instantaneous motion of the disk is rotation about the diameter Y 8 that contains the point of contact. As the disk rolls to a stop, a goes to zero, and the precession rate V of Z8 about Z goes to infinity.",
        "texts": [
            " In this Rapid Communication we present measurements of the spinning motion of heavy steel disks and rings on a variety of surfaces and find that the precession rate of all these objects increase with a power law as suggested by Moffatt @3#: V(t)}(t2to)21/n. However, n varies between 2.7 and 3.2 under different experimental conditions rather than being equal to 6. The exponent of the power law, as well as the systematic dependence of the precession rate on coefficients of friction, establishes that the primary mechanism of energy dissipation is rolling friction, rather than the viscous drag of the air. The dynamical problem is shown in Fig. 1. In the situation sketched therein, the symmetry axis (Z\u03028) of a disk of mass M and radius a is tipped at an angle a to the direction \u00a92002 The American Physical Society02-1 Z\u0302 normal to the horizontal plane. The angular velocity of precession of the symmetry axis, denoted by VW , points along the Z axis. If the disk rolls without slipping, there is no angular momentum component about the symmetry axis. The instantaneous state of motion, therefore, is rotation about the diameter (YW 8) that contains the point of contact of the disk with the plane",
            " As the tip angle a gets smaller, the viscous dissipation rate Fvisc increases, both because the precession rate goes up and because the layer is thinner and has to support a larger gradient in velocity. For small angles the dissipation rate is estimated @3# as Fvisc;a22. The total energy of the coin is E5Mga sin a1 1 2IV2sin2a5 3 2Mga sin a. Integrating dE/dt52Fvisc yields the principal result of Ref. @3#: V(t)}(t2to)21/6. We have made measurements of the motions of a disk, a ring, and coins by high-speed video imaging. The disks are spun on a variety of surfaces, by hand. In the early stages of the disk\u2019s motion there are degrees of freedom other than those described in Fig. 1 and the associated calculation. Initially, the point of contact of the disk can roll in a larger circle than the one of radius a cos a. This is apparent from a slow rotation of the body-fixed axes (XW 8 and YW 8) over one rotation of the ZW 8 axis about the Z axis. Depending on the way in which the disk was set into motion, the center of mass may also have some linear momentum. However, the disk rapidly settles into the motion described by Fig. 1, and all other motions appear to be damped out. In this regime we have not observed any significant deviations from Eq. ~3!. In Fig. 2 we present measurements of the angular precession 04510 rate V(t) versus (t2to). The triangles represent data from five different measurements of a steel disk spun on a flat steel surface. As shown in the figure, the data are quite reproducible and in this regime of time do not reflect irreproducibilities in the initial motions discussed above. In the figure we also show data for the same steel disk spinning on a glass surface ~plus signs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003077_pesc.2005.1581746-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003077_pesc.2005.1581746-Figure6-1.png",
        "caption": "Fig. 6: A cell of the multilevel Inverter, a) Top Side b) Bottom side.",
        "texts": [
            " Despite the advantages that the common mode voltage reduction offers, the number of commutations for some voltage phasor transitions with this algorithm is not minimum. Furthermore it must be used in combination with an over-modulation strategy, if the performance of the DTC in the high speed range wants to be reached. IV. SIMULATION AND EXPERIMENTAL RESULTS A 15kW prototype of a multicell inverter was developed in order to verify the proposed control method. Each cell is composed of a three-phase rectifier, a DC-link of 250V and 4 IGBTS IRG4PH40UD of 21A nominal current with their respective Drivers (fig. 6). A floating point DSP platform ADSP-21062 of Analog Devices was used for the implementation of the digital control. The modulator, the timers and the incremental encoder were programmed in a FPGA included in the board. The sample period was set up in 200\u00b5s, far more than a conventional DTC. The multicell inverter was connected to a 5.5kW induction machine for the first tests. Fig. 7a presents a simulation of the dynamic performance of the control algorithm. A step in the torque reference of 2Nm was applied with a DC-link voltage of 120V and with the machine running at 240min-1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000948_s0967-0661(02)00075-8-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000948_s0967-0661(02)00075-8-Figure1-1.png",
        "caption": "Fig. 1. X-38 control surfaces definition.",
        "texts": [
            " It is the most complicated part for control systems design, where the control needs to be transferred from the small thrusters to the aerodynamic control surfaces, as the atmospheric density increases with decreasing altitude. Correspondingly, two kinds of controls, the thrusters and the control surface deflections, are used in different combinations during the re-entry phase, depending on the environmental dynamic pressure level or Mach number (Wallner, Burkhardt, Zimmermann, Schottle, & Well, 1999; Wu & Chu, 1999). The vehicle possesses four aerodynamic control surfaces, as shown in Fig. 1. The left and right rudders are located on the fins and a pair of body flaps is located at the bottom of the vehicle. The body flaps (termed \u2018elevon\u2019) function as ailerons as well as elevators for asymmetric and symmetric deflections, respectively. In addition, cold gas reaction jets for control during the early phases of re-entry are located in two pods in the rear of the vehicle. Their nozzles are positioned in such a way that they can produce control torque around pitch, roll and yaw axes. Their $Partial content of this paper was presented in the 38th AIAA Aerospace Sciences Meeting & Exhibit, paper AIAA2000-0174, Reno, NV, USA, 10\u201313 January 2000"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002427_50009-5-Figure7.37-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002427_50009-5-Figure7.37-1.png",
        "caption": "FIGURE 7.37 Methods for the local measurement of hysteresis loop and power losses in magnetic sheets. (a) The applied field is provided by a yoke and the local field is detected by means of a magnetoresistive sensor (sensing area 1.5 mm \u2022 10 ~m). The flux in the measuring region is obtained, upon suitable calibration, by measuring the flux in the yoke (adapted from Ref. [7.115]). (b) Local measurement of the induction by needle probes in one dimension [7.117] and in two dimensions [7.118]. The local field is determined either by means of a Hall sensor or an H-coil. (c) The voltage V12 = V34 measured by using needle probes over a distance l much greater than the lamination thickness (exaggerated for clarity here) and the domain wall spacing is V12 = 89 Vc, where Vc is the voltage induced in a one-turn search coil wound around the same portion A,, of the lamination cross-sectional area. The horizontal lines schematically represent the eddy current trajectories.",
        "texts": [
            " The quest for local power loss measurements is motivated by the desire to investigate the behavior of the material to a scale suggested by the geometrical features of the sample (for example, the teeth in the statoric core of a motor), the structure of the material (e.g. individual crystal in grain-oriented laminations), or even the domain structure. To this end, a number of techniques, besides the thermal one, have been implemented, differing in the methods used to detect local field and induction. In the scheme reported in Fig. 7.37a, the local tangential field is measured by means of a miniature magnetoresistive sensor made of permalloy, biased by a small permanent magnet (for a discussion on magnetoresistive magnetometers, see Section 5.2.2), and the corresponding magnetization is induced from the signal detected by a coil wound around the yoke limb [7.115]. This flux-sensing method requires a calibration procedure on a test sheet of known properties. The local induction value can actually be determined in a most simple way by making holes and threading a few-turn winding through them. A non-destructive approach is, however, preferred for practical and quick material testing and, whenever sensitivity is not a big problem, needle probes can be advantageously employed. Figure 7.37b schematically shows two possible arrangements for local induction measurement with needle probes, and Fig. 7.37c illustrates the underlying working principle. If the contacts are placed at a distance l much greater than the lamination thickness and the flux variation occurs homogeneously upon such a scale, it is obtained from FaradayMaxwell's law that 1 ~ dBy 1 Via = 734 = - 2 A,, - ~ dan = 2 Vc~ (7.43) where V12 is the voltage measured between the contact points of the needles, A n is the portion of the cross-sectional area of the sheet lying beneath the contacts, By is the y-directed induction, and Vc the voltage induced in the one-turn search coil wound around the same area",
            " Detailed theoretical analysis shows that the presence of the domain walls does not introduce impor tant differences be tween the t ime evolution of the fluxes detected by the single turn and the needles. Discrepancies can be of the order of a few percent when the domain wall spacing D becomes a substantial fraction of the measur ing distance (D >---0.21) [7.116]. Reasonable figures are therefore expected using needle probes placed at a distance around 10 mm in grain-oriented laminations, as this arrangement, illustrated in Fig. 7.37b, provides a reasonable D/I value, while allowing one to put in evidence the grain-tograin loss fluctuation. Notice that the needle leads must always be arranged in such a way that as shown in the figure, they do not embrace a significant area. In the examples here reported, the local field is detected either by means of a Hall plate [7.117] or by a small H-coil [7.118]. A combination of double flat H-coil and double B-sensing needle pairs in a hand-held device has also been developed as a practical means for the analysis of the local distribution of fields and losses in laminated soft magnetic cores [7",
            " A pair of flat H-coils, orthogonally placed on the sample surface across the region of homogeneous magnetization (Figs. 7.11-7.14 and 7.39) can be employed to detect the components Hy and Hx. Alternatively, a pair of RCPs covering the same region can be used [7.128]. The use of Hall sensors can also be envisaged. In this case, however, the measurement is somewhat localized and the active character of the device is a disadvantage. The polarization components Jy and Jx can be obtained either with B-coils or needle probes, as illustrated in Fig. 7.37. The measuring region, however, must be sufficiently large to encompass the structural inhomogeneities of the tested material. With grain-oriented laminations this is not easily achieved and averaging of the results obtained on a number of samples might be required. The directly detected signals are obviously proportional to the time derivative of the above quantities, which are then obtained by numerical integration (Fig. 7.39). In this way, we have all we need for the measurement of the 2D power losses",
            " By integrating the instantaneous value of the surface integral of the Poynting vector over a full period we obtain the energy loss W. Under normal measuring conditions, the edge effects are irrelevant and the energy streams only through the top and bottom surfaces of the lamination and we can conclude that the energy loss throughout the whole sample volume can be determined by means of a surface measurement of the electric and magnetic fields. These are exactly the quantities we obtain by means of our needle probes (Fig. 7.37), which provide the voltages Vy = Eyl and Vx = Exl, and by the H-coils, from which the field components Hy and Hx are obtained after integration. With the symmetry of our problem, where the field is applied in the lamination plane and E and H do not have components along the z direction and are constant upon the measuring region of area l 2, we obtain that the instantaneous power dissipated in the volume 12d, where d is the lamination thickness, is P(t) = -21(E x H)I.I 2 -- 212(EyHx - ExHy ) = 2l(VyHx - VxHy), (7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001904_iros.2001.976254-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001904_iros.2001.976254-Figure4-1.png",
        "caption": "Figure 4: Measurement of 201 and 81",
        "texts": [
            " The body and arm are made of balsa wood. The whole mass of the jumping machine is 0.72 [kg], and the mass of the arm is 0.028 [kg]. The length of the foot is 0.25 [m] (= l j ) , the height of the body is 0.25 [m] (= 11), and the length of the arm is 0.20 [m] (= Z2). The normal power and the rated torque of the servo motor are 6.4 [W] and 0.215 [kgcm] respect ively. The experimental system is required to measure the jumping height. A sensor of the jumping height consists of two links attached to the both sides of the foot as in Fig.4. The ends of these links rotate freely, and the other ends are in contact with the ground. The angles of these links with respect to the foot are measured by two potentio-meters. The geometrical relation in Fig.4 gives the equations concerning 201 and 191 as follows: lf 201 + - sin81 = Lsin(cpL - 81) (2) If 201 - - sin81 = Lsin(qR + 01) (3) Although the horizontal translation is not measured, the jumping height and the posture are measured by this sensor. 2 2 3.2 Examination of Jumping Up After trial-and-error tests, we decided to input a rectangle command voltage to the servo motor of the experimental jumping machine. Then the jumping machine was able to jump up and land on the ground again. The command voltage and the jumping height are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001463_robot.1990.126233-Figure3.7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001463_robot.1990.126233-Figure3.7-1.png",
        "caption": "Figure 3.7 Graspable configuration on three vertices in the normal circle",
        "texts": [
            " Selection of grasp in this case follows a similar procedure used in section 3.3 for triangle grasp on two edges and one vertex[l2]. To find a grasp on one edge and two vertices, computation takes about 0.031 second. 4. 5. 6. 7. 8. 3.6 Grasp on Three Vertices When three vertices are used to grasp, there are four different normal circle configurations as a feasible vertex ranges arrangement That is, when each cone of vertex range in normal circle is grouped by pair, four different cases are possible depending on number of pair which has a counter-overlap, Figure 3.7. The following algorithms describe the grasp construction procedure for three vertices depending on number of pair which has counter-overlap in a normal circle. In these algorithms, CO, represents the cone in a normal circle formed by ith vertex range. Algorithm 3.8 Grasp on Three Vertices : Case 1. None of pair has counter-overlap in normal circle as Figure 3.7 (a). 1. Check whether three vertices are located on a line. If so, stop. Construct the normal circle by each vertex range. 2. Find convex addition of CO, and CO*, CO = CO1 + CO? Check whether CO has counter-overlap with CO3. If not, stop. Find intersection of vertex feasible regions, CF = CF(Cl) n CF(C2) n CF(C3). If empty, stop. Find force focus point as center of intersection C F . Define first, second and third grasp point at each vertex location. Use step 8 of Algorithm 3.5 to find a force direction at each vertex",
            " When the intersection of vertex feasible regions is not a single convex region, it is divided into several convex regions. Also if it is not bounded, the points located at large distance from the origh are assumed to make it a bounded convex polygon. To select a force focus point, the center of each bounded convex polygon is computed first. Then using each center as a force focus point, a grasp is constructed. The grasp which has the best heuristic value is selected as the final grasp. Figure 3.8 (a) shows the grasp on three vertices when three vertex ranges have normal circle as Figure 3.7 (a). 3. 4. 5. Algorithm 39 Grasp on Three Vertices : Case 2. One pair has counter overlap in normal circle as Figure 3.7 (b) where CO1 and CO2 have counter-overlap. 1. 2. 3. Same with step 1 of algorithm 3.8. Same with step 2 of algorithm 3.7. Divide normal circle into two sectors by the line which coincides with ul. Divide vertex range if it is located in more than one sector of divided normal circle. Select subrange C1 from CO1 and subrange C, from CO2 such that C1, C2 and CO, are not located at one side of normal circle dividing line simultaneously. Construct vertex feasible regions, CF(CI) and CF(C2). of selected subranges",
            " Find intersection of vertex feasible regions, C F I = CF(C1) n CF(Cz) . If subranges CI and Cz have counter-overlap, define direction of base vector as a vector passing through the middle of CO3. Apply algorithm 3.6 to find usable region CFU of CF1. If empty, stop. Find intersection of third vertex feasible region and CFU, CF2 = CFU n CF(C3). If empty, stop. Find force focus point from CF2 and grasp points with force directions by step 4 and 5 of algorithm 3.8. When three vertex ranges have a normal circle configuration as in figure 3.7 (b). three different grasps, (Cl2 , CzJ, (CII, CZI) and (Clz, C& pair with CO,, need to be evaluated. Figure 3.8 (b) shows the grasp on three. vertices where normal circle is given in Figure 3.7 @). When two pairs have counter-overlap in normal circle as shown Figure 3.7 (c), construction of grasp can be done by following similar procedure with algorithm 3.9. For this case, normal circle is divided into four sectors. Then, for each feasible combination of subranges, a gmsp is constructed. The maximum number of feasible subranges pairs will be nine. Also, when all three cones have counter-overlap. the normal circle is divided into six sectors and the maximum number of feasible subrange pairs will be thirty six. When this case arises, a grasp using subrange pairs which has none or has only one counter-overlap in a normal circle is constructed first"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002668_05698190500414300-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002668_05698190500414300-Figure4-1.png",
        "caption": "Fig. 4\u2014Dynamic and kinematic relations in ball motion.",
        "texts": [
            " [10a] and [10b] gives \u03b1i + \u03b1o = 2\u03b1 [25] Substitution of Eqs. [23] and [25] into Eq. [14] gives { 2r \u2212 D+ [( Ko sin \u03b1o Ki sin(2\u03b1 \u2212 \u03b1o) ) 2 3 +1 ] \u03b4o } cos(\u03b1\u2212\u03b1o)\u2212 A= 0 [26] where \u03b4o in Eq. [26] can be deleted by the substitution of Eq. [24]. The resulting equation is thus expressed as a function of \u03b1o; then \u03b1o can be solved by a numerical method. The other unknowns such as \u03b1i Qi , Qo, and \u03b4i , are thus obtained from Eqs. [25], [18a], [18b], and [23]. Angular Velocities of Ball and Inner and Outer Raceways As Fig. 4 shows, A\u2032 is the contact point of a ball and the outer raceway, whereas B\u2032 is the contact point of the same ball and the inner raceway. The ball\u2019s angular velocity relative to the rotating cage is defined to be \u03c9b. Then \u03c9b = \u2212\u03c9b(cos \u03b2 i\u0302 + sin \u03b2k\u0302) [27] Because the outer raceway is assumed to be stationary, the angular velocity of the outer raceway, \u03c9o, relative to that of the cage is \u03c9o = \u2212\u03c9c i\u0302 [28] where \u03c9 is the cage\u2019s absolute angular velocity. Similarly, the angular velocity \u03c9 of the inner raceway relative to that of the cage is written as \u03c9i = (\u03c9 \u2212 \u03c9c)i\u0302 [29] where \u03c9 denotes the absolute angular velocity of the inner raceway. In the case of outer raceway control (the ball\u2019s angular velocity relative to the outer raceway, \u03c9so = 0), the angular speeds of the cage and the inner raceway satisfy the following relationship (Jones (2)) \u03c9c \u03c9 = 1 \u2212 D dm cos \u03b1i 1 + cos(\u03b1i \u2212 \u03b1o) [30] As Fig. 4 shows, the angle formed between the negative x\u2032 axis and the \u03c9b vector is \u03b2, this angle is stated as (Jones (2)) \u03b2 = tan\u22121 ( sin \u03b1o cos \u03b1o + D dm ) [31] The angular velocity (\u03c9c) of a cage can be obtained from Eq. [30] if the angular velocity of the inner raceway (\u03c9) is given; the angle \u03b2 is easily obtained from Eq. [31] if \u03b1o is obtained. The ratio of \u03c9 to \u03c9c is given as (Jones (2)) \u03c9b \u03c9c = cos \u03b1o + dm D sin \u03b1o sin \u03b2 + cos \u03b1o cos \u03b2 [32] The equation is applied to evaluate \u03c9b if \u03c9c and \u03b2 are obtained. Slip Velocity at Contact Area between Ball and Inner Raceway As Fig. 4 shows, the position vector ( rA\u2032 ) connecting contact point A\u2032 at the outer raceway and the ball center is rA\u2032 = D 2 (\u2212 sin \u03b1oi\u0302 + cos \u03b1ok\u0302) [33] Similarly, the position vector ( rB\u2032 ) linking the contact point B\u2032 at the inner raceway and the ball center is rB\u2032 = D 2 (sin \u03b1i i\u0302 \u2212 cos \u03b1i k\u0302) [34] The velocity of the ball evaluated at point A\u2032 relative to the rotating cage is expressed as VbA\u2032 = \u03c9b \u00d7 rA\u2032 = 1 2 D\u03c9b(sin \u03b1o sin \u03b2 + cos \u03b1o cos \u03b2) j\u0302 [35] Similarly, the velocity of the ball at point B\u2032, which is evaluated relative to the cage, is expressed as VbB\u2032 = \u03c9b \u00d7 rB\u2032 = \u22121 2 D\u03c9b(cos \u03b1i cos \u03b2 + sin \u03b1i sin \u03b2) j\u0302 [36] The velocity of the outer raceway at the contact point A\u2032, relative to the cage, is stated as VoA\u2032 = \u03c9o \u00d7 ( rA\u2032 + dm 2 k\u0302 ) = 1 2 D\u03c9c ( cos \u03b1o + dm D ) j\u0302 [37] where the position vector of the rotational arm is the connection of bearing center to contact point A\u2032"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000974_20.717704-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000974_20.717704-Figure4-1.png",
        "caption": "Fig 4 (a) Eiieigy and (b) Co-eiieigy in a permanent magnet fiorn expiessions ( I ) and (9)",
        "texts": [
            " These forces are called by convenience \"intrinsic magnetic force densities\", as they are supposed to represent the magnetic forces on the magnet due to its intrinsic magnetization. The summation of these forces for a single magnet is, of course, null. (a) Vectoi potential 1 (b) Scalar potential ~ - . __ __ ._ __________ -J Fig '3 Local toice densities of a magnet alone (intrinsic forces) These distributions completely differ. This can be explained by the fact that the expressions of the energy and c.o-energy from which the above electromagnetic forces derive are simplified models and do not account for the same quantities. Fig. 4 presents the energy and the co-energy in a magnet from expressions (1) and (9). These expressions assume a linear-rigid model for the magnet which accounts for the variation of energy or coenergie from the remanent or coercitive point to the working point B. They obviously do not represent correctly the actual energy implied in the non linear magnetizing process. That energy will be called \"intrinsic magnetic energy\". The value of this intrinsic magnetic energy is unknown. At least, no clear value is given",
            " The necessary energy to magnetize the magnet is, in the most of the cases, over two to twenty times the energy of the single magnet [8]. The exceeding energy is lost in heat form, magneto mechanical form, ... [71[81[91[101. We have seen that when a magnet is magnetized, during the magnetizing process, most of the supplied energy is lost in heat or magneto mechanical form while only a small part of this energy is stored in the magnet under magnetic form. Then, one should be able to affirm that in the remanent point B, (in fig. 4), the magnet has a certain magnetic energy stored, which we shall call \"intrinsic initial energy\" which is the intrinsic magnetic energy at the remanent point. This energy is not taken into account by the expression (I), for which the magnetic energy is null if the magnet works on the remanent point (B = Br). Thus, one must take care that the classical expressions of forces in a permanent magnet obtained by the usual magnetic energy and co-energy expressions are so simplified that they do not represent the reality any more"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001559_b978-0-08-092509-7.50008-7-Figure4.3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001559_b978-0-08-092509-7.50008-7-Figure4.3-1.png",
        "caption": "FIGURE 4.3. The Puma'spostures.The four physicalsolutionswhichposition theendeffectorat (0,30,40).",
        "texts": [
            " In general,ill-posednessof the lattertypecanbe interpretedas arising fromtwo distinctphenomena.First, the inverseis nonuniqueina global sense(but perhapsstill well-definedlocally) becauseof the existenceof multiplesolutionbranches.This occursfor manipulatorsbothwith and withoutexcessDoF.Forexample,considerthenonredundanttwo-linkplanarmanipulatorwithunlimitedrotationaljointsshownin Figure4.2. There are two configurationswhichplacethe endeffectorat anygiven pointin the reachableworkspace.The nonredundantPuma560can placetheend effectorat a specifiedlocationinfour distinctways,asshownin Figure4.3. problemis locallywell-posed. Second,the inversekinematicsproblemfora manipulatorwith redundantDoFis locallyill-posedin thateachsolutionbranchcontainsaninfinite numberof solutions.Asingle inversesolutionbranchconsistsofasetof configurationswhichhavea manifoldstructurein thejointspaceof dimensionequalto thenumberof redundantdegreesof freedom.Theexistenceof suchnontrivialpreimagemanifoldsfor redundantDoF manipulatorsallows configurationmotionsto occurwhilekeepingtheendeffectorfixedat some desiredlocation",
            " The fiber T'\":\"' correspondstoa manifoldof manipulator self-motions,whichwe identifywith asingle solutionbranch,andtheset B correspondsto thepossiblesolutionbranches(disjointpostures)of the manipulator. For example,for the nonredundant,wristless(positioningonly) Puma manipulator(wheren == m == 3), the \"fibers\"T'\":\"' == TO are discrete points,representingthefact thatnonredundantmanipulatorshavenoselfmotionsoutsideof singularconfigurations.Therearefour discretepoints in B which indexthe possiblepostures,e.g.,\"elbowup, shoulderleft.\" Figure4.3 illustratesthefour postureswhichpositionthemanipulatorat aspecifiedlocationin theworkspace. Restrictingour attentiontoan individualw-sheetWi, wedefinea solution branchof j (.) over the w-sheetWi tobea maximallyconnected subsetof j-l(Wi). The solutionbranchesover Wi are denotedby 81, j == 1, ... , IBil, IBil denotingthe numberofsuch branches.The w-sheets Wi are maximallyconnectedregionsofregularvaluesintheworkspaceW 1A metricspaceY is solidiffor anyclosedsubsetA ofa normalspaceX with map I : A -+ Y, thereexistsa mapI' :X -+ Y suchthat I' IA == I"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002767_978-3-642-71015-5-Figure3.8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002767_978-3-642-71015-5-Figure3.8-1.png",
        "caption": "Fig. 3.8. Investigated system",
        "texts": [
            " The solution of our problem - which we phrase as follow: \"What is the proximity effect between a rectilinear current-carrying wire and a thin plane metal sheet?\" - is also relevant to the behavior of ground wires and counterpoises [e.g. Ref. 3.2]. A very long (\"infinite\") wire of circular cross section (diameter 2ro) carries an alternating current whose return path is provided by a conducting plane sheet of uniform thickness ~ located at a distance h ~ roo The sheet exhibits an electric conductivity (f and a magnetic permeability 110 and extends infinitely along the \u00b1 x and \u00b1 y axes in a rectangular frame of reference x, y, z (Fig. 3.8) incorporating also the time parameter t. We seek: a) The per-unit length equivalent impedance change of the wire, due to the finite conductivity of the metal sheet. b) The flow pattern of the induced current in the extended conductor under an applied current step in the wire. To simplify the problems posed and their relevant solutions, we shall assume that the wire, characterized by an \"infinite\" conductivity, comprises a continuous array of internal current generators providing the required excita tion (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000059_971101-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000059_971101-Figure4-1.png",
        "caption": "Figure 4: The tire ring and the deformation and the coordinate system used.",
        "texts": [
            " THEORETICAL MODAL ANALYSIS USING THE FLEXIBLE RlNG MODEL THE EQUATIONS OF MOTION OF THE FLEXIBLE RING MODEL - The flexible ring model, shown in Figure 3, consists of a circular ring representing the tire tread-band; a mass representing the rim; circumferentially distributed radial and tangential springs representing the tire sidewalls and pressurized air in the tire. The rim has three degrees of freedom in the plane of the wheel: the vertical and horizontal displacements and the rotation about the The equations of motion of the flexible ring model, according to the coordinate system introduced in Figure 4 read [6]: +cbw (w, - xa cos 9 + za sine) + where q, and q, are the external distributed forces acting on the ring in the tangential and radial directions; F, and F, are the external forces acting on the rim; M,, is the external torque acting on the rim; vb and w, are the tangential and radial displacements of the ring element; xa and za are the horizontal and vertical rim displacements and 0, is the small deviation of the angular displacement of the rim on top of the displacement due to steady speed of rotation a"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000141_s0043-1648(97)00190-7-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000141_s0043-1648(97)00190-7-Figure4-1.png",
        "caption": "Fig, 4. Dia~'n~i(m.,, of the sliding shoes.",
        "texts": [
            "r\u00a2 ,) ) and the friction at the moment of possible velocity reversal F ( t , ) . 3 . E x p e r i m e n t a l 3. L Test rig and lesI preparat ion A schematic view of the rotary stick-slip tester used in the premnt research is presented in Fig. 3. The test rig basically 140 F. Van De Velde et al. / Wear 216 t1998~ 138-149 consists of a rotating bath ( l ) driven by a frequency controlled a/c. motor, in which a ring (2) is mounted. Two centre-pivoted sliding shoes ( 3 ), with dimensions as shown in Fig. 4, are connected to an arm (4) by means of pins (5) and are pressed against the ring by a dead weight-lever system (6-7) . The arm (4) is connected to the frame by a roller bearing with the same centre as the bath and ring. Rotation of the arm is prohibited by a linear spring (8), connected to the frame. Three springs with different stiffness can be mounted: the most flexible one is a torsion bar (shown in Fig. 3 ), the stiffer two are leaf springs Fig. 5b. Rotation of the bath causes sliding of the ring against the shoes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001248_1.2826898-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001248_1.2826898-Figure2-1.png",
        "caption": "Fig. 2 Six solutions for the Stevenson six-bar of Fig. 1 for a given value of 0c- For the specified value of dc point C is always at the location shown and point D must lie on the circle centered on C. The couplercurve described by point D as constrained by the four-bar cell OAABOB is also shown. Its six intersections with the circle define six possible positions of the linkage, which are shown using different line weights or dashes for each.",
        "texts": [
            " 1, has four solutions if OA or OB is considered to be the driving joint, but six if Oc is the driving joint. If OA is the driving joint, there are two possible positions of the dyad OBBA for any given value of 9A. Hence there are two possible positions for point D. For any given position of point D there are two possible positions of the dyad OQCD. Hence there is a total of 2^ solu tions. This is characteristic of solution by dyadic decomposition with the linkage driven by a crank of the four-bar cell. If the linkage is driven via joint Oc, as is shown in Fig. 2, for any given value of Qc point D can lie anywhere on the circle shown. Point D is also constrained by the four-bar cell OAABOB for which it is a coupler-point. The coupler-curve that is the path of any point on the coupler-plane of a four-bar linkage is, in general, a tri-circular sextic curve (Hunt, 1978). A circle has at most six real, finite intersections with a tri-circular sextic. The six intersections of the circular locus of point D determined * Presently with the Department of Mechanical Engineering, University of Texas, Austin, TX 78712. Contributed by the Mechanisms Committee and presented at the Mechanisms Conference, Minneapolis, MN, September 11 -14, 1994, of THE AMERICAN SOCI ETY OF MECHANICAL ENGINEERS. Manuscript received July 1995; revised March 1996. Technical Editor: B. Ravani. by rotation about C for given 6c with the coupler-curve are shown on Fig. 2. Each intersection gives a distinct solution position of the linkage. However, this latter difficulty is not the primary issue which is to be discussed in this paper. Rather, for planar linkages with 8 or more members it is not necessary that there be a four-bar circuit in the mechanism. As appears to have originally been shown by Alt (1955), there are 16 possible topologies for an 8 member planar mechanism with mobility one, and with all joints having connectivity one, one of which does not have any four-bar circuits"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002427_50009-5-Figure7.12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002427_50009-5-Figure7.12-1.png",
        "caption": "FIGURE 7.12 Vertical-type double-yoke magnetizer.",
        "texts": [
            " By increasing its width, we also obtain that geometrical imperfections of sample and pole faces have little effect. Tapering is also associated with the rapid decrease in the field strength on leaving the sample surface (see Fig. 4.24). Consequently, it requires precise positioning of specimen and H-coils. The horizontal-type double yoke magnetizer is of simple construction and it has been adopted, with more or less significant variations (e.g. flat H-coil vs. RCP, tapered vs. untapered poles), by a good number of laboratories [7.46-7.49]. The more complex vertical double-yoke 2D magnetizer, sketched in Fig. 7.12, is sometimes preferred to the horizontal-type 2D magnetizer because the two orthogonal applied field components are generated by means of two nearly independent magnetic circuits [7.50, 7.51]. It is generally recognized, however, that with both these types of magnetizers it is difficult to control accurately the rotation of the magnetization in strongly anisotropic materials. This typically applies to grain-oriented Fe-Si laminations, which are very soft along RD, but quite hard along the direction making an angle of 54"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000440_0302-4598(95)01856-a-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000440_0302-4598(95)01856-a-Figure4-1.png",
        "caption": "Fig. 4. Cyclic voltammetric curves of 5 mM dopamine in phosphate buffer (pH 7.4) at polycarbazole electrode (14 p.). (1) 20 mV s- l; (2) 50 mV s - t ; (3) 100 mV s; (4) 200 mV s; (5) 400 mV s -1.",
        "texts": [
            "22 V was not observed here. Ascorbic acid undergoes a two-electron oxidation to produce a product which undergoes a fast irreversible hydration reaction [19,20]. It is a quasi-reversible system with an anodic-cathodic peak separation of 100 mV at a recorded sweep rate of 1000 V s -1. At slower sweep rates, the hydration reaction is too fast for any complementary peak to be observed. The electrochemical oxidation of dopamine at a polycarbazole electrode was also examined as a function of sweep rate. Fig. 4 shows the typical behaviour of a polycarbazole wire electrode (A = 0.064 cm 2) for 5 mM dopamine. The current function remains constant with increasing sweep rate. An interesting feature of the cyclic voltammetric curve is that the anodic peak reaches a plateau instead of following the characteristic decay observed for a diffusion controlled process. This feature is certainly helpful in the determination of dopamine concentration as the current in this region is constant over a large potential range"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003889_3-540-29461-9_55-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003889_3-540-29461-9_55-Figure2-1.png",
        "caption": "Fig. 2. Schemes for the 1-DOF leg for: (a) kinematic analysis; (b) dynamic analysis",
        "texts": [
            " Numerical and experimental results in [15] show that good kinematic features can be obtained when points C and P in Fig. 1 are not coincident. In particular, it has been shown in [14, 15] that better features can be obtained if the transmission angles \u03b31 and \u03b32 have suitable large values. Kinematic and Dynamic analyses have been carried out in order to evaluate and simulate the performance and operation of the leg system. In particular, the mechanical design is based on the Chebyshev design [12, 13]. Three reference systems have been considered, as shown in Fig. 2. The position of point B with respect to CXY frame can be evaluated as a function of the input crank angle \u03b1 as XB = \u2212a+ n cos\u03b1+ (c+ f) cos \u03b8; YB = \u2212n sen\u03b1\u2212 (c+ f) sen \u03b8 (1) where \u03b8 = 2 tan\u22121 sen\u03b1\u2212 (sen2\u03b1+B2 \u2212D2)1/2 B +D (2) Coefficients B, C and D can be derived by the closure equation of the mechanism. By considering the five-bar linkage CDBGP in Fig. 2, one can write the closure loop equation to obtain \u03d51 and \u03d52 as \u03d51 = 2 tan\u22121 1\u2212\u221a1 + k1 2 \u2212 k2 2 k1 \u2212 k2 ; \u03d52 = 2 tan\u22121 1\u2212\u221a1 + k3 2 \u2212 k4 2 k3 \u2212 k4 (3) where k1 = xB \u2212 p yB \u2212 h ; k2 = b1 2 + (yB \u2212 p)2 \u2212 (l2 \u2212 b2)2 + (xB \u2212 h)2 2b1 (yB \u2212 h) k3 = p\u2212 xB yB \u2212 h ; k4 = \u2212b12 + (yB \u2212 p)2 + (l2 \u2212 b2)2 + (xB \u2212 h)2 2 (l2 \u2212 b2) (yB \u2212 h) (4) Consequently, from Fig. 2a, transmission angles \u03b31 and \u03b32 can be evaluated as \u03b31 = \u03d51 + \u03d52 and \u03b32 = \u03c0 \u2212 \u03b8 \u2212 \u03d51 . The position of A can be given as XA = XB + b2 cos\u03d52 \u2212 (l1 \u2212 b1) cos \u03d51 YA = YB \u2212 b2 sen\u03d52 \u2212 (l1 \u2212 b1) sen\u03d51 (5) The position of C with respect Axy reference frame can be written as xC = l1 cos\u03d51 \u2212 l2 cos\u03d52 \u2212 p; yC = l1 sen\u03d51 + l2 sen\u03d52 \u2212 h (6) Acceleration of point A, with respect to Axy frame can be obtained as aAX = aBX \u2212 b2 ( \u03d5\u03082 sen\u03d52 + \u03d5\u03072 2 cos \u03d52 ) \u2212 (l1 \u2212 b1) ( \u03d5\u03081 sen\u03d51 + \u03d5\u03072 1 cos \u03d51 ) aAY = aBY \u2212 b2 ( \u03d5\u03082 cos \u03d52 \u2212 \u03d5\u03072 2 sin \u03d52 ) \u2212 (l1 \u2212 b1) ( \u03d5\u03081 cos \u03d51 + \u03d5\u03072 1 sin \u03d51 ) (7) The walking performances can be also evaluated from dynamic viewpoint by using the Newton-Euler method to obtain the equations to derive the actuating torque \u03c4. In the following analysis 3 assumptions have been made [14]: 1) concentrated masses; 2) no friction forces; 3) no elastic deformations. Expressions of the velocity and acceleration are evaluated by using (1) to (7) for the center of masses for each link. A suitable model for the dynamic analysis is shown in Fig. 2b. The force acting on the i-th link of the leg can be evaluated in the form 7\u2211 i=1 (Fexi + FIxi) = 0; 7\u2211 i=1 (Feyi + FIyi) = 0; 7\u2211 i=1 (Mei +MIi) = 0 (8) in which Fe and Fi represent respectively the acting and inertia forces and Me and Mi represent respectively acting and inertia moments. The equation\u2019s system in (8) can be rewritten in the form AX = F (9) where A is a (21\u00d7 21) matrix, X is the vector containing 21 unknown forces and torques. F is the vector of 21 known forces and torques. Kinematics and Dynamics have been considered for numerical simulations with data of Table 1. In particular, results have been obtained without considering the leg\u2019s interaction with the ground. It has been shown in [14, 15] that the best motion characteristics for the leg can be obtained when p and h in Fig. 2a are equal to 20 mm and 30 mm. Figure 3 shows results of the numerical simulation that has been carried out with p = 20 and h = \u221230 and the angular velocity \u03c9 of the input crank is chosen as a constant value and equal to 2.3 rad/s. Figure 4 shows transmission angles and the actuating torque. Simulations have been also carried out by removing the hypothesis of input constant velocity. Indeed, the angular velocity \u03c9 can be considered as \u03c9 = \u2212 cos(\u03bd) (10) A prototype of low-cost biped walking machine has been built as based on the proposed 1-DOF leg at LARM in Cassino",
            " A scheme of the measuring system that has been settled up, is shown in Fig. 5b. It is composed of commercial measuring sensors and LabView software [16] with NI 6024E Acquisition Card [17]. Referring to Fig. 5 one biaxial accelerometer Ac, [18], has been installed at point A. It gives the possibility to measure and monitor the acceleration at the extremity of the leg. Numerical results are shown in Figs. 6 and 7 in which the acceleration components aAx and aAy are expressed in the AXmYm reference frame, as shown in Fig. 2a. In this paper a 1-DOF pantograph-leg is presented. Kinematics and Dynamics have been solved to obtain suitable simulation of its operation. A low-cost biped machine has been built at LARM in Cassino by using the proposed 1-DOF leg. First experimental results has been presented. 1. Rosheim, M.E. (1994) Robot Evaluation, Wiley, New York 2. Chernousko, F.L. (1990) On the Mechanics of a Climbing Robot, Jnl. of Mecha- tronics Systems Engineering, Vol. 1, pp. 219\u2013224 3. Morecki, A., Waldron, K.J. (1997) Human and Machine Locomotion, Springer, New York 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003299_tsmc.1987.289354-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003299_tsmc.1987.289354-Figure1-1.png",
        "caption": "Fig. 1. Planar articulated robotic manipulator.",
        "texts": [
            " Planar manipulators occur naturally within horizontally jointed (SCARA) type arms which are often used for high-precision assembly work. Here the use of more than two horizontal joints makes the arm redundant with respect to controlling the horizontal position of the end effector. Similarly, in a vertically jointed (articulated) arm, the use of more than two consecutive,vertical joints makes the arm redundant with respect to controlling the radial position of the wrist. As an example of a redundant robotic manipulator, consider the planar n-axis articulated arm shown in Fig. 1. If we regard the last link of the manipulator as an end effector, then the gripper configuration space is of dimension m = 3. The first two components of x e R3 represent the coordinates of the position of the tip of the end effector, while the last component of x represents the orientation of the end effector. The kinematic model of this arm is particularly simple when formulated in terms of the absolutejoint angles q E Rn. From Fig. 1 it is evident that the gripper configuration is given by n xl= E, akCk (12a) k=1 n x2= E, akSk (12b) k=1 X3 =qn (12c) Here the notation Ck ^ cos(qk) and Ak- sin(qk) is used to simplify the development of subsequent equations. Although the formulation of the kinematic model in terms of q is quite simple, it is the vector of relative joint angles 0 E Rn whose rates we control. Here -01 = ql, while 0k = qk - qk-I for 2 < k < n. The vector of relative joint angles can be recovered from the vector of absolute joint angles using 0 = Cq",
            " In the {I}-inverse formulation of the rate equations, these unused degrees of freedom manifest themselves as the n - 3 components of the redundant joint velocity vector r(t). Potentially, the redundant joint rates might be specified in many ways. In this section we outline one approach to selecting them which is useful for avoiding obstacles in the work space. Let wk-denote the position of the start of link k for 1 < k < n. Then wl = 0 represents the position of the base, while Wn = z' is the prescribed position of the wrist. Using (14) and Fig. 1, and working backwards from the wrist, the position of the start of link k is n- wk( q) = z' - Eaj [Cj Sj] 3 < k A n -1. (25) j=k Next let { h3, h4** hn ) denote a set of desired positions for the start of links (3,4,. .., n - 1}, respectively. In a work space containing obstacles, the set fhk) might represent points in a free space path between the base and the wrist. To place n - 3 additional position constraints on the arm, consider the following sequence of performance indices, one for each redundant joint: Vk(q) =wk(q)-hkj I/2, 3 < k < n-1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000810_s0924-0136(02)00356-4-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000810_s0924-0136(02)00356-4-Figure8-1.png",
        "caption": "Fig. 8. Effective strain rate distribution during wheel rolling.",
        "texts": [
            " This clearly has resulted in an increased problem size, a situation that was partially reduced by excluding the boss section of the wheel from the model. Historical observations of the process has lead to the general assumption that the boss section is unaffected by the rolling process. This assumption suggests that the inner radius of the meshed region, the boundary with the boss can be assumed to be fixed during the process. Hence velocity boundary conditions have been applied in all directions to the inner ring of nodes in the mesh. The importance of extending the dense mesh region can be seen in Fig. 8, which shows the effective strain rate in the workpiece during the process. Strain rate in the vicinity of the drive roll is much smaller, suggesting that the dense region close to that roll could be made smaller. 1. The ALE update strategy allows the use of a non- uniform mesh and means that the dense mesh region does not follow the material out of the roll gap, as would be the case for a standard updated Lagrangian approach. 2. The mandrel rotation speed is determined as an additional unknown in the problem in an extension of the method of Yang and Kim [1]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003023_001-Figure23-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003023_001-Figure23-1.png",
        "caption": "Figure 23. A schematic drawing of the end of a flexible bilumen mass spectrometer probe (after Parker and Delpy 1983). intravascular blood gas catheter",
        "texts": [
            " Various slits or holes have been cut into the steel catheter to allow the gas molecules to diffuse to the mass spectrometer head, and the geometrical design of these catheters was examined by Seylaz and Pinard (1978) and Pinard et al(l978). In more recent years several reports (Lundsgaard et al 1980, Parker and Delpy 1983, Hansen et a1 1986) have described catheter probes with the tip consisting of a sintered, porous substrate (typically bronze) covered with a permeable membrane. Two examples are shown in figures 22 and 23. The Hansen et a1 (1986) design (figure 22) uses the conventional stainless steel tube connection to the mass spectrometer, but the Parker and Delpy (1983) design (figure 23) uses a flexible plastic catheter, coated on the inside with polyurethane to minimise the problem of water vapour diffusion through the catheter walls. This latter design also includes a bilumen tube, one lumen being used for blood sampling. 9.1.2. Non-invasive probes. A transcutaneous mass spectrometer non-invasive probe is shown schematically in figure 24. It is essentially a heated gas collection chamber, and was described by Delpy and Parker in 1975. A plastic body enclosed a stainless steel chamber, and a porous metallic plug supported a gas permeable membrane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001630_robot.1999.772552-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001630_robot.1999.772552-Figure3-1.png",
        "caption": "Fig. 3: Infliicncc of obstacle on the gait",
        "texts": [
            " Two types of obstacle influcncc arc classified: (a) Wlicn the o1)stac:lc is very near to or overlaps with the front tmindary of t,he reachable area of the leg, it affects the placing position and transfer time. The influcncc is tlicrcforc defiricd as DIO (Double Infliicncc of 0bstac:lc) (1)) Whcn the obstacle is far away from the front 1)oiindary of thc rcachablc area of the leg, but near to tha front boiindary of the reachable area of the next lcg which will be liftcd, thc obstacle affects only the transfcr time of t,hc currently considered leg. This influcric:o is tlcfimd as S I 0 (Singlc Influcncc of Obstadc). The two typcs of influcncc arc demonstrated by Fig. 3. In Fig. 3(a), thc obstaclc has an influcncc of DIO on leg 3 and an influcncx of S I 0 011 lcg 2, while in Fig. 3(b), it has a DIO on leg 2 and a SI0 on leg 4. 5.3 Determination of Gait Parameters set, to the rriaxirriiim transfer time, Without any ol)stac:lc, the leg transfer time can be t.f = Tf , and t,hc leg is p1ac:otl Iicar to thc anterior cxtrcmc position (AEP). If thcrc is an obstaclc of SIO, thc placing position is not affcctcd and aquals to A E P , and the transfer time is set t,o the rriinimiim transfer time, t f = TfO . (19) Her(:, thc: rriiriirriiim t,rarisfcr time Tfo is the time for leg transfcrrcd with t,hc maximiim speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002584_tnn.2004.824418-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002584_tnn.2004.824418-Figure5-1.png",
        "caption": "Fig. 5. The BTT missile diagram.",
        "texts": [
            " And the solution of Ricatti-like equation for disturbance rejection control signals can be simplified to be easy to determine in this paper. For ridge Gaussian neural networks, not only the input-to-hidden and hidden-to-output layers weights but also the orientations and shapes of Gaussian functions can be tuned and that improves the flexibility of Gaussian neural networks. The proposed controller was applied to BTT missiles and simulations demonstrated the effectiveness successfully. APPENDIX I STATE NOTATIONS AND DYNAMIC EQUATIONS OF BTT MISSILES Assuming the BTT missile shown in Fig. 5 is a rigid body, the complete 6 degrees-of-freedom (DOF) dynamics of BTT missiles can be given by , , , , , , , , and (see equation at the bottom of the page) where , , , , , , and . The ac- tuator is modeled by a first-order system as follows: , , . The nine elements of the gain matrix derived by input-output linearization technique are as follows: , , , , , , , , and , where s are aerodynamic coefficients that are complex functions of and and not given here. The above 6-DOF missile dynamic equations and detailed process of derivation can be referred to [12]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003746_1.2159036-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003746_1.2159036-Figure3-1.png",
        "caption": "Fig. 3 Displacements of ball, inner, and outer races",
        "texts": [
            "org/about-asme/terms-of-use Downloaded F mb v\u0308r v\u0308z = Qi cos i \u2212 Qe cos e + Fe Qi sin i \u2212 Qe sin e 3 where Qi,e are contact loads, mb is the mass of a ball and i,e are contact angles in Fig. 1. Assuming the outer race is fixed in the Z-axis the radial motion of the outer race is described as me + mj \u00b7 x\u0308e y\u0308e = j=1 n Qe cos e j \u00b7 cos j j=1 n Qe cos e j \u00b7 sin j + Fs 4 where me and mj are the masses of the outer race and the damper journal, respectively, and Fs is the force vector from the damper. Displacements of the groove centers p ,q and the ball center b are shown in Fig. 3. Let wr be the radial displacement of the outer-race groove center q. The lengths loi , loe represent the distances between the ball center and race groove centers under no external force, and the lengths li , le the distances under external forces. Likewise, the angle o is the initial contact angle and the angles i,e are the contact angles under external loads. From the relative geometric relation 10 , the contact angles and the lengths after external forces are applied including thermal expansions are obtained from tan i = loi sin o + uz \u2212 vz loi cos o + ur + i \u2212 vr , tan e = loe sin o + vz loe cos o + vr \u2212 wr \u2212 e 5 204 / Vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003409_s0737-0806(84)80050-7-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003409_s0737-0806(84)80050-7-Figure4-1.png",
        "caption": "Figure 4. The moments of the legs overall. 140",
        "texts": [
            " F together with the respective moment arms for these tendons and the ground reaction force, F, 139 extensor taken to be operating as one. The passive action of the common and lateral extensors is considered further with the experimental results. The interosseous medius is taken to include the proximal sesamoid bones and the straight distal sesamoidean ligament as its functional, distal continuation and attachment. The moment arms are indicated by the lower case letters. All the moment arms are approximately anatomical constants with the exception of 1, f, and p. In Figure 4, -Mh is a clockwise moment caused by the weight of the horse caudal to the foreleg, acting around the moment arm, h, the center of rotation being at the coffin joint. Mmh is the counter-clockwise moment caused by the weight of the head and neck. Rh' is the counter-clockwise moment caused by the weight of the horse in front of the rearleg, acting around the moment arm, h'. This equation is included, so that the proximal end of the foreleg is in equilibrium and will not move parallel to the ground as the hoof angle is changed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001707_s0094-114x(03)00091-0-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001707_s0094-114x(03)00091-0-Figure2-1.png",
        "caption": "Fig. 2. (a) The location of the instant center I136. (b) The location of the instant center I236. (c) The location of the instant center I36. (d) Location of the instant centers that lie on page.",
        "texts": [
            " First, remove link 5 (link 4 could also have been chosen) which results in a two-degree-of-freedom six-bar mechanism. In other words, let the pin connecting links 5 and 6 (i.e., point E) float freely in link 6 with the length of link 5 remaining unchanged. Second, choose any point on link 7, or link 7 extended (i.e., the line connecting the instant centers I17 and I67), as the instant center I116. Then use the Aronhold\u2013 Kennedy theorem to locate the corresponding instant centers I126 and I136, see Fig. 2a. Third, choose a different point on link 7, or link 7 extended, as the instant center I216 and again use the Aronhold\u2013 Kennedy theorem to locate the corresponding instant centers I226 and I236, see Fig. 2b. Fourth, draw a line through the instant centers I136 and I236 which represents the locus of all possible instant centers I36 for the two-degree-of-freedom six-bar mechanism. The intersection of this line with link 5, or link 5 extended, of the geared seven-bar mechanism is the instant center I36, see Fig. 2c. Finally, the point of intersection of the line connecting I13 and I36 and the line connecting I17 and I67 is the instant center I16. The location of the remaining secondary instant centers can now be obtained directly from the Aronhold\u2013Kennedy theorem. The secondary instant centers that lie on the page are shown in Fig. 2d. Special configurations. There are certain configurations where the geared seven-bar mechanism will instantaneously gain a degree of freedom (commonly referred to as a stationary configuration) or lose a degree of freedom (commonly referred to as a singular configuration). In these configurations, the graphical procedure outlined above will simplify and the instant center for the coupler link I16 can be obtained in a more direct manner. For purposes of illustration, consider the following three configurations",
            " The procedure to find an equivalent five-bar linkage is to draw a line through pins A and D and a line through pins B and E. The intersection of these two lines is a point fixed in the coupler link 6 and will be denoted as point M , see Fig. 3. The center of curvature of point M for 6/2, denoted as O0 M , can be obtained by writing the Euler\u2013Savary equation for points D and M fixed in link 6, respectively, as 1 P26JD \u00bc 1 P26D 1 P26OD \u00f01a\u00de and 1 P26J 0 M \u00bc 1 P26M 1 P26O0 M \u00f01b\u00de where the pole P26 is coincident with instant center I26 (see Fig. 2d) and OD is coincident with pin A. Since D and M lie on the same line then the inflection points JD and J 0 M are coincident; i.e., P26JD \u00bc P26J 0 M . Therefore, equating Eqs. (1a) and (1b) and rearranging will give the center of curvature O0 M , i.e., 1 P26O0 M \u00bc 1 P26M \u00fe 1 P26OD 1 P26D \u00f02\u00de Similarly, the center of curvature of point M for 6/3, denoted as O M , can be obtained by writing the Euler\u2013Savary equation for points E and M fixed in link 6, respectively, as 1 P36JE \u00bc 1 P36E 1 P36OE \u00f03a\u00de and 1 P36J M \u00bc 1 P36M 1 P36O M \u00f03b\u00de where the pole P36 is coincident with instant center I36 (see Fig. 2d) and OE is coincident with pin B. Since E and M lie on the same line then the inflection points JE and J M are coincident; i.e., P36JE \u00bc P36J M . Therefore, equating Eqs. (3a) and (3b) and rearranging will give the center of curvature O M , i.e., 1 P36O M \u00bc 1 P36M \u00fe 1 P36OE 1 P36E \u00f04\u00de The centers of curvature O0 M and O M will henceforth be denoted as T and U , respectively, as shown in Fig. 3. Note that the links of the constrained five-bar linkage O2TMUO3, also denoted as links 1, 2, 8, 9 and 3, are equivalent in motion to the corresponding links of the original geared seven-bar mechanism. Also note that since link 2 is in rolling contact with link 3 then the instant centers of the five-bar linkage can be obtained directly from the Aronhold\u2013Kennedy theorem. The first intermediate four-bar linkage can now be obtained from a study of the kinematic inversion 2/3. The pole P23 is coincident with the point of contact of the two gears (i.e., the instant center I23 shown in Fig. 2d), the pole normal PN is coincident with the line of centers O2O3, and the pole tangent PT is perpendicular to this line through the pole P23, see Fig. 4a. The inflection point for the point O2 can be obtained from the Euler\u2013Savary equation. Since the inflection point lies on the pole normal then this point is also the inflection pole J23. Therefore, the inflection circle for 2/3 can be drawn with diameter P23J23. Then the inflection point JT for the coupler point T can be obtained; i.e., the point of intersection of the line P23T with the inflection circle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003976_1.3452904-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003976_1.3452904-Figure4-1.png",
        "caption": "Fig. 4 Cross section of the two-disk test rig",
        "texts": [
            " Despite the smaller viscosity temperature dependency of test oil 6 compared with the test oils 2 and 3, the viscosity of oil 6 increases much more with increasing pressure. Considering the viscosity pressure behavior it has to be taken into account that the viscosity pressure coefficient also depends on the temperature. This effect is shown in Fig. 3 for the test oils. The small influence of temperature on the a-value of the silicone oil (test oil 1) and the much more pronounced temperature effect on test oil 3, one of the high viscosity mineral oils, can be recognized. Test Rig and Measuring Equipment Two-Disk Test Rig. Fig. 4 shows a cross section of the two-disk test rig used for this investigation. The loading force is applied by the upper yoke (1) from the upper to the lower disk. This upper yoke is connected with the lower yoke by two tension rods (2). The lower yoke is applied by the force of a hydraulic cylinder (4) mounted on the base plate (3). -Nomenclature. R\\, #2 = electrical resistances of the trans ducers u = surface velocity of solids in x direction (circumferential speed) w = load per unit length of cylinder x = coordinate of the contact length v - viscosity pressure coefficient deter mined by viscosity measurement up to 2000 bar v* = viscosity pressure coefficient correct ed by grafical extrapolation for that test oils not corresponding to the simplified relationship -r\\p = i)o-eap )jo = viscosity at conditions of entry to con tact rip = viscosity at pressure p t"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001756_jsvi.2001.4016-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001756_jsvi.2001.4016-Figure3-1.png",
        "caption": "Figure 3 shows a pair of spur bevel gears arranged perpendicularly. This pair can be simpli\"ed as a pair of virtual cylindrical gears in the co-ordinate frames ox y z , i\"1, 2, which are \"xed on rotors 1 and 2 respectively. As done in reference [1], the relationship between the lateral translations x , y , x and y of two virtual cylindrical gear centers",
        "texts": [
            " KINETIC CONSTRAINT FOR A PAIR OF SPUR BEVEL GEARS The tooth surface of a pair of spur bevel gears is the envelope of a family of spherical involute curves. Figure 1 shows a pair of bevel gears, whose transmission can be simpli\"ed as a pair of virtual cylindrical gears shown in Figure 2. In this study, the following assumptions upon the system of concern will be used hereinafter: and the torsional angles and can be simpli\"ed to x sin #y cos #r \"x sin #y cos #r , (1) where is the pressure angle of gear, r and r are the radii of base circles of the two virtual cylindrical gears. As shown in Figure 3, the motion described in the co-ordinate frame ox y z can be determined from x y z \" cos 0 sin 0 1 0 !sin 0 cos x y z , (2) where \" ,! , i\"1, 2 are the pitch cone angles. For the virtual cylindrical gears and the bevel gears, the following kinetic relation holds true: r \"r , (3) where r , i\"1, 2 are the radii of base circles of bevel gears. Substituting equations (2) and (3) into equation (1) yields x sin cos #y cos #z sin sin # r \"x sin cos #y cos !z sin sin # r . (4) Now, let each torsional angle be composed of two parts as \" # , i\"1, 2, (5) where , i\"1, 2 represent the rotating angles of two rotors and yield the transmission relationship of bevel gears r \" r "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003346_j.jsg.2004.07.005-Figure21-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003346_j.jsg.2004.07.005-Figure21-1.png",
        "caption": "Fig. 21. Geometrical construction for Eqs. (28) and (41).",
        "texts": [
            " Line length preservation requires that: BCZBC0 CC0D (20) BCZAB\u2020cot\u00f0b2 or b1\u00de (21) being either b2 (Step I) or b1 (Step II) the hanging wall central ramp cut-off angles: BC0 ZAB\u2020\u00f0d2 or d 0 1\u00de (22) where either d2 (Step I) or d01 (Step II) are the apical angles of the circular sector pinned at the central ramp upper inflection point: C0DZAB\u2020cot\u00f0b3 or b 0 1\u00de (23) being b3 (Step I) or b 0 1 (Step II) the forelimb or the CP 0 panel cutoff angle. Substituting Eqs. (21)\u2013(23) into Eq. (20) and simplify- ing: cot\u00f0b2 or b1\u00deZ \u00f0d2 or d 0 1\u00deCcot\u00f0b3 or b 0 1\u00de (24) d2 Z b3 Kb2 Ca2 Ka3 (25a) d01 Z b0 1 Kb1 Ca2 Ka3 (25b) Substituting Eqs. (25a) or (25b) into Eq. (24) we obtain: cot\u00f0b3\u00deCb3 Za3 Ka2 Ccot\u00f0b2\u00deCb2 (26a) cot\u00f0b0 1\u00deCb0 1 Za3 Ka2 Ccot\u00f0b1\u00deCb1 (26b) f2 Z 90K \u00bd180K \u00f0b3 Ka3\u00deK \u00f0a3 Kb4\u00de =2 (27) Simplifying: f2 Z \u00f0b3 Kb4\u00de=2 (28) During contraction, triangle ACD (Fig. 21a) becomes AC 0D 0 (Fig. 21b). Line length preservation imposes: CDZC0DKAC0 (29) CDZH\u2020cot\u00f0a3\u00deKH\u2020cot\u00f0a2\u00de (30) B0C0 ZH=cos\u00f0f2\u00de (31) C0D0 ZB0C0\u2020\u00bdsin\u00f090Cf2 Kb3\u00de=sin\u00f0b4\u00de (32) AC0 ZB0C0\u2020\u00bdsin\u00f090Cf2 Kb3\u00de=sin\u00f0b3\u00de (33) Substituting Eq. (31) into Eqs. (32) and (33), we obtain: C0D0 ZH\u2020\u00bdcos\u00f0f2 Kb3\u00de=sin\u00f0b4\u00de =cos\u00f0f2\u00de (34) AC0 ZH\u2020\u00bdcos\u00f0f2 Kb3\u00de=sin\u00f0b3\u00de =cos\u00f0f2\u00de (35) Substituting Eqs. (30), (34) and (35) into Eq. (29) and simplifying: \u00bdcos\u00f0f2 Kb3\u00de=cos\u00f0f2\u00de \u2020\u00bd1=sin\u00f0b4\u00deK1=sin\u00f0b3\u00de Z cot\u00f0a3\u00deKcot\u00f0a2\u00de (36) Eq. (36) can also be written as: cos\u00f0f2 Kb3\u00de=\u00bdcos\u00f0f2\u00de\u2020sin\u00f0b4\u00de Kcos\u00f0f2 Kb3\u00de=\u00bdcos\u00f0f2\u00de\u2020sin\u00f0b3\u00de Z cot\u00f0a3\u00deKcot\u00f0a2\u00de (37) cos(f2Kb3) can also be written as cos(f2Cb4), which substituted into Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003318_s0022-0728(83)80439-2-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003318_s0022-0728(83)80439-2-Figure1-1.png",
        "caption": "Fig. 1. Cyclic voltammogram for 10 - 3 M Ru(bpy) 3 (C104) 2 in 0.1 M H 2 S O 4. Scan rate = 100 mV s -1.",
        "texts": [
            "100 V) of 20 ms duration to the cell and monitoring the resulting current transient on the Norland scope; only background currrents (i.e., capacitive and residual faradaic) are observed over this potential range. The amount of compensation was increased until oscillations were observed in the current transient. The compensation value where oscillation was first observed was applied during the determinations of k \u00b0. 269 R E S U L T S A cyclic voltammogram (CV) for the oxidation of Ru(bpy) 2+ is shown in Fig. 1. The oxidation of water at the glassy carbon commences at about 0.75 V vs. SMSE; this causes the flattening at the anodic current immediately following the anodic peak. A formal potential, E \u00b0', of 0.624 V vs. SMSE (corresponding to 1.27 V vs. NHE) was determined from CVs at slow scan rates, v (50-200 mV s- l ) , where Nernstian behavior is observed. The diffusion coefficients obtained for the 2 + (D R) and 3 + (Do) forms from CV peak current vs. v 1/2 plots or from potential steps to values where Cottrell behavior [12] is observed are D R = 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002804_j.mechmachtheory.2005.07.008-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002804_j.mechmachtheory.2005.07.008-Figure2-1.png",
        "caption": "Fig. 2. Geometric setup for the generation of the spiral bevel pinion.",
        "texts": [
            " Adopting the notation already introduced in Section 4, let a be the axis of the machine cradle and b, the axis of the pinion blank. As well known in gear literature [21], during generation of a spiral bevel pinion axes a and b are skew and can experience a relative translating motion. As suggested in [1], points Oa and Ob(/) are not taken on the line of shortest distance, but according to common practice they are displaced with respect to such line. A schematic representation of the geometric set up during generation is given in Fig. 2. Point Oa, which is a fixed point on the fixed axis of the machine, is moved along a by a variable parameter called sliding base DXB1 \u00f0/\u00de, while point Ob(/) is moved along b by the machine center to back DXD1 , which has a constant value. Quantity DEM1 \u00f0/\u00de, called blank offset, is indeed the shortest distance between a and b and is a function of the motion parameter /. In the Gleason s implementation of the face-milling process, blank offset DEM1 \u00f0/\u00de and sliding base DXB1 \u00f0/\u00de are polynomial functions of the motion parameters of the following types DEM1 \u00f0/\u00de \u00bc DEM10 \u00fe V 1/\u00fe 1 2 V 2/ 2 \u00fe 1 3 V 3/ 3 \u00f0115\u00de DXB1 \u00f0/\u00de \u00bc DXB10 \u00fe H 1/\u00fe 1 2 H 2/ 2 \u00fe 1 3 H 3/ 3 \u00f0116\u00de where DEM10 and DXB10 are constant values and Vi and Hi (with i = 1,2,3) are called, respectively, vertical and helical motion coefficients"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003945_rnc.1206-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003945_rnc.1206-Figure2-1.png",
        "caption": "Figure 2. Finding a periodic solution in a system with the twisting algorithm.",
        "texts": [
            " Using the notation of the twisting algorithms, this equation can be rewritten as follows: W\u00f0jO\u00de \u00bc 1 N\u00f0a1;O\u00de \u00f06\u00de where the function at the right-hand side is given by 1 N\u00f0a1;O\u00de \u00bc 1 N\u00f0a1\u00de \u00bc pa1 c1 \u00fe jc2 4\u00f0c21 \u00fe c22\u00de The negative reciprocal of the DF is a function of the amplitude only and does not depend on the frequency of the oscillation. Equation (5) is equivalent to the condition of the complex frequency response characteristic of the open-loop system intersecting the real axis in the point \u00f0 1; j0\u00de: The graphical illustration of the technique of solving equation (5) is given in Figure 2. The function 1=N is a straight line the slope of which depends on c2=c1 ratio. This line is Copyright # 2007 John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control 2008; 18:502\u2013514 DOI: 10.1002/rnc located in the second quadrant of the complex plane. The point of intersection of this function and of the Nyquist plot W\u00f0jo\u00de provides the solution of the periodic problem. This point gives the frequency of the oscillation and the amplitude a1: Therefore, if the transfer function of the plant (or plant plus actuator) has relative degree higher than two, a periodic motion occurs in such a system. For this reason, if an actuator of first or higher order is added to the plant of relative degree two driven by the twisting controller a periodic motion occurs in the system. The conditions of the existence of a periodic solution in a system with the twisting controller can be derived from analysis of Figure 2 Obviously, every system with a plant of relative degree three and higher would have a point of intersection with the negative reciprocal of the DF of the twisting algorithm and, therefore, a periodic solution would exist. Another modification of the twisting algorithm is its application to a plant with relative degree one with the introduction of the integrator. This is usually referred to as the \u2018twisting-as-a-filter\u2019 algorithm. The above reasoning is applicable in this case too. The introduction of the integrator in series with the plant makes the relative degree of this part of the system equal to two. As a result, any actuator introduced in the loop increases the overall relative degree to at least three. In this case, there always exists a point of intersection of the Nyquist plot of the serial connection of the actuator, the plant and the integrator and of the negative reciprocal of the DF of the twisting algorithm Figure 2. Thus, if an actuator of first or higher order is added to the plant with relative degree one, a periodic motion occurs in the system with the twisting-as-a-filter-algorithm. Let us describe propagation of averaged signals through the nonlinear functions using the concept of the equivalent gain [8, 9] Assume that the input to the first relay is an asymmetric harmonic signal s\u00f0t\u00de \u00bc s0 \u00fe a1 sin\u00f0Ot\u00de \u00f07\u00de Define the equivalent gain as the derivative of the averaged output of the nonlinearity with respect to the averaged input noting that the averaged input is s0: For the first relay, Copyright # 2007 John Wiley & Sons, Ltd"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001463_robot.1990.126233-Figure2.2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001463_robot.1990.126233-Figure2.2-1.png",
        "caption": "Figure 2.2 Two finger grasp versus three finger grasp",
        "texts": [
            "1 Vertex Range : The vertex range represents the applicable force direction at a vertex, which makes an obtuse angle with both sides of the vertex. The vertex range vector of vertex range is a vector located at extreme of vertex range. 2.3 Two Finger Grasp versus Three Finger Graqp Force closure grasp in a plane is possible when there are four wrenches where three are independent. That is, when two friction contacts are located appropriately in the plane, force closure can exist without a third contact. Figure 2.2 (a) shows force closure grasp by two friction point contacts with the thud contact as a redundant contact. Even though two friction point contacts are enough to mathematically have force closure in a plane, it may not be a stable grasp due to the possible errors. As an example, consider a small m r in positioning the finger as shown in Figure 2.2 @) where pi is intended and p,, is the actual contact location. When this happens, the object will start to rotate and can slip away from the grasp. But if the grasp is constructed as shown in Figure 2.2 (c) it is much safer than the grasp of Figure 2.2 (b) with respect to possible errors. So when grasps are constructed on all feasible combination of edges and/or vertices, we consider only those grasps where all three contacts explicitly participate.. 3. Construction of Force Closure Grasp To find the best grasp on a polygon, construction of a force closure grasp on each feasible combination of edges and/or vertices is required. In this section, algorithms to construct force closure grasp on six different combination of edges and/or vertices are presented"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000516_20.952635-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000516_20.952635-Figure1-1.png",
        "caption": "Fig. 1. Cross-section of SRM for electromagnetic field analysis.",
        "texts": [
            " With a smaller air gap, this phenomenon especially becomes severe. Therefore, it is necessary to predict the dynamic response caused by the electromagnetic unbalance force and mechanical unbalance mass to reduce the vibrations. This paper investigates the various dynamic response of the rotor caused by the mechanical and magnetic coupled origins according to the variation of the unbalance mass and bearing stiffness. The rotor behavior is analyzed by the coupled electromagnetic and structural time stepping FEM. The rotor in a SRM is used in this study. Fig. 1 shows the cutaway view of a SRM with four rotor poles and six stator poles with three phases winding in the stator, which is used for two-dimensional electromagnetic field analysis. Fig. 2 shows the rotor configuration supported on both bearings and its mesh for rotor dynamics analysis. For the structural FEM, the analysis model is divided into 23 beam elements. The 0018\u20139464/01$10.00 \u00a9 2001 IEEE beam elements are defined by two nodes having four degrees of freedom at each node. Two independent element meshes are created to analyze the coupled problem"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002591_0094-114x(85)90040-0-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002591_0094-114x(85)90040-0-Figure7-1.png",
        "caption": "Fig. 7. Involute interference limit.",
        "texts": [
            " 4(c) with a zero value for re, eqn (20) describes the trochoid portion of the tooth flank which blends the bottom land arc into the bottom of the tooth 's involute profile. The presence of undercutting on the gear tooth can be determined by comparing the rack form addendum to the location of the tangent point, B, between the gear 's base circle and the line of action, BO, of the cutting mesh. If the perpendicular dis. tance from the rack 's pitch line to point B is greater than the addendum on the rack form, then no involute interference will occur. This condition is shown in Fig. 7. This inequality can be expressed a s a, <~ R sin-\" 6 (21) for no involute interference. If this relation is satisfied, the full filet is cut with 13 sweeping from ~r/2 to 6 and the fillet and involute curves tangent at the position where 13 equals ~b. If relation (21) is not satisfied, involute interference exists and the trochoid will cross the involute above the base circle with 13 greater than 6 at the point of intersection. The determination of this point of demarcation between the fillet and the involute is best found by a double iteration, At this point of demarcation the radius vector of eqn (7) equals the radius vector of eqn (20)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001156_s0301-679x(01)00108-6-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001156_s0301-679x(01)00108-6-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of a three-pad journal bearing.",
        "texts": [
            " This paper employs a Newton\u2013Raphson scheme to conduct a TEHD analysis in which the models of elastic deformation and temperature are all three-dimensional (3D) for the purpose of predicting the behavior of the tilting-pad journal bearing more accurately and efficiently. The 20-node isoparametric finite element method is used to calculate the elastic and thermal deformation of the pads. A sequential sweeping approach is presented to solve the temperature profiles. The model of this paper is based on a three-pad-journal bearing. A cross-section of the journal bearing showing the nomenclature of the problem is presented in Fig. 1. For the sake of reducing the CPU time, the pad is assumed to be symmetric axially and the model is offered on half of the pad. All of the equations and boundary conditions are presented in non-dimensional form. The dimensionless quantities are defined as follows: C\u03041 C1cr0T0, C\u03042 C2cr0T0, C\u03043 C3T0, C\u0304b Cb /Cp, d\u0304 d /Cp, e\u0304x ex /Cp, e\u0304y ey /Cp, h\u0304 h /Cp, k\u0304 kR / (kpCp), L\u0304 L /R, p\u0304 C2 pp / (h0u0R), r\u0304 r /h, r\u0304p rp /R, T\u0304 T /T0, U\u0304 U /u0, u\u0304 u /u0, v\u0304 v /u0, W\u0304 WC2 p / (h0u0R3), y\u0304 y /R, a\u0304 ah0u0R /C2 p, b\u0304 bT0, d\u0304 dR /Cp, h\u0304 h /h0, h\u0304e he /h0, h\u0304 e h e /h0, q\u0304 q, r\u0304 r /r0, r\u0304e re /r0, r\u0304 e r e / (r0 /h0), r\u0304 e r e / (r0 /h0), r\u0304\u2217 r\u2217 /r0, r\u0304h e rh e| r0 h0 ",
            " The new value of unknown quantities can be obtained by the following: p\u0304(new) m,i,j p\u0304(old) m,i,j \u0304pm,i,j (m 1, 2, 3; i 1, 2, \u2026, 19; j 0, 1, \u2026, 9) d\u0304(new) m d\u0304(old) m \u0304dm (m 1, 2, 3) e\u0304(new) x e\u0304(new) x \u0304ex e\u0304(new) y e\u0304(new) y \u0304ey (15) It is obvious that the notable advantage to employing this scheme in the present problem rests in simultaneous acquisition of various types of quantity. It is unnecessary to conduct the calculation pad by pad and to modify the eccentricity artificially. Another merit of the method is the quick convergence. For instance, only 170 s is spent to obtain the solution for the present problem with a 586 PC of 400 Hz CPU. Calculations using the method outlined above were performed for the three-pad bearings (Fig. 1). The input data are given in Table 1. Table 2 shows the simulated results under different cases. Case 1 shows the results without tking the pressure deformation and temperature elevation into consideration. Case 2 shows the results only considering the pressure deformation. It is known that elevation of the temperature influences the behavior of the bearing via the thermal expansion of the pads as well as by altering the viscosity and density of the lubricant. Case 3 shows the results considering only the influences of the viscosity and density alterations caused by the temperature elevation but without pressure deformation and thermal expansion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000601_s0003-2670(00)01020-5-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000601_s0003-2670(00)01020-5-Figure10-1.png",
        "caption": "Fig. 10. Bienzymatic OPEE assembly for the analysis of phosphatidylcholine.",
        "texts": [
            " recently carried out a research aiming to construct a bienzymatic OPEE able to determine phosphatidylcholine working also dipped directly in organic solvents in which lecithin is more soluble and to apply it to the analysis of the lecithin content in food [54] and pharmaceutical [55] matrices. At this aim a biosensor was studied, that was obtained by using a gas diffusion amperometric electrode for oxygen as electrochemical transducer and two enzymes, phospholipase D and choline oxidase, both immobilized in kappa-Carrageenan gel (Fig. 10). This biosensor was used to study the possibility of determining lecithin content in several food samples (egg yolk, soy flour, diet integrators, etc.) as well as in several pharmaceutical formulations, operating in a chloroform\u2013hexane, or chloroform\u2013hexane\u2013methanol, mixture and working in batch conditions. Results (see Fig. 11) clearly show that the bienzymatic OPEE can be used directly in organic solvents to analyze real matrices containing lecithin with the added advantage of being able to perform the test directly in the same solvent mixture as was used to dissolve or extract the species to be determined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003678_00022660510597223-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003678_00022660510597223-Figure2-1.png",
        "caption": "Figure 2 Characterization of each vector component with respect to axis XYZ",
        "texts": [
            " The orthogonal systems used to describe the plane behavior are the terrestrial axes (coordinate system X0Y0Z0) and rotating axes (coordinate system XYZ). We will assume that the plane total mass and mass distribution remain constant. This is a reasonable assumption for mass that changes less than 5 percent within the first 30-60 s of flight, with respect to the fuel consumption. We apply Newton\u2019s second law to a wing profile over the non-inertial rotating axes XYZ (Figure 1), characterizing each vector component on the coordinate axes system (as shown in Figure 2). Noting that the inertia moment Ixy \u00bc Iyz \u00bc 0; because of the plane symmetry in the XZ plane, we obtain the following linear and angular momentum equations (Roskam, 1995b) . Scalar equations of linear momentum m\u00f0 _U 2 VR \u00fe WQ\u00de \u00bc mgx \u00fe FAx \u00fe FTx m\u00f0 _Y 2 UR \u00fe WP\u00de \u00bc mgy \u00fe FAy \u00fe FTy m\u00f0 _W 2 UQ \u00fe VP\u00de \u00bc mgz \u00fe FAz \u00fe FTz . Scalar equations of angular momentum _PIxx 2 _RIxz 2 IxzPQ \u00fe \u00f0Izz 2 Iyy\u00deRQ \u00bc LA \u00fe LT _QIyy \u00fe \u00f0Ixx 2 Izz\u00dePR \u00fe Ixz\u00f0P2 2 R2\u00de \u00bc MA \u00fe MT _RIzz 2 _PIxz \u00fe \u00f0Iyy 2 Ixx\u00dePQ \u00fe IxzQR \u00bc NA \u00fe NT where I denotes the moment of inertia. The plane forces, momentum and velocities are defined as follows (Figure 2): . Forces Aerodynamic force components: the drag, side and lift forces, respectively. ~FA \u00bc i \u00a3 FAx \u00fe j \u00a3 FAy \u00fe k \u00a3 FAz Trust force components ~FT \u00bc i \u00a3 FTx \u00fe j \u00a3 FTy \u00fe k \u00a3 FTz Gravitational acceleration components ~g \u00bc i \u00a3 gx \u00fe j \u00a3 gy \u00fe k \u00a3 gz . Momentum Aerodynamic momentum components: rolling, pitching and yawing momentum, respectively, ~MA \u00bc i \u00a3 LA \u00fe j \u00a3 MA \u00fe k \u00a3 NA Trust momentum components: rolling, pitching and yawing momentum, respectively, ~MT \u00bc i \u00a3 LT \u00fe j \u00a3 MT \u00fe k \u00a3 NT Control of longitudinal movement of a plane Manuel A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002196_ac0350615-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002196_ac0350615-Figure1-1.png",
        "caption": "Figure 1. (left) Top view and cross section of the spectroelectrochemical cell: (a) cell body, (b) platinum wire, (c) porous frit, (d) metal working electrode, (e) glass disk, and (f) solution layer. (right) Sketch of the moving spectroelectrochemical cell mounted under the Raman microscope.",
        "texts": [
            "18,21 In this paper, we present a linearly moving low-volume spectroelectrochemical cell that is small and can be easily placed under a Raman microscope with the working electrode facing up. This cell has been specifically designed to work with low amounts of proteins; it is small, easily cleaned, and photodegradation of the sample is prevented. Its efficiency is demonstrated by studying cytochrome c adsorbed on a roughened silver electrode coated with a self-assembled monolayer (SAM) of mercaptopropionic acid (MPA). Cell Design. In Figure 1, a sketch of the spectroelectrochemical cell is shown. The cell body (a) is a cylinder of PEEK which is 16 mm in diameter and 10 mm in height, in which three holes (b-d) of different diameters were made. One hole houses a fixed platinum wire (b), the second hole a fixed porous frit (c), and the third one a removable metal electrode (d). A 0.2-mm-thick glass disk (e) covers the thin (0.5 mm) solution layer (f). The total internal volume of the cell is 50 \u00b5L. PEEK was chosen as the cell material because of its chemical resistance and mechanical characteristics. The porous frit is in contact with a reference electrode through a Teflon capillary filled with electrolyte solution (KCl 0.1 M). The cell is put on the tip of the metal electrode (Kel-F body with a metal disk fixed inside), and the electrode itself is put in a moving holder (Figure 1, right), which ensures a constant linear movement of the metal electrode surface under the microscope objective in order to prevent photodegradation of the sample. The design of the moving device is similar to that described by Niaura et al.20 The cover glass disk is held tightly to the cell by a PEEK ring screwed onto the cell body. Potential-controlled SERRS measurements performed using this spectroelectrochemical cell were done with a silver electrode (IJ Cambria Scientific, Carms, U.K.) as working electrode (WE), a platinum wire as counter electrode (CE), and an SCE as reference electrode (RE) (AMEL Instruments, Milano, Italy)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003715_026-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003715_026-Figure2-1.png",
        "caption": "Figure 2. Nonlinear pendulum.",
        "texts": [
            "0, 1 )1( ,0, 1 )(~ 1' 0 , i i k i i j tt tt hc i k jtt k ij j jmim jm ik m For calculation, equation (17) can be rewritten as mk k i imikm fhgxcx 1 , (18) where 0, , , ~ ~ k ik ik c c c , 0, ~ 1 k k c g . Equation (18) is known as k step algorithm of GEAR method. According to formula (15) the truncating errors of GEAR method can be given by )( ~ ' ,, mkmkm thsR k j ttjm k m tt k xh 0 ' )1( )]( )!1( )( [ mkm k k ttth k x , 1 )( 1 )1( (19) According to formula (19) the truncating errors of k step algorithm of GEAR method is O(hk+1). The flow chart of GEAR method for program can be obtained in reference [5]. 4. Calculation examples 4.1. Nonlinear pendulum In figure 2 mass m is attached to a lever with l length. The corresponding equation of motion of the mass is given by 0sinmgml (20) namely 0sin2 0 (21) where 2 0 = lg / . Given l=1m, g=9.8m/s, (0)=0 rad, 3.0)0( rad/s the pendulum equation can not simplified as a linear differential equation by sin for the large motion. But according to the conservation theory of mechanical energy 2 max(1/ 2) [ (0)] (1 cos )m l mgl the analytical maximum angle Table 1 shows the results of GEAR method and other numerical calculation methods"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003716_ip-epa:20050466-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003716_ip-epa:20050466-Figure3-1.png",
        "caption": "Fig. 3 Rotor equivalent circuit of DWIM (i) Cage-rotor equivalent circuit (ii) ith rotor-loop turn and winding functions for skewed rotor",
        "texts": [
            " A method to model a cage rotor adequately has been set forth in [8, 15]. The cage rotor with n (even or odd) bars and two end rings to short-circuit all the bars together is considered as n identical magnetically coupled circuits. Each circuit is composed of two adjacent rotor bars and segments of the end rings connect two adjacent bars together at both ends of the bars. Each bar and end-ring segment of the rotor loop is equivalently represented by a serial connection of a resistance and an inductance, as shown in Fig. 3(i). The resistance and the inductance of the rotor bar are represented by rb and lb, respectively; the resistance and inductance of the partial end winding in the rotor loop are represented by re and le, respectively. Three rotor loops are shown in Fig. 3(i) and the currents flowing through the rotor loops are represented by ik 1, ik and ik\u00fe1, respectively. Since every rotor loop is treated as an independent phase, a healthy cage rotor having n rotor bars becomes an n-phase balanced system. The turn function of the ith rotor loop is shown in part (a) of Fig. 3(ii) where ar is the bar spacing angle. Since the airgap length is constant, the winding 390 IEE Proc.-Electr. Power Appl., Vol. 153, No. 3, May 2006 function of the ith rotor loop is shown in part (b) of Fig. 3(ii). The expressions for turn and winding functions are ni y\u00f0 \u00de \u00bc 0 y 2 0; yi b\u00bd \u00de 1 b y yi \u00fe b\u00f0 \u00de y 2 yi b; yi\u00bd \u00de 1 y 2 yi; yi \u00fe ar b\u00bd \u00de 1 b yi \u00fe ar y\u00f0 \u00de y 2 yi \u00fe ar b; yi \u00fe ar\u00bd \u00de 0 y 2 yi \u00fe ar; 2p\u00bd \u00de 8>>>>>< >>>>>>: 9>>>>>= >>>>>>; \u00f029\u00de Ni y\u00f0 \u00de \u00bc ar 2p y 2 0; yi b\u00bd \u00de 1 b y yi \u00fe b\u00f0 \u00de ar 2p y 2 yi b; yi\u00bd \u00de 1 ar 2p y 2 yi; yi \u00fe ar b\u00bd \u00de 1 b yi \u00fe ar y\u00f0 \u00de ar 2p y 2 yi \u00fe ar b; yi \u00fe ar\u00bd \u00de ar 2p y 2 yi \u00fe ar; 2p\u00bd \u00de 8>>>>>>>< >>>>>>>: 9>>>>>>>= >>>>>>>; \u00f030\u00de where b \u00bc skew factor ar. Substituting the turn and winding functions of the ith rotor loop into the general expression for the self-inductance calculation as shown in (19), the self-inductance of the ith rotor loop (which is the same for all loops) is Lrr \u00bc m0rl g0 ar b 3 a2r 2p \u00f031\u00de The winding functions of the adjacent rotor loops will overlap each other when the skew rotor is considered, such that the mutual inductances between the ith and i+1th will be different from those between the ith and i+kth \u00f0k 2 \u00bd2; n 1 \u00de, where n is the number of rotor bars"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002348_robot.1994.351251-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002348_robot.1994.351251-Figure3-1.png",
        "caption": "Figure 3: Configuration of the ultrasonic transducers for the measurement of the normal direction of the wall. \u201cT\u201d denotes the transmitter and \u201cR\u201d denotes the receiver.",
        "texts": [
            " The position of m object can only be estimated in the wide area of the beam width. The position cannot be limited to the transducer line-of-sight when the distance is measured by using this sensor. In order to compensate, plural receivers can be used. Furthermore, the normal direction of the object surface can be measured if the characteristics of the reflective surface of the object are considered. Nakajima et d.[7J controlled a manipulator tracing curved surface using the sensor based on this technique. Such a sensor is constructed by the arrangement shown in Fig.3. The inclination of the surface is calculated from the phase difference of the reflected wave using the method of Nakajima et al. In this method, the measurable range of the angle is limited by the wave length of the ultrasound and the geometricd configuration of the receiver. This limited range is insufficient for the sensor of the mobile robot. In our studies the angle is calculated from the difference of the round-trip timeof-flight. With such a method, the problem of missing detection of the leading edge from the received signal must be solved"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003307_s10704-005-8546-8-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003307_s10704-005-8546-8-Figure5-1.png",
        "caption": "Figure 5. Transformation of real gear pair to equivalent contact model.",
        "texts": [
            " The conditions for crack propagation are most favourable in this region due to initial crack orientation and surface traction direction, which are opposite to the rolling contact direction, Figure 4. 4.2. Normal and tangential loading conditions The distribution of normal loading in non-lubricated contact can be estimated by using the classical Hertzian theory (Johnson, 1994). The real contact geometry (e.g. gear tooth flanks) can be transformed into a pair of equivalent contacting cylinders with the radii corresponding to curvature radii of analysed mechanical elements (Figure 5). The two cylinders are then further transformed into equivalent contact cylinder of equivalent radius R\u2217, for which the Hertzian normal contact pressure distribution p(x) can be estimated with simple analytical relationships. Detailed description of the equivalent contact model and relevant equations is given in reference (Glodez\u030c et al., 1998). It has been shown, that for small coefficients of friction the distribution of tangential contact loading q(x) due to relative sliding can be estimated with a simple Coulomb friction law within the Hertzian model (Ren et al",
            ", 1985) assumption of specific circumferential stress intensity factor K\u03c3(\u03b8, r), where the critical load case corresponds to the maximum K\u03c3(\u03b80, rc) when the load moves over crack mouth. By applying the minimum strain energy density theory, the critical load case corresponds to the maximum value of minimum strain energy density factor Smin(\u03b80, rc). The classical and modified fracturing criteria have been applied to simulation of surface crack propagation on a gear tooth flank under lubricated contact loading conditions, with the objective to evaluate the modified criteria. 5.1. Computational model data The derived equivalent contact model (Figure 5b) has the following geometrical data: the upper cylinder of radius R1 = 10.285 mm corresponds to the radius of pinion at the inner point of single teeth pair engagement [so called point B (DIN 3990, 1987)] with number of teeth z1/2 = 16/24, gear module m = 4.5 mm, centre distance a = 91.5 mm, addendum modification coefficients x1/2 =0.18/0.17 and standard gear profile angle \u03b1n =20\u25e6. The pinion is made of carburized steel 16MnCr5 (according to the ISO standard) with Young\u2019s modulus E = 206 GPa and Poisson\u2019s ratio \u03bd = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002597_j.chaos.2004.06.052-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002597_j.chaos.2004.06.052-Figure6-1.png",
        "caption": "Fig. 6. Dynamics of the beam system alone computed for b = 0.45, n = 0.005 and X = 0.5935: (a) basins of attraction for 3 period one attractor, (b) corresponding set of phase plane portraits, superimposed on the same plane.",
        "texts": [
            " 5(b) shows the phase plane of the period three attractors, note that the oscillations are still greater than beam length, and thus physical reality is yet to be applied. When the forcing amplitude and the magnitude of oscillations are within beam length, the system is behaving within the boundaries of physical realism. As before, with the reduction in magnitude of oscillations comes a loss of complex dynamical responses across an increasing parameter range. However, interesting nonlinear behaviour can be found with even modest values for angle of deflection from equilibrium position. Fig. 6(a) shows the basins of attraction for 3 coexisting period one attractor and Fig. 6(b) shows the corresponding set of phase plane portraits. The response of smaller magnitude has an angle of deflection of 35 or x/L of 0.55, the other two make an angle of 52 or x/L of 0.78, this is a significant increase in magnitude, which in an engineering system could be the difference between normal function and catastrophic breakage. Interesting behaviour can be found with yet smaller oscillations. Fig. 7(a) shows the basins of attraction for 2 coexisting period one attractor. Fig. 7(b) depicts the corresponding phase planes, superimposed on the same plane for clarity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002779_s0166-526x(05)44002-7-Figure2.7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002779_s0166-526x(05)44002-7-Figure2.7-1.png",
        "caption": "Fig. 2.7. Scheme of the electron transfer in multi-centre enzymes containing heme according to Refs. [7,8].",
        "texts": [
            " This process is measurable when gluconate is in the concentration range of tLM-mM. 94 Third generation biosensors--integrating recognition It has been proposed tha t the substrate conversion is at the flavin site and the electrons are then transferred via F e - S - and the heme to the electrode (ubiquinone in the native system). The electron transfer at the heme moiety has been confirmed with another quinohemoprotein using electroreflectance [114]. Since then a number of examples supporting this model have appeared (Fig. 2.7). Detailed mechanistic studies were also published by Gorton's group for the flavohemoprotein cellobiose dehydrogenase [8,26,109,110,225,226]. Cellobiose dehydrogenase (EC 1.1.99.18, CDH) is an extracellular flavoheme-glycoprotein from white rot fungi [223,224]. It catalyses the oxidation of cellobiose and related oligosaccharides by a number of acceptors including cytochrome c. Typically, CDH is a monomeric protein with a molecular mass of about 100 kDa and an acidic pI of around 4. The three-dimensional structure of CDH has one 55 kDa domain carrying FAD and a second 35 kDa domain carrying the cytochrome b type heine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.69-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.69-1.png",
        "caption": "Figure 3.69 Measurement of the moment of inertia of a flywheel, (a) Horizontal axis pendulum, (b) Multifilar suspension",
        "texts": [
            " In order to obtain an accurate reading the period of oscillation should be as long as possible and, above all, the value of the radius of inertia of the flywheel must be greater than length L. If this is not the case the difference in equation (3.254) is the difference between two similar values. Small errors on the measured value of T can lead to large errors in the results. A simple way to implement this method with rotors having a central hole is to drive the knife-edge into the bore; the suspension length is then coincident with the inner radius (Figure 3.69a). In the multifilar suspension system, the flywheel is suspended from a horizontal surface by a certain number of wires (usually three). The length of the wires must be equal, and the attaching points must be equally spaced on a circumference whose centre must lie on the rotation axis of the rotor which is assumed to coincide with a principal axis of inertia (Figure 3.69(b)). In this case the length of the wires has to be greater than the radius of the circumference of the flywheel on which the attachment points are located. The moment of inertia is given as a function of the period of the small oscillations T by the formula: J = m^lT2 ( 3 . 2 5 5 ) If the wires are attached to a fixture of mass m1 to which the flywheel is then connected, it is easy to take into account the inertia of the apparatus simply by first measuring the period (Tx) of oscillation of the device without the flywheel, then hanging the flywheel and measuring again the period of oscillation (T2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003091_taes.2005.1541428-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003091_taes.2005.1541428-Figure2-1.png",
        "caption": "Fig. 2. Solar forces on control plate.",
        "texts": [
            " Since the radiation forces on these control surfaces are directed along the surface normals, only pitch movement is produced by the solar pressure controller. The equation of motion describing the pitch dynamics of the satellite is given by [13, 14, 18] d2\u00b8=d\u00b52 =Mg +Ms (1) where Mg and Ms denote normalized gravity gradient and solar torque, respectively. The gravity gradient and the radiation torques are given by Mg =\u00a13K sin\u00b8cos\u00b8 Ms = C[(jcos\u00bb1j)cos\u00bb1 cos\u00b11 \u00a1 (jcos\u00bb2j)cos\u00bb2 cos\u00b12] (2) where \u00bbi (i= 1,2) is the angle of incidence on the ith solar control plate shown in Fig. 2. The radiation force is shown in Fig. 2, and the incidence angle is SINGH & YIM: NONLINEAR ADAPTIVE SPACECRAFT ATTITUDE CONTROL 771 given by cos(\u00bbi) = \u00be 0:5 sin(\u00b5+\u00af+\u00b8+ \u00b1i) \u00be(\u00c1) = 1\u00a1 sin2\u00c1sin2 i \u00af(\u00c1) =\u00a1 tan\u00a11(tan\u00c1cos(i)): (3) Since the solar aspect angle \u00c1 varies from 0 to 2\u00bc radians in a year, \u00be and \u00af are extremely slow variables. The solar parameter C is given by C = 2\u00bdpA\u00b2=(\u22122Ix): (4) Let \u00ae be the orientation of the satellite with respect to the inertially fixed axis Y, then one has \u00ae= \u00b8+ \u00b5 (5) where the orbital angle is \u00b5 =\u2212t, and \u2212 is the orbital rate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001559_b978-0-08-092509-7.50008-7-Figure4.1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001559_b978-0-08-092509-7.50008-7-Figure4.1-1.png",
        "caption": "FIGURE 4.1. Denavit-Hartenbergparameters.FollowingCraig[10],theoriginof thereferenceframeforlink i-I is locatedat theintersectionofaxis Z, -1 andthe line betweenZi-l andZ, whichis normalto both.ThisdefinesXi-I. Thetwist angleai-l isdeterminedusingtheright-handrulelookingalongXi-I. Theoffset d; is thedistancealongZ; from thecommonnormalwith Zi-l to thecommon normalwith Z\u00ab. The joint angle (h is the angle betweenX i - 1 andXi looking alongz..",
        "texts": [
            " Welet8 == 8 n denotethen-dimensionaljointspaceandW == wm == f(8) denotethem-dimensionalworkspace,withelements() E 8 n andx E W, respectively.Fora redundantmanipulatorn > m,fora nonredundant manipulatorn == m. Theforwardkinematicsfunctionis representedby the map f : 8 --+ W; f(f}) == x, (4.1) Theforwardfunctioncanbe computedasa sequenceof rigid-bodytransformations,givena descriptionof thewaythelinksconnect.TheDenavitHartenbergconventionisalink frameparameterizationgenerallyusedto describerobotjoints,abbreviatedastheD-H parametersof therobot[10]. Figure4.1 illustratesthelink-to-linkassignmentofD-H parameters.Axis Zo is theworldframe,locatedat thebaseof therobot,andisalways(by convention)collinearwith Zl; thusaoandaoarealways O. Thereisno do, anddl isgenerallysetto O. Theparameterf}i is thevariableparameterfor a rotationaljoint,whiletheparameterd; is thevariablefora slidingjoint. ThepositionandorientationofframeOi, whichisattachedtolink i, can becomputedbyaseriesoffour transformationsofframeOi-l- First,rotate aboutX i- l by angleai-l. Second,translatealongX i-l by the distance ai-l"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003496_ias.2005.1518531-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003496_ias.2005.1518531-Figure2-1.png",
        "caption": "Figure 2. A layered rotor.",
        "texts": [
            " Analysis is based on the magnetic equivalent circuit approach that considers most important factors affecting the motor behavior. Experimental results are also provided to support the analysis. II. MODELING OF THE AIR GAP A rotor misalignment fault is shown in Fig. 1. The air gap length is a function of the rotor angle and the position along the axial dimensions. Fig.1 (a) depicts a pure misalignment fault and Fig.1 (b) illustrates a simultaneous static air gap eccentricity and rotor misalignment faults. To formulate both faults, we need to model the machine in a 3-dimensional space. Figure 2 shows a part of an unskewed rotor having some degree of misalignment fault. The rotor is divided into 4 layers. Each layer has some radial displacement with respect to the neighboring layers. Rotor bars are shown with solid black lines and the rotor core and the rotor teeth are shown with white color. The air gap length in different layers is dependent on the axial position of the layers, but in each layer it is assumed to be constant. Fig. 3(a) shows the cross sectional view of each layer of the Fig. 2. A few stator and rotor teeth around the air gap of the IAS 2005 1324 0-7803-9208-6/05/$20.00 \u00a9 2005 IEEE machine are shown. At a time, each stator (rotor) tooth can face a few rotor (stator) teeth. Fig. 3(b) shows the crossing air gap flux from a stator tooth to a rotor tooth. Since the length of air gap between each two stator and rotor teeth is much smaller than each tooth width, a trapezoidal flux tube such as shown in Fig. 4(a) and (b) can be imagined for each two stator and rotor teeth. Based on the geometric dimensions defined in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002997_j.mechmachtheory.2004.02.005-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002997_j.mechmachtheory.2004.02.005-Figure3-1.png",
        "caption": "Fig. 3. Scheme of the starting angle.",
        "texts": [
            " The axial errors are defined by the deviation between the axial curve of the noninvolute beveloid gear 2 and the corresponding curve of involute helicoid. The axial errors can describe the change of the tooth thickness. The equation of involute helicoid can be written as follows: x20 \u00bc rb2 cos\u00f0l2 \u00fe h2 \u00fe /0\u00de \u00fe rb2l2 sin\u00f0l2 \u00fe h2 \u00fe /0\u00de y20 \u00bc rb2 sin\u00f0l2 \u00fe h2 \u00fe /0\u00de rb2l2 cos\u00f0l2 \u00fe h2 \u00fe /0\u00de z20 \u00bc p2h2 9= ; \u00f011\u00de where l2; h2 are the parameters of the involute helicoid; rb2 is the base circle radius (mm); p2 is the corresponding helical parameter; /0 is the starting angle which is shown in Fig. 3. The calculation procedure of axial errors is: (1) As shown in Fig. 3, ab is theoretical curve of involute helicoid, and cd is practical curve of gear 2. Given the zero deviation between the curves ab and cd on the pitch circle, /0 can be obtained by the equations as follows: z2 \u00bc z20 \u00bc p2h2 x22 \u00fe y22 \u00bc r022 \u00f0r02 is the pitch circle radius\u00de \u00f0x2 x20\u00de2 \u00fe \u00f0y2 y20\u00de2 \u00bc 0 U \u00bc 0 (2) The section of the gear 2 can be determined by the equation z2 \u00bc z20 \u00bc zk (zk is the z-coordinate of the section), then according Eqs. (8), (10) and (11), we can obtain: z2 \u00bc z20 \u00bc zk x22 \u00fe y22 \u00bc x220 \u00fe y220 \u00bc r02 U \u00bc 0 from these equations, we can obtain the five values: l, h, l2, h2 and u1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003099_j.actamat.2004.04.025-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003099_j.actamat.2004.04.025-Figure7-1.png",
        "caption": "Fig. 7. (a) A thermal barrier system with wrinkled TGO film from [26]. (b) A model structure with elastic constraint on top of the film.",
        "texts": [
            " Although the equilibrium state is energetically unstable, subsequent evolution toward longer wavelengths is extremely slow due to the kinetic constraint of ratcheting, which was not observed in our simulations. A perturbation to the equilibrium state may be necessary to numerically trigger the evolution. In a thermal barrier system (Fig. 1), the TGO film is under compression due to lateral growth at high temperatures. As temperature cycles, ratcheting of underlying bond coat allows the TGO film to grow wrinkles. The TBC layer on top, however, constrains upward deflection of the TGO film. Consequently, the wrinkle tends to grow into the bond coat. Fig. 7(a) shows a wrinkled TGO film in a thermal barrier system observed by Mumm et al. [26]. Fig. 7(b) sketches a model structure to be used for simulations. Assume a clamped boundary condition at both ends of the film. Within the span, the TBC layer provides an elastic constraint against upward deflection, but downward deflection is not constrained, resembling the case when the TBC layer is debonded from the TGO film due to interface cracking. Outside the span, the film is clamped between the bond coat and the TBC layer with perfect bonding. To approximate this elastic constraint, we add a term linearly proportional to the upward deflection to Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000867_i2002-00157-x-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000867_i2002-00157-x-Figure1-1.png",
        "caption": "Fig. 1 \u2013 Sketch and photograph of the experiment. A rectangular plate clamped at two sides (at x = \u00b1d/2) has its centre pushed down. Two d-cones linked by a ridge of length 2D appear at small vertical displacement (here Z = 5 mm). The origin of axes is at the initial plate centre.",
        "texts": [
            " Energies are measured by integrating the plate resisting force as a function of the imposed displacement. The energy difference between drilled and undrilled plates gives the core energy. Our second achievement was to model the behaviour of the plate when plastic deformations occur in the core. The experiment. \u2013 A thin elastic plate of length L = 35 cm and width W = 25 cm is clamped on two sides and free on the other two sides. The distance d between the clamped sides as well as their inclination angle \u03b1 can be adjusted (fig. 1). A conical tip pushes the plate at its centre. The control parameter is the vertical displacement Z of the centre. A piezoelectric cell gives the plate resisting force F . Initially (when Z = 0), the plate is cylindrical, and we measure its curvature 2k at x = 0. As plates, we use: i) mylar sheets of thickness h = 0.25 mm, bending modulus \u03ba = 8.3 \u00b7 10\u22123 N m and Poisson ratio \u03bd = 0.4 (as a reference case); ii) the same mylar sheets but pierced with 2 holes of radius Rt, located at (x = \u00b1D0, y = 0); iii) bronze sheets of thickness h = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003819_rspa.2005.1452-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003819_rspa.2005.1452-Figure5-1.png",
        "caption": "Figure 5. Processed high pressure paper results. (a) Two-dimensional quarter contour plot, (b) three-dimensional full contour plot.",
        "texts": [
            " After this period, the bolts were loosened in the order described for tightening and removed. The wheel carrier was carefully separated from the disc, and finally, the pressure-sensitive paper removed and sent to the supplier for processing. Computer analysis of the pressure-sensitive paper provides pressure distribution and magnitude. The system renders high resolution, colour-calibrated images that reflect pressure distribution at the interface. The results obtained from the analysis include twodimensional and three-dimensional contour plots, as shown in figure 5 for the high-range paper. The pressure paper contour plots (figure 5) also indicate two distinctive areas, one with high pressure, around the bolt holes (1), and one with low pressure, between the bolts (2). The highest pressure is at the group of two holes between the jacking hole (smaller diameter hole). High pressure is also seen close to the internal diameter concentrating at the regions close to the boltholes. The pressure reduces from the internal diameter towards the outside diameter of the contact area. The boltholes continue to influence the pressure distribution close to the outside diameter. The low pressure, in the region of the outside diameter between the boltholes, is not registered in the shown contour plots (figure 5). The pressure in this region is below the threshold of the high-pressure paper, that to Proc. R. Soc. A (2005) say, it is below 49 MPa. However, the medium paper provides more details in this region and the results have been carefully analysed. In order to reduce the amount of data presented, these results have not been shown. The measured pressure-sensitive paper results (figure 5) are very close to the stress results from the FE analysis (figure 3). Note that results in figure 5 are obtained from the high-range paper, which cannot measure pressures lower than 49 MPa. FE analyses and pressure-sensitive paper measurements results are compared in table 2 (for maximum bolt torque), at positions (1) and (2). The results show that the FE modelling can reliably predict pressure distribution in bolted brake component interfaces. This gives confidence in designing new bolted joints with predictable interface pressure distributions. 8. Thermal contact resistance measurement (a) Experimental set-up The experimental part of the study was conducted using a specially developed spin rig (see Voller 2003)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000308_s0020-7462(98)00001-8-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000308_s0020-7462(98)00001-8-Figure1-1.png",
        "caption": "Fig. 1. Mechanical model.",
        "texts": [
            " Two time histories are compared, showing how, after global bifurcations, a chaotic transient is observed before settling on one of the three periodic, attracting solutions. Furthermore, the basins of attractions of these attractors are shown and the manner in which they change as a consequence of the global bifurcations and achieve a completely fractal nature as the amplitude of the excitation increases, are discussed. In this section the dynamics of a beam resting on a non-linear elastic substrate, fixed at its base and subjected to a vertical load pL , which in general is not constant in time (Fig. 1), is analyzed. The beam is modelled as an \u2018\u2018elastica\u2019\u2019 (see Articles 262 and 263 of [5]), that is, we assume that it is a slender, incompressible, uniform rod with infinite shear modulus and that the bending moment depends linearly on the curvature (the constant of proportionality will be denoted by EJ ). The lateral displacement of the centroid, yL , its vertical displacement, xL , and its deflection angle, u, depend on the arc length sL , which is contained in the interval [0, \u00b8], and on time t",
            " In Eqs. (2a)\u2014(2c) we have retained only terms up to a6. This permits workable calculations and it is sufficient to capture the main phenomena we are interested in. The stationarity of the action integral \u00b8\":q 2 q 1 (\u00b9!\u00ba#\u00bc ) dq furnishes the equation of motion a\u0308 (1#d 2 a2#d 3 a4)#aR 2 (d 2 a#2d 3 a3)#a N (d 4 #k!pd 11 )#a3 2(kd 6 #k 1 d 7 !pd 12 ) #a5 3(kd 8 #k 1 d 9 #k 2 d 10 !pd 13 )\"0, (4) where d i \"c i /c 1 . Eq. (4) governs the single-mode, fifth-order, unperturbed dynamics of the system in Fig. 1. Let us simplify Eq. (4) slightly by changing variable aPb(a). In the considered range of parameters, the coefficient d 2 and d 3 are always positive, so that we can define b(a) as the increasing function solution of db da (a)\"J(1#d 2 a2#d 3 a4) , (5a) b (0)\"0 (5b) and then compute b\u00ae \" a\u0308 (1#d 2 a2#d 3 a4)#aR 2(d 2 a#2d 3 a3) J(1#d 2 a2#d 3 a4) . (6) Inserting these last two expressions in Eq. (4), one has b\u00ae # 1 2 d db Ma2 (d 4 #k!pd 11 )#a4(kd 6 #k 1 d 7 !pd 12 )#a6 (kd 8 #k 1 d 9 #k 2 d 10 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003819_rspa.2005.1452-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003819_rspa.2005.1452-Figure2-1.png",
        "caption": "Figure 2. Disc and wheel carrier FE model (mesh removed).",
        "texts": [
            " The average interface contact pressure (Pavg) can be calculated by dividing the total clamp force (product of the number of bolts nb and the individual bolt clamp force (F ) with the interface contact area (Aint): Pavg Z nbF Aint : (4.1) The values of bolt clamp force and average contact pressure, for the applied bolt torque, are included in table 1. As expected, average contact pressure is a linear function of bolt torque. Proc. R. Soc. A (2005) In order to study contact pressure in more detail, SDRC I-DEAS software was used to create a FE model of the CV brake disc and wheel carrier assembly. Both the disc and wheel carrier were truncated to reduce model complexity, while maintaining accuracy, as shown in figure 2. Making use of the circumferential symmetry, a three-dimensional segment of 368 was modelled, which included one bolthole. The 10 bolts connecting the disc and the wheel carrier are not equally spaced, but grouped in five equally spaced \u2018pairs\u2019. Appropriate boundary conditions were applied. The disc and wheel carrier were modelled with 3900 solid linear brick elements and 286 gap elements, having a total of 4577 nodes. The disc was modelled with grey cast iron material properties and the wheel carrier was modelled with SG iron properties",
            " In such modelling, the relative movement (sliding) of interfaces can only be artificially included, since the user must define fixed nodes (that do not move), which will determine the direction of sliding. In practice, some relative movement of components is inevitable during assembling, which combined with gradual increase of clamp force makes the \u2018non-friction\u2019 approach the most suitable. For interface pressure and TCR measurements, the disc and wheel carrier were bolted to the very stiff spin rig adapter (see figure 6). This enabled simplified (\u2018rigid\u2019) but realistic modelling of the underside surface of the disc hat (see \u2018clamped\u2019 nodes in figure 2). To model the bolt clamp force, a continuous load was applied to 120 nodes under the bolt head on the surface of the wheel carrier (see bolt force, figure 2). At the symmetry planes of the model (368 apart), appropriate boundary conditions were introduced, ensuring nodes remained within these planes during loading. Figure 3 shows the contour plot of the ZZ stress component (perpendicular to the interface), representing interface pressure distribution. The applied bolt force of 120 kN is resulting from the maximum torque applied to the bolt (300 Nm; see table 1). High interface pressure can be clearly seen around the hole, the maximum value being 124 MPa (the negative sign in figure 3 indicates compression)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003023_001-Figure17-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003023_001-Figure17-1.png",
        "caption": "Figure 17. A schematic diagram of a combined O,/CO, transcutaneous sensor (after Mahutte et a1 1984).",
        "texts": [
            " What was clear, from the outset, was that the transcutaneous Po, sensors over-read true arterial Pco2 by a factor between 1.2 and 1.6. Several factors contribute to this, including heating of the capillary blood beneath the sensor and the increase in local cellular metabolism. The readings are also affected by the metabolic sequelae of inadequate perfusion and hypoxia beneath the sensor. The next logical development was that of a combined Pco,-Po, transcutaneous sensor, and an outline diagram showing its construction is presented in figure 17. The dual sensor is essentially a skin surface Pco, sensor with a cathode incorporated in it to measure Po,. The sensor uses a common buffer electrolyte, in addition to a common membrane and reference anode. Any OH- ions produced by the cathode are buffered by the electrolyte and their production is too small to affect the Pco, readings. Advantages of the dual sensor include convenience, lower potential cost for two simultaneous on-line blood gas measurements and the minimising of skin damage by measuring on one site"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000910_20.877800-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000910_20.877800-Figure3-1.png",
        "caption": "Fig. 3. Random distribution algorithm tests and thermal sensor position.",
        "texts": [
            " But in the fabrication stage, the conductors are randomly distributed in the machine slots. As a result, the maximum temperature, , of the winding is a random variable. To obtain the statistical distribution of we used the Monte-Carlo reject method with uniform distribution to disperse randomly the conductors in the slot [6]. In fact, we distribute a set of points as centers of circular conductors. To avoid object superposition in geometry definition, we must consider the proximity of these points with the outer of the slot or with other conductors previously distributed (see Fig. 3). The distribution algorithm is defined as follow: A) Generate two uniform random numbers and between 0 and 1. B) Define the point by - coordinates in a rectangular box surrounding the slot and using the previous random numbers ( = width * & = height * ). C) If the point is out of the slot then go to A. D) If the point is too close to the boundary of the slot (i.e. distance lower than the conductor radius) then go to A. E) If the point is too close to a conductor (i.e. distance between the center of two conductors is lower than conductor diameter) then go to A",
            " As for high filling rates, the maximum temperature is practically independent of the conductor distribution, we try to correlate it with a measurable physical characteristic of the machine. The most evident one is the temperature of an easily accessible point. The other solution is to compare it with the mean temperature of the winding which can be obtained through the measurement of the resistance of stator windings. Fig. 5 shows temperature values for these different solutions. One of the easiest points accessible near the winding and after manufacturing is the free area at the entry of the slot. Here we have enough space to put a thermal sensor as shown in Fig. 3. For each distribution at different filling rates, we test the correlation between the maximum temperature of the winding and the computed temperature of a midpoint in the entry of the slot. Fig. 6 shows the dispersion of differential temperature of this point to the maximum temperature in the slot. Because of the substantial drift greater than 10%, we can assume that the temperature of this point is not correlated enough to the maximum temperature to have good information on it. This can be explained by the fact that this point is placed in a high temperature gradient area, between the winding and free air (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001819_rob.4620100104-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001819_rob.4620100104-Figure1-1.png",
        "caption": "Figure 1. Planar redundant manipulator: do = 0.7, dl = 0.6, d2 = 0.85, d3 = 0.2.",
        "texts": [
            " In summary, the proposed approach for the numerical solution of the inverse kinematics problem has the properties that: (1) The automatic adjustment of the damping factor is theoretically justifiable; (2) It is in general faster to compute than the previous version presented in ref. 20; and (3) it is a powerful and effective procedure to deal with the singularities avoidance problem of manipulators operating in a redundant fashion. Here, eq. (22) using the numerical procedure described in the previous section is tested for a simulated three degree of freedom planar redundant manipulatorI4 shown in Figure 1. The following task is considered. Given an initial end effector position [ x l ( t o ) , x z ( to ) ] = L0.991421, 1.4414211 5% Journal of Robotic Systems-1 993 with a corresponding initial configuration (rad.)I4 specified by it is required to move the end effector along a straight line with constant speed for t f = 10.0 secs to the final position with a corresponding singular configuration given by The task is simulated on a SunSparc server 330 digital computer with a program written in FORTRAN and double-precision arithmetic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003084_s00422-005-0008-x-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003084_s00422-005-0008-x-Figure1-1.png",
        "caption": "Fig. 1 Two degrees of freedom kinematic chain model of a limb for simulating planar reaching movements",
        "texts": [
            " Accordingly (see the proof for details), if z1 f , . . . , zn+1 f is a minimum variance solution, then so is Qz1 f , . . . , Qzn+1 f for any orthogonal change of basis Q. Note 13 The sphere where zf is distributed may be centered in any position other than the origin. If the center is zc the minimal variance solution can be easily proven to be the translation of the solution above, i.e. zc + z1 f , . . . , zc + zn+1 f . In this section we apply the proposed spinal field paradigm to control a 2DOF (two degrees of freedom) planar chain (see Fig. 1); this system has been used as a simplified model of the human arm in (Morasso 1981) and (Mussa-Ivaldi and Bizzi 2000). The dynamics of this model can be expressed in the form (1) with m = 2 and q = [\u03b81 \u03b82] ; the inputs are the torques applied at the joints, u = [u1 u2] , and the task is the control of the cartesian position of the extremity P , i.e. y = [xP yP ] . Table 1 gives the kinematic and dynamic parameters that we used in the simulations. Table 2 gives the expressions of the matrices M and C (see Mussa-Ivaldi and Bizzi 2000 for details)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001343_1.2832457-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001343_1.2832457-Figure6-1.png",
        "caption": "Fig. 6 Spatial distribution of tPie contact force at resisting (a) and as sisting (b) contact regions",
        "texts": [
            " Each local contact force contributes to the overall contact force at the interface of a friction pair. The net sum of the components of the local forces at all asperities normal to the mean planes of the interacting surfaces is equal to the normal load at the interface of the two nominally parallel surfaces Si and ^2. Similarly, the net sum of the components of all the local forces tangential to the mean planes of the interacting surfaces is the dry-friction force. Here, contact forces are formulated by a distributed force g(Ps) over each local contact area as shown in Fig. 6. The distributed force g(p,,) is then expressed as a vector sum of the two forces as g(/0.) = p(p.,) + q(p,) . The force p(ps) is tangent while the force q(ps) is normal to the (local) contact surface. The independent variable p,, is used to indicate that the contact forces are functions of the contact surface coordinates x,,, ys, Zs- The equal but opposite contact force for each resisting asper ity pair can be expressed in terms of their components in the normal and tangential directions to the mean planes of the sur faces",
            "v) = -p'ni - P'mn, qi(p,,) = -q'at + q'\u201e2n (18) where, pU = Pn, p'n\\ = p'm, qU = q'12 and q'\u201et = q'\u201e2, and for the case of assisting asperity pairs Pi(Ps) = p/it - piiTi, q((p,) = -qjit - qUn PUPS) = -pht + piin, (iiips) = q'ni + qiiTi (19) where, p'n = ph and pL = pii, qU = qk and qU = qii. The unit vectors t and n are in the tangential and normal directions to the mean planes of the surfaces, respectively. Since the ratio of the components of the contact force at a contact point is equal to the slope of the contacting surfaces at that point, referring to Fig. 6 and considering Eqs. (11), (18), and (19), slope at a contact point can be expressed in terms of force components as: (9Zi dZa dX'2 dX{ dXi = 111 q'ni g/1 _ q'nx qa ^ q'n2 qii Pni ^ p'n ^ pin ph Pn2 Pn pL ph (20) (21) Relationships between contact forces, rate of deformations and relative velocity of the interface can be obtained for a resisting contact region by substituting (20) into the velocity equation (12). h = (s P'a h = (s - 6',) qn OK dt dt 1, i = 1, (22) In a similar manner, for an assisting contact region, from Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002662_0301-7516(89)90007-0-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002662_0301-7516(89)90007-0-Figure1-1.png",
        "caption": "Fig. 1. Collision mechanisms in deep-bed filtration.",
        "texts": [
            ", 1985). Hencl et al. recognized that a modified physical picture was needed and, although some of their fundamental arguments are invalid, their paper can serve as a starting point for a more realistic description of the process of particle capture in a real matrix. In the present work, the transport mechanisms of particles in HGMS were analysed, and a static model of particle a t tachment is described in outline. with the matrix element (collector) by virtue of its finite size, as is shown in Fig. 1, case A. This transport mechanism, which is called interception and straining, is not caused by any force acting on the particle; it is induced by the geometry of the system. the fluid. It will therefore leave the streamlines and come into contact with a collector (Fig. 1, case B). In wet filtration, the efficiency of collection of such particles is negligible but, in air filtration, the transport of particles by inertia can be important. If the density of the suspended particles is greater than that of water, the trajectory fbllowed by the particles will be influenced by the gravitational force field (case C in Fig. 1). This gravitational t ransport process is often called sedimentation. Particles in a suspension are subject to the Brownian motion of the medium in which they are suspended and, for small particles, diffusion can be an important t ransport mechanism (case D in Fig. 1 ). The velocity of the liquid can also be greater on one side of a particle than on the other, causing the particle to rotate. As a result, pressure difference develops laterally to the direction of flow and the resultant force causes the particles to move across the flow field. This hydrodynamic effect will appear as a random drifting motion across the streamlines, which also contributes to the retention of the particles on the matrix (Rajagopalan and Chi Tien, 1973; Ives, 1975). The fundamental equations describing the retention of particles in a filter bed are the macroscopic conservation equation and the rate equation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000710_mech-34246-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000710_mech-34246-Figure6-1.png",
        "caption": "Figure 6. The Locus of the Instant Centers 59I .",
        "texts": [
            ", 1992, \u201cAn Analytical Method for Locating Velocity Instantaneous Centers,\u201d Proceedings of the 22nd Biennial ASME Mechanisms Conference, DE-Vol. 47, Flexible Mechanisms, Dynamics, and Analysis, pp. 353- 359, Scottsdale, Arizona, Sept. 13-16. 11. Yang, A.T., Pennock, G.R., and Hsia, L-M., 1994, \u201cInstantaneous Invariants and Curvature Analysis of a Planar Four-Link Mechanism,\u201d ASME Journal of Mechanical Design, Vol. 116, No. 4, December, pp. 1173-1176. APPENDIX Consider the six-bar linkage comprised of the left-hand loop of the double butterfly linkage and the slider link 9 attached to the coupler point B, see Figure 6. The appendix will prove that the locus of instant center 59I , for all possible lines of motion of link 9, is a straight line which is parallel to the line connecting point B to point 0T ; i.e., the intersection of lines AO2 and CD . Note that the procedure to find the instant center, 59I , for an arbitrary line of motion of link 9, is to: (i) find the point of intersection of the lines AO2 and BI19 (i.e., the instant center 13I denoted here as 1T ); (ii) find the point of intersection of lines 15TO and CD (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000423_s0301-679x(98)00085-1-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000423_s0301-679x(98)00085-1-Figure1-1.png",
        "caption": "Fig. 1 Rolling\u2013sliding contact of rough surfaces, showing definition of axes and surface speeds relative to body 1 (the specimen). A diagrammatic representation of the distribution of pressure and the direction of the tangential traction due to the sliding are also shown. Slide\u2013roll ratio is defined as s 5 (U1 2 U2)/(U1 1 U2) and has a negative value for all the examples given in this paper",
        "texts": [
            " the applied load, geometry of the bodies (radii of curvature), roughness and the material, the model determines the pressure distribution 728 Tribology International Volume 31 Number 12 1998 in the contact. The pressure distribution is then used in turn to determine the stresses in the specimen close to the area of contact using the subsurface stress model. In this paper we present the stress distributions and the stress histories of a specimen loaded by a counterbody rolling\u2013sliding over it (Fig 1). Various contact conditions from smooth-on-smooth, smooth-on-rough, rough-on-smooth and rough-on-rough have been investigated. The profiles of rough surfaces used, which represent typical ground finish of 0.18 mm rms, are shown in Fig 2. In order to generate the full stress history experienced by the material, a series of contacts was made over a small area in the specimen by loading the counterbody across it in sequence. The parameters used in this study were; radius of curvature 5 10 mm, load per unit length 5 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003444_1.2176121-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003444_1.2176121-Figure5-1.png",
        "caption": "FIGURE 5 \u2014 Fabrication process of the encapsulated ChLCD on the single textile substrate.",
        "texts": [
            " The conducting polymer exhibits high transmission, high conductivity, and flexibility, which make this material a promising alternative for conventional ITO electrodes. To increase the durability of the display, a protective clear layer is deposited on the top conducting polymer electrode. The total thickness of the coatings on the fabric surface is on the order of 30\u201335 \u00b5m. Flexible printed circuits are bonded to the flexible display using conductive tape over the conductive polymer electrodes on the fabric substrate. Figure 5 illustrates all the steps in the fabrication process and is a schematic representation of the final display assembly. A distinctive feature of the ChLCDs is their reflectivity and bistability. The color of cholesterics originates from the pure selective reflection sensitive to the wavelength and polarization of the incident light. The helical molecular structure of ChLCs exhibits two stable textures controllable by the applied electric field. The first texture, planar, is reflective for the incident light with one of the circular polarizations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000363_s0168-874x(99)00042-6-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000363_s0168-874x(99)00042-6-Figure1-1.png",
        "caption": "Fig. 1. Solid model of a ball bearing with an integrated sensor module.",
        "texts": [
            " The quality of the input signal therefore depends on the interface between the bearing and the housing as well as the coupling between the sensor and the housing. Furthermore, with the sensor secured to a supporting structure instead of to the bearing itself, the measurement is prone to contamination from structure-borne vibration. The measurement quality can be substantially improved if the condition monitoring sensors are directly embedded into the bearing itself [4,5]. This approach is illustrated in Fig. 1, which shows a solid model of a conventional ball bearing with a sensor module embedded in its outer ring. The sensor module consists of sensing elements and on-board microelectronics (hardware and software) for bearing condition monitoring and assessment. The establishment of assessment algorithms can be based on guidelines that relate a bearing's operation condition to various physical quantities, which includes, for example, the interpretation of machinery vibration measurements given by Jones [6,7], and description of the various phases of bearing wear presented by Berggren [8]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002320_irds.2002.1041626-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002320_irds.2002.1041626-Figure4-1.png",
        "caption": "Figure 4 : Mobile objects may also appear in the shadows of static.obstacles",
        "texts": [
            " 2 Two caies may occur depending on the No obstacles in Cui, In the simple case where the robot\u2019s position is such that no static obstacle lies inside C,;,, a moving object may appear (at time t = 0) anywhere onto Cvjs\u2019s boundary (Fig. 3). At time t o (ie. when the robot is stopped), the distance crossed by the object is d,bj(u) 5 UobjUvob/am. Avoiding any potential collision imposes that &, 2 drob(w) + d,bj(u). The condition relates the maximal robot\u2019s velocity vmaZ to the sensor\u2019s range RD;s: = -Uobj t 4- (1) Influence of shadowing corners Static obstacles lying inside Cui, may create shadows (eg. see the grey region of Figure 4) succeptible to contain mobile objects. The worst-case situation occurs when the mobile remains unseen until it arrives at the shadowing cornerof a polygonal obstacle. Since the mobile\u2019s motion direction is not known it is best modeled for a worst case scenario as an expanding circular wave of radius U&jt centerd at (d, 0) ( X ( t ) - dcosO)*+ (Y(1) - dsinB)2 = u2b,t2 Let us first consider that the robot\u2019s path r is a straight segment. Considering that the intersections between the circular wave and the robot\u2019s segment path, should never reach the robot before it stops at time t o yield to the following velocity constraint: - d(a,dcos B + ~ : ~ ~ ) t ~ f , ~ + 4&d2 2 0 (2) This solution only exists under the condition W & j > Ja,d(l - cosO), ie"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003520_12.7973908-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003520_12.7973908-Figure6-1.png",
        "caption": "Fig 6. Schematic showing the effect of material conductivity on the shape of cross -sectional isotherms.",
        "texts": [
            " Therefore a special effort was made to determine what characteristics of the thermal field, if any, were related to the depth of penetration. Data concerning the depth of penetration were gathered from microstructural examinations of the welds. This consisted of cutting the plates through the weld and then polishing, etching, and photographing the exposed surfaces. Temperature- dependent microstructural changes allowed the identification of surfaces that reached particular temperatures during the welding process. Figure 6 shows the theoretical temperature distribution through a cross section of a plate, of arbitrary thickness t1 and thermal conductivity k1, in contact with a backing material, of thermal conductivity k2, on one side and under the influence of an arc on the other side. Malmuth et al.27 have shown that for a given thickness of material this temperature distribution is a function only of the ratio k1 /k2. Figure 6 shows the top extreme cases for this thermal field (k) /k2 = 0 and k1 /k2 = oo) and one intermediate case (k1 /k2 < 1). Two important conclusions may be drawn from the work done by Malmuth et al.: (a) the thermal distribution across the surface determines the thermal field throughout the material, and (b) the shape of the isotherms inside the weld metal is determined solely by the surface position of that isotherm (the thickness and k1 /k, being fixed). These two facts allow us to develop a method for predicting the depth of penetration of an isotherm, given only its shape and position on the surface as well as the thickness t and the ratio k1 /k, for the material",
            " ( the general relationship betw en cro s- l l de of penetrati B an surfa l i ( ti lat cr se ti sho i r l f l. re s l wa ma to determine t ri ti s t f pe t ata con ti n f microstr exa  s th wel Thi con cutti the plate t p l ,  ing t exposed surfaces. Temperature-depende t tr ctural anges llo ed the tification  ces t rea parti r te tures ing t l i i ure s t t i i l of arbitrary thickness tj t al ctivity p i t a backi i l, , nce f the other side. Malmuth et al. 27 ve own that a give thic s mat l t perature distribution is a nction only f r j/k2 . Figure 6 shows the top extre e cases for t is t l j/k2 /k 00 o i ter i t ca j/k2 < ). T o i rt rk e l th t  n a ss t surfa deter es t ther fiel ( t s t is t ide ld t l ly s ition t isot (th thick a k/k? bei i ed). hese two facts al ow us t lop icting the th an isother , give ly ts e ition s ll i ness t j/k2 l. ( ) icts t ll t trol er t e t , respecti l , if t i . . e i relationship betw en cro s-sectio l ii t i i i t a elli ill str t i i . 7( t ti l f ,/k and t  endent f r ture). th is rk t . , i t on the surface of the plate rea ti full penetration is ac i ti n de t t ti it it t i er f r , co  as th functi t l t r li i r or sug r i ure s e th exi g fi t th t b / OPTICAL EN RING / J "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000902_s0302-4598(98)00066-x-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000902_s0302-4598(98)00066-x-Figure2-1.png",
        "caption": "Fig. 2. Typical cyclic voltammograms observed for 1 mM Indole at PGE \u017d . \u017d . y1A pH 6.0; B pH 9.0 at a sweep rate of 100 mV s .",
        "texts": [
            " The E of the two peaks was so close that mostp of the times, they were merged to a single peak. At pH)6.0, the two reduction peaks clearly merged to a single peak. The peak potentials of peaks II and III werec c also dependent on pH and shifted to more negative potential with increase in pH. When the direction of sweep was further reversed, peaks II and III were observed, whicha a formed quasi reversible couples with peaks II and III inc c the pH range 2.0\u20136.0. Some typical cyclic voltammograms of Indole are presented in Fig. 2. \u017d .Fig. 4. Variation of the peak current function i r6\u00d5 with the logarithmp of the voltage sweep for 1 mM Indole at pH 6.0 at PGE. \u017d .The peak current for the oxidation peak I was morea or less constant in the entire pH range studied. However, the i increased with increase in concentration of Indole.p Fig. 3 presents the plot of peak current values observed at different concentrations of Indole. It was found that the peak current increased linearly up to about 2 mM concentration and attained more or less constant value at higher concentrations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000099_(sici)1521-4109(199912)11:18<1333::aid-elan1333>3.0.co;2-6-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000099_(sici)1521-4109(199912)11:18<1333::aid-elan1333>3.0.co;2-6-Figure1-1.png",
        "caption": "Fig. 1. Scheme of the \u00afow cell used for FI and LC measurements: A) polypropylene pipet tip in which the modi\u00aeed CFME is inserted; B) block containing the Ag=AgCl reference electrode; C) steel \u00afow outlet tube-auxiliary electrode.",
        "texts": [
            " Voltammetric measurements were made using a BAS MF 2063 Ag=AgCl reference electrode and an auxiliary electrode consisting of a Pt wire directly immersed in the solution. A Metrohm 6.0804.010 conventional glassy carbon electrode (3 mm o.d.) has been also used as a working electrode for comparison purposes. A 10-mL electrochemical cell from BAS, Model VC-2 was also used. A \u00afow cell based on a T-shape con\u00aeguration previously described [20] was employed for FI and LC measurements. The scheme of this \u00afow cell is depicted in Figure 1. Basically, it consisted of a homemade methacrylate block provided with a 4- mm f \u00afow-channel where the microelectrode is inserted perpendicularly to the \u00afow solution, which passes through the whole active surface of the electrode, thus assuring the smallest possible dead volume. The above mentioned Ag=AgCl reference electrode is also inserted in the \u00afow cell, and the steel \u00afow outlet tube was used as the auxiliary electrode. Stock 5.0610\u00ff4 mol L\u00ff1 solutions of dopamine (Sigma) and serotonin (Fluka), and 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001707_s0094-114x(03)00091-0-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001707_s0094-114x(03)00091-0-Figure6-1.png",
        "caption": "Fig. 6. (a) The vectors for the geared seven-bar mechanism. (b) The angular displacements of the geared seven-bar mechanism.",
        "texts": [
            ", OEE \u00bc \u00f0P16E\u00de2 JEE \u00f09\u00de The center of curvature of the path traced by the coupler point E and the osculatory circle is shown in Fig. 5. The following section presents an analytical method that will be used as an independent check of the graphical technique. The method, commonly referred to as the method of kinematic coefficients [19], will provide an equation for the radius of curvature of the path traced by the coupler point E. A fixed Cartesian coordinate reference frame, henceforth referred to as the fixed frame, is denoted as XO2Y , see Fig. 6a. The origin is coincident with the ground pin O2 and the X -axis is chosen to pass though the ground pin O3. The vectors that describe each link of the mechanism are shown in Fig. 6a. Vector R1 points from O2 to O7, R2 points from O2 to A, R3 points from O3 to B, R23 points from O2 to O3, R4 points from A to D, R5 points from B to E, R6 points from D to C, R62 points from D to E, and R7 points from O7 to C. The constant angle between the two vectors R6 and R62 is denoted as a. The angular displacement hj (j \u00bc 1, 2, 3, 4, 5, 6, and 7), which indicates the direction of vector Rj, is measured counterclockwise from the X -axis, see Fig. 6b. The vector RE, which points from O2 to coupler point E, is used to define the path of coupler point E. The radius of gear 2 and the radius of gear 3 are denoted as q2 and q3, respectively. The configuration of the geared seven-bar mechanism can be described by two independent vector loops. The two vector loop equations that will be used in this paper are R2 \u00fe R4 \u00fe R6 R7 R1 \u00bc 0 \u00f010a\u00de and R2 \u00fe R4 \u00fe R62 R5 R3 R23 \u00bc 0 \u00f010b\u00de The X and Y components of Eqs. (10a) and (10b), respectively, are R2 cos h2 \u00fe R4 cos h4 \u00fe R6 cos h6 R7 cos h7 R1 cos h1 \u00bc 0 \u00f011a\u00de R sin h \u00fe R sin h \u00fe R sin h R sin h R sin h \u00bc 0 \u00f011b\u00de 2 2 4 4 6 6 7 7 1 1 R2 cos h2 \u00fe R4 cos h4 \u00fe R62 cos h62 R5 cos h5 R3 cos h3 R23 cos h23 \u00bc 0 \u00f011c\u00de and R2 sin h2 \u00fe R4 sin h4 \u00fe R62 sin h62 R5 sin h5 R3 sin h3 R23 sin h23 \u00bc 0 \u00f011d\u00de where h4, h5, h62 and h7 are the four unknown joint variables",
            " (13a)\u2013(13d) with respect to the input position h2, and writing the resulting equations in matrix form, gives \u00bdA h04 h05 h06 h07 2 664 3 775 \u00bc R2 ch2 \u00fe R4 ch4h24 \u00fe R6 ch6h26 R7 ch7h27 R2 sh2 \u00fe R4 sh4h24 \u00fe R6 sh6h26 R7 sh7h27 R2 ch2 R3 ch3h23 \u00fe R4 ch4h24 \u00fe R62 ch62h26 R5 ch5h25 R3 sh3h03 R2 sh2 R3 sh3h23 \u00fe R4 sh4h24 \u00fe R62 sh62h26 R5 sh5h25 \u00fe R3 ch3h03 2 664 3 775 \u00f019\u00de where c and s are used as abbreviations for cosine and sine, respectively, the (4\u00b7 4) coefficient matrix \u00bdA is given by Eq. (17b), and h0j \u00bc d2hj dh2 2 ; \u00f0j \u00bc 3; 4; 5; 6; and 7\u00de \u00f020\u00de is referred to as the second-order kinematic coefficient of link j. Note that the second-order kinematic coefficient of link 3, obtained by differentiating Eq. (16) with respect to the input position h2, is h03 \u00bc 0 \u00f021\u00de The vector equation for coupler point E, see Fig. 6b, can be written as RE \u00bc R2 \u00fe R4 \u00fe R62 \u00f022\u00de The X and Y components of this equation, respectively, are XE \u00bc R2 cos h2 \u00fe R4 cos h4 \u00fe R62 cos h62 \u00f023a\u00de and YE \u00bc R2 sin h2 \u00fe R4 sin h4 \u00fe R62 sin h62 \u00f023b\u00de Then differentiating Eqs. (23a) and (23b), with respect to the input h2, gives the first-order kinematic coefficients for the path of point E; i.e., fXE \u00bc dXE dh2 \u00bc R2 sin h2 R4 sin h4h4 R62 sin h62h6 \u00f024a\u00de and fYE \u00bc dXE dh2 \u00bc \u00feR2 cos h2 \u00fe R4 cos h4h4 \u00fe R62 cos h62h6 \u00f024b\u00de The velocity of point E can be written as V E \u00bc VE ut \u00f025a\u00de where ut \u00bc fXE i\u00fe fYE j fE \u00f025b\u00de is the unit tangent vector to the path of point E, and the speed of point E can be written as VE \u00bc fEx2 \u00f026a\u00de where fE \u00bc \u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f 2 XE \u00fe f 2 YE q \u00f026b\u00de Substituting Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002487_j.enconman.2004.05.005-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002487_j.enconman.2004.05.005-Figure2-1.png",
        "caption": "Fig. 2. Stator flux linkage vector diagram.",
        "texts": [
            " Finally, Section 5 summarizes the main contributions of this paper. Using the d\u2013q transformation, the voltage equations of an IPM machine in the rotor reference frame are as follows: vd \u00bc Rsid \u00fe dkd dt xekq; \u00f01\u00de vq \u00bc Rsiq \u00fe dkq dt \u00fe xekd ; \u00f02\u00de where kd \u00bc Ldid \u00fe km, kq \u00bc Lqiq and the stator flux linkage is ks \u00bc \u00f0kd \u00fe kq\u00de 1 2. The corresponding equivalent circuits are shown in Fig. 1. It has been shown that the electromagnetic torque in an IPM machine can be regulated by controlling the magnitude and angle of the stator flux linkage or load angle d as seen in Fig. 2 [2]. This can be performed by applying the proper output voltage vectors of an inverter to the machine. There are six nonzero voltage vectors and one zero voltage vector for a two level inverter as depicted in Fig. 3. They can be represented by: Sa, Sb and Sc are used to show the state of each leg in the inverter, which is either 0 or 1. They are 0 when the leg is connected to zero and 1 when it is connected to the DC bus voltage VDC. It has also been proved that the torque dynamics is dependent on the speed of rotation of the stator flux linkage with regard to the magnet flux linkage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001396_s0022-5096(01)00130-2-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001396_s0022-5096(01)00130-2-Figure10-1.png",
        "caption": "Fig. 10. Shapes of a rod with = 5 7 at constant R=4:265 (rad). (a) is for d=0:115, just after the buckling instability. A loop starts to develop in (b) (for d=0:69), but no dynamic jump takes place. Instead, the rod reaches con(gurations in which the clamps are inverted, as in (c) (d= 1:06) and (d) (d= 1:53). Note that at d = 1 the rod forms a closed stable planar loop.",
        "texts": [
            " Since we no longer consider just the homoclinic orbits in the phase space but any orbit that ful(ls the boundary conditions, the number of static con(gurations is larger and the post-buckling surface becomes more complicated (Neukirch and Henderson, 2001). Also, as shown in van der Heijden et al. (2001), the force vector no longer lies along the \u2018-axis as it did in the in(nite length case. As done for the previous model, we will plot D\u2212T and R\u2212M distinguished diagrams to check the stability of the static con(gurations under (xed-R and (xed-D experiments, respectively. Here D, for an arbitrary con(guration, is given by Eq. (9). It takes values between 0 and 2L (for D\u00bfL the rod leaves the clamps on the outside, see Fig. 10). For details on the numerical techniques used we refer to van der Heijden et al. (2001). Fixed R experiment: The D\u2212T response diagram for any (nite-L rod with = 5 7 is drawn in Fig. 8. We see that bucking (d def= D=L = 0) may happen for negative t (compression). We also note that as in Fig. 5 not all the curves have a D-fold, which means that there are again two regimes for the curves emerging from the (rst buckling mode: \u2022 For high end-rotation, R\u00bf 2 , there will be a jump to self-contact at a certain limiting d (see Fig. 9). \u2022 For low end-rotation, R\u00a1 2 , the buckled con(gurations are stable up to d=2 (for the present value of ), which includes, for d\u00bf 1, rod con(gurations with inverted clamps (see Fig. 10). Change in the value of will qualitatively change the stability features of this experiment. For instance, we note that when is increased beyond\u221a 3, the curve with R = 0 acquires instability. This instability takes place at d = 1 when the rod forms a closed loop with one turn of twist put in. Since = \u221a 3 this implies that the twisting moment is \u221a 3, which is the buckling load for a planar ring (Zajac, 1962). The same argument can be used to show that curves with 0\u00a1R6 2 will acquire instability for larger values of "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000121_s0167-8396(97)00002-2-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000121_s0167-8396(97)00002-2-Figure4-1.png",
        "caption": "Fig. 4b. Axonometric view of a Dupin ring cyclide.",
        "texts": [
            " 3). (cyc7) According to property (cyc6) an offset surface of the symmetric Dupin horn cyclide is obtained by translating each of the circles k of the first system of circles along the generating lines of its cone of revolution Ck through the offset distance d. G. Albrecht, W.L.E Degen / Computer Aided Geometric Design 14 (1997) 349-375 355 Fig. 2b. Cross sections of the symmetric Dupin horn cyclide. The resulting surface is again a Dupin cyclide (see, e.g., (Pascal and Timerding, 1922, p. 872)). Fig. 4a illustrates the effect of the offsetting procedure for the cross sections of the cyclide. The circles c and cl thus become circles c d and c~ a with radius r - d and r + d respectively. Different values of d imply different shapes of the offset surface resulting in the following classification: 1 .0 = d < e < r: symmetric Dupin born cyclide in Case 3 c d touches el a from the inside. In Cases 4 and 6 c d and c~ do not have real intersection points, and c a lies inside c~. In Case 5 c d degenerates to a point inside c~"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001343_1.2832457-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001343_1.2832457-Figure4-1.png",
        "caption": "Fig. 4 Deformed surface roughness functions at a contact region",
        "texts": [
            " 3, separation h be tween the two bodies and their relative tangential displacement s are dependent on displacements arising from deformation and sliding of the surfaces. Separation h is expressed using functions representing the deformed surfaces and s is expressed as a com bination of the tangential components of the local sliding and deformation of each asperity pair: h = Zi{X\\) + Z2(X^) s = riL + ii (1) (2) where, Zi and Z2, describe the deformed surfaces. They are functions of undeformed surface functions zi and zi and the normal deformation functions 6\u201e\\ and 6\u201e2 as illustrated in Fig. 4. Zi{X\\,t) = Zi{X\\)- 6',.i{X\\,t) (3) Z2{X'2, t) = 22(XD - 6'\u201e2{X'2, t) (4) X\\= x + (rj, T 6',i) X'2=x- a,T 6\\2) S\u201e = 6\u201ei + 6\u201e2, (5\u201e > 0 and. In Eqs. (1) through (4) 0 = i,j with i = I, . . . , kj = 1, . . . , / corresponding to resisting and assisting contacts, respectively. The negative of the + in the parentheses is used for resisting contacts, while the positive sign is for assisting contacts, [k and 20 / Vol. 119, JANUARY 1997 Transactions of the ASME Downloaded From: http://tribology.asmedigitalcollection",
            " (1) and (2) with respect to time yields, h = (f], -t- 5Ji) dZj dXt (L T S'a) dZ2 dXi dt s = r), + t where 06'\u201e ^ 86^ d6\\a dt dt dt (8) (9) (10) where L = i, j i = \\, . . . , k j = 1, . . . , / and (\u2022) indicates derivative with respect to time. Equation (8) is valid in the contact region; selection of minus sign yields an expression for the resisting contacts, whereas, the positive sign gives a similar relationship for the assisting contacts. The slope of each surface at every material point must be equal to each other during contact, as illustrated in Fig. 4. Hence, the spatial derivatives of the deformed surface functions Z| and Z2 in equation (8), representing the slopes of the de formed surfaces at contact points, must be equal at each contact region t = i,j in the interface: dZj dX\\ dx'2 (11) The minus sign in (11) is because Z2 is measured positive away from the surface ^2. Equation (11) also represents a necessary condition for contact between two surfaces. Substituting (9) into (8) and using the necessary condition for contact, expressed by (11), yield the relative velocity equa tions for the resisting and assisting contacts in terms of contact slopes and deformations: ; , \u2022, dZ2 d6'\u201e "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000861_(sici)1097-4628(20000628)76:14<2062::aid-app9>3.0.co;2-t-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000861_(sici)1097-4628(20000628)76:14<2062::aid-app9>3.0.co;2-t-Figure3-1.png",
        "caption": "Figure 3 Nonlinear Maxwell model.",
        "texts": [
            " The relaxation time T would be proportional to the slippage speed of the fibers when subjected to a given strain, that is, for very long relaxation times, there would scarcely be any slippage between the fibers and, therefore, the yarn would behave like an elastic solid. The Maxwell model does not fit the behavior of some of the yarns under study. The response of these was nonlinear with respect to deformation. Thus, if the deformation X of the sample is replaced by (X^C) so that it can be adapted to a nonlinear response, the nonlinear Maxwell model is obtained, as shown in Figure 3. Model fitting was made in two steps: First, using the logarithmic transformation of the models, a linear regression was performed to obtain the initial estimators of the parameters. The models were linearized as follows: \u25cf Potential model: LOG(F) 5 LOG(A) 1 C 3 LOG(X), giving the initial estimation of A and C. \u25cf Maxwell model: LOG(F/X) 5 LOG(A) 2 K 3 X, K 5 1/T 3 r, giving the initial estimation of A and T. \u25cf Nonlinear Maxwell model: The initial estimators were those obtained by the Maxwell model, the initial estimation of C 5 1 (linear behavior)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002517_iros.2005.1545360-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002517_iros.2005.1545360-Figure5-1.png",
        "caption": "Fig. 5. The high speed Cartesian position feedback loop with velocity feedforward controls the joint velocities of the manipulator.",
        "texts": [
            " [p\u00d7] is a 3\u00d73 skew-symmetric matrix representing the cross product with p as defined in equation (7). The diagonal matrix K\u2032 s approximates the stiffness expressed at the center of the flexible mounting part. Finally, the twist ts is transformed into joint velocities q\u0307 for the velocity controlled manipulator. We use a high speed control loop with Cartesian position feedback on the integrated twist xf of the manipulated object, to eliminate drift on the manipulator position. A control scheme of this feedback loop is shown in figure 5, in which J is the manipulator Jacobian and K p F B the Cartesian position feedback constant. PSfrag replacements VI. EXPERIMENTAL RESULTS This paragraph describes the experimental setup and the obtained results of the real world experiment we used to verify our approach. In our experiments we use the Kuka 361, a six degrees of freedom velocity controlled industrial manipulator, which is shown in figure 6. The manipulated object, a cube, is attached to the manipulator with a flexible mounting part"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001811_ip-cta:20030966-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001811_ip-cta:20030966-Figure1-1.png",
        "caption": "Fig. 1 Longitudinal forces and moment acting on missile",
        "texts": [
            " The rigid body equations of motion reduce to two force equations, one moment equation, and one kinematic equation _U \u00fe qW \u00bc P FBX m \u00f036\u00de _W qU \u00bc P FBZ m \u00f037\u00de _q \u00bc P MY IY \u00f038\u00de _ \u00bc q \u00f039\u00de where U and W are components of velocity vector V * T along the body-fixed x- and z-axes; is the pitch angle; q is the pitch rate about the body y-axis; m is the missile mass. The forces along the body\u2013fixed co-ordinates and moments IEE Proc.-Control Theory Appl., Vol. 150, No. 6, November 2003 579 about the centre of gravity are shown in Fig. 1. The force and moments about the centre of gravity areX FBX \u00bc L sin a D cos a mg sin \u00f040\u00de X FBZ \u00bc L cos a D sin a\u00fe mg cos \u00f041\u00de X MY \u00bc M \u00f042\u00de where a is angle of attack; L denotes lift; D denotes drag and M is the pitching moment. L \u00bc 1 2 rV2SCL; D \u00bc 1 2 rV2SCD; M \u00bc 1 2 rV2SdCm \u00f043\u00de The normal force coefficient CZ is used to calculate the lift and drag coefficients CL \u00bc CZ cos a; CD \u00bc CD0 CZ sin a \u00f044\u00de where CD0 is the drag coefficient at the zero angle of attack. The nondimensional aerodynamic coefficients at 6096m altitude are: CZ \u00bc ana 3 \u00fe bnajaj \u00fe cn 2 M 3 a\u00fe dnd \u00f045\u00de Cm \u00bc ama 3 \u00fe bmajaj \u00fe cm 7 \u00fe 8M 3 a\u00fe dmd\u00fe emq \u00f046\u00de In this paper we adopt Mach number M, angle of attack a; flight path angle g; and pitch rate q as the states since they appear in the aerodynamic coefficients"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001024_978-1-4757-5070-6_3-Figure3.14-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001024_978-1-4757-5070-6_3-Figure3.14-1.png",
        "caption": "FIGURE 3.14. Experimental device for measuring the Volta-potential difference between an electrode surface emersed from an electrolyte (cell) and a reference surface (vibrator). The inert atmosphere in the stainless steel chamber is water-saturated. The position of the Kelvin vibrator in front of the withdrawn electrode surface is adjusted with a micrometer drive.",
        "texts": [
            " The new Donnan potential leads to a new value of (4)Me - cjl'0ly) that differs from the old one by the change in the Donnan potential (see Fig. 3.9). The Volta-potential measurements are conducted with the aim of determining such variations of (4)Me - cjl'oly) and thus of fl.4>D. 3.3.3. Volta-Potential Difference dl/l Measurements For the Volta-potential measurements, the coated electrodes are withdrawn from the electrolyte under potential control. (73) Experimen tally this is done in the device shown in Fig. 3.14. The electrode is mounted vertically in a holder that enables it to be moved down (immersion into the electrolyte for electrochemical equilibration) and up (removal from the electrolyte and positioning in front of the Kelvin vibrator). The fl.\", measurements are conducted in an atmosphere of nitrogen saturated with water. The water-saturated atmosphere is neces sary to keep the state of the polymer the same as in the electrolyte, and oxygen must be excluded to avoid electrode reactions that can change the value of (~Me - ql'0ly) in the withdrawn (emersed) state"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002314_1.1814390-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002314_1.1814390-Figure3-1.png",
        "caption": "Fig. 3 The ith leg of a translational 3-URC mechanism",
        "texts": [
            " Hereafter a 3-URC mechanism that meets the above-mentioned conditions will be called translational 3-URC. With reference to Fig. 2, points Ai , i51, 2, 3, are the centers of the universal joints. Points Bi , i51, 2, 3, are the intersections of the cylindrical pair axes with the revolute pair axes adjacent to them. Moreover, Sp is a reference system fixed in the platform and Sb is a reference system fixed in the base. Point P is the origin of Sp . 004 by ASME NOVEMBER 2004, Vol. 126 \u00d5 1113 17 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F Figure 3 shows the ith leg, for i51, 2, 3, of the translational 3-URC. With reference to Fig. 3, wj i , j51, 2, 3, and u j i , j51, 2, 3, are the axis\u2019 unit vector and the joint coordinate, respectively, 1114 \u00d5 Vol. 126, NOVEMBER 2004 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/22/20 of the jth revolute pair where the j index increases from the base towards the platform. w4i , u4i , and si are the axis\u2019 unit vector, the angular coordinate, and the linear coordinate, respectively, of the cylindrical pair. ui is a unit vector fixed in the platform and perpendicular to w4i . vi is a unit vector fixed in the base and perpendicular to w1i . Point Ci is the foot of the perpendicular through Ai to the axis of the revolute pair adjacent to the cylindrical pair. Point Bi0 is a platform point lying on the cylindrical pair axis. hi and di are the lengths of the segments AiCi and BiCi , respectively. With this notations and the conventions on the unit vectors shown in Fig. 3, conditions ~i! and ~iii! can be analytically expressed as follows: w1i5w4i , i51,2,3 (1a) w2i5w3i , i51,2,3 (1b) If the three legs of a 3-URC mechanism are separately analyzed, the platform angular velocity, v, can be written in three different ways as follows: v5 u\u03071iw1i1 u\u03072iw2i1 u\u03073iw3i1 u\u03074iw4i , i51,2,3 (2) where u\u0307 j i , j51, 2, 3, 4, are the time derivatives of the joint coordinates u j i , j51, 2, 3, 4, respectively. Taking into account Eqs. ~1!, Eqs. ~2! become v5~ u\u03071i1 u\u03074i!w1i1~ u\u03072i1 u\u03073i",
            ", which is linear and homogeneous, will admit the only solution v50 (4a) ~ u\u03071i1 u\u03074i!50, i51,2,3 (4b) ~ u\u03072i1 u\u03073i!50, i51,2,3 (4c) Differentiating relationships ~2! and taking into account geometric conditions ~1!, the following three different expressions of the platform angular acceleration, v\u0307, can be deduced: v\u03075~ u\u03081i1 u\u03084i!w1i1~ u\u03082i1 u\u03083i!w2i1 u\u03074iw\u03074i 1~ u\u03072i1 u\u03073i!w\u03072i , i51,2,3 (5) where u\u0308 j i , j51, 2, 3, 4, w\u03074i , w\u03072i are the time derivatives of u\u0307 j i , j51, 2, 3, 4, w4i , w2i , respectively. In addition, by considering the notations of Fig. 3, relationships ~1! and the timedifferentiation rule for constant-magnitude vectors, the following analytic expressions of w\u03072i and w\u03074i result: w\u03072i5 u\u03071iw1i3w2i (6a) w\u03074i52~ u\u03072i1 u\u03073i!w1i3w2i (6b) Finally, substituting expressions ~6a! and ~6b! for w\u03072i and w\u03074i , respectively, into Eqs. ~5! and taking into account ~4c! yield v\u03075~ u\u03081i1 u\u03084i!w1i1~ u\u03082i1 u\u03083i!w2i , i51,2,3 (7) Since Eq. ~4c! has been used to obtain Eqs. ~7!, Eqs. ~7! hold when the mechanism does not assume a singular configuration",
            " Since the platform of a translational 3-URC translates when the mechanism is out of singular configurations, the position analysis of a translational 3-URC can be addressed by assuming that the platform orientation is constant and known with respect to the base. This assumption yields that the rotation matrix, Rbp , which transforms the vector components measured in Sp into the vector components measured in Sb , is constant and known. Therefore, the translational 3-URC DPA analytically consists of determining the positions of point P ~see Fig. 2! compatible with given values of the joint coordinates u1i , i51, 2, 3 ~Fig. 3!. On the contrary, its IPA consists in calculating the u1i , i51, 2, 3, values compatible with an assigned position of point P. With reference to Figs. 2 and 3, the constraint equations of a translational 3-URC can be written as follows: w2i\u2022~Bi2Ai!52di , i51,2,3 (9a) ~Bi2Ai! 25hi 21di 2, i51,2,3 (9b) with Bi5P1Rbp p~Bi02P!2siw4i , i51,2,3 (10) where all the vectors are measured in Sb and the bold capital letters without a left-hand superscript point out position vectors measured in Sb , whereas the left-hand superscript p, added to a vector symbol, indicates that the vector is measured in Sp ~Fig. 2!. The substitution of expression ~10! for Bi into Eqs. ~9!, by taking into account condition ~1a! and expanding the resulting expressions, yields the following relationships: w2i\u2022P1w2i\u2022@Rbp p~Bi02P!2Ai#1di50, i51,2,3 (11a) P21p~Bi02P!21si 21Ai 212P\u2022@Rbp p~Bi02P!2siw1i2Ai# 22siw1i\u2022@Rbp p~Bi02P!2Ai#22Ai\u2022Rbp p~Bi02P! 5hi 21di 2, i51,2,3 (11b) rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/22/20 The analysis of Fig. 3 reveals that the analytic expression of the unit vector w2i is w2i5cos~u1i!vi1sin~u1i!w1i3vi , i51,2,3 (12) Since w2i depends only on u1i ~Eq. ~12!!, Eqs. ~11! are a system of six scalar equations in the following nine unknowns: the three coordinates of P, si , and u1i for i51, 2, 3. Therefore, by assigning three out of these nine unknowns, the remaining unknowns can be computed by solving system ~11!. Direct Position Analysis \u201eDPA\u2026. The direct position analysis consists in solving system ~11! for assigned values of the joint coordinates u1i , i51, 2, 3",
            "50 (15) Condition ~15! is verified if and only if the w2i , i51, 2, 3, vectors are all parallel to a single plane. When this geometric condition occurs, the platform can carry out a finite translation along a straight line perpendicular to the plane, the w2i , i51, 2, 3, vectors are parallel to, even if the revolute pairs adjacent to the base are locked. Since each w2i vector is perpendicular to the plane, p i , located by the segment AiCi and the ith leg\u2019s revolute pair axis fixed in the base ~Fig. 3!, condition ~15! is satisfied if and only if either ~I! at least two out of the planes p i , i51, 2, 3, are parallel to each other or ~II! the planes p i , i51, 2, 3, intersect one another in parallel lines. Figure 4 shows the geometric condition ~II!. Finally, since the w2i vectors are given and the coordinates of point P are the unknowns in system ~11a!, it is worth noting that the ith equation of system ~11a! is geometrically represented by a plane perpendicular to w2i and the solution of system ~11a! is the common intersection of three planes, which gives an alternative geometric interpretation of condition ~15!. Inverse Position Analysis \u201eIPA\u2026. The inverse position analysis consists in finding the actuated-joint coordinates for an assigned platform pose. From a geometric point of view, once the platform pose is given, the location of the straight line parallel to w4i and passing through Bi0 is assigned in the ith leg ~see Fig. 3 and geometric condition ~1a!!. This line and the line parallel to it and passing through Ai uniquely locate one plane that is rigidly connected to the plane p i , parallel to w1i and containing the segment AiCi . Thus the plane p i is uniquely located, which brings one to the conclusion that only one value of u1i ~see relationship ~12!! is solution of the IPA of a translational 3-URC. NOVEMBER 2004, Vol. 126 \u00d5 1115 17 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F From an analytic point of view, the inverse position analysis requires the solution of system ~11! for assigned values of the coordinates of point P. If the position vector P is given, at most two values for each si , i51, 2, 3, can be determined by solving Eqs. ~11b! ~in this case, the ith Eq. ~11b! is a quadratic equation whose only unknown is si). Therefore, two positions, lying on a straight line parallel to the unit vector w1i , can be determined for point Ci ~see Fig. 3! in the ith leg. Once the position vectors Ci , i51, 2, 3, are known, the w2i , i51, 2, 3, unit vectors can be computed as follows: w2i5 w1i3~Ci2Ai! iw1i3~Ci2Ai!i , i51,2,3 (16) Since the ith position vector Ci has two values, whose difference is a vector parallel to w1i , expressions ~16! give only one value for the ith unit vector w2i . Expressions ~12! and ~16! make it possible to determine in a unique way the actuated-joint coordinates, u1i , i51, 2, 3, as follows: cos~u1i!5 vi\u2022@w1i3~Ci2Ai!# iw1i3~Ci2Ai",
            " is also the singularity condition that allows all the translation singularities to Transactions of the ASME 17 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F be found and these singularities always make a finite translation of the platfom possible even if the actuated joint are locked. Finally, the analysis of the ith Eq. ~18b! shows that the time derivative u\u03071i is not determined when the following condition holds: ~Bi2Ai!\u2022ni50 (23) Condition ~24! is matched when the vector (Bi2Ai) lies on the plane located by the unit vectors w1i and w2i ~see Fig. 3!. A new translational parallel mechanism ~TPM!, named translational 3-URC, has been presented. The proposed TPM is a special 3-URC architecture where, in each URC leg, ~i! the revolute pair axis fixed in the base is parallel to the cylindrical pair axis fixed in the platform, ~ii! the cylindrical pair axis intersects and is perpendicular to the adjacent revolute pair axis, and ~iii! the axes of the two revolute pairs that are not adjacent to the base are parallel to one another. Its actuated pairs are the three revolute pairs adjacent to base"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003310_1.2400209-Figure14-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003310_1.2400209-Figure14-1.png",
        "caption": "FIG. 14. A schematic sketch showing the placement of the vortices in the opposite-signed symmetric equilibrium in the case N=2.",
        "texts": [
            " It is interesting to observe that in cases a and c , the vortices and cylinder move apart and settle down into a regular motion which for the vortices, interestingly enough, is a leapfrogging sequence. In b the orbits appear to densely fill a compact neighborhood of the equilibrium points and the corresponding cylinder velocity shows rapid oscillations with an envelope that appears to be bounded. Consider now the special case in which 1 = \u2212 2 = . Equilibrium configurations again exist in which the two symmetric vortex pairs are also symmetrically placed about the y axis. In this case, the circulations of the vortices are reflected about the y axis. A schematic sketch is shown in Fig. 14. The equilibrium curve is given by the equation x\u0304*12 y\u0304*2 \u2212 2 + x\u0304*10 \u2212 2 \u2212 8y\u0304*2 + 6y\u0304*4 + x\u0304*8 4 + 39y\u0304*2 \u2212 10y\u0304*4 + 15y\u0304*6 + 4x\u0304*6 1 + 2y\u0304*2 + 20y\u0304*4 + 5y\u0304*8 + x\u0304*4 \u2212 2 + 23y\u0304*2 + 34y\u0304*6 + 10y\u0304*8 + 15y\u0304*10 + 2x\u0304*2 1 + y\u0304*2 3 \u2212 1 + 3y\u0304*2 \u2212 5y\u0304*4 + 3y\u0304*6 + y\u0304*2 y\u0304*2 \u2212 1 2 y\u0304*2 + 1 4 = 0. 14 The curve is plotted in the full space in Fig. 15. There are again four branches of the curve symmetric about the x and y axes in the full space or, equivalently, two branches symmetric about the y axis in the half-space"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001328_3.20929-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001328_3.20929-Figure1-1.png",
        "caption": "Fig. 1 Nomenclature for helicopter near hover.",
        "texts": [
            " Minimax Compensator Design If we could minimize Jw with respect to the compensator parameters Kc while simultaneously maximizing Jw with re- spect to A/7 with a specified norm, we would have the best compensator with the specified order for the worst parameter change with the specified norm. This would optimize the compensator for parameter robustness. This problem is not yet solved. With a norm on disturbances, it is a minimax problem; however, there is no closed-form expression for JW(KC) as there is in Eq. (6). Example: Control of a Helicopter in Hover We consider a helicopter near hover disturbed by horizontal wind gusts (see Fig. 1). We shall evaluate two types of position-hold autopilot designs: one with full state feedback and the other with a dynamic compensator that uses only a measurement of position. We expect that the former designs will be quite robust and the latter designs quite nonrobust to plant parameter changes. The plant model is xu xq -g o Mu Mq 0 0 0 1 0 0 1 0 0 0 6 + -Aftt 0 0 (69) where g is the force per unit mass due to gravity, u the forward velocity, q the pitch angular velocity, 6 the pitch angle, y the postion deviation from desired hover point, 6 the longitudinal cyclic stick deflection, and uw the horizontal wind velocity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000475_ac951033d-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000475_ac951033d-Figure2-1.png",
        "caption": "Figure 2. Reactions of HRP with H2O2 (a-c) and with cyanide (d). The heme moiety and imidazole ring of proximal histidine are illustrated.",
        "texts": [
            " The potential is then stepped to 0 mV, at which H2O2 is reduced but O2 is not (Figure 1B). Therefore, a transient current for H2O2 reduction flows until the accumulated H2O2 is consumed at the PG surface and/or diffused out of the interfacial region. Since this H2O2 reduction current is catalyzed by HRP adsorbed on the PG surface, it is inhibited by cyanide. HRP has a heme moiety as the active center to which the imidazole ring of the histidine residue is coordinated (fifth coordination site). The vacant sixth coordination site of the heme iron(III) is the reaction site for H2O2 (Figure 2, reactions a-c). Therefore, a strong ligand for heme impedes approach of H2O2 to the active site, and as a result, the H2O2 reduction current is depressed (Figure 2, reaction d). Inhibition of the transient reduction current is monitored for the cyanide determination. A PG disk electrode (0.05 cm2) was immersed in a 1/15 M (\u223c0.067 M) phosphate buffer (pH 7.4) containing HRP (from (1) Scheller, F.; Schubert, F. Biosensors; Elsevier: Amsterdam, 1992. (2) Albery, W. J.; Cass, A. E. G.; Mangold, B. P.; Shu, Z. X. Biosens. Bioelectron. 1990, 5, 397-413. (3) Smit, M. H.; Cass, A. E. G. Anal. Chem. 1990, 62, 2429-2436. (4) Smit, M. H.; Rechnitz, G. A. Anal. Chem. 1993, 65, 380-385",
            " On a bare PG electrode, a steady-state cathodic current observed upon the addition of 2 \u00b5M H2O2 was almost negligible at 0 mV vs Ag/AgCl (\u2206i < 0.2 nA). However, for the HRP/PG electrode that had been prepared from 1 g/L HRP solution, a cathodic current was observed upon the addition of H2O2 (2 \u00b5M). The current decreased gradually, and the steady-state response was about 13 nA. Thus, HRP obviously contributes to the electrocatalytic reduction of H2O2. That is, direct charge transfer from compounds I and II of HRP to the PG electrode surface (Figure 2, reactions b and c) proceeds in the absence of any mediators and promoters, as has been reported.7-12 The HRP/PG electrodes obtained from 10 mg/L-10 g/L HRP solutions exhibited similar responses to 2 \u00b5M H2O2: cathodic currents decreased gradually, and the steadystate responses were 10-13 nA. The current decrease before the steady state implies that the H2O2 reduction is probably diffusioncontrolled under these conditions. The H2O2 reduction currents were suppressed upon the addition of NaCN solutions. For the HRP/PG electrode that had been prepared from 1 g/L HRP solution, the depression was observed at a cyanide concentration of g5 \u00b5M (final concentration). The reduction current decreased with increasing cyanide concentration and almost disappeared at 1 mM. This observation clearly indicates that the catalytic activity of HRP is inhibited by cyanide, and it is consistent with the report of Smit and Cass.3 In the case where reaction a in Figure 2 is sufficiently slower than reactions b and c (namely, the rate-determining step is reaction a), the cathodic current density i should be given by where ka is the rate constant for reaction a in Figure 2, \u0393 is the surface coverage of active HRP, C* and C0 are the H2O2 concentrations in solution bulk and on the electrode surface, respectively, D is the diffusion coefficient of H2O2, and d is the diffusion layer thickness. Equations 1 and 2 yield the following relation between i and C*: i ) 2Fka\u0393C0 (1) i ) 2FD(C* - C0)/d (2) i ) 2FC* d/D + 1/ka\u0393 (3) Analytical Chemistry, Vol. 68, No. 9, May 1, 1996 1613 In the presence of cyanide, \u0393 is a function of the cyanide concentration CL: where \u03930 is the intrinsic surface coverage of HRP (total coverage of active and inactive HRP) and K is the dissociation constant (K ) [HRP][CN-]/[HRP-CN-] ) 4 \u00d7 10-6 M13 )"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003409_s0737-0806(84)80050-7-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003409_s0737-0806(84)80050-7-Figure9-1.png",
        "caption": "Figure 9. The linear forces of the metacarpus. P was the force recorded by the load cell.",
        "texts": [
            " There is considerable similarity and a nearly linear relationship between hoof and fetlock angles (correlation coefficients .98 and .99). As the wedges were removed, the fetlock dorsal angle increased as already noted. Also, the force recorded at the upper load cell of the Instron (force, P, equation (5)) dropped as each wedge wag removed.~ This is shown schematically in Figure 8, representative of a series of tests. This is explained as follows. The force, P, the force being measured by the load cell, is equal to the sum of the ground reaction force, F, and the tensile forces in the tendons, as equation (5), (Figure 9). As the wedges were removed, P decreased because, (1) the H force, equation (8) (Figure 7), decreased a s the angle of the pastern increased. That is, F decreased because H decreased with V constant. (2) As the fetlock joint dorsal angle increased, the tensile force in the interosseous medius, SL, decreased. In additional tests, there was a slight decrease of P when the extensor branches were transected. There was, also, a slight decrease when the common extensor tendon was transected just distal to the fetlock and a barely perceptible decrease when the lateral extensor was cut above the fetlock"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003160_0022-0728(85)80080-2-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003160_0022-0728(85)80080-2-Figure1-1.png",
        "caption": "Fig. 1. Anodic E/I curves with a platinum rotating disc electrode for a 1.10 x 10-2 mol dm-3 N204 solution in sulfolane ( + 0.1 mol dm-3 TEAP) at various temperatures. T = 298 (1); 303 (2); 309 (3); 313 (4); 318 (5); 324 K (6).",
        "texts": [
            " The different values for AG, AH and AS, Table 2, are in reasonable agreement with the earlier NMR work in acetonitrile [5]. It should be noted that the thermodynamic stability of N204 in solution increases in the same way as the donicity [15] (DN) of the solvent. The rotating disc voltammograms of N204 dissolved in anhydrous and deoxygenated sulfolane and propylene carbonate containing 0.1 mol dm -3 TEAP are shown in Figs. 1 and 2. The shape of the anodic wave exhibits a dramatic change with temperature (Fig. 1). The height of the wave increases as the temperature increases and the half-wave potential is shifted to lower potentials with the temperature increase: E l ~ 2 = + 1.63 V at 298 K shifts t o El~ 2 - - + 1.50 V at 324 K with 109 reference to the half wave potential of the ferrocene/ferricinium system. We have also noticed that the limiting current as a function of the rotation speed, ~0, of the platinum electrode, is unchanged in the range: 20.9-83.7 rad s -1. In addition, the peak potentials (Ep, E~) of the cyclic voltammograms corresponding to the oxidation of N204 and the reduction of NO~- are almost the same [16] (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003779_s11044-006-9028-0-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003779_s11044-006-9028-0-Figure1-1.png",
        "caption": "Fig. 1 An example for the graph description of a MBS",
        "texts": [
            " An edge J\u03b1 \u2208 is an unordered pair J\u03b1 \u2261 (Bk, Bl ) (for brevity, the notations \u03b1 \u2208 or (k, l) \u2208 and J\u03b1 \u2261 (k, l) are used). A spanning tree of is denoted as G = (B, J G), and the corresponding cotree as H ( , G) = (B, J H ), or simply as H. Vertex B0 is chosen as the root of the tree. J G is the set of tree joints, and J H := J\\J G is the set of cut-joints. G comprises n tree joints. Let Gd be the directed tree w.r.t. to the root B0, that is the directed subgraph of G such that to every vertex there is a path starting from the root of G (Figure 1). The directed tree induces the following ordering relation of joints and bodies w.r.t. topological tree: Bl is the direct predecessor of body Bk , denoted with Bl = Bk \u2212 1, (l = k \u2212 1 for short) iff1 (k, l) \u2208 Gd , J\u03b2 is the direct predecessor of joint J\u03b1 , denoted with J\u03b2 = J\u03b1 \u2212 1 (\u03b2 = \u03b1 \u2212 1 for short) iff J\u03b2 = (\u00b7, k) \u2208 Gd \u2227 J\u03b1 = (k, \u00b7) \u2208 Gd , J\u03b2 is a predecessor of joint J\u03b1 , denoted with J\u03b2 \u2264 J\u03b1, iff there is a finite m, such that \u03b2 = \u03b1 \u2212 1 \u2212 1 \u00b7 \u00b7 \u00b7 \u22121 (m times \u22121). Note that possibly k \u2212 1 = l \u2212 1 for k = l. For, e.g., in Figure 1, J1 = J2 \u2212 1, J2 = J6 \u2212 1, J6 = J7 \u2212 1, so that J1 < J7. For each body Bk , there is a unique tree joint J\u03b1 1(k, l) \u2208 Gd means that Bk is the source and Bl is the target of the edge. Notice that (l, k) /\u2208 Gd , since Gd is directed. Springer connecting Bk to its predecessor, i.e., J\u03b1 = (\u00b7, k) \u2208 Gd . This fact will be denoted with \u03b1 = J (k) (Body Bk is connected to Bk\u22121 via J\u03b1). Finally, Jroot (k) denotes the smallest \u03b1 \u2264 J (k). This is the index of the joint connecting the branch containing Bk to the ground B0. In Figure 1, J (6) = 7, J (5) = 6 and Jroot(k) = 1 for all k. An orientation of G w.r.t. Gd is an indicator function s such that s(J\u03b1) = 1 or s(J\u03b1) = \u22121 if J\u03b1 \u2208 G is, respectively, positively or negatively orientated w.r.t. Gd . Also, s(\u03b1) is used for short. Springer 2.2 Kinematics of tree-topology systems An inertial frame (IFR) is fixed at the ground B0. The configuration of body Bk is expressed as C k \u2208 SE (3) C k = ( E p 0 1 ) , with E \u2208 SO (3), p \u2208 R3, (1) with the rotation matrix E and the position vector p describing the relative rotation and displacement of the body-fixed reference frame (RFR) w",
            "3 Constraints for kinematic loops: cut-joint constraints MBSs with kinematic loops are described as MBS with tree topology subject to holonomic constraints. The tree kinematics is built upon a chosen spanning tree as in the preceding section, and holonomic constraints describe the closure conditions imposed by the cut-joints J\u03b1 , \u03b1 \u2208 H . Each FL comprises exactly one cut-joint. Therefore, and to account for this oneto-one correspondence, the FL containing cut-joint J\u03b1 is denoted with \u03b1 . Body Bk is the root body of the FL iff Bk < Bl\u2200l \u2208 \u03b1 . For, e.g., in Figure 1, the root body of 8 is B2 and that of 3 is B1. Denote with H d the directed cotree such that all J\u03b1 \u2208 H are positively orientated. The geometric closure condition for \u03b1 with cut-joint J\u03b1 \u2261 (l, k) \u2208 H d is M\u22121 \u03b1 C\u22121 l C k = e Z\u0302 \u03b11 q\u03b11 . . . e Z\u0302 \u03b1\u03bd q\u03b1\u03bd . (16) Equation (16) contains the cut-joint variables q\u03b1i , which are no generalized coordinates. Moreover, they yield the joint motion that must not be constrained. The closure constraints are the independent components of the relative configuration M\u22121 \u03b1 C\u22121 l C k for which the right- hand side of Equation (16) is identically zero",
            " Clearly, the relative configuration of the two bodies only depends on the joints that comprise the FL \u03b1 , so that the right-hand Springer side of Equation (16) is given in terms of the relative configurations of these joints: M\u22121 \u03b1 C\u22121 l C k = M\u22121 \u03b1 R\u22121 \u03b3 R\u22121 \u03b3\u22121 . . . R\u22121 r (l) R r (k) . . . R \u03b2\u22121 R \u03b2 , where \u03b2 = J (k), \u03b3 = J (l). r (k) and r (l) denote the indices of the joints that connect to the root-body of the FL, that is r (k) \u2264 J (k), r (l) \u2264 J (l) and r (k) \u2212 1 = r (l) \u2212 1. For, e.g., in Figure 1, the root-body of 8, with cut-joint J8 \u2261 (7, 6), is B2, and r (6) = 6 and r (7) = 9. In Equation (18), the summation over generalized velocities of the loop joints is sufficient. Assumption 1. It is assumed hereafter that the motion space of the cut-joint J\u03b1 is a subgroup, so that (19) is valid. Springer In order to determine redundant equations in the system of cut-joint constraints (19), it is necessary to investigate the vector space of relative velocities of the bodies Bl and Bk , that can possibly occur in the tree topology system, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003779_s11044-006-9028-0-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003779_s11044-006-9028-0-Figure2-1.png",
        "caption": "Fig. 2 Relative kinematics of two bodies Bl and Bk connected by joint J\u03b1",
        "texts": [
            " Gd is an indicator function s such that s(J\u03b1) = 1 or s(J\u03b1) = \u22121 if J\u03b1 \u2208 G is, respectively, positively or negatively orientated w.r.t. Gd . Also, s(\u03b1) is used for short. Springer 2.2 Kinematics of tree-topology systems An inertial frame (IFR) is fixed at the ground B0. The configuration of body Bk is expressed as C k \u2208 SE (3) C k = ( E p 0 1 ) , with E \u2208 SO (3), p \u2208 R3, (1) with the rotation matrix E and the position vector p describing the relative rotation and displacement of the body-fixed reference frame (RFR) w.r.t. to the IFR. A joint J\u03b1 \u2261 (l, k) is characterized by three consecutive transformations (Figure 2): the constant transformation S \u03b1,l from the RFR to the joint frame (JFR) on Bl , the constant transformation S \u03b1,k from the RFR to the joint frame (JFR) on Bk , the variable transformation due to the joint\u2019s DOF. The variable transformation is expressed as a series of successive screws, i.e., 1-DOF, motions. For, e.g., a revolute joint allows for rotations about its axis of revolution, a prismatic for translations along its joint axis, a universal joint comprises successive rotations about mutually orthogonal axes of revolution, while a spherical joint is considered as three consecutive rotations. If J\u03b1 has a DOF2 \u03bd, the individual intermediate one-parametric motions are given in terms of a set of relative (generalized) coordinates for J\u03b1 , denoted with q\u03b11 , . . . , q\u03b1\u03bd , and a set of screw coordinate vectors Z \u03b11 , . . . , Z \u03b1\u03bd (Figure 2). The screw coordinate vectors are expressed in the joint frame on either Bl or Bk , depending on which one is the source according to the orientation of J\u03b1 . Given a topological tree G for the MBS, then the configuration of body Bk is determined by that of its predecessor and by the relative transformation R \u03b1 due to the tree joint J\u03b1 connecting 2Indeed the DOF is diffierent for the particular joints, which should be indicated by \u03bd\u03b1 . For simplicity the joint index will be omitted, however. Springer Bk and Bk\u22121 [11] C k = C k\u22121 R \u03b1 , \u03b1 = J (k) (2) The transformation due to the tree joint J\u03b1 \u2261 (l, k) \u2208 Gd (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001024_978-1-4757-5070-6_3-Figure3.40-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001024_978-1-4757-5070-6_3-Figure3.40-1.png",
        "caption": "FIGURE 3.40. (Continued).",
        "texts": [
            " At a finite thickness existence of the plateau depends on the ratio between d and the screening length of the polymer phase Lljfly or d\u00bb Lljfly (69) ( E RDl/2 Lpoly = -p- [(k + k N )k C S ] -1/4 D 8;rF2 ox K ox X (70) The ratio between d and L1fflY can be expressed by dimensionless constants d {[ (Fcf>Me)] } 114 L1fflY = {) NK + Nox exp RT Nx (71) Several different types of profiles cf>(Xi) can be expected when the metal potential is varied in the positive direction. Among them the most interesting variants for electro active materials are as follows: 1. Within the whole interval of available metal potentials, Eqns. 72 and 73 are fulfilled (72) (73) Then according to Eqns. 68 and 71, the concentration of cations cIJ(ly is much greater than that of electronic species Cox, and the profile ~(x) is 432 KARL DOBLHOFER AND MIKHAIL VOROTYNTSEV 90 Polymer 60 -60 -90 a FIGURE 3.41. See Fig. 3.40. Transformation of the potential distribution from the membrane type into the electronic one by sweeping the polarization in the positive direction. (From Ref. 162.) (a) Variation of the metal solution potential difference NK = Nx = 1 (equal resolvation energies of cations and anions in the film), Nox = 1. (b) Variation of Nox (i.e., the electronic energy in the polymer phase or the bulk electrolyte concentration CS ), NK = Nx = 1, Nox = 0 (a), 0.01 (b), 0.1 (c), 1 (d). There is no marked effect at negative polarization, but there is a strong shift of the plateau value of <P(x) at positive polarization",
            " Therefore in this case there is a plateau region inside the polymer phase whose potential is independent of the polarization, so that the variation of cl>Me leads to a parallel shift of the metal/polymer potential drop within the interfacial region. The potential drop across the polymer/electrolyte interface is determined completely by ionic equilibria, as discussed in Sections 2.3, 3, and 4.1. Since such potential profiles are characteristic of electrodes THE MEMBRANE PROPERTIES OF ELECTROACTIVE POLYMER FILMS 433 90 Polymer 60 d 30 c ~ ~ 0 e \"- '0 :g Xi ~ ~ w -30 -60 -90 b FIGURE 3.41. (Continued). coated with membrane films, we can refer to this case as membrane behavior of electroactive materials. Fig. 3.40 illustrates this case. 2. Equation 73 is again fulfilled, but within the accessible potential range of the metal, there is a point cl>Me* at which concentrations of electrons and coions in the film are identical. Then at more negative potentials, the effect of electrons on the profile is again negligible, and the picture corresponds to Case 1. However when the metal potential has passed through cl>Me*, electrons (and counterions) determine the profile. Within this polarization interval the plateau is retained, but its potential becomes strongly dependent on cl>Me"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000698_1.1326030-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000698_1.1326030-Figure4-1.png",
        "caption": "FIGURE 4. The elevation of the long axis is considered as a rotation of the long axis from a0 to a1 about a rotation axis presented by unit vector n that is perpendicular to the plane formed by initial attitude a0 and final attitude a1 of the long axis, and is defined as n\u00c4a0\u00c3a1 \u00d5za0\u00c3a1z. Axial rotation angle g can be about a0 before the long axis rotation or about a1 after the long axis rotation.",
        "texts": [
            " In this paper, the three-dimensional rotation of a limb segment or joint is considered to be composed of two primary rotations\u2014a long axis rotation and an axial rotation. There are two possible combinations for the two rotation sequences. The first is an axial rotation followed by a long axis rotation. In this sequence, the axial rotation of an angle g is about the long axis at initial position a0 , and the long axis rotation of angle b is from initial position a0 to position a1 about an rotation axis with an unit vector n in the reference coordinate system XYZ ~Fig. 4!. The second rotation sequence consists of a long axis rotation followed by an axial rotation. The long axis rotation in this case is the same as in the first, but the axial rotation of an angle g is about the long axis at displaced position a1 . In the follow paragraphs we will derive an integrated rotation matrix for each of the two rotation sequences and show that the two integrated rotation matrixes are the same. Therefore, the sequence independence of the long axis rotation and the axial rotation can be proved and a unique integrated rotation matrix can be obtained. The integrated rotation matrix of each rotation sequence can be obtained by multiplication of two rotation matrices: one rotation matrix describing the long axis rotation and another rotation matrix describing the axial rotation. We first investigate the long axis rotation to obtain its rotation matrix. The long axis rotation ~Fig. 4! from initial position a0 to position a1 by an angle b about axis n can be described by a rotation matrix Rl(b ,n) as a15Rl~b ,n!a0 , ~15! where a05e1 ~16! can be written as a05@a0#5@e1#5F 1 0 0 G . ~17! e1 is the unit vector of the X axis. The matrix form of unit vector a1 can be written in terms of three compo- nents a11 , a12 , a13 in the reference coordinate system or in terms of two angles a, b in the spherical rotation coordinate system as a15@a1#5F a11 a12 a13 G5F cos b sin b cos a sin b sin a G "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001551_robot.1996.503859-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001551_robot.1996.503859-Figure6-1.png",
        "caption": "Figure 6: Initial configuration of the space robot",
        "texts": [
            " The arrangement of each links and joints is given in Fig.5. The positions of the center of mass of each link are assumed at the geometric center of the link. The initial state of the space robot is q = ( ~ 1 3 , - ~ / 3 , ~ / 3 , - - ~ / 3 , ~ / 3 , -~/3)*[rad] with the configuration of Fig.5 as the origin. The desired trajectory is t o move the end-effector for l[s] at the constant speed 0.5[m/s] in the positive x-axis direction with the satellite orientation maintained. The initial configuration and the desired trajectory are given in Fig.6, where the broken line stretched from the end-effector denotes the desired trajectory. X 0 :joints Figure 5: Structure of a space robot Figure 7 shows the satellite orientation variation in response to the end-effector desired trajectory without spiral motion. The solid, broken and chained line denotes the 3 vector elements of the Euler parameters in the order. Figure 8 shows the same motion every 0.2[s]. The results of the single-turn spiral motion are shown in Figs.9 through 11. In Fig.9, the solid line denotes xcoordinates variation of the end-effector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003264_j.jmatprotec.2004.01.030-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003264_j.jmatprotec.2004.01.030-Figure8-1.png",
        "caption": "Fig. 8. The seventh order of the mode shape.",
        "texts": [
            " Normal velocity root-mean square values of some selected points of the gearbox are shown in Table 2. Radial and axial vibration velocity root-mean square values of the transmission system are shown in Table 3. The normal vibration velocity in the frequency-domain of a node (No. 39078) of the gearbox model is shown in Fig. 5. Radial displacement vibration in the time-domain of input-end shaft is shown in Fig. 6. Radial displacement vibration in the time-domain of the output-end shaft is shown in Fig. 7. The seventh order of mode shape of the gearbox with the input shaft is given in Fig. 8. Value of calculation 0.0258 0.0518 0.1913 0.0739 0.0360 0.0454 The following conclusions may be drawn from the results of FE dynamic analysis of the gearbox: 1. The curve of meshing stiffness can be computed using a 3D contact finite element method for gearing. The curve of error may be expressed by a simple harmonic function. A procedure using a numerical simulation method for gear meshing dynamic excitation analysis has been introduced. 2. A 3D finite element model for dynamical analysis of the speed-increase gearbox was created with a view to studying its normal characteristics and its vibration response"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002525_s0022-460x(85)80146-2-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002525_s0022-460x(85)80146-2-Figure8-1.png",
        "caption": "Figure 8. Half-section views of a meridionally symmetric mode for N = I with dominant mot ion in both transverse and meddional directions. M W = 5, M U = 4.",
        "texts": [
            " The 3-D graphical display software was then used to study the predicted natural mode shapes. Figures 6(a) and 7(a) display two major spin modes for N = 0. It is noted that the 3-D tire mode shapes presented in this paper are exceptionally enlarged for the purpose of illustration. Since the displacements ofthe two modes are in the circumferential direction, their side views, as shown in Figures 6(b) and 7(b), further illustrate the details of these mode shapes. In order to observe the N = 1 transverse mode shown in Figure 8(a), the same view with 90-degree rotation about the tire axis, as shown in Figure 8(b), appears to be quite informative. It is of interest to illustrate a natural mode shape composed of displacements in all the w, u and o directions. The side view of one of these mode shapes is shown in Figure 9(a), and a half-section view is shown in Figure 9(b). Since the present computer graphics software can plot the 3-D views for any mode shape from the various viewing angles, a more thorough understanding of the tire natural mode shapes can be achieved. Experimental natural frequencies were measured on the P185/80R13 tire in the following manner"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000964_robot.1991.131992-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000964_robot.1991.131992-Figure6-1.png",
        "caption": "Fig. 6. Example of a precedence graph",
        "texts": [
            " to pick up an object) but not the way this goal can actually be achieved (e.g. FIND(Object), APPROACH, GRASP(Object), DEPART(0bject)). In contrast to the explicit command interface of the robot (EEOs, see Chapter 2), these operations are called Implicit Elementary Operations (LEOS). At execution time, each IEO is decomposed into a sequence of explicit robot commands (EEOs) depending on the present state of the robot's environment. The complete set of sequence constraints of an assembly is represented by using a precedence graph (PG), Fig. 6. Two nodes A and B are connected by an arc A+B if the corresponding operations are in order OA e OB. Because and Background Knowledge target station. Having reached this position, a sensorguided docking manceuvre is started which results in a defined spatial contact between the robot and the target station. The two manipulators are now located above the surface of the work table (Fig. 4). To initialise the assembly, KAMRO activates its onboard camera system and determines the position and orientation of the parts on the work table"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003828_tmag.2005.844561-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003828_tmag.2005.844561-Figure5-1.png",
        "caption": "Fig. 5. Thin air gap synchronous machine with polar pieces. Mesh 1 with 81 edges on .",
        "texts": [
            " The rotor displacement step is set in a way that five steps are necessary to overpass one element on . Fig. 4 shows better results with the MEM than MB, for first order interpolation on . As shown in Fig. 4, the experimental and simulation results are in very good agreement. Only with a zoom can we see the oscillations due to the movement. With second order the oscillations due to the movement are eliminated in the two methods. For this machine, which has a thin airgap (0.3 mm) with iron in both sides, two discretizations are used: mesh 1 with 81 edges (Fig. 5) and mesh 2 with 162 edges on both interface sides. The airgap has two layers of quadrilaterals elements. The interface is placed between them for MEM and the MB is placed in the lower one. Although a nonregular mesh in the airgap (dense near the rotor tooth corners and coarse in the airgap regions between tooth) may produce better magnetic induction results concerning torque evaluation, for the e.m.f., as it is calculated on the coils (relatively far from de airgap), a regular mesh avoids very deformed elements (producing discontinuities) and the final results are better with the regular mesh"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003053_02678299008047378-FigureI-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003053_02678299008047378-FigureI-1.png",
        "caption": "Figure I . Definition of the vectors in the present model. Here n is the director along the average direction of the long molecular axes. v and c are the layer normal unit vector and the c director, respectively. p is defined by v x c . a denotes the wave vector.",
        "texts": [
            " According to the conventional terminology of the ferroelectricity of SE liquid crystals [ 11, let us call the total contribution of the piezo and flexoelectricities as ferroelectricity in the ferroelectric SE liquid crystal. In this sense we have certainly to distinguish the ferroelectricity in liquid crystals from that in solids [ 11. Now we shall first note that c and v are related to the n director by the following relation: n = vcos0 + c s i n 0 , (4) where 0 is the molecular tilt angle with respect to the layer normal and is assumed to be constant throughout the material in the present model (see figure I). Here it is convenient to introduce an auxiliary unit vector p defined by p = v x c . ( 5 ) then c-p-v make a right handed orthogonal triad. Since v and c are assumed to be genuine vectors as well as P,, p is axial. It is noticeable that P, is introduced as a vector independent of p = v x c in the present model although P, is often assumed to be always parallel to p in a simple treatment [I]. Now a scaler quantity K(r) is assumed to be related to a(r) and v(r) = a(r)/la(r)l in the following manner: a(r) = 11 + Kcr>>v<r>, (6 a) or K(r) - a(r) - v(r) - 1, (6 b) D ow nl oa de d by [ D uk e U ni ve rs ity L ib ra ri es ] at 1 0: 40 0 7 D ec em be r 20 15 654 M"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002597_j.chaos.2004.06.052-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002597_j.chaos.2004.06.052-Figure5-1.png",
        "caption": "Fig. 5. Dynamics of the beam system alone computed for b = 0.73, n = 0.005 and X = 0.842: (a) basins of attraction for period 3 and period 1 motion, (b) phase plane for period 3 motion.",
        "texts": [
            " However, such phenomena are usually found for parameters which in the given system would be physically meaningless. Chaotic motion as shown in Fig. 4 is rare in our system until the system is forced with an amplitude approximately 10 times greater than the length of the beam. This behaviour, though interesting, is not realistic. See Fig. 4. As the forcing amplitude is brought down the rich dynamics become less prevalent, with chaos disappearing. However, coexisting attractors as well as subharmonic and superharmonic motion can occur for significant parameter ranges. Fig. 5(a) shows the basins of attraction with the coexistence of two attractors, one period three, the other period one. Fig. 5(b) shows the phase plane of the period three attractors, note that the oscillations are still greater than beam length, and thus physical reality is yet to be applied. When the forcing amplitude and the magnitude of oscillations are within beam length, the system is behaving within the boundaries of physical realism. As before, with the reduction in magnitude of oscillations comes a loss of complex dynamical responses across an increasing parameter range. However, interesting nonlinear behaviour can be found with even modest values for angle of deflection from equilibrium position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002531_rspa.2004.1439-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002531_rspa.2004.1439-Figure3-1.png",
        "caption": "Figure 3. Representation of the single state of self-stress (a) and mechanisms (b)\u2013( j), of rings of rotating tetrahedra, shown as decorations of a torus. For NZ6: (a) shows A00 2; (b) shows A00 1. For NZ8: (a) A1u; (b) A2u; (c) B1g; (d ) B1u. For NZ10: (a) A 00 2; (b) A 00 1; (c) and (e) E0 2; (d ) and (f ) E00 2. For NZ12: (a) A1u; (b) A2u; (c) and (e) E2g; (d ) and (f ) E2u; (g) B1u; (h) B1g. For NZ14: (a) A 00 2; (b) A 00 1; (c) and (e) E 0 2; (d ) and (f ) E 00 2; (g) and (i) E 0 3; (h) and ( j) E 00 3.",
        "texts": [
            "18) resolves into separate expressions for the symmetries spanned by the states of self-stress and mechanisms: G\u00f0s\u00deZG3; (4.19) G\u00f0m\u00deZGz C\u00f0GL KGTKGR\u00de; (4.20) valid for generic configurations of rings with even NR6. The angular-momentum description of GL (equation (4.3)) gives a physical picture of the sets of mechanisms for NO 6 that are additional to the characteristic anapole rotation. As noted earlier, (GLKGTKGR) has terms of two types. In DNh, the representations E2g, E3u, E4g,. are those of scalar cylindrical harmonics, which can be visualized with appropriate patterns of shading on the torus (figure 3c,e,g,i). A given En(g/u) in this series describes a pair of functions that are interconverted on rotation of p/2n about the main toroidal axis, each having n nodal planes containing that axis. Both members of the pair are symmetric with respect to reflection in the horizontal mirror plane. The alternative representations E2u, E3g, E4u,. are those of vector cylindrical harmonics, and describe pairs of vector fields on the torus, again interconverting under rotation by p/2n and again having n nodal planes containing the vertical cylinder axis, but now antisymmetric with respect to reflection in the horizontal plane; each vector symmetry is related to a scalar harmonic symmetry through multiplication by Gz (Eng!A1uZEnu). The vector harmonics can also be visualized with appropriate shading of the torus (figure 3d,f,h,j). Physical models of the mechanisms of the ring of tetrahedra follow from the visualizations of figure 3; for simplicity, we shall consider these in the standard setting. The case NZ12 is shown in the standard setting in figure 4. The ring of N tetrahedra in the standard setting has N/2 vertical and N/2 horizontal hinges. A full description of the mechanisms is given if the freedoms of these two sets of hinges are treated separately, considering in turn one set to be locked and the other free to move. Consider initially the case where the horizontal hinges are locked. The freedoms of a planar cycle of rigid bodies connected pairwise by N/2 perpendicular revolute hinges can be represented by sets of N/2 scalars (C for opening, K for closing, say)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000413_s11661-000-0143-x-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000413_s11661-000-0143-x-Figure4-1.png",
        "caption": "Fig. 4\u2014Diagram illustrating the locations in the weld where residual stress determination was carried out using the neutron diffraction technique.",
        "texts": [
            " For the purposes of the present experiment, the testpieces The residual-stress state in the testpiece welded at a 120 mA defocus was characterized using the neutron diffractionwere mounted on a purposely built fixture that imposed no constraint or loading other than that by gravity. This allowed technique at the ISIS facility of Rutherford Appleton Laboratory (Didcot, Oxfordshire, United Kingdom). The measure-the free deformation of the testpieces during welding and on subsequent cooling. Thermal isolation was achieved by ments were performed at seven measurement locations across the center of the testpiece, as illustrated in Figure 4.inserting glass slides between the sample and fixture. METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 31A, SEPTEMBER 2000\u20142263 believed that the treatment of the composite diffraction pattern as a single pattern does not generate erroneous results.[22] Consequently, the average strain in the sample was obtained by performing a Reitveld refinement on each full spectrum, Fig. 3\u2014Schematic illustration of the two modes of distortion considered assuming only a single-phase fcc material. Conversion ofin the present article: (a) angular distortion and (b) cambering"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002015_bf02996108-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002015_bf02996108-Figure2-1.png",
        "caption": "Fig. 2",
        "texts": [
            "1 Experimental setup Parameters governing the workings of the hydrostatic sliding bearing precedently mentioned can be explained theoretically with certain assumptions, but experimental determination of the values closest to reality is the most favorable scientific approach. In this study, the effects of slippers, which enhance the efficiency of axial piston pumps and motors on lubrication are examined under various working conditions. An experimental setup has been designed to examine the performance of slippers, in various working conditions of the axial piston pump. The schematic experimental setup is shown in Fig. 2. Copyright (C) 2003 NuriMedia Co., Ltd. (a) Fig. 3 (b) Part No Par t Name I stud bolts 2 t o p table 3 hotlom tame _ _ 5 h ostafic bearm oil e x i ~ 7 I oll barricade -- T ~ ' I moving plate in vertical d~rection cylinder cov~r cJ.Imdcr block \" hydrostatic bearing The main setup Fazd Canbulut, Cem S]nanoght and ~ahin Yildirim 436 with control and measurement devices. 3.2 Main test unit The slippers in axial piston pumps and motors working on the hydrostatic bearing principle were taken into account in this study"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003335_0020-7403(81)90025-4-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003335_0020-7403(81)90025-4-Figure10-1.png",
        "caption": "FIG. 10. An example of a pure shear plane deformation, through a discontinuity plane a of any orientation with respect to the vectors \u2022 and i.",
        "texts": [
            " This is simply a geometrical consequence of the equality of the normal components e. and i.. The velocities parallel to e in the first half-space and to i in the second, are obviously parallel to the plane containing e and i: also the discontinuity between the tangential components i , - e , = l - e of the velocities, is parallel to the same plane: hence the deformation of a solid element, which is displaced parallel to e in the first half-space, and parallel to i in the second, is a pure shear plane deformation, as is illustrated in Fig.10. It is not possible to obtain a spatial deformation by a pure homogeneous shear through a plane of any orientation. This fact is very interesting, and was used to make the SERR kinematical model of three-dimensional deformation, which is the natural extension of the PERR model, concerning the plane deformation. Such a model can be described as follows: three-rigid regions in the space are considered, see Fig. 11, which are separated by two shear planes a and LO; the discontinuities of the velocities AV"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002135_026387602753581980-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002135_026387602753581980-Figure10-1.png",
        "caption": "Figure 10. (a) Flat sheet membrane ow cell; (b) cross-corrugated membrane ow cell.",
        "texts": [
            " The catalysed plate reactor concept15 is yet another innovative PI technology for achieving ef cient heat transfer for performing exo and endothermic reactions on opposite sides of a catalysed plate. A schematic diagram representing the coupling of Trans IChemE, Vol 80, Part A, April 2002 methane steam reforming and combustion of methane can be seen in Figure 9. This technology enables the reduction in the size of equipment by several orders of magnitude, and eliminates NOX emissions as the process is operated at lower temperatures. Cross-corrugatedmembrane modules, as shown in Figure 10, offer the potential of developing multi functional units for performing reaction as well as product separation in one miniaturized module16. The use of microporous membrane to a reaction system is a relatively new method of solving various reaction=separation problems. Miscible uids may be kept apart to control the rate of transport of reactant or product, and thereby controlling the overall reaction rate. Alternatively, the membrane may be designed to be permselective; that is to say it will allow a desired species to pass through it, say the product of an organic synthesis, while holdingbackanother, say a byproduct,or unreactedfeed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002767_978-3-642-71015-5-Figure2.19-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002767_978-3-642-71015-5-Figure2.19-1.png",
        "caption": "Fig. 2.19. Metal sheet moving in air gap of rectangular electromagnet",
        "texts": [
            " To this end, two idealized cases will be considered: (a) a conducting sheet of \"infinite\" horizontal extent; (b) a conducting sheet \"infinite\" in the direction of motion, but of finite width. The initial braking problem is formulated in analogy to the cases outlined in Sects. 2.2 - 4, i.e., an \"infinite\" horizontal nonmagnetic metal sheet, of thickness L1 and electrical conductivity a, glides at a constant speed v along the x-axis in the very narrow air gap of a direct-current electromagnet whose pole pieces are rectangular (Fig. 2.19). With the reaction field disregarded as in (2.3.15), what is the braking force acting on the sheet? The electromagnetic analogy introduced in Sect. 2.3.2 is now somewhat ex tended so as to cover the specific problem under consideration. The stream function D satisfies here the differential equation, compare (2.3.28), a2D + a2D = -(aL1)v 8Bz(x, Y) , ax2 ay2 ax (2.5.1) again with the induction component Bz = Bz (x, y) prescribed in the z = 0 plane; the magnetic vector potential of the above analogy once more obeys exactly (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002149_sme-120001477-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002149_sme-120001477-Figure5-1.png",
        "caption": "Figure 5. Modeling of a 2 d.o.f. universal joint.",
        "texts": [
            " This allows us to define the so-called augmented position vectors: diiz \u00bc z i \u00fe dii, for center of mass CMi; dijz \u00bc z i \u00fe dij, for joint connection point Oj. . a relative angle if i is revolute (units\u00bc [rad ]), characterizing the rotation along the unit vector e\u0302 i of body frame fX\u0302 i g with respect to body frame fX\u0302 h g. Since O0i \u00bc Oi for a revolute joint, zi\u00bc 0. More elaborate joints (spherical, universal, or even a general 6 d.o.f. joint*) can be straightforwardly modeled as a succession of these elementary joints and intermediate fictitious bodies, as shown in the example of Fig. 5 which refers to the universal joint of Fig. 3. A fictitious body i has neither dimension (Ii\u00bc 0; d j\u00bc 0 8 body j child of i) nor mass (mi\u00bc 0; Ii\u00bc 0), but is considered in the same way as other bodies in the multibody topology (numbering, filiation). These additional fictitious bodies do not affect the symbolic results provided by ROBOTRAN nor, thus, the resulting Figure 4. Elementary joint. *For instance, between a \u2018\u2018flying\u2019\u2019 body and the base. 36 FISETTE ET AL. D ow nl oa de d by [ U ni ve rs ity o f C on ne ct ic ut ] at 0 8: 14 2 8 O ct ob er 2 01 4 ORDER REPRINTS performances, since all zero quantities are simply disregarded during the symbolic manipulations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000974_20.717704-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000974_20.717704-Figure5-1.png",
        "caption": "Fig 5 Supplied energy duiing the magnetizing piocess",
        "texts": [
            " These expressions assume a linear-rigid model for the magnet which accounts for the variation of energy or coenergie from the remanent or coercitive point to the working point B. They obviously do not represent correctly the actual energy implied in the non linear magnetizing process. That energy will be called \"intrinsic magnetic energy\". The value of this intrinsic magnetic energy is unknown. At least, no clear value is given. Indeed, each permanent magnet material has his own behaviour when submitted to an exterior magnetic field. Fig. 5 presents the energy supplied during the magnetizing process. This supplied energy is the total energy supplied magnetically by the magnetizing circuit used to magnetize the magnet. This total energy is the energy that must be supplied to saturate the magnet. In any way that energy represents the stored magnetic energy. Indeed, only a part of this supplied energy is stored in the magnet under magnetic form. The necessary energy to magnetize the magnet is, in the most of the cases, over two to twenty times the energy of the single magnet [8]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002151_j.wear.2004.08.002-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002151_j.wear.2004.08.002-Figure1-1.png",
        "caption": "Fig. 1. (a) Thin walled plates model used to obtain 1.5, 2, 3, 4 and 9 mm thickness samples, (b) detail of the plate dimensions in mm [11].",
        "texts": [
            "1 mg precision scale and then converted into volume loss, assuming densities of 7.0 and 7.8 g/cm3 for iron and steel, respectively. Each E value reported, corresponding odulization procedures were carried out by using convenional techniques in a 30 kg ladle with nodulization pocket. he chemical composition of the melts, listed in Table 1, as determined by means of a Baird spark emission optic pectrograph. Plates of different thickness, for abrasion samples, were btained by using the model shown in Fig. 1 [11] and stanardized 13 and 25 mm Y-blocks (ASTM A 395). All the cast amples were then heat treated in order to obtain the desired atrix microstructures and to eliminate any carbide preciptated during the solidification process [7]. Table 2 lists the eat treatment cycles used in order to obtain fully ferritic, earlitic, martensitic and ausferritic matrices, respectively. able 2 ample identification, heat treatment parameters and hardness ample identification Heat treatment Temperature/tim austenitizing, T erritic Ferritizing 910 \u25e6C/180 min earlitic Normalizing 910 \u25e6C/120 min artensitic Q&T 910 \u25e6C/120 min usferritic Austempering 910 \u25e6C/120 min AE 1010 Ferritizing 900 \u25e6C/180 min Furnace 198 Air 312 Water quenched and tempered @ 250 \u25e6C 700 Salt bath @ 280 \u25e6C 435 Furnace 136 to the different nodule count and matrix combination, was obtained from a group of three individual tests"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001024_978-1-4757-5070-6_3-Figure3.31-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001024_978-1-4757-5070-6_3-Figure3.31-1.png",
        "caption": "FIGURE 3.31. Equilibrium state of PANI-E/PVS-a molecular mixture of polyaniline- and poly(vinyl sulfonate) chains-in equilibrium with an HCI solution (see Fig. 3.30 and the text for further explanations).",
        "texts": [
            " First, H+ is partitioned into the polymer matrix (34) Second in the polymer matrix, the protonation/deprotonation of PANI-E proceeds (PANI-E)H+ :;:= H;o/y + PANI-E (35) According to Eqn. 35 (PANI-E)H+ constitutes a Br~nsted acid, for which the dissociation equilibrium was characterized by a value of pKa = 5. (88) Like the PMPy /PSS example, polyaniline can be prepared in the presence of poly(vinylsulfonate), PVS. Volta-potential experiments demonstrated(88) that the produced PANI-E/PVS matrix constitutes a cation exchanger, also in the protonated state. The protonation/ deprotonation equilibrium in the PANI-E/PVS matrix is illustrated in Fig. 3.31. It is important to consider that the protonation/deprotonation equilibrium involves the concentration (activity) of protons in the polymer. However in experiments the activity of H:Jm i.e., the pH of the bathing solution, is controlled. Therefore the membrane state of the polymer, i.e., the Donnan potential, which affects the partitioning 412 KARL DOBLHOFER AND MIKHAIL VOROTYNTSEV PANI-E (base form = electronic insulator) equilibrium of protons, influences the acid/base equilibrium state. This fact can be demonstrated conveniently via the conductivity of the polymer, which is directly related to the degree of protonation in the PANI-E matrix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002848_0020-7462(84)90034-9-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002848_0020-7462(84)90034-9-Figure2-1.png",
        "caption": "Fig. 2. Deformed configuration of axi-symmetrically loaded membrane.",
        "texts": [
            " (6) The set of-equations (3)-(6) describes any axi-symmetr ical ly wrinkled region completely and can be solved analytically or numerical ly depending on the form of the function for q. If the m e m b r a n e mater ial is considered to be inextensible, the solution must also satisfy the compat ibi l i ty condit ion that the meridional arc length is unchanged during deformation. 3. A X I - S Y M M E T R I C A L L Y A P P L I E D C O N C E N T R A T E D L O A D Consider a spherical m e m b r a n e subjected to constant internal pressure, qo, and a concentra ted load, P, applied at the apex, (see Fig. 2). F r o m equat ion (4) we have Q = rcr2qo - P (7) while equat ion (3) takes the simple form dr P 2ztr tanq5 d(/) = ~rr2 - --- (8) qo the solution to which can be expressed as Z r = + C sin q5 (9) v~here C is a constant of integration. The boundary condit ions are given by r(--O~,) = O; r((/)l) = Rosin eft1 (10) whereas the assumed inextensibility of the m e m b r a n e dictates f '~ R,j, d O = Ro(/)]. ( ) 1 1 P whele F 2 = 7tR2qo \" After transformations, equat ion (11) is written as E [\"*' d42 427 (13) ",
            " 2w/s' in 42o ~,/,,, v /s in0o + sin4) Thus for a given P (or F), 42o and ~bl can be evaluated using equations (12) and (13) as a result of which the shape of the wrinkled region is determined as /1 sin(/) F R o S ' sin42 d42 r(42) = F R o + -\" h ( 4 2 ) - .. . (14) N sin420 2\\/sin42o -e,,,\\/sin(/)o + sin~ Singularities in equations (1 3) and (14) (at -420) are handled during the integration process, unless 42o = ~z/2. In stating the boundary conditions (10), it was assumed that the membrane is flee to deform into the shape depicted in Fig. 2. If the initial central angle of the membrane is rio (see Fig. 3) the above relations will be applicable until the angle qS~, denoting the slope of the tangent of the deformed membrane at the support, reaches the central angle value rio. When (h, = [~o and under increasing load the following conditions must be met r((/;i ) - Ro sinfio. (1 5) Introducing equation (1 5) in to the boundary conditions and rearranging the inextensibility condition, one arrives at a new relation fiom which the values of (ho and (/)~ can be found sin&l sine/fo = - 1 (16) sin&c, 1 \"'2 f: -,I,~ dO [~o = ~ ~ ( 1 7 1 2\\, sin42(~ "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001282_bf00369977-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001282_bf00369977-Figure1-1.png",
        "caption": "Fig. 1. a Gear model; b spring constant",
        "texts": [],
        "surrounding_texts": [
            "1 Introduction\nWith increased demands for high speed, heavy load, light weight and quiet-running in modern gears, the fatigue damage analysis of gears and the reducing gear noise have become a critical design step. Specifically, these require an accurate evaluation of the dynamic tooth loads and vibrations. Among the many factors that contribute to the dynamic tooth loads and vibrations are the variable mesh stiffness, the backlash and the gear transmission error, which is a total error consisting of the manufacturing errors, mounting errors, and the tooth deflection under the applied load. The effect of these factors on the dynamic tooth loads and vibrations has been investigated experimentally, and analytically by a number of researchers (Terauchi et al. 1967; Opitz 1967; Rettig 1965; Aida and Sato 1968; Gregory et al. 1963; Umezawa 1982). In these studies, the gear transmission error is assumed to be sinusoidal wave forms and the gear system is modelled as a single degree of freedom for the main purpose of determining the dynamic factor that can be used in gear root stress formulae. The underlying assumption in these studies is not that the transmission error can be considered as a small amplitude sinusoidal wave form and that the gear system parameters do not vary. However, in reality, because of the fluctuation of the various time dependent factor such as tooth wear, bearing wear and lubricating oil temperature etc., the gear system parameters vary from the values at the design stage, and because of a small static tooth load or of the manufacturing errors of large gears such as gear for rolling mill derive and marine gear etc., the transmission error is not always small. Therefore, the separation of tooth meshing is caused by the large amplitude torsional vibrations of gear system. Hence, a nonlinear treatment of the gear dynamics problem is essential.\nGregory et al. (1963), Retting (1965), Terauchi et al. (1967) and the present authors (1979) showed the occurrence of jump phenomena and subharmonic oscillations. The random-looking vibration was originally pointed out by Terauchi et al. (1967) and the similar results were obtained by the present authors (1979). If the above random-looking response is a chaos, then it is impossible to evaluate accurately the dynamic tooth loads and vibrations, and furthermore, if the bifurcation phenomena occur due to the variation of gear parameters, then the large dynamic tooth loads are caused by the tooth separation. However, very little information relating to nonlinear phenomena of gear system parameters is available. The purpose of the present work is to show the numerical method in order to obtain the bifurcation sets and to verify the existence of chaotic motion numerically.",
            "2 Bifurcation sets\nGear systems represent one of the most complex and less unders tood of mechanical vibration problems because of the difficulty involved in their modelling. Hence, numerous mathematical models have been developed for different purpose in the past three decades (Ozgtiren and Houser 1988). In this paper, a simple single degree of freedom model is used. The equations of mot ion for a gear system (Fig. la). in terms of the relative mot ion will be\nT~ i3T * ~O* + 2 ~ * + k(t*)g(T* + e*(t*), t/) - 1 + i 2 | 1 + i 2 (1)\nwhere\n11,12\nTo\nC~ k t r\ner t i\n8 k tr m a x\nD m a x\n0st\nIc\nI / , t *\ne*\ns n t* T*\ng(','7) k(t*)\nmoments of inertia of the gear 1 and gear 2, respectively angular displacements of gear 1 and gear 2, respectively input torque output torque damping between the meshing gear teeth variable mesh stiffness transmission error time gear ratio relative angular displacement between gear 1 and gear 2 = ku 1 - ~P2/i backlash max imum variable stiffness (the max imum of ktr ) max imum input torque (the max imum of To) angulardisplacementofthemeshinggearteeth=Tomax/ktrmax/(l+l ) equivalent mass m o m e n t of inertia of the two mat t ing gears = 1 Tll\ndimensionless relative angular displacement between gear 1 and gear 2 = T/0st dimensionless transmission error = e/0s,\ndamping ratio = C J2 natural frequency = 1 / ~ dimensionless time = co,t dimensionless input torque = To/Tomax dimensionless output t roque = TL/Tomax dimensionless backlash = e/0st nonlinear function representing gear teeth backlash model dimensionless variable mesh stiffness (Fig. lb).",
            "Letting x = ~u, + e* assuming the transmission error and the external torques to have the same frequency as the meshing frequency, Eq. (1) becomes\nd2x dx d t ,~ + 2( ~t ~ + k(t)g(x, tl) = Bcos(vt* + O) + B o. (1)\nDepending upon the operat ional situation, the nonlinear function representing gear teeth backlash model is defined in the following manner:\nx, x > 0 - q < x < 0\nx < - t /\n( o(x , ,1 ) = o,\nx+tl ,\nwhere\nv dimensionless B dimensionless B0 dimensionless 0 phase angle L dimensionless L1 dimensionless meshing frequency ampli tude of sinusoidal excitation static componen t of excitation meshing period = 2n/v meshing interval with double tooth pair contact.\nLetting vt* = ~, Eq. (1) becomes\ndx 1 dr - x2 - f l (x l ' x2, z)\nd x 2 _ 2 ~ x 2 k (z ) B B o d'c v F 2 g(Xl'tl)+~COS('~ + O ) + 7 - = f2(Xl'X2\"C)\"\n(2)\nSince k(z) and cos (z + 0) is now periodic with period 2ir, there exists a periodic solution with period 2m Hence, the following t ransformation theory is useful. (Sato, Kamada and Takatsu 1979).\nLet the solution of Eq. (2), which phases th rough any point Zo = (Xlo, X2o) on the Xlxz-plane at z = 0, be z(z) = ~(z, %). And let T be the Poincar6 map of phase plane R 2 (i.e., x , x z plane) into itself, then the following relation holds (Tomita 1984; Codding ton and Levinson 1955).\nT : R 2 , R 2 )\nZo ---+ Zx = z(2~z) = ~(2~z, Zo) }\" (3)\nNow, a fixed point of the mapping T is given by\nT(z) - z = 0. (4)\nLet the parameters of a gear system be 2 = ((, t/, v, B, B o, 0, L~). The fixed points of the mapping T or the roots of Eq. (4), zoeR 2, are grouped into four classes by characteristic roots, pl and P2, which are the solution of the following equat ion (Coddington and Levinson 1955; Furuya and N n a g u m o 1962; Shiraiwa 1975);\nh(zo, 2, p) = det (DT(zo) - pI) = 0, (5)\nwhere DT(zo) denotes the differentiation of T at Zo, and I is the 2 x 2 unit-matrix. As is generally known, the bifurcation phenomena are the phenomena in which the fixed point changes its topological proper ty due to the variation of the gear system parameter 2. Hence, the bifurcation analysis follows from Floquet theory for linear periodic-time varying systems and Eq. (5) determines the characteristic values p of a fixed point of order one which loses its stability when p = _+ 1. They are named as follows;\n(1) In the case of P l = 1 and P2 = e - 4 { = / v , it is named as a tangent bifurcation and corresponds to appearance and disappearance of a pair of the fixed points.\n(2) In the case of PI = - 1 and P2 = - - e - 4 { ~ t / v , it is named as a pitchfork bifurcation and corresponds to appearance and disappearance of 2-periodic point."
        ]
    },
    {
        "image_filename": "designv11_11_0002364_robot.2001.933087-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002364_robot.2001.933087-Figure1-1.png",
        "caption": "Fig. 1. Geometry for contacts located on edges or convex vertices.",
        "texts": [
            " Six test objects and three quality metrics, including a new metric for measuring the sensitivity of the grasp to positioning errors, will be employed. 2. Problem Definition It is assumed that a three fingered dexterous hand, or similar device, capable of independently controlling the finger forces is available. The finger to object contacts are modeled as hard contacts with Coulomb friction. The perimeter of the object is modeled as a polygon. The origin of the coordinate system is located at its center of mass. It ,is assumed that the finger forces are applied 0-7803-6475-9/01/$10.000 2001 IEEE 3061 normal to the edge as shown in Figure 1 . For the case of a finger located at a convex vertex, a locally radiused corner is assumed such that the contact normal bisects the included angle, as shown. While convex vertices have been rejected as contact locations for valid reasons by other researchers [9], our emphasis here is not to subjectively rule out any potential solutions. Contacts at concave vertices are modeled in the same manner as in [9]. The problem to be solved by each of the planning methods is to determine the best location for three such contacts so that an optimal (or near optimal) 2D forceclosure grasp is obtained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003611_bf02692330-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003611_bf02692330-Figure1-1.png",
        "caption": "Fig. 1 Physical model of the two-stage gear system Fig. 2 Nonlinear dynamic model of the two-stage gear system",
        "texts": [
            " This paper focuses on the nonlinear dynamic behavior of a two-stage gear reducer and integrates into that behavior the mesh stiffness fluctuation and the phenomenon of contact loss during working.[6,8,10] An example gear train was used to investigate the influence of gear mesh damping, backlash amplitude, and time step. In this paper, the dynamic behavior of a two-stage gear reducer is analyzed while taking into account teeth flexibility and nonlinear behavior resulting from contact loss during service.[6,8,10] The physical model of the studied system is presented in Fig. 1. The reducer elements are modeled by lumped parameters. The gears are modeled by concentrated masses,[13,15] and the rigidities are modeled by nonlinear springs with fluctuated stiffness and a linear damping element. At this level, the shafts and bearings are considered to be rigid. The dynamic model associated with the physical model is represented in Fig. 2 and is characterized by two degrees of freedom that are the result of teeth deflections at every stage. Every deflection represents the relative displacement of the teeth projected by the lines of action and can be expressed by:[16] \u03b41(t) = r1\u03b81(t) + r2\u03b82(t) and \u03b42(t) = r3\u03b83(t) + r4\u03b84(t) (Eq 1) Table 1 Parameters of the Studied System Material: 42CrMo4 Motor Torque Pressure Angle Average Mesh Stiffness Teeth Module Teeth Width \u03c1 = 7860 Kg/m3 Cm = 1000 Nm \u03b1 = 20\u00b0 kmoy = 108 N/m m = 410\u20133 b = 10\u20133 m Teeth Number Contact Ratio First Gearmesh Contact Second Gearmesh Contact First Gearmesh Contact Second Gearmesh Contact Z1 = 25; Z2 = 40 Z3 = 30; Z4 = 35 \u03b5\u03b11 = 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003849_03ye0551-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003849_03ye0551-Figure4-1.png",
        "caption": "Fig. 4. Top foil and bump foil schematic.",
        "texts": [
            " xx x x T xy x x yx y T yy y xx x T xy x yx y T yy y K K K A K K K K K A K K D D A D D D D A D D , ! ! ! ! ! ! ! ! ! ! (24) The coefficients Kij, Dij (i, j = x, y) defined in formula (24) exactly describe the dynamic characteristics of a compliant foil bearing in the small perturbation state. 5 Numerical results and discussion The static and dynamic characteristics of a certain aerodynamic compliant foil bearing are calculated based on the presented theory by means of the finite element method (FEM). Fig. 4 is the schematic of the top foil and bump foil, in which tT is the thickness of the top foil, pB the bump pitch, lB BB the bump length, hB the bump height, and tB BB the thickness Copyright by Science in China Press 2005 Bearing configuration and operation conditions are listed in Table 1, and the corresponding numerical results are listed in Table 2, where L is bearing length, and G0 dimensionless load capacity. www.scichina.com Fig. 6 shows the changes of the dynamic stiffness coefficients K and the dynamic damping coefficients D with 0 at = 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000560_s0167-8922(98)80096-5-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000560_s0167-8922(98)80096-5-Figure1-1.png",
        "caption": "Fig. 1 : ~ e t w o - d i s k m a c h i n e pr inc ip l e",
        "texts": [],
        "surrounding_texts": [
            "Tribology for Energy Conservation / D. Dowson et al. (Editors) 1998 Elsevier Science B.V. 399\nI n f l u e n c e of the n a t u r e and s ize of sol id par t i c l e s on the i n d e n t a t i o n f e a t u r e s in EHL c o n t a c t s\nFabrice VILLE and Daniel NELIAS European Institute of Tribology Laboratoire de M~canique des Contacts, UMR CNRS/INSA n\u00b05514 INSA B~t. 113, 20 av. A. Einstein, 69621 Villeurbanne Cedex, France.\nAn experimental study of the influence of several contaminant types on the surface indentation in EHL contacts is presented. An original lubrication system with a controlled level of contamination has been developed. The contaminant distribution and concentration are measured on-line by an automatic particle counter called CM20. Experiments are conducted on a two-disk machine with different operating conditions. The oil is a synthetic one qualified under the MIL-L23699 specification. An optical profilometer is used to describe the indent topography and concentration.\nThe test bench is described and the experimental procedure is presented. Particles from four different materials (SAE Fine Test Dust, M50 steel, SiC, B6C) with several size ranges have been tested. Results show the influence of the particle nature and size on the indentation features i.e. dent shape and concentration.\n1. INTRODUCTION\nThe constant improvements in material quality and manufacturing process increase the rolling bearing life. On the other hand, the increase of the contact severity as higher temperature and lower amount of oil available, reduces the EHL film thickness. So the proportion of rolling bearing failures initiated from the surface increases.\nSurface damages could be due to solid particles in suspension in oil which may pass through the contact and indent the surfaces. That may be at the origin of rolling bearing failures. So the interest in oil contamination effects on fatigue life is more and more important.\nSome authors have experimentally studied the particle entry and deformation in EHL contacts (1, 2, 3, 4, 5). Generally an optical interferometry technique is used to observe the particles' behaviour. The contact is\nformed by a steel ball rolling against a glass disc. A microscope coupled with a high speed video camera is positioned directly above the contact and allows observation of particles and dents. Other authors theoretically studied the influence of a dent on the pressure distribution and evaluate the tensile stress around it (6, 7, 8, 9, 10, 11).\nIn a previous work (12), the authors presented an experimental study on the concentration and shape of dents caused by spherical metallic particles in EHL contact. For their tests, they used a two-disk machine coupled with a specific lubrication system allowing to have a controlled level of contamination. Particles were composed of M50 powder with a diameter ranging from 32 to 40 t~n and the effect of concentration of contaminant and test time was studied. They observed a good linearity between the number of dents and the product of test concentration by test duration. It was shown",
            "that the number of indents on the raceways can be estimated from the contaminant concentration and thus, that the particle entry ratio is close to one. Conclusions concerning sliding conditions were also presented. It appears that, under pure rolling conditions, the initially spherical particles are flattened looking like a \"camembert\" and not remaining imbedded, whereas under sliding conditions, they are spread and have been observed embedded on the both surfaces. Finally the indentation and deformation of ductile particles process was assumed to be divided in 3 steps. First there is an elastoplastic indentation, afterwards the particle is laminated and finally ejected or embedded.\nIn this paper, the influence of the nature and size of particles is presented. The contamination is composed of M50 high carbon steel powder with various size ranges, SAE Fine Test Dust, silicon and boron carbides. The oil is a synthetic one qualified under the MIL-L-23699 specification. Tests were conducted on the two-disk machine coupled to the specific lubrication system. The effects of the particle nature on the dent shape and the indentation process were first studied. Finally, some results on the shape and concentration of dents versus the initial particle size are presented.\n2. TEST B E N C H\nHydraulic Jack\n2.1 The t w o - d i s k m a c h i n e The high-speed two-disk machine available at LMC facilities was used for these tests. It reproduces the operating conditions of gears or rolling bearings, respectively at the contact between gear teeth or between the ring and the rolling element. Mechanical parameters which manage this contact are imposed and/or measured. These ones are rolling and sliding speeds, contact pressure, lubricant, temperature, material and surface finish. The test ring is shown in figures I and 2.\nEach disk is driven in rotation by a spindle of a three-phase a-c motor. The motor 1 is fixed to the machine housing. The other one is connected to the frame via two hydrostatic bearings which axis are normal to the rotational axis of the motor. So, this motor has two degrees of freedom : a translation and a rotation. The translation provides the desired normal load in the contact owing to an hydraulic jack. The rotation converts the motor 2 into a dynamometer and the friction force is measured through a stiff load cell (see fig. 2).\nLoad Pick Up\nFi~. 2 : M e a s u r e m e n t of fri, c t ion fo rce\n2.2 The c o n t a m i n a t i o n b e n c h An oil jet feeds the EHL point contact between the disks. To ensure a controlled level of contamination (number and size distribution of solid particles in suspension in oil), it was necessary to develop a specific lubrication system called the contamination bench (see fig. 3). It is composed of a tank, a",
            "mixing pump, a free way gate, ~12~a=200 and ~3~a---200 cleaning filters and a head race. The contamination bench could be linked with the two-disk machine during a given test time using the flow coming from the head-race.\nThe qualification of the contamination bench was described in a previous paper (12). The main conclusions were\"\n1. The gear pump and other internal components do not generate particles so there is no internal source of contamination. 2. The oil system is dust-proof and airtight to state that there is no external source of contamination. 3. The contamination size distribution is not altered during operations, there is no sedimentation of the heaviest particles. 4. The concentration of solid contaminants in the lubricant flow stays uniform during the test length. 5. The particles may travel through the EHL contact only one time to not have size or shape modification during a test. 6. Finally the contamination bench is able to clean the lubricant between each test.\n2.3 The p a r t i c l e c o u n t e r To complete this test bench, an automatic particle counter is used to measure on-line the contamination distribution and concentration during tests. The principle of operation is an optical scanning analysis (see\nfig. 4). The theoretical particle size is ob~ined by integrating the fall voltage value with the crossing time which corresponds to the absorbed light intensity. The size given is an evaluation of the diameter of the particle.\nI&~ 14. o~cal Scanner i I ~ c h . ~ , ~ ~v , , ! e. o ~ o ~ e o . s y , ~ Pump i \" n \u00b0 \" P\"~\",,,\u00b0~,\" ................\nFig. 4.: Automat.i..c. oa r t i c l e c o u n t e r\nTests results presented here are given according to the cleanliness code ISO DIS 4406. The particle counts, for this code, are for an oil volume of 100 ml and for particles greater than 2, 5, 15, 25, 50 and 100 pro. The ISO code is created by selecting the values for particles greater than 2, 5 and 15 tun. For example, a contamination level of ISO 21/18/15 corresponds to an 100 ml of oil that contains 1.2 106 particles over 2 tun, 250 103 over 5 pm and 30 10~ over 15 pro. The different codes are described elsewhere (12).\nData transfers are allowed by mean of a RS232 serial port towards a PC computer.\n3. TEST CONDITIONS\n3.1 O p e r a t i n g cond i t ions Test disks have a spherical shape with a radius (in both directions) of 40 mm in such a manner that the contact conjunction is circular. They were made in AISI 52100 steel. The surface roughness corresponds to a complete finishing of the samples, which means a Ra value of about 0.1pro. The operating conditions correspond to pure rolling ones with a rolling speed of 20 m.s -I and a maximum hertzian pressure of 1.5 GPa for each test.\nThe lubricant used is a tetra-ester of 5 cst viscosity at 100\u00b0C, qualified for use in gas turbine engine lubrication systems under the MIL-L-23699 specification. The tribological and rheological properties of this lubricant"
        ]
    },
    {
        "image_filename": "designv11_11_0003987_j.surfcoat.2006.06.035-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003987_j.surfcoat.2006.06.035-Figure8-1.png",
        "caption": "Fig. 8. Estimation of area overlap. D is measured as the average width of the treated zone and d is estimated from the values of frequency, scan rate and width of treated zone using Eq. (3). Area overlap is given by Eq. (1).",
        "texts": [
            " It has been found that approximately a linear relationship exists between the melt zone dimensions and ln J 2h Uw . The variations of melt depth and melt width as a function of ln J 2h Uw is shown in Fig. 6. Both the melt width and depth increased linearly with increasing ln J 2h Uw . In pulsed laser treatments, crescent shaped visible markings can be found on the surface (Fig. 7). These correspond to the overlapping menisci of the freezing zone. The extent of overlapping is influenced by the pulsing frequency and the scan rate. The area of the overlapping region on the surface was estimated (Fig. 8) using the expression: Ao \u00bc 0:25D2\u00f02h\u2212sin2h\u00de \u00f01\u00de where h \u00bc cos\u22121 D\u2212d D ; \u00f02\u00de d \u00bc \u00f0h\u22121\u00deD\u2212U \u00f0h\u22121\u00de ; \u00f03\u00de and D is the measured width of the treated zone. The variations of area overlap due to variations in pulse frequency and scan rate calculated based on the measured values of melt zone width is shown in Fig. 9. The overlapping area increased with increasing frequency and decreasing scan rate. Fig. 10 shows the distributions of micro hardness along the treated zone centreline with depth at different peak powers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001202_10402009808983741-Figure24-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001202_10402009808983741-Figure24-1.png",
        "caption": "Fig. 24ontactlng rough surfaces model.",
        "texts": [],
        "surrounding_texts": [
            "218 A. A. POLXARPOU AND I. ETSION\nOne of the reasons is that undesirable high values of static friction, referred to as stiction, are occasionally encountered. The problem of stiction is exacerbated with the use of smoother thin-film disks in order to allow lower head/disk separations and accomplish higher information storage densities.\nMany experiments were conducted to study the role of surface roughness, lubricant (liquid film) type and thickness, and relative humidity (RH) on stiction at head/disk interfaces. A brief chronological summary is given in Ref. ( I ) . Basically, it is always found that, for a given roughness, there exists a critical liquid film thickness above which the friction force increases sharply. Below this critical thickness, friction is low and insensitive to liquid thickness.\nThe earlier published experimental research work on hard disk interfaces dealt primarily with the effect of \"ultra-thin lubrication\" (2) or humidity on stiction (3), (4), and somewhat neglected the surface roughness effects. More recent experiments (5)-(7) investigated the effects of lubricant thickness, surface roughness, and lubricant properties. In all cases, the critical thickness phenomenon is observed, along with higher critical thickness and a lower friction coefficient with increasing surface roughness. In Ref. (8), comprehensive experiments on long-term stiction at thin-film interfaces are reported. It was found that stiction increases with dwell time. This was explained by the effect of the contact and adhesion forces on the surfaces separation. A different type of experiment was performed by Etsion and Amit (9) to investigate the effect of small normal loads on the static friction coefficient. They found a sharp increase in the static friction coefficient with decreasing loads.\nConcerning the modeling efforts of the effects of roughness and liquid film thickness on stiction after a sufficiently long rest time, a number of analytical meniscus models have been suggested (3), (6), (10)-(12). These models share the common assumption that stiction results from a significant increase in adhesion due to the meniscus forces (13) of the adsorbed film at the interface. The time dependence of stiction was modeled in Ref. (8) by considering the time dependence of the contact and adhesion forces (including meniscus) through gradual changes in the surfaces separation. Meniscus-based models have been successfully used to calculate the strong adhesion forces that are developed due to surface tension effects associated with liquid bridges that are formed by pulling lubricant off the surrounding solid areas. Meniscus models are very useful when the lubricant at the interface is abundant, relatively thick and mobile. However, when the lubricant thicknesses are extremely small, on the order of a few monolayers that strongly adhered to the solids (immobile), the meniscus model breaks down (13).\nFor these cases, an alternative to the meniscus model has been suggested in Ref. (14). This alternative model, termed subboundary lubrication (SBL), is more likely for strong lubricant-solid bond and extremely thin lubricant thickness, and was used in Ref. ( I ) to develop the SBL static friction model. The difference between the meniscus model, on the one extreme, and the SBL model, on the other extreme, is that the former contains liquid bridges with negative mean curvature and a pressure difference that will pull lubricant\noff the surrounding solid areas. On the other hand, the SBL model considers the case in which there is a strong interaction between the lubricant and substrate, i.e., a large negative amount of energy is associated with the formation of a unit area of solid lubricant interface. In such a case, the energy cost for liquid bridge formation is too high. Meniscus formation is energetically unfavorable and lubricant layers remain essentially uniform and of quasi-solid nature. The quasi-solid behavior of extremely thin liquid layers has been studied by many researchers in their studies of \"molecularly\" thin liquid films. For a comprehensive review, see Ref. (15).\nAnother problem usually associated with all the meniscus models is that the stiction force calculations are based on assuming a certain empirical value for the coefficient of friction. For example, a value of 0.2 is assumed in Refs. (3), (6), ( lo) , and (11). Even the most recent improved meniscus-based stiction model, suggested by Gui and Marchon (12), still uses an empirical friction coefficient, p, = 0.2, in order to calculate the stiction force.\nContraly to the semiempirical nature and the difficulties associated with the meniscus-based stiction models, the SBL static friction model is derived from first principles. The tangential (friction) force needed to shear the junctions between the contacting surfaces is calculated by considering the actual stress field at the contacting asperities of the interface and not from an arbitrary empirical value of the friction coefficient.\nIn this paper, the SBL static friction model of Ref. ( I ) is compared with experimental results from three different references--Refs. (6), ( 7), and (9)-that were performed independently and represent two types of tests. The first type of test involves experiments performed on thin-film disks with different surface roughness conditions, variable lubricant and adsorbed water vapor film thickness, and constant normal loads, (6), (7). The other type of test includes experiments that were performed at a constant water film thickness and variable small normal loads (9).\nBACKGROUND\nThe static friction coefficient after a sufficiently long rest time is defined in the form (see Fig. 1)\nD ow\nnl oa\nde d\nby [\nG az\ni U ni\nve rs\nity ]\nat 1\n1: 54\n0 9\nJa nu\nar y\n20 15",
            "Comparison of the Static Friction Subboundary Lubrication Mc ode1 with Experimental Measurements on Thin-Film Disks 219\nwhere p. is the static friction coefficient, Q is the tangential force necessary to shear the junctions between the contacting asperities, and F is the external normal force, which is equal to the actual contact load, P, minus the adhesion force, F,, acting between the surfaces in contact.\nThe contacting surfaces are modeled using the CEB elasticplastic model ( 1 6 ) which is based on the Greenwood and Williamson (GW) model ( 1 7 ) . It assumes that when two nominally flat surfaces touch, contact occurs at discrete contact spots due to surface roughness. Deformation occurs in the contacting regions and can be elastic, plastic or elastic-plastic, depending on the nominal pressure, surface roughness i d material properties. Based on this model, the two rough surfaces are represented by an equivalent rough surface in contact with a smooth plane. The geometry of this model is shown in Fig. 2. The rough surface is modeled by a collection of asperities having spherical summits with a uniform radius R and a standard deviation a, of their heights, u. The separation of the surfaces, measured from the mean of the a s perity heights, is d, h is the separation of the surfaces measured from the mean of the surface heights, y, is the distance between the means of asperity and surface heights and to is the lubricant layer thickness, which is equal to the sum of the two uniform lubricant layers that are present on each surface ( 1 4 ) .\nThe dimensionless contact load, P*, for an elastic-plastic contact of rough surfaces is given in Ref. ( 1 6 ) by\nn*-y,+o:\n9 ( h * ) = [ ( 3 R I o * 2 + * ( ~ * ) du*\nh* -y: PI\nIn Eq. [2], the first and second integrals are the contributions of the elastically and plastically deformed asperities, respectively. +*(u*) is the normalized distribution of the asperity heights which is assumed to be Gaussian. His the hardness of the softer material and E' is the equivalent elastic modulus given by\nand is another form of the plasticity index, JI, defined by GW ( 1 71, i.e.,\nNote that Eq. [2] was also used by Gitis et al. ( 8 ) in their long-term stiction model.\nThe adhesion force ( 1 4 ) in dimensionless form ( I ) is\nE;* (h*) = hq R A y l ~ * 2 3E' {\"'r '1(E* - o* 1 - t,*12 - m\n- E*6 ]s*+*(u*) ds*du* (Z* - t,*19\nEach integral in Eq. [7] corresponds to one of three components of the adhesion force as follows. The first component is from completely noncontacting asperities where u 5 d - to (see Fig. 2 ) . The term in the denominator (E* - w* - t,*) is the dimensionless distance from the asperity tip to the lubricant layer surface. The second component is for solid noncontacting but lubricant contacting asperities where d - to l u l d. The last component is for solid contacting asperities with u > d.\nThe adhesion force originates from the Lennard-Jones interactive ptential that forms the basis for the adhesion models in Refs. ( 1 4 ) and ( 1 8 ) . Since the lubricant is assumed to behave as a quasi-solid, the energy of adhesion Ayl in Eq. [7] is Ayl = 2y, see for example Ref. ( 1 9 ) . Also in Eq. [7] E(E* = \u20ac /a ) is the interatomic spacing (0.3-0.5 nm) used in the Lennard-Jones potential. For more details see Refs. ( I ) , ( 1 4 ) and ( 1 8 ) .\nGitis et al. ( 8 ) used exactly the same formulation of the first and second components in Eq. [7] for their adhesion force, but assumed an empirical exponential form for the solid contacting asperities, corresponding to \"not fully equilibriated\" menisci.\nFinally, the dimensionless tangential force is given in Ref.\n(20) by\nD ow\nnl oa\nde d\nby [\nG az\ni U ni\nve rs\nity ]\nat 1\n1: 54\n0 9\nJa nu\nar y\n20 15",
            "220 A. A. POLXARPOU AND I. ETSION\nThis force (the static friction force) is based on Hamilton's analysis of the stress field for combined normal and tangential forces in a sphere contacting a flat. A major assumption of the model developed in Ref. (20) is that plastically deformed asperities, which have already failed due to local contact pressure, are unable to support any tangential load. Hence, only the elastically deformed asperities can resist sliding. Further improvement in the calculation of Q can be achieved by using the approach of Halling (Zl), where a general stress/strain relationship that accounts for both elastic and plastic behavior of the contacting surfaces is used.\nThe dimensionless function f (a function of v, K, o , and o,) in Eq. [8] depends on the asperities failure inception location for yielding below the surface at the Hertz location, or on the surface at the trailing edge of contacting asperities.\nAs discussed earlier, the calculation of the friction force from first principles without the usual assumption of an empirical friction coefficient is a unique feature of the SBL stiction model.\nAVAILABLE EXPERIMENTAL DATA\nOf all the relevant experimental research work published so far, only three papers--Refs. (6), ( 7) and (9)-were identified that contain enough information to enable comparisons with the SBL friction model. A description of the data in these references, and the associated parameters needed in the SBL model, is given below. The data of four different cases will be presented in a descending order of surface roughness in terms of the standard deviation of surface heights, a, and the plasticity index, (I, starting from the roughest surfaces (largest u and JI).\nThe first (roughest) case for comparison is by Etsion and Amit (9), who studied the effect of small normal loads on the static friction coefficient for \"very smooth surfaces.\" The experiments were performed in a controlled humidity environment and consisted of measuring the static friction for different aluminum samples in contact with a nickelcoated disk. The surface roughness parameters and mechanical properties of the Ni disk and one of the Al samples are listed in Table 1, while those of the combined friction pair are listed in Table 2. Note that the values of R corresponding to Ref. (9) in Tables 1 and 2 vary by 220% of their reported values. This is because some uncertainties are involved in the\n'value for diamond (25). PHardness value as per Ref. (24). Walue for alumina/TiC (25). 'From Ref. (23) .\nTABLE 1-EXPERIMENTAL SURFACE ROUGHNESS PARAMETERS AND MECHANICAL PROPERTIES OF THE INDMDUAL MATERIALS FROM REFS. (6), (7), (9) AND (23)-(25)\nREF.\n( 9)\n( 9)\n(6)\n( 7)\n( 7)\n(6)\nMATERIAL\nNi Disk\nA1 Sample\nDisk 1\nDisk 2\nDisk 3\nIBM Slider\nu (nm)\n8.24\n42.26\n7.76\n4.79 f 20%\n1.74 + 20%\n2.38\nR ( ~ m )\n310.8 f 20%\n312.0 f 20%\n13.0\n28.0 f 20%\n100.0 2 20%\n52.0\n\"l ( ~ m - ~ )\n0.00924\n0.00473\n-\n0.745\n0.508\n-\nH (GPa)\n5.884\n0.698-0.872\n(1.42-~.59)~\n(1.42-2.591~\n(1.42-2.59)\n2 ~ . 6 ~\nv\n0.291\n0.334\n0.20'\n0.20'\n0.20~\n0 . 2 1 ~\nE (Cpa)\n206.8\n71.7\n90.0\n100.0\n100.0\n450.0\nD ow\nnl oa\nde d\nby [\nG az\ni U ni\nve rs\nity ]\nat 1\n1: 54\n0 9\nJa nu\nar y\n20 15"
        ]
    },
    {
        "image_filename": "designv11_11_0003734_j.bioeng.2006.04.001-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003734_j.bioeng.2006.04.001-Figure2-1.png",
        "caption": "Fig. 2. Gaseous diffusion amperometric electrode and biosensor assembly: (a) electrode body; (b) internal solution (phosphate buffer); (c) reference electrode (Ag/AgCl) (anode); (d) platinum electrode (cathode); (e) teflon cap; (f) gaspermeable membrane; (g) teflon O-ring; (h) dialysis membrane; (i) enzyme immobilized in kappa-carrageenan. \u2018\u2018Reprinted from Campanella et al., 2001c, with permission from Elsevier\u2019\u2019.",
        "texts": [
            " Campanella et al. (2001c) have reported a number of organic phase enzyme electrodes using tyrosinase and other enzymes (monoenzymatic and bienzymatic systems), and operating in different organic solvents or solvent mixtures. As enzyme immobilisation system they propose kappa-Carrageenan gel in which enzyme was entrapped. The gel loaded with the enzyme was placed on the head of an amperometric GDE for oxygen, between the gas permeable membrane of the electrode and a dialysis membrane as is illustrated in Fig. 2. Applications performed in the field of foodstuff and cosmetic control (Campanella et al., 1999a,b) supported the correlation between classical indicators such as log P values of the solvent and empirical new indicators such as \u2018\u2018maximum current variation\u2019\u2019 (MCV) or \u2018\u2018current variation rate\u2019\u2019 (CVR) of the enzyme biosensor. A close correlation exists between the trends of log P and CVR indicator assuming that the enzyme molecules involved in the catalysis are those at the interface and neglecting any diffusion phenomena and solvent effects in the kappaCarrageenan gel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003335_0020-7403(81)90025-4-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003335_0020-7403(81)90025-4-Figure4-1.png",
        "caption": "FIG. 4. Tirlateral figure. Analysis of the internal velocity as a function of the two given external velocities e~ and e2.",
        "texts": [
            " If a multilateral figure is considered, its rigid internal velocity is fully known, when the normal components of the external velocities (equal to the corresponding internal components), are known on two adjacent or non-adjacent sides. The absence of one of these pieces of information can be overcome if the direction of the internal motion is prescribed. The following cases are of interest: side A C , see Fig. 3. The direction of the internal velocity vector is obviously parallel to A B and hence the problem is the same as that given in Example I. The external velocity vectors e, and e~ are given on the sides A B and BC, see Fig. 4. The flux of material through the sides A B and BC is respectively given by: Analysis of plastic deformation according to the SERR method 131 The internal velocity i, must simultaneously meet the continuity conditions across A B and B C If the two sides A B and B C in Fig. 4 are displaced parallel to themselves, by quantifies respectively equal to the normal components of the vectors et and e2 (i.e. equal to PZ and P S ) , then their intersection P determines, together with the point B, the internal velocity i. We obtain, P Z = P B \u2022 sin y; P S = P B \u2022 Sin and Hence, A H A B C H B C B C siny sinO\" sin8 = s i n ( * r - O ) =s inO\" A H A B . sin y C H B C . sin S\" Further we see that, A H A B \u2022 sin y A C A B \u2022 sin y + B C \u2022 sin 8' and hence, from equations (1), we obtain, From Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.68-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.68-1.png",
        "caption": "Figure 3.68 Flywheel test facility of Politecnico di Torino. A four-pole asynchronous motor capable of 30000 rev/min is shown. (Genta [80-28], [82-7])",
        "texts": [
            " As an example, a two-pole motor on a 1000 Hz converter will be allowed to reach 60000 rev/min with low values of the torque, a four-pole motor will reach 30 000 rev/min with higher torques and a ten-pole motor allows the testing of very large flywheels requiring high accelerating torques up to 12 000 rev/min. The author uses coaxial motors with different numbers of poles in order to obtain high torques to go through the critical speeds with high acceleration and then to shift to the high-speed motor. An example of this approach is the flywheel test facility of the Dipartimento di Meccanica of the Politecnico di Torino shown in Figure 3.68. It is a very versatile device, designed for a large spectrum of applications, spanning from burst testing of the usual rotating machine elements to research work on highenergy density flywheels. An intermediate-speed four-pole motor is shown in the figure. Other types of electric motor can be used, but they require a transmission with speed-increaser and a vacuum seal on the shaft particularly for d.c. motors, thus losing the advantages of simplicity and cost. Internalcombustion engines are very powerful and are relatively cheap, but they required a transmission (usually a continuously variable one) and a vacuum seal",
            " The 'catcher' is also useful as an amplitude limiter, should the passage through a critical speed cause large deflections. An upper amplitude limiter can be useful, particularly in order to stabilize a rotor when it spins on the 'catcher' after a quill shaft failure. The usefulness of such devices is, however, still controversial, but the author has had some flywheels rescued by them. A good precaution is to have a safety valve on the spin chamber, should combustion of rotor debris or of oil from the motor follow the loss of vacuum. In the example shown in Figure 3.68 the lid acts as a safety valve, being kept in position by springs which allow it to rise if the internal pressure exceeds the external pressure by more than 50 kPa. In normal operation the lid is kept in position by atmospheric pressure. The vacuum system and the burst containment devices will be described in Chapter 4, and the rotor dynamics problems will be dealt with in Chapter 5. For a spin test it is necessary to have a speed meter, if possible of the recording type, and monitoring instruments for the vacuum and power plants"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000765_s0043-1648(02)00108-4-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000765_s0043-1648(02)00108-4-Figure5-1.png",
        "caption": "Fig. 5. (a) Conditions of restrain and load of wheelset and (b) finite element mesh of half wheelset.",
        "texts": [
            " That is why the reduced contact stiffness increases the ratio of stick/slip area of a contact area and decreases the total tangent traction under the condition of the contact area without full-slip. In order to calculate the SED described in Fig. 1b\u2013d, and Fig. 2, discretization of the wheelset and the rail is made. Their schemes of FEM mesh are shown in Figs. 5, 7 and 9. It is assumed that the materials of the wheelset and rail have the same physical properties. Shear modulus: G = 82,000 N/mm2, Poisson ratio: \u00b5 = 0.28. Fig. 5 is used to determine the torsional deformation of the wheelset. Since, it is symmetrical about the center of wheelset (see Fig. 1b), a half of the wheelset is selected for analysis. The cutting cross section of the wheelset is fixed, as shown in Fig. 5a. Loads are applied to the tread of the wheelset in the circumferential direction, on different rolling circles of the wheel. The positions of loading are, respectively, 31.6, 40.8 and 60.0 mm, measured from the inner side of the wheel. Fig. 6 indicates the torsional deformations versus loads in the longitudinal direction. They are all linear with loads, and very close for the different points of loading. The effect of the loads on the deformation of direction of y-axis, shown in Fig. 5a, is neglected. Fig. 7 is used to determine the oblique deformation of the wheelset. The oblique deformation is unsymmetrical about the center of wheelset, so it is necessary that discretization of the whole wheelset is made. According to the situation of the loads and deformations of a wheelset moving on track, the restrain and load conditions of it are selected as shown in Fig. 7a. The center of the left nominal rolling circle of the wheelset is fixed in the directions of x-, y- and z-axis, respectively, and that of the right is fixed in the directions of x- and z-axis, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001825_bf03263391-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001825_bf03263391-Figure2-1.png",
        "caption": "Fig. 2. Master chart of objective function for fusion welding.",
        "texts": [
            " The following augmented sum-of-squares function (objective function) is taken to be a criterion of IHCP solution accuracy: F(p)=\u2211 J j=1 w \u0192 j [\u0192m j \u2013 \u0192 j(p)]2+\u2211 K k=1 w p k [p0 k \u2013 pk]2+wq [qm net \u2013 qnet(p)]2 +w 0 \u2211 N n=1 [p n]2 +w 1 \u2211 N\u20131 n=1 [p n+1 \u2013 pn]2 +w 2 \u2211 N \u20132 n=1 [p n+2 \u2013 2p n+1+pn]2 (4) where J is the number of observations, K the number of unknown parameters, and N the number of unknown values of power density, N \u2264 K. Let us look at the physical meaning of the above function F of the parameter vector sought p, where p = {p1, p2, ..., pK}. Unknown parameters pk can be the power density at a fixed point, welding speed \u03bd, etc. (Fig. 2) and the parameter dimensions are arbitrary. In equation (4) the first N parameters are the heat power densities q3 app at the fixed points xn, yn, zn, pn = q3 app (xn, yn, zn). Response functions: values of \u0192j m and \u0192j are the respective measured and calculated temperature-related (heat-induced) thermophysical, metallurgical, chemical and/or mechanical weld characteristics at point j (Fig. 2). Constraints may include an a priori (i.e. guessed) value of the k-th parameter pk 0, restrictions on the parameter sign and value, the measured (prescribed) values of the net heat power q m net, etc. (Fig. 2). The inequation pk > 0 is obeyed by the substitution: pk = exp (p\u0303k) where p\u0303k is the new variable. Weighting factors wj \u0192 and wq are recommended to be proportional to the reciprocal of the variance of the random measurement error of the measurement of \u0192j m and q m net [3]. The weighting factor wk p is the reciprocal of the square of a typical interval within which parameter pk is allowed to vary around an a priori parameter pk 0 [16]. If the net heat input q m net is unknown then wq is taken as zero",
            " The temperature field is described by the following equation: T(x, y)= 1 \u2211 N\u20131 n=1 \u222b xn+1 xn [q2 app n + q2 app n+1 \u2013 q2 app n (\u03be \u2013 xn)]\u03c0\u03bb xn+1 \u2013 xn exp[\u2013 \u03bd(x \u2013 \u03be)]K0 ( \u03bdr \u221a 1 + 8a\u03b1 )d\u03be + T0 ; (8) 2a 2a c\u03c1h\u03bd2 r = \u221a(x \u2013 \u03be)2 + y 2 where a is the thermal diffusivity, K0 is the Bessel function of the second kind of zero order, \u03b1 is the coefficient of heat transfer from plate to ambient air and T0 is the initial temperature. The temperature is finite everywhere including the plate edge (y = 0) where the surface heat source is acting. Using equation (8) one can calculate the thermophysical response function \u0192 (Fig. 2) including the weld pool boundary T(x,y) = Tmel and angle \u03b2 between temperature gradient gradT and x-axis at any point on the weld pool boundary (Fig. 3b): \u03b2 = \u03c0 + arctan \u2202T /\u2202x 2 \u2202T /\u2202y The IHCP is solved by using the iterative technique outlined above (Fig. 4). At every iteration the direct problems are solved successively: the heat transfer problem to find the weld pool shape and the metallurgical problems to evaluate the texture orientation angle \u03b3 by the grain boundary evolution method [20]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003849_03ye0551-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003849_03ye0551-Figure3-1.png",
        "caption": "Fig. 3. Deflection of bump foil subjected to forces.",
        "texts": [
            " tb tb tb z A A A z A A (5) Similar to the expression of the deformation of the top foil, deformation of the bump foil due to contact load W( , z) can be always expressed in the following form by using the deflection coefficient fb of the bump foil. www.scichina.com ( , ) ( , ) ( , , , )d db b A H W z f z z z ( , ) ( , , , )d d tb b A W z f z , (( , ) ;( , ) )tbA z A . (6) It must be pointed out that for the calculation of the deformation of the bump foil, reacting forces Ni and friction forces Fi, as shown in Fig. 3, also play important roles and must also be taken into account besides W( , z), and consideration of the action of Ni and Fi can be dealt with by using the method presented in ref. [8], and details are neglected here for simplicity. Copyright by Science in China Press 2005 Substituting eq. (4) into eq. (3) yields ( , ) ( , ) ( , , , )d d ( , ) ( , , , )d d tb t t A A H P z f z z W z f z z . (7) Denote ( , ) ( , ) ( , )p wH H H , where ( , )pH is the deformation of the top foil at point ( , ) due to the gas film pressure P( , z) alone, and Hw ( , z) the deformation of the top foil due to contact load W( , z)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001165_s11664-003-0054-x-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001165_s11664-003-0054-x-Figure3-1.png",
        "caption": "Fig. 3. The ion angular distributions: (a) for < c, no etch lag occurs; (b) for = c; and (c) for > c, where etch lag predominates.",
        "texts": [
            " For plasmas reported in the literature as etchants for HgCdTe, examples of these three would be Ar+; H that reacts with tellurium to form TeH2, which is volatile and pumps off;5,6,12 and N2, used with plasmas containing methane to slow the etch rate,5,6 respectively. Such a plasma process can be described as ion induced, reactive ion etching (RIE). Ionic paths acquire a preferred directionality because of the various self and applied biases, while radicals and inhibitors are directionally random. The ion angular distribution (IAD) is predicted by Jansen and Elwenspoekto have a strong effect on the shapes of etched features. This effect is described in Fig. 3, where the aspect ratio of a trench is described by an angle . The critical angle c is the angle that is approximately equal to the maximum of the IAD,17 labeled as in Fig. 3. In this model, trenches with \u2264 c do not suffer etch lag. Trenches with > c do show etch lag because fewer directional ions reach the bottom of the trench. 1 ARc = 2 tan( c) \u2248 2 tan( ) (1) Thus, the path to achieving values of IARc is reduced to reducing the value of of the plasma. To reduce , we chose to vary the DC bias. The heated wave resonance zone of the PlasmaQuest 357 is 25.3 cm from the sample; therefore, changes in DC bias are expected to vary the IAD of our plasma while having a minimal effect on other plasma parameters, such as species type, electron likely reach the ECR region where a small density of H2 + and H+ will be produced"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001563_a:1008185917537-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001563_a:1008185917537-Figure11-1.png",
        "caption": "Figure 11. View of active dual-wheel caster assembly.",
        "texts": [
            " The reference trajectory was a straight line, whose gradient was 0 rad for the first 3 s, and \u03c0/3 rad for the rest. The control purpose was that the c.g. of the robot should follow this trajectory, and also that the azimuth of the robot \u03c6 satisfies the line gradient. Resultant simulation results are shown in Figures 9 and 10. From the control results, we see that the robot moved toward 0 rad direction for the first 3 s, and after that the azimuth of the platform was changed to the same direction as the reference trajectory. The actual view of active dual-wheel caster assembly mechanism is shown in Figure 11. The specifications were as follows: r = 0.05 m, s = 0.075 m, b = 0.26 m. The width of the wheel was 0.04 m, the DC motor was used as an actuator. Torque was transmitted by the gear between the motor and wheel. Furthermore, to take the balance of assembly or robot, a passive free caster was arranged on the front of steering axis of each assembly as an auxiliary wheel. The view of the prototype of the omnidirectional mobile robot with two active dual-wheel caster mechanisms is shown in Figure 12, in which two casters are arranged in the front and rear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000621_s0039-9140(01)00330-7-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000621_s0039-9140(01)00330-7-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of flow injection dialyzer manifold for determination of sulfite: (A) 10\u22122 M MES buffer pH 5; (B) 5\u00d710\u22121 M H2SO4; (C) sulfite test sample solution; (D) peristaltic pump; (E) pulse suppressor; (F) mixing coil; (G) flow injection valve; (H) dialysis chamber; (I) gas permeable membrane; (J) waste; (K) flow through TP\u2013epoxy membrane sensor; (L) Ag/AgCl reference electrode; (M) electric ground attached to a metal inlet tube; (N) electrolyte solution; (O) pH/mV meter; and (P) chart recorder.",
        "texts": [
            " Standard working sulfite solutions (10\u22121\u201310\u22125 mol l\u22121) were freshly prepared daily and stabilized by dilution of appropriate aliquots of the stock sodium sulfite solution with distilled de-ionized water containing 5% (v/v) glycerol to mask the heavy metals. 2.2. Equipment All potentiometric measurements were made at ambient temperature (25 1\u00b0C) using an Orion digital pH/mV meter (Model SA 720) and TP\u2013epoxy membrane based sensor in conjunction with Hana silver-chloride single junction reference electrode filled with 10% (w/v) KCl. A combination Ross glass pH electrode (Orion 81-02) was used for all pH measurements. A schematic diagram of the flow injection analysis (FIA) system manifold used for sulfite quantitation is shown in Fig. 1. The system consists of a laboratory made flow cell containing the sulfite sensor, peristaltic pump (MSREGLO), and an Omnifit 4-port injection valve (Omnifit, Cambridge, UK). A home made modified gas dialyzer similar to that described earlier [32] was used. Each channel contains two support ribs to hold the gas-permeable membrane securely in place, in order to reduce the movement of the membrane. The dialyzer was fitted with a polytetrafluoroethylene membrane (0.2 m pore size). The recipient buffer (10\u22122 mol l\u22121 MES, pH 5",
            " Sensor characteristics and origin of response Epoxy membrane based sensor containing TP, showed strong potentiometric responses for many common anions such as SO3 2\u2212, NO2 \u2212, Br\u2212, I\u2212, Cl\u2212, F\u2212, NO3 \u2212, HPO4 2\u2212, SO4 2\u2212, CrO4 2\u2212, IO4 \u2212 and S2\u2212. Evaluation of the sensor under static mode of operation according to IUPAC recommendations [34] indicated that the sensor displayed a sub ment, not to retain any of the flowing solution after injection cycle. The whole cell acted as a potentiometric flow-through detector with adjusted zero dead volume. The cell was assembled and integrated with the flow injection system as shown in (Fig. 1). A gas dialysis unit similar to that described earlier [32] was used in the flow injection system. The upper channel of the dialyzer acted as an injection loop. The used valve has two positions; one to allow the carrier buffer stream (10\u22122 mol l\u22121 MES, pH 5.0) to flow through the upper channel of the dialyzer and then downstream through the flow detector. The second position of the valve allowed separation of the upper channel of the dialyzer, and released the recipient stream to flow directly through the sensor detection unit"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002868_tpas.1983.317740-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002868_tpas.1983.317740-Figure5-1.png",
        "caption": "Fig. 5. Vector diagram for three-winding transformer",
        "texts": [
            " When the armature winding operates as a winding of an exciter of the number of poles 2p, the revolving speed Ns of the rotating field made by the exciting power is Ns = 120 f/2p = 60 f/p ----------------------(2) We can get the slip s from the equations (1) and (2). s = (Ns + n)/Ns = 3 -------------------------(3) Therefore, P1 : P2 : P3=l : s : l-s = 1 : 3 :-2 -----(4) where, PI, P2, P3 are respectively secondary input power, electric power and mechanical output power. Thus, the exciting winding of the rotor is supplied with twothirds of the total electric power from the mechanical shaft and with one-third of the total electric power from the secondary winding of the transformer. Fig. 5 shows a simple vector diagram by which the operation of the three-winding transformer can be explained. In no load condition of the generator, the transformer has a magnetic flux \u00a20 made by an exciting current in the primary voltage winding and linked with the three windings. The primary voltage winding is supplied with a voltage % o balanced with a voltage Eso induced in the primary voltage winding or converted to the primary circuit when induced in the secondary winding by the magnetic flux b0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000858_cta.4490220606-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000858_cta.4490220606-Figure6-1.png",
        "caption": "Figure 6. \u2018First-polarization\u2019 curve, limit cycle and saturation values of the piecewise function Q( e)",
        "texts": [
            ", N (8) where x for x > 0 0 for x < 0 r ( x ) = (9) Then the charge Q, which is the sum of the N capacitor charges q; = Ciu;, depends on the voltage e as N Q ( e ) = C ; r ( e - u i ) f o r O < e < e , i = l The value Q, of Q for e = e, is N N N Q, 4 Q ( e , ) = c C;r(e , - u ; ) = c c C;Vj ; = I j = i For e > e, the voltages across all the non-linear resistors are set to their upper limits Vk; hence Q, is the upper limit of Q and we can write The piecewise linear function Q ( e ) defined by (10) and (12) is shown in Figure 6 together with the two limit branches of the hysteresis cycles. 3.2. Limit descending branch Starting from e = e,, let the voltage e be monotonically reduced until it reaches the value - e,. As stated before, at e = e, the voltages across all the capacitors are set to their upper limit values. When e is lowered under the threshold value e,, we have v1 = e and the charge of CI is reduced accordingly. When e becomes smaller than e, - 2u2, also the voltage v2 across C2 conforms to the change in e, and so on",
            " Starting from this situation and increasing the input monotonically, arguments similar to those in the previous subsection lead to the results u ; ( e ) = - ( e s - u i ) + r ( e s + e-21.4;) for i = 1 , 2 , ..., N (16) N Q ( e ) = - QS + C;r(e , + e - h i ) i = l which completely define the characteristic of the limiting ascending branch and the related behaviour of the capacitors for eE [ - e s , e s l . The limit branches given by (14) and (17) define the limit hysteresis cycle, whose general features are shown in Figure 6. For the sake of completeness, the initial polarization curve (10) is plotted too, thus giving an idea of a possible evolution of the state starting from the \u2018virgin\u2019 state in which all the capacitors are uncharged. The number of points in the ( e , Q ) plane that can be reached from the \u2018virgin\u2019 state by applying proper input wave-forms e ( t ) is bounded by the limit cycle. The limit hysteresis cycle may be thought of as the result of the composition of Nelementary cycles related to the single charges q;"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002767_978-3-642-71015-5-Figure1.1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002767_978-3-642-71015-5-Figure1.1-1.png",
        "caption": "Fig. 1.1 a-c. Highly conducting plates (a) Short-circuit; (b) Open-circuit; (c) Resistive termination",
        "texts": [
            " When dealing with electromagnetic induction, the problem is very often of a magneto-quasistatic nature; how can quasistatics, in which the finite speed of light plays no specific role, be reconciled with restricted relativity? Before considering this, let us review our treatment of quasistatics. quoted (see, however, [1.13] and [Ref. 1.8, pp. 45 - 47]). The formal approach is somewhat handicapped by the need to incorporate considerations not explicitly stated by differential laws. For example (Fig. 1.1) two perfectly conducting plates (dimensions b, I, and spacing h) excited, e.g., by a low-frequency sinusoidal power supply, represent a magneto-quasistatic approximation so long as they are short-circuited at one end, but when they are open-circuited, an electro-quasistatic situation results; further, a quite different situation is to be expected if the open- or short-circuit is replaced by a finite conductivity [1.14]. The usual definitions of quasistatics are thus somewhat loose, often neces sitating intuition and experience, and may give rise to certain questions of principle; thus, one approach to quasistatics is through the in-vacuo wave length A of the considered field which oscillates at frequency f",
            " We supplement our review of quasistatics by a short digression to stationary charge flow, i.e., stationary current. For such fields, Maxwell's laws reduce to 'V xH =j , 'V xE = 0 (1.5.1) (1.5.2) being often supplemented by Ohm's law. Obviously, Ollendorff-Cerenkov electrodynamics with n = V.Llr er formally incorporates this case as well, with .Llr = er = O. Stationary fields arise in practical cases in which the wave-propagational properties of the fields are irrelevant, yet quasistatics is adequate. Such a situation may be visualized by considering, e.g., Fig. 1.1 c, where the con ducting plates terminate in a resistive sheet. With dc excitation, a stationary current arises in the configuration; E and H fields coexist. However, when the overall load resistance R of the resistive sheet is low, the E-field is \"weak\" and the configuration models an inductor, whereas when it is high the H-field is relatively unimportant and a model for a capacitor ensues. Where is the boundary between these two cases? As already hinted, when the specific magnetic energy density Wm greatly outweighs the electric specific energy density We' it is the inductor case, whereas when wm <1!: we' it is the capacitor case; finally, when an intermediate case ensues (we are still dealing with a dc situation). Thus, in Fig. 1.1 c, approximate expressions for Wm and We read Wm ~ ~ Po (~ )'. w,~ >oe~Ry, (1.5.3) (1.5.4) (1.5.5) so that (1.5.3), in fact, implies lr;;;~~R. V -; h Or, with band h of the same order - lr;;;~R . V-; 1.5 Further Remarks on Quasistatics 19 (1.5.6) (1.5.7) Conversely, it is clear that the condition for magneto-quasistatics may now be rewritten in the form i.e., ~o b -~-R , eo h lr;;;~R, V-; or and that for electro-quasistatics in the form ~ Po ( ~ ) 2 .. ~ eo ( l~ ) 2 , leading towards ~o b -<t,-R , eo h i.e. (1.5.8) (1.5.9) (1.5.10) (1.5.11) (1.5.12) (1.5.13) Under a different point of view - which we very briefly mention - we can try to determine up to what (angular) frequency the system of Fig. 1.1 c (analyzed for dc) still represents a \"resistor\", i.e., the power dissipated at the load greatly exceeds the magnetic and/or electric energy stored in the volume (blh) per cycle. Thus the first case prevails as long as (1.5.14) 20 1. Introduction i.e., dispensing with the factor 112 which is redundant in our far-reaching approximations, as long as R w~--- hi /10- b For the second case we have or (1.5.15) (1.5.16) (1.5.17) Obviously, /1ohl1b and eobllh represent, respectively, the relevant static plate inductance and capacitance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000976_20.728299-Figure16-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000976_20.728299-Figure16-1.png",
        "caption": "Fig. 16. Starting characteristics (two phase, 12 poles).",
        "texts": [
            " Motor C is generally extremely small in pull-out torque The reason that the pull-out torque of motor A is smaller than that of motor B is because as the number of poles increases, the magnetic flux passes nearly radially through the rotor ring, whereas the magnetic anisotropy is circumferentially oriented so that the area of the hysteresis loop of the rotor ring becomes small (a loop having small and in the direction that the magnetic flux passes. In addition, the reaction torque adds little to hysteresis torque Simply stated, it is desired that a motor having 12 poles should be made to have nearly radial magnetic anisotropy. Fig. 16 shows the starting characteristics of two-phase, 12- poles, CF-type motors. From the figure, it is established that motor A is greater in starting torque and smaller in in the high voltage range of than motor B, and hence motor A is superior to motor B. However, the disadvantage of motor A is that starting torque is almost zero in the low voltage range of This disadvantage is removed by making the gap length larger. In general, a RF-type motor, in comparison with a CF-type motor, is characterized by smaller input current, higher efficiency, etc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002189_mech-34368-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002189_mech-34368-Figure2-1.png",
        "caption": "Fig. 2 X1 Y1 coordinate is needed according to the definition",
        "texts": [
            "org/about-asme/terms-of-use Downloaded From: htt 2.5 Location of Standard Test Plane and Coordinate System On page 23, Figure 15 has the same errors as figure 14 mentioned above. 5 5 Copyright \u00a9 2002 by ASME p://proceedings.asmedigitalcollection.asme.org/ on 04/11/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: ht Table 1. List of Errors page No. Before Revised After Revised 11 In Fig. 4, the position of the working space center point is positioned incorrectly. Along the same x-axis See Fig.1 See Fig. 2. 11 X1Y1 coordinate is needed. See Fig. 3 See Fig. 4. 22 In Figure 14, the Y-axis should be X. The X-axis should be Yaxis in the opposite direction. See Fig. 9 See Fig. 10 23 Figure 15 has the same errors as Figure 14. See Fig. 11 See Figure 12. 25 In item 4. STP Cycle Test, Deviation From STP, Section is \"8.4.2.8\". There is no section with that number. It should be \"8.4.2.7\". 26 Section 7.3 second line is \"(Table 2)\". Table 2 should be \"(Figure 17)\" On page 10 of the standard, the explanation of the working space center point conflicts with the definition of how to find it, given on page 24 of the standard"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002090_j.scriptamat.2004.08.003-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002090_j.scriptamat.2004.08.003-Figure1-1.png",
        "caption": "Fig. 1. Unit vectors n and m. (a) Both n and m lie in a plane containing one of the coordinate axes and (b) m belongs to a plane containing one of the coordinate axes and n is orthogonal to this plane.",
        "texts": [
            " Analogously, if m is a unit vector orthogonal to n (m \u00c6 n = 0), the lateral strain in the direction m induced by rn is given by e\u00f0m\u00de \u00bc rnm m S\u00bdn n \u00bc: em: \u00f02\u00de The lateral strain em is related to the longitudinal strain en through the Poisson s ratio as em = mnm en, so that: mnm \u00bc m\u00f0n;m\u00de \u00bc e\u00f0n\u00de e\u00f0m\u00de \u00bc m m S\u00bdn n n n S\u00bdn n ; \u00f03\u00de or, in terms of cartesian components (assuming the usual summation rule over repeated indices) mnm \u00bc em en \u00bc mimjSijhknhnk npnqSpqrsnrns : \u00f04\u00de The anisotropic elastic nature of the material is obviously reflected on Poisson s ratio, which is therefore a function of the two orthogonal directions n and m. We assume that the unit vectors n and m are directed as shown in Fig. 1. The axes xi, xj, xk will be selected according to the presence of a plane of elastic mirror mnm \u00bc 1 8 s11 \u00fe s33 s55 \u00fe 6s13 \u00f0s11 \u00fe s33 s55 2s13\u00de cos 4h 2\u00f0s15 s35\u00de sin 4h s11cos4h \u00fe 2s15 sin hcos3h \u00fe \u00f02s13 \u00fe s55\u00desin2hcos2h \u00fe 2s35sin 3h cos h \u00fe s33sin 4h : \u00f05\u00de symmetry and, due to its dominant role in the mechanical response, the two loading conditions cover all the significant situations. The monoclinic crystal system is characterized by one plane of elastic reflective symmetry. The normal to the plane of mirror symmetry (according to the data in Landolt and Bo\u0308rnstein [20]) is taken here to be in the x2 direction",
            " Three crystal classes exist in the monoclinic system: the domatic, spheroidal and prismatic: all these classes are associated to the same structure of the elasticity matrix [sij] and the number of independent elastic constants is reduced from 21 (complete anisotropy) to 13 (Cowin and Mehrabadi [21]). The sij are the reduced compliances according to the Voigt s notation: s11 = S1111, s12 = S1122, s13 = S1133, s22 = S2222, s23 = S2233, s33 = S3333, s15 = 2S1131, s25 = 2S2231, s35 = 2S3331, s44 = 4S2323, s46 = 4S2312, s55 = 4S3131, s66 = 4S1212. Due to the presence of the plane of elastic reflective symmetry x1x3, the loading cases of Fig. 1 are assumed with i = 1, j = 2 and k = 3. As an example, the behavior of Poisson s ratio is shown in Fig. 2 for cesium dihydrogen phosphate, when both the unit vectors n and m lie on the plane containing x3. The surface representing the function mnm intersects the horizontal plane mnm = 0 and the Poisson s ratio results to be negative, for every h, in a rather wide range of values for the angle a. In Fig. 3, three particular cases of the loading condition of Fig. 2 are shown. In the case where both n andm are on the plane of elastic symmetry (Fig",
            " 2 where the Poisson s ratio is always negative is shown in the right plot of Fig. 4, corresponding to the third loading case of Fig. 3. Here the function mnm becomes negative for values of the angle a belonging to the interior of a wedge having amplitude Da = 0.66 rad (in the figure, a1 = 1.24 rad and a2 = 1.90 rad); in this case, the minimum value of the Poisson s ratio is mmin = 1.34. For cesium dihydrogen phosphate, Fig. 5 shows the function representing the Poisson s ratio and its intersection with the horizontal plane mnm = 0 for the case (b) of Fig. 1. Also in this case a wide range of angles a and h characterize the auxetic behavior of the crystal. Particular cases of the loading condition of Fig. 5 are given in Fig. 6. In the first case, with n directed along x1 dihydrogen phosphate, corresponding to the cases of Fig. 3. Grey areas in the plane x1x2 and m in the plane orthogonal to n (left), for the monoclinic lanthanum niobate (LaNbO4): s11 = 66.8, s22 = 14.8, s33 = 146.0, s44 = 22.8, s55 = 1060.0, s66 = 18.7, s12 = 16.9, s13 = 94.8, s23 = 30"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002414_027836403128965277-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002414_027836403128965277-Figure6-1.png",
        "caption": "Fig. 6. A cubic polynomial spiral. Clockwise from top left, a curve of cubic polynomial curvature, its curvature, and the first and second derivatives of curvature versus distance.",
        "texts": [
            " In this context, \u201cestimated well\u201d means well enough to determine end posture to perhaps a few millimeters in position and a few milliradians in heading. When coefficients are large in magnitude, it may be necessary to perform many integrand evaluations in Simpson\u2019s rule. At some point, large coefficients correspond to infeasible inputs and the difficulty in computation indicates difficulty or even impossibility of execution. In rough terms, curves that cannot be computed, cannot be executed anyway. The appendix provides a straightforward mechanism to reuse computations while refining the estimate of the quadratures. Figure 6 shows a typical member of the cubic curvature polynomial family of curves computed. Curves must be much at WESTERN MICHIGAN UNIVERSITY on June 4, 2016ijr.sagepub.comDownloaded from more aggressive than this one to present difficulty in the forward solution. All forms of the inverse solution require an initial estimate in order to start the iterations. Estimates must be very good to have a significant impact on the efficiency because most of the time is spent fine tuning the answer. Therefore, efficiency is not a strong motivation to produce good initial estimates"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001384_epjap:2002122-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001384_epjap:2002122-Figure1-1.png",
        "caption": "Fig. 1. Drawing of the studied motor.",
        "texts": [
            " They are grouped together in two phases, named \u03b1 and \u03b2 respectively fed by the voltages v\u03b1 and v\u03b2 , the RMS value of which are V\u03b1 and V\u03b2 . The poling direction of these elements let an elastic flexural wave travel. This wave is assumed to be purely sinusoidal (hypothesis H1). Moreover, we count k piezoelectric elements per phase with the same poling direction. The traveling wave bending the ring uses friction to transmit torque to the rotor shaft, a metal component placed on the stator. The mass of the rotor shaft is called mR. Figure 1 shows an illustration of the major components of the motor and several notations used along this article: \u2013 a and b the respectively inner and outer radius of the stator; \u2013 h the length between the undeformed centerline of the stator, and the position of the contact point; \u2013 F\u03c4 an axial force pressing the stator and the rotor together. The rotor drives a load, and the inertia of the load and the rotor is named J . A load torque Cr acts on the mechanical system. In order to make the modelization easier, and thus well adapted for a control scheme, we introduce the concept of ideal rotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002997_j.mechmachtheory.2004.02.005-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002997_j.mechmachtheory.2004.02.005-Figure2-1.png",
        "caption": "Fig. 2. Conversion relationship between the coordinate systems.",
        "texts": [
            " Finally, this paper has finished the simulation of the new type of noninvolute beveloid gears by applying the CAD system, Pro/Engineer. The motion coordinate systems r1 \u00bc \u00bdo; i*1; J * 1; k * 1 and r2 \u00bc \u00bdo; i*2; J * 2; k * 2 , as shown in Fig. 1, are attached to the involute beveloid gear (gear 1 in short) and to the tooth profile (gear 2 in short) of the gear which is conjugated with gear 1, respectively. r10 \u00bc \u00bdO10;~i10;~j10;~k10 and r20 \u00bc \u00bdO20;~i20;~j20;~k20 are the original coordinate systems of gear 1 and gear 2, respectively. The conversion relationship of all the coordinate systems is shown in Fig. 2. Thus the coordinate transition matrix can be expressed as follows: M21 \u00bc cosu1 cosu2 sinu1 sinu2 cosd sinu1 cosu2 \u00fe cosu1 sinu2 cosd sinu2 sind cosu1 sinu2 sinu1 cosu2 cosd sinu1 sinu2 \u00fe cosu1 cosu2 cosd cosu2 sind sinu1 sind cosu1 sind cosd 2 4 3 5 \u00f01\u00de where d is the shaft angle between gear 1 and gear 2; u1 and u2 are the rotation angles of gear 1 and gear 2, respectively. Their relationship can be represented as u1 \u00bc i12u2, where i12 is the angular speed ratio. The tooth profile P 1 of the standard beveloid gear 1 can be represented as follows: ~r1 \u00bc x1~i1 \u00fe y1~j1 \u00fe z1~k1 \u00f02\u00de It can be rewritten as follows: x1 \u00bc rb1 cos\u00f0 l \u00fe h\u00de rb1l sin\u00f0 l \u00fe h\u00de y1 \u00bc rb1 sin\u00f0 l \u00fe h\u00de rb1l cos\u00f0 l \u00fe h\u00de z1 \u00bc ph 9= ; \u00f03\u00de where p rb1 tgbb1 is helix parameter, bb1 is the base cylinder helix angle; rb1 is the base circle radius (mm); l and h are the parameters of the involute helicoids"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002427_50009-5-Figure7.15-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002427_50009-5-Figure7.15-1.png",
        "caption": "FIGURE 7.15 Rotating field and magnetization in the plane of an open test plate. The applied field Ha leads the magnetization by the angle ~a. The field FI1 measured by a flat H-coil at a distance h 1 from the sample surface is H1 = Ha - klJ and leads by the angle ~1. If the distance is increased to h 2 > h i , the field becomes H 2 - - H a - k2J , w i t h k 2 < k 1 and the leading angle becomes ~2 < ~1. The vector diagram shows that Ha sin ~a = /-/1 Sin ~1 = /-/2 Sin ~ , which implies that the measured loss does not depend, in principle, on the distance of the H-coil from the test plate surface.",
        "texts": [
            " The energy loss per cycle and unit volume can be expressed (see also Section 7.3) as W -- H. ~-~ dt, (7.8) where T is the period. Since f ~ ~ dj Nd J. ~-~dt = 0, /z0 we can equivalently write dj W -- Ha\" - ~ dt. This is obviously unders tood as due to the demagnet iz ing field being in phase with the magnetization. It also means that whatever the distance h of the H-coil from the test plate surface, the phase shift be tween the detected field H(h) and J will change in such a way that the integral in Eq. (7.8) will not change at all. Figure 7.15 shows this clearly for the 2D case [7.55], where the vector J trails the measured field H(h) by an angle ~, which depends on h in such a way that the quanti ty H(h)sin~(h)), proport ional to the loss, is constant. The example reported in Fig. 7.16, which compares the hysteresis loops measured on the same lamination, first as a single strip in a closed circuit, then as a disk in a 2D yoke, both using a I m m thick flat H-coil, further illustrates the point. The loop measured on the single strip can be considered as intrinsic because the demagnet iz ing field is very small as is the increase of the tangential field versus distance from the strip surface (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001366_pime_proc_1992_206_183_02-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001366_pime_proc_1992_206_183_02-Figure1-1.png",
        "caption": "Fig. 1 Principal frictional elements in a reciprocating engine",
        "texts": [
            " The mechanical losses in an engine are only a small proportion of the total losses, but they represent a significant fraction of the output power. A reduction in the internal combustion engine losses is important to produce energy saving; reduction in fuel consumption and wear are two important effects of it. Furthermore, a reduced fuel consumption reduces gaseous emissions. Thus it is very useful to study in detail how and where these losses are produced to know how to design correctly the different components and the complete engine. The piston-liner system, valve train and bearings (Fig. 1) are the most important components for the mechanical friction losses in reciprocating engines. The M S was received on I S November I991 and was accepted for publication on 15 April 1992. Because they are the major lubricated components in an engine and for a better comprehension of the lubrication concepts expressed later, the principal lubrication regimes are shown in Fig. 2. The piston skirt-liner lubrication is predominantly hydrodynamic, with surfaces completely separated by a relatively thick oil-film; localized contacts between the ring and liner are present at the dead centres (at the top, in particular, in firing conditions) because of zero and low velocities (mixed lubrication, with part of the load carried by the fluid film and the rest by contacting asperities, and the boundary lubrication regime, with the surfaces, wet by absorbed oil, in contact)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001370_elan.1140050103-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001370_elan.1140050103-Figure2-1.png",
        "caption": "FIGURE 2. Modification of the activated silicon surface with (1,l '-ferrocenediy1)dichlorosilane.",
        "texts": [
            ")des were removed from the reaction solution, rinsed thoroughly in ethanol, and then air dried. The electrodes were stored in vacuo over silica gel until required. The reactions involved in this step are summarized in Figure 1(A). Mod@cution Using (1,l '-fewocenediylJDichlorosilane. This moisture-sensitive strained Si-C moiety can be made to react in the presence of trace amounts of water with surface -OH groups to form a covalent linkage between the ferrocene and the surface of the silicon electrode [6, 71 (see Figure 2). As well as the direct linkage, it has been suggested that polymerization between neighboring ferrocene groups can also occur [lo]. Following pretreatment and drying, the electrodes were placed in flat-bottomed tubes and sparged with dry oxygen-free N, for 20 minutes. Degassed isooctane (2.5 ml) was syringed into each tube followed by 0.3 ml of (1,1 '-ferrocenediy1)dichlorosilane solution in isooctane (0.1 M). The electrodes were allowed to react, with stirring, for periods of time ranging from 5-48 hours"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002495_ac051178c-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002495_ac051178c-Figure2-1.png",
        "caption": "Figure 2. Process of finding the tip position above a microcell by using SECM scan curve (current versus tip position curve).",
        "texts": [
            " The tip current decreased with the distance due to negative feedback as the tip was close to the slide. When i was 80% of the steady-state current, the tip was stopped. In this case, the distance between the tip and the slide surface could be estimated using the fit of the experimental normalized approach curve to theory based on the method reported by Bard et al.58 From this fitting, the distance was estimated to be \u223c20 \u00b5m. Then, the tip was moved laterally toward the microcell at a constant height according to the traces shown in Figure 2, to search the microcell center. When the tip was moved along the x-axis above a microcell (solid line 1), i increased, because the effect of the negative feedback was reduced. When i decreased, implying that the tip left the microcell, the tip was moved back (dashed line 2) and stopped at the position of maximum current. Then, the tip was moved along the y-axis (dashed line 3) and crossed the whole microcell, which could be observed as i was reduced. Finally, the tip was scanned reversely along the same trace (solid line 4) and stopped at the position of the maximum current, meaning the position of the microcell center"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001321_s0013-7944(03)00050-x-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001321_s0013-7944(03)00050-x-Figure3-1.png",
        "caption": "Fig. 3. Transformation of gearing to mechanical model.",
        "texts": [
            " In the calculation in our model we take into account the actual loading so that the gear tooth is loaded at various points of engagement by currently corresponding force F . We can accurately take into account these loadings in the calculation only by mean of the mathematical model of a real gearing in the form of equation of motion, which in general represent a non-conservative non-linear system of differential equation of the second order. For a spur gear pair the replacement mechanical model is shown in Fig. 3. For a gearing consisting of such gears we can write the system of equations of motion in the matrix form [6]: I \u20acH \u00feD _H \u00fe K\u00f0H \u00fe q\u00de \u00fe F\u00f0t\u00de \u00bc 0 \u00f03\u00de where: I \u00bc diag\u00bdI1; I2; . . . ; In matrix of inertia moments D \u00bc diag\u00bdD1;D2; . . . ;Dn damping matrix H \u00bc \u00f0H1;H2; . . . ;Hn\u00de vector of angular turns K \u00bc diag\u00bdK1;K2; . . . ;Kn rigidity matrix q vector of clearance between tooth flanks during engagement F\u00f0t\u00de vector of external loadings In general, depending on the number of gears we obtain the number of differential equation of second order, which, in our algorithm is solved by the conventional method of Runge Kutta",
            " The results of calculation are angular turnings, which indicate the point of engagement on the tooth and loading occurring in this point. To be able to determine the properties of very short cracks, it is important in the analytical models describing the S\u2013N curves to consider the dominant properties of the fields of the crack tip as well as the crack growth rate, which is high in the beginning but then decreases [2]. This can be reached by considering the separate regimes in the Kitagawa\u2013Takahashi diagram, which gives a significant advance in the understanding of short crack behaviour (Fig. 3). This diagram shows the effect of defect size on the fatigue limit stress; see, for example, Fig. 2. For large defects, the allowable stress for infinite life must be low, within linear elastic fracture mechanics regimes, and, therefore, the limiting condition is given by a straight line of slope minus one half of the threshold stress intensity factor DKth, such that DKth \u00bc Y \u00f0a=S\u00deDr ffiffiffiffiffiffiffiffi path p \u00f04\u00de where Y \u00f0a=S\u00de is shape factor [3], Dr is stress ratio and ath is a threshold crack length"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000666_s0022-2860(00)00629-3-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000666_s0022-2860(00)00629-3-Figure1-1.png",
        "caption": "Fig. 1. Chemical formulae of 1,10-phenanthroline.",
        "texts": [
            " Power at the sample was restricted to 0.5 mW in the case of measurements with a Raman microscope. Prior to the spectroscopic measurements, the polycrystalline copper electrode was roughened by anodic \u201cactive\u201d dissolution in 0.2 M CuSO4 1 0.4 M H2SO4 at E 10:5 V for 40 s. A typical three-electrode potentiostatic system was used. A platinum wire was used as the counter electrode and a silver chloride electrode as the reference. All potentials are reported with respect to the Ag/AgCl electrode. SERS studies on phenanthroline (Fig. 1) containing systems are scarce and were confined to the Ag surface [8,9]. As far as we know no results have been published until now for the Cu\u2013phenanthroline system. In this study SERS spectra were recorded at the Cu electrode/0.003 M 1,10-phenanthroline 1 0.1 M KCl solution interface under a potential controlled within a range of 20.15 V (open circuit potential) to 21.1 V vs Ag/AgCl. The pH of the investigated solutions was changed from neutral to acidic (pH 2). In order to characterise the surface species, the SERS spectrum was compared with the normal Raman spectra of o-phenanthroline monohydrate and its copper (I) complex in the solid state (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002807_j.optlastec.2004.08.015-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002807_j.optlastec.2004.08.015-Figure2-1.png",
        "caption": "Fig. 2. Recorded profile.",
        "texts": [
            " Since the information received by the sensor comes through a small section, the resulting resolution is high. The system moves under the protection nozzle as in real working conditions, concerning the gas flow (oxidation protection, \u2018\u2018plasma hunting\u2019\u2019, etc.). Consequently, the pressure evolution in the gas-influenced zone can be recorded. This work presents the results obtained with two nozzles, coaxial with the laser beam, in the case of surface treatment and welding using an Nd:YAG laser. Nevertheless, the methodology that we propose can be employed for other laser sources. Fig. 2 presents the pressure evolution in the nozzleinfluenced zone. A pressure value is recorded when the sensor is centered on the base followed by a relaxation that appears with the sensor movement. This depression is due to the speed difference between the assistant gas molecules and the ambient air ones. Actually, in the case of an incompressible flow, the total pressure measured by the sensor is composed by two terms: static and dynamic pressures. The dynamic pressure, which contains the speed factor, changes its direction when the gas stream is tangent to the pressure-recording hole (just before reaching it and right after this hole), which explains the measured depression"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001044_cdc.2003.1272865-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001044_cdc.2003.1272865-Figure3-1.png",
        "caption": "Fig. 3. Position servomechanism",
        "texts": [
            "1 Intel Pentium 3 733MHz 256MB. A. Description of Constrained System To perform a control experiment for validation of the proposed reference governor, we need to design a control system and coustruct a reference management rule by offline calculation following to the proposed way. Additionally, we will show a time response of the designed closed-loop system under a constraint. I ) Plant description: We consider a control of the practical plant E,, which consists of a DC-motor, a gear, a hard shaft and a load in Fig. 3. Ignoring the t w small motor electrical time constant and denoting by OL the load angle and by xp = [ OL Or. ]', then from the dynamic equations the model of C, can be described by the following state space form, where the control U = V and the output z1 = OL which is measured by encoder. Next, we have identified both parameter values from the experimental step response data of tJL = 90 [deg] = 1.5708 [rad]. As a result, c = 0.7 and w, = 7'. Moreover, E, has the saturation constraint about the input volt "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002847_b:tril.0000044500.75134.70-Figure13-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002847_b:tril.0000044500.75134.70-Figure13-1.png",
        "caption": "Figure 13. Different EHL films under pure rolling and pure sliding conditions, PB1300 with a load of 16 N and an entrainment speed of 598.5 lm/s: (a) fringe pattern under pure rolling; (b) fringe pattern at pure sliding; and (c) film profiles along the center line in the entrainment direction.",
        "texts": [
            " During the tests, an average of 11 sets of film thickness data around the contact centre in the centerline along the entrainment was taken as the central film thickness for one measurement. For each experimental condition, the film thickness was measured six times and the mean was taken as the final result. Figure 12 provides also the standard deviation bars along with some thin film thickness data, which illustrates the uncertainty of measurements in the region of ultra thin film lubrication. For values less than 10 nm, the results have an average standard deviation of 0.89 nm. Interferograms, as shown in figure 13, were obtained from a purposely designed experiment to demonstrate the existence of an inlet dimple in an EHL film theoretically predicted about a decade ago by Lee and Hamrock [29] and Shieh and Hamrock [9], based on the concept of limiting shear stress. A polybutene PB1300 of very high viscosity was selected as the lubricant to ensure typical EHL film thickness at the ultra slow entrainment speeds under employed for suppressing shear heating at large slide/roll ratios. It can be seen that under pure rolling, there is a typical EHL film profile with a distinct outlet constriction",
            " Under simple disc sliding (disc sliding and ball stationary) conditions, a quite different film profile occurs even at the same entrainment speed. An obvious dimple appears at the inlet region. In the central region, the film gap is more a wedge-like other than the conventional parallel one. Furthermore, the outlet constriction is not so a distinct as that in pure rolling, indicating a local pressure distribution with significant deviations from the well-known second pressure spike. All the above experimental observations are well correlated with the theoretical predictions [9,29]. Figure 13 shows that under simple disc-sliding conditions, the film thickness changes from a minimum of 432.4 nm to a maximum of 1255.4 nm within the contact region. At the inlet, the film thickness is at a typical micrometer level, while the depth of the dimple is 99.5 nm. It can be seen that the MBI method can give an accurate description of such a non-conventional film shape. The MBI thin lubricating film measurement scheme has been integrated with an optical EHL test rig successfully. Software has been written for efficient film profile reconstruction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003823_icar.2005.1507430-Figure13-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003823_icar.2005.1507430-Figure13-1.png",
        "caption": "Fig. 13. The path that the robot traverses in the face of a biased distribution, where the chance of the ball appearance is 60% in region 2, 30% in region 1 and 5% in regions 3 and 4.",
        "texts": [
            " Because whatever the distribution, the average detection time for each event is constant and equal to the half of the whole traversing time. 3) Biased Distribution: In our next experiment we tested the robustness of our approach in a scenario such that the balls appear in all the regions but with different probabilities. In the biased distribution, with probability 60% the ball appears in region 2, with probability 30% it appears in region 1, with probability 5% in 3, and with probability 5% in 4 (Peg = .6/50, .3/50, .05/50, and .05/50 respectively). The path that the robot traverses is approximately the one in Figure 13. The time needed for the robot to change its path from the uniform case to the path shown in Figure 13 is based on how fast it can learn the distribution, which itself is based on frequency of ball appearances. In our experiment, every 50 seconds an average of 1 ball appeared. In this setting, the robot took 9 complete traverses (1734 seconds or 35 ball appearances) to start traversing the shown path. After the 1734 seconds, when the robot learned the distribution, on average every ball was visited 79\u00b11.2 seconds after its appearance. In the experiment, 200 balls were shown to the robot. This result is significantly better than uniform traversal which results in average detection time of 106 or ideally 100 seconds",
            " In particular, we consider a scenario in which at some unknown point in time the probability of appearance of the balls changes abruptly. The initial distribution of the ball appearance was the same as the biased case discussed in previous section, that is 60% in region 2, 30% in region 1, 5% in region 3, and 5% in 4. After 100 ball appearances, the distribution changes to the uniform appearance of the ball. The path that the robot found with the starting distribution is the same as the one in Figure 13. It took the robot about 1820 seconds or 36 ball appearances to adapt to the second distribution and approximately follow the path in Figure 10. In this paper, the problem of continuous area sweeping is introduced. The problem is defined as one in which a robot must repeatedly visit every part of the environment in order to detect a set of events of interest. The frequency of the events can possibly be non-uniform, thus the robot should visit the points with non-uniform frequency. Examples of continuous area sweeping tasks are surveillance and cleaning"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003206_j.mechmachtheory.2003.12.003-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003206_j.mechmachtheory.2003.12.003-Figure3-1.png",
        "caption": "Fig. 3. Stephenson six-link mechanism in the Chase and Mirth example [3] and five domains of the driving link.",
        "texts": [
            " For that reason, we have to discriminate the domains of motion of the driving link. According to the definitions in Section 1, the branch corresponds to the domain of motion on the coupler curve separated by two limit points or the connection of two parts separated by limit and turning points. The circuit corresponds to the coupler curve or the domain of motion on the coupler curve separated by two turning points. Moreover, the circuit corresponds to the connection of adjacent domains of motion on the coupler curve. Fig. 3(a) is the Stephenson-3 six-link mechanism of the Chase and Mirth example [5]. Numbers of circuits and branches are three and five, respectively. Fig. 3(b) and (c) are five domains of motion of the driving link on the coupler curve and five relationships between the input angle and the coupler angle of the constituent four-link mechanism, respectively. That is, the number of domains of motion of the driving link is accounted to five. Besides, a more valid variable than the output angle is adopted for discriminating domains of the driving link, which corresponds one to one to the point of the coupler curve. So, two circuits to be illustrated one over another in the Chase and Mirth Fig",
            " When the input angle h6 takes a value within the interval whose lower and upper bounds correspond to the point of marks h and the upper limit point on the h6 / curve, respectively, two roots of the sixth order polynomial of the displacement analysis belong to one domain of motion of the driving link, that is, one branch. The variable to be newly adopted is suited to the procedure for discriminating the domains of motion of the driving link in consideration of the complicated property above-mentioned. The similar treatment need to apply the long part (circuit 1, branch 2) of the curve of reciprocating rotational-oscillating motion in the case of the Chase and Mirth example as shown in Fig. 3(c), where the driving link may rotate through greater than 2p without inversion of linkchain configuration. The number of solutions in the displacement analysis of Stephenson-3 six-link mechanisms is even and less than six and as many link-chain configurations of moving links are formed from the set of solutions of angular displacements. The domain of motion of the driving link is defined by such a domain of the displacement or the angular displacement that the driving link is possible to move without inversions of the link-chain configuration of moving links",
            " If signs \u00f0S1k; S2k\u00de of the link-chain configuration to correspond to the real root h2k coincide with signs \u00f0S 1 ; S 2\u00de, the real root h2k corresponds to the value of the input angle apart from h 6 by 2p, and this link-chain configuration is contained also in the domain of motion \u00bd/l;/u . Namely, two real roots of Eq. (20) correspond to a same link-chain configuration. Then, newly, let h2k (k \u00bc 1 or 1\u20132) denote such real roots of Eq. (20) and let /k denote the value of / which corresponds to h2k. If there is not exist the real root of h2k which are secured for the lower limit position /l in the above-mentioned manner, let the value of k be zero. The domain of motion [1.924, 10.226, d\u00f0h6\u00de > 0] of the six-link mechanisms of Fig. 3 and two domains of motion [6.169, 15.809, d\u00f0h6\u00de > 0], [6.169, 15.809, d\u00f0h6\u00de < 0] of the six-link mechanisms of Fig. 4 are examples of such six-link mechanism that the driving link rotates greater than 2p and less than 4p. If the domain of motion \u00bd/l;/u has the point /k, the driving link oscillates within an interval of the input angle such that 2p < h6 < 4p. In such cases, we deal with the calculated interval \u00bdh6l; h6u of the input angle as two intervals \u00bdh6l; h6l \u00fe 2p and \u00bdh6l \u00fe 2p; h6u \u00fe 2p which correspond to two jointed domains \u00bd/l;/k , \u00bd/k;/u , respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002427_50009-5-Figure7.63-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002427_50009-5-Figure7.63-1.png",
        "caption": "FIGURE 7.63 (a) Pickup coil type permeance meter developed by Yamaguchi et al. [7.173] for magnetic film testing in the frequency range 1-3.5 MHz. The drive parallel plates are terminated with a short circuit and are 50 f~ matched to the reflecting port of a network analyzer. The standing-wave generated magnetic field amplitude varies appreciably with distance from the termination only on approaching the GHz range, as shown in (b) for f -- 3 GHz (A/4 = 25 mm). The pickup coil, which is matched to the receiver port of the network analyzer, is realized by means of a central conductor and outer conductors. The latter provide shielding against the electric field and are connected to the ground plane of the driving coil near the termination.",
        "texts": [
            " The need to achieve the GHz range in the characterization of thin magnetic films, instigated by their increasing applications in UHF devices (for example, mobile phone handsets), has prompted both further development of the just described pickup coil methods and adaptation to the thin-film geometry of the TEM transmission line techniques solidly assessed with ferrites. Good progress towards extended frequency permeance meters of the pickup coil type has been achieved in the last decade at the Tohoku University laboratory in Sendai [7.171-7.173]. An example of a permeance measuring jig with 1 MHz-3.5 GHz capabilities developed in this laboratory is shown in Fig. 7.63. The measuring jig is made of a pair of current-carrying driving plates, shorted at the end and connected via an SMA connector to the reflection port of a network analyzer. Its dimensions are such as to provide 50 12 matching. In addition, it is sufficiently short to avoid higher-order resonating modes in the GHz range (\u2022/2 = 43 mm at 3.5 GHz). The pickup coil, which is connected to the receiver port of the network analyzer, is especially designed to be insensitive to the electric fields. As discussed in detail in Ref",
            "93) on a shorted transmission line loaded by the sample under test has been demonst ra ted up to a few GHz by a number of authors [7.174, 7.175]. The procedure in essence is no different from the previously discussed method of characterizing a toroidal ferrite specimen placed at the bot tom of a shorted line, but for the sensitivities required and the obvious use of a microstrip line instead of a coaxial line. The termination is in the shape of a loop, similar to but smaller than the one made with the drive plates in Fig. 7.63 (width w ~ 5 -10 ram, length l --- 10 mm). At a frequency f = 2 GHz, these dimensions are still safely lower than ~/4. With a radiofrequency current i circulating in the loop, the generated field, directed along the loop axis, is H = k(i/w), with k -< 1 and the flux additionally linked with the loop after introduction of a film sample of cross-sectional area As is z ~ = AsJ = As/z0(/Zr - 1)H. This brings about a variation of the coil impedance AZ -- joJ/z0(/zr - 1)k(As/w), with complex relative permeability/zr =/Zr - j/z\", which is then determined by difference of a double measurement with empty and loaded fixtures",
            " Again, calibration with a reference sample amenable to good theoretical prediction is recommended. Korenivski et al. [7.174] take a YIG thin film as a model reference sample because of its near-zero internal anisotropy (/z = Js/HDc), lack of eddy current effects, and narrow ferromagnetic resonance line. Yamaguchi et al. have carried out a comparison of permeability measurements up to 3 GHz in a number of amorphous C o - N b - Z r and Fe~-Co-Mo-Si -B thin films by means of two independent methods: the two-port setup method illustrated in Fig. 7.63 and the approach based on the loading of a shorted microstripline [7.176]. The values found differ, on average, by + 15%, the major reason for the found discrepancies being attributed to the calibration procedure. Figure 7.64 illustrates a case where good agreement was found. It relates to a 0.14 ~m thick C o - N b - Z r film with anisotropy field Hk = 4537 A/m, characterized along the direction orthogonal to the easy axis. 7.1. IEC Standard Publication 60404-4, Methods of Measurement of the d.c"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003399_j.ijmecsci.2005.04.003-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003399_j.ijmecsci.2005.04.003-Figure2-1.png",
        "caption": "Fig. 2. Geometry of a cylindrical helix.",
        "texts": [
            " (9) The values of o which make the determinant of the system dynamic stiffness matrix zero are the natural frequencies of the problem. For the case of free vibrations the dynamic stiffness matrix is obtained by applying the complementary functions method described in Appendix B. Both the element dynamic stiffness matrix and the fixed-end forces are determined by the method of the complementary functions in the Laplace domain (see Appendix C). The parametric equations of a helix is given by Temel and C- al\u0131m [17] (see Fig. 2) as x \u00bc a cosf; y \u00bc a sinf; z \u00bc hf, (10) where f is the horizontal angle of the helix. The infinitesimal length element of the helix is defined as c \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 \u00fe h2 p ; ds \u00bc cdf; cos a \u00bc a=c; sin a \u00bc h=c, (11) where a and a are pitch angle and centerline radius of the helix, respectively. The curvatures of a cylindrical helical spring are w \u00bc a=c2 \u00bc constant; t \u00bc h=c2 \u00bc constant. (12) The relationship between the moving triad \u00f0t; n; b\u00de and the fixed reference frame \u00f0i; j;k\u00de are (Fig. 2) fVgTtnb \u00bc \u00bdB fVgTijk; Vt Vn Vb 8>< >: 9>= >; \u00bc \u00f0a=c\u00de sinf \u00f0a=c\u00de cosf \u00f0h=c\u00de cosf sinf 0 \u00f0h=c\u00de sinf \u00f0h=c\u00de cosf \u00f0a=c\u00de 2 64 3 75 Vi Vj Vk 8>< >: 9>= >;, (13) where Vi;Vj;Vk are the vector components in the fixed reference frame and Vt;Vn;Vb are the vector components with respect to the moving triad. Assuming that the centroid and the shear center of cross-section coincide, the n, b axes become the principal axes and the effect of warping of the cross-section is neglected. If the selected section is considered symmetric in terms of geometry and material, the system of 12 ordinary differential equations governing the dynamic behavior of the helical bar with respect to the moving coordinate system, is obtained in canonical form in the Laplace domain as dU\u0304t df \u00bc a c U\u0304n \u00fe cA0 11T\u0304 t \u00fe cA0 12T\u0304n, \u00f014a\u00de dU\u0304n df \u00bc a c U\u0304t \u00fe h c U\u0304b \u00fe cO\u0304b \u00fe canA0 22T\u0304n \u00fe cA0 21T\u0304 t, \u00f014b\u00de dU\u0304b df \u00bc h c U\u0304n cO\u0304n \u00fe cabA0 33T\u0304b, \u00f014c\u00de dO\u0304t df \u00bc a c O\u0304n \u00fe cD0 11M\u0304t \u00fe cD0 12M\u0304n, \u00f014d\u00de dO\u0304n df \u00bc a c O\u0304t \u00fe h c O\u0304b \u00fe cD0 22M\u0304n \u00fe cD0 21M\u0304t, \u00f014e\u00de dO\u0304b df \u00bc h c O\u0304n \u00fe cD0 33M\u0304b, \u00f014f\u00de dT\u0304 t df \u00bc cz2 ~AU\u0304t \u00fe a c T\u0304n \u00fe cB\u03047, \u00f014g\u00de dT\u0304n df \u00bc cz2 ~AU\u0304n \u00fe h c T\u0304b a c T\u0304t \u00fe cB\u03048, \u00f014h\u00de dT\u0304b df \u00bc cz2 ~AU\u0304b h c T\u0304n \u00fe cB\u03049, \u00f014i\u00de dM\u0304t df \u00bc cz2 ~I1O\u0304t \u00fe a c M\u0304n \u00fe cB\u030410, \u00f014j\u00de dM\u0304n df \u00bc cz2 ~I2O\u0304n \u00fe h c M\u0304b a c M\u0304t \u00fe cT\u0304b \u00fe cB\u030411, \u00f014k\u00de dM\u0304b df \u00bc cz2 ~I3O\u0304b h c M\u0304n cT\u0304n \u00fe cB\u030412"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000514_1.1286271-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000514_1.1286271-Figure2-1.png",
        "caption": "Fig. 2 Thermocouple arrangement",
        "texts": [
            " Power oscillator controls the load frequency and amplitude. The oil temperature is measured by 12 chromel-alumel thermocouples using a temperature scanner. The temperature scanner is based on CMOS IC technology and can be operated in \u2018\u2018manual\u2019\u2019 or \u2018\u2018auto\u2019\u2019 mode. In auto mode, the scanner indicates temperature readings at 1\u201312 channels at an interval of 8 s sequentially. Automotive cold compensation is in-built and linearized accuracy is 61\u00b0C. Thermocouple wire is fed in 3.175 mm ~1/89! screw drilled ~Fig. 2!, and screw is fixed in the tapped copper rivet ~Fig. 2!. The supply pressure of lubricant is controlled by two-valves and flow is measured by rotary piston flow meter. A monograde oil ~kinematic viscosity of 20.437 cSt at Transactions of the ASME /data/journals/jotre9/28691/ on 03/06/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: http of Tribology ://tribology.asmedigitalcollection.asme.org/pdfaccess.ashx?url= 40\u00b0C, 3.95 cSt at 100\u00b0C and density of 873.5 kg/m3! is used for bearing lubrication. The oil feed pressure is maintained at 206"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003160_0022-0728(85)80080-2-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003160_0022-0728(85)80080-2-Figure5-1.png",
        "caption": "Fig. 5. Anodic E/I curves for N204 + H 2 0 mixtures in sulfolane (+0.1 mol dm -3 TEAP) at 303 K. [N204]=12.0X10 -3 mol dm -3, [H20 ] = 0 (1), 1.1X10 -3 (2), 2 .1x10 -3 (3), 4 .4x10 -3 mol dm -3 (4).",
        "texts": [
            "1 \u00d7 10 -s mol dm -3 at 303 K [7]. Thus, it may be concluded that the dissociation according to: N204 ~ NO; + NO 2 (8) is very weak with regard to those according to equilibria (1) and (7), and can therefore be neglected in this solvent. The solvents used in the present work have been claimed anhydrous. In order to establish the reaction of N204 with water, by means of electrochemical techniques, small calculated quantities of water were introduced into an anhydrous sulfolane solution of N204. In Fig. 5 the (RDEV) voltammograms thus obtained are shown. When water has been introduced into the solution, a supplementary wave appears at a potential corresponding to the oxidation of N203. This latter species is probably produced through the following reaction sequence: N204 + H 2 0 ~- H N O 2 + H N O 3 (13) HNO2 + N204 ~ N 2 0 3 + HNO3 (14) Following the present work, a general mechanism of the electrochemical oxidation of N204 in aprotic media can be proposed: kl N24 ~ 2 NO 2 ~ 2 NO~- + 2 e- k-I The equilibrium and the rate constants of the homolytic dissociation of N204 have been determined in sulfolane, propylene carbonate and nitromethane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002661_bf03258605-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002661_bf03258605-Figure1-1.png",
        "caption": "Figure 1. Spray forming of tubular preform.",
        "texts": [
            ", Mannesmann-Demag5 in Germany, Sumitomo Heavy Industries in Japan, Sandvik Steel in Sweden, and MIT (Liquid Dynamics Compaction)6 and Drexel University in the U.S. A recent review by Singer4 discusses some appli cations of the process. General Electric is a licensee of Osprey Metals and has been investigating spray-forming technology for the production of nickel-base superalloys. NEAR NET\u00b7SHAPE MANUFACTURE To produce a tube preform, atomized droplets are deposited onto a rotating, tubular collector which traverses through the spray (Figure 1). Located at Sand vik Steel in Sweden, the largest tube plant in operation is being used to produce stainless steel tubing up to 8 m long, in sizes ranging from 100-400 mm OD, and with wall thicknesses up to 50 mm. Molten alloy is bottom poured from a one metric-ton or seven-metric-ton induction heated ladle directly into a gas-atom izing device. Metal dispensing and atomizing rates are typically in the range 80- lDO kg per minute with the flow rate of metal being controlled by argon gas overpressure above the melt"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001358_s0094-114x(03)00090-9-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001358_s0094-114x(03)00090-9-Figure8-1.png",
        "caption": "Fig. 8. Assembly modes of the triad with one external prismatic joint.",
        "texts": [
            " The six solutions for this polynomial are inserted in the Table 1, where two real roots and four complex roots are obtained for the specific geometry here considered. For each real value of the displacement s, the coordinates x and y of the internal joint B are determined using the Eqs. (22) and (23). The values of the coordinates of the joint B are inserted in the Table 1. After that the coordinates of the internal joint E are calculated with the aid of Eqs. (4) and (5) while the coordinates of the internal joint C are obtained with Eqs. (16) and (17). The two configurations of the triad corresponding to the real solutions are presented in Fig. 8. Others input data of the triad can lead to six, four or zero real solutions. In the second example, using the procedure described in Section 3, the position analysis of a triad with one internal joint is considered (see Fig. 5). The geometrical data and the coordinates of the external joints A, D and F of this triad are inserted in the left part of the Table 2. The coefficients of the polynomial equations (36) and (37) are calculated and the extraneous roots are eliminated. The solving of the final sixth order polynomial leads to four real roots and two complex roots (see Table 2) for the input data here considered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001704_s0022-5193(03)00015-8-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001704_s0022-5193(03)00015-8-Figure1-1.png",
        "caption": "Fig. 1. (a) Schematic diagram of a copepod and a bead (not to scale) The copepod\u2019s swimming trajectory is assumed to lie along its body axis and the orientation angle of the bead (see Table 2) is as shown. (Diagram based on Fig. 1 of Bundy et al., 1998). (b) Possible long-range perception field of a copepod which, based the experimental data of Bundy et al. (1998) appears to be closely correlated with the directions of its antennae. (c) Diagram illustrating the assumed perception field of a planktonic predator to be used in this work. It is made up of a right circular cone of semi-vertex angle a, together with a base from a segment of a sphere of contact radius R. All prey entering this \u2018ice cream\u2019 cone will be perceived. Generally the predator\u2019s line of sight will lie in the direction of its swimming motion.",
        "texts": [
            " Typical values of R range from 1 to 40 10\u20133 m for fish larvae (Muelbret et al., 1994). However, there are many experimental studies which show that planktonic predators perception capabilities are not isotropic. Copepods, for example, typically perceive their prey (and avoid predators themselves) by detecting tiny disturbances in the local fluid environment generated by a moving body close by. They do so by the movement of tiny sensory hairs or satae, found all over their bodies but especially on their antennae (Fig. 1a), which generate electrical signals in sensory neurons found at the base of each hair (French, 1988; Corey and Garc!\u0131aAn\u0303overos, 1996). A number of different components of the local fluid disturbance (those derived from changes in deformation rate, vorticity and arising from density differences between fluid and microorganism) were examined by Ki^rboe and Visser (1999), who calculated each of these for the idealised case of a rigid sphere moving through a fluid at very low Reynolds number. Their results clearly show that the size and extent of the *Corresponding author",
            " (1992), Sundby and Fossum (1990), Viitasalo et al. (1998), Ki^rboe et al. (1999) and Hwang et al. (1994). It would therefore seem somewhat paradoxical to highlight some observations that were carried out in still fluid, when this paper is primarily concerned with turbulent encounter rates. However, they do bring out the connection between predator perception and foraging strategy rather well, which is one of the aims of this paper. What follows is a brief summary. The copepod species studied in Bundy et al. (1998) was Diaptomus sicilis (see Fig. 1a), specimens of which were collected from Lake Michigan. After some acclimatisation procedures (see Bundy et al., 1998 for full details), a number of captured copepods were transferred to a 1800 ml Pexiglas tank containing filtered lake water. In addition the tank contained a species of phytoplankton Cryptomonas refexa B360 cells ml\u20131 and a number (3\u20136 ml\u20131) of 50 10\u20136 m polystyrene beads (specific gravity 1.05 g cm\u20133). Individual copepods were then filmed for periods of 30\u201360 min using a videotracking system similar to that used by Bundy and Paffenh ",
            " The third set of columns shows the mean \u2018swimming trajectory\u2019 during these times. This was actually defined as the change in direction between sequential digitised positions, with 0 indicating no change in direction between two successive positions. So a small angle would indicate prominently straight line motion, a large angle many direction changes. Table 2 shows a summary of the same six copepods behaviour in the time interval immediately prior to an attack sequence (column 2). Column 3 shows the orientation angle of the bead to each copepod (Fig. 1a) before it began its slow approach towards it. (Although it is not entirely clear from Bundy et al. (1998), this appears to approximate the orientation angle when the copepod first perceives the bead.) Column 4 shows the distance of the bead from the copepod at this point. Columns 5 and 6 show the new orientation and distance before the attack jump is made. (Note the feeding current plays no role in the capture, as the beads have a tendency to be displaced away from a copepod as it makes its slow approach.) A number of interesting features can be discerned from these results. The copepods initially tend to perceive a bead over a limited range of orientation angles 102\u2013125 (column 3 Table 2), before their attack response. This suggests that they possess only a narrow field of long-range perception roughly aligned with their antennae, which support very many sensory satae (perhaps something along the lines of Fig. 1b). Notice too (column 4 Table 2) that the copepods seem to perceive the beads at a number of different distances (some caution is needed here as the distances represent two dimensional projections). The subsequent maneuvering of the copepods, so that they lie roughly at right angles to the bead, is probably to maximise their capture chances by using feeding appendages attached to the sides of their bodies. As regards the foraging strategy before a bead is encountered, the high velocity jumps are probably a defensive mechanism aimed at avoiding predators, by not lingering too long in a small portion of the water column",
            " This is usually the case for most species of phytoplankton but not for copepods, typically B1 10\u20133 m in length, in highly turbulent regions. However, as high turbulence seems likely to disrupt a predators perception capabilities (Ki^rboe and Visser, 1999), it will be assumed that copepods restrict their foraging to less-disturbed parts of the water column, where the assumption holds. It will be further assumed that both the predator\u2019s and prey\u2019s swimming motion is uncorrelated with the turbulent flow. A perception field of the type illustrated in Fig. 1b aligned closely with the copepod\u2019s antennae is too complicated to model here. Instead for this work it will be assumed that the predator\u2019s perception field is an \u2018icecream\u2019 cone centred on its head, defined by a contact radius R and semi-vertex angle a as shown in Fig. 1c. The case a=p gives a predator with an isotropic perception field considered in previous papers. Here though it will be assumed that aA[0, p/2] and that the predator\u2019s line of sight is always directed along vP its swimming velocity vector. In what follows no attempt will be made to model any particular mode of perception, such as the size of any fluid disturbance that takes place near the predator. Simply any prey particle entering the perception cone will assume to have been encountered. The problem then is to determine the encounter rate, or number of encounters over some fixed period T say"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001467_cdc.1989.70174-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001467_cdc.1989.70174-Figure3-1.png",
        "caption": "Figure 3: Equipment plan of the test stand for the hydraulic system",
        "texts": [
            " Analogous to the procedure for the observer design stated before, the algorithm to calculate the matrices appearing here can be found in 141. In Fig. 2, the blockdiagram of the resulting observer system is shown. IV. EXPER IMENT bilinear observer As described in [7], [18], a secondary controlled hydraulic rotary drive consists of a pressure generating unit (primary unit), a line-network with a hydraulic accumulator for the distribution and reservation of hydraulic energy and a secondary drive which has to be controlled in the presence of changing load (see Fig. 3). This system can be described by the bilinear model given in (6) [7], [18]. The values of the system matrices are given in Appendix. The complete control concept proposed in the previous sections is implemented in a microprozessor (VME 133, 68020) with the sample time 2ms [8], [9]. This controller works on-line. To study the performance of the observer on the test stand, Fig. 4 shows the estimated state variables in comparison with the measured state variables. For the state variables which are not measurable, the comparison with the simulation results of a nonlinear model that gives a exact description of the hydraulic drive is carried out"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002645_1.394920-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002645_1.394920-Figure4-1.png",
        "caption": "FIG. 4. Effect of compliance on computed force histories for striking point a =0.185 L and mass ratio m/M= 1.5, with F(t) in dimensionless form F?(2TV?c) vst/O. Curves are labeled with parameter C/Co. With no compliance, there are three recontacts, while increasing values of\u2022r = C/Co give two, one, and no recontacts.",
        "texts": [
            " When waves with n as large as 6 were included, slight irregularities in the graphic output suggested that the large number of arithmetic operations was leading to visible roundoff errors. This problem could be reduced by using a different computer that would retain more than seven significant digits. There are three main parameters for the problem, with cr = C/Co now to be considered along with m/Mand a - a/ L. The complete dependence on all three parameters involves far too much information to show exhaustive results, so only representative samples are presented here. First, Fig. 4 illustrates the effect of increasing compliance upon force histories for fixed values of rn/M and a. Besides generally rounding off these curves, the compliance tends to lengthen the initial contacts and reduce the incidence of recontacts. The reduction of recontacts in this case is shown in more I I I I I I I I MASS -1.5 ALPHA-. 185 I I I I .2 .4 .6 .8 1 COMPL I ANCE RAT I O FIG. 5. Times of making and breaking contact (in units of 0) and fractional energy transfer from hammer to string as a function of C/Co for the same values m?M = 1.5 and a = 0.185 used in Fig. 4. 551 J. Acoust. Soc. Am., Vol. 81, No. 2, February 1987 Donald E. Hall' Piano soft narrow hammer 551 Downloaded 13 Oct 2013 to 152.3.102.242. Redistribution subject to ASA license or copyright; see http://asadl.org/terms ! I I I I 0 Ref. 2, which differs only in having c = 0, one sees again a tendency toward longer contacts, fewer recontacts, and reduced energy transfer with greater compliance. The compliance does not, however, eliminate discontinuities in the dependence of contact times and energies upon striking position and mass"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002889_0301-679x(84)90095-1-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002889_0301-679x(84)90095-1-Figure1-1.png",
        "caption": "Fig 1 Schematic diagram of bearing",
        "texts": [
            " Theoretical and experimental studies on circular thrust bearings have been made 11,12 and an analytical expression for porous oil bearings for very small eccentricity has been obtained 13 . The aim of the present study is to solve the equations for hydrostatic porous oil bearings with slip and to investigate the steady state characteristics of load capacity, friction coefficient, attitude angle and oil flow rate. The effect of various parameters on the performance has been investigated and presented in the form of graphs. Theoretical analysis For the bearing configuration shown in Fig 1, pressurized off is fed to the entire outer surface of the bearing at a supply pressure Ps. It flows through the bushing and out from the bearing ends. It is assumed that H/R and C[R are small, so that cartesian coordinates may be used without serious error. TRIBOLOGY international 0301/679X]84/060317-07 $03.00 \u00a9 1984 Butterworth & Co (Publishers) Ltd 317 Chattopadhyay and Majumdar -- hydrostatic porous oil bearings with slip ~)2p, 82p, a 2 p , kx a -~ +ky 0 - 7 +kz ~ =0 (1) and the modified Reynolds equation in the film region considering slip and anisotropic permeability is: ~p ~ ap /) [h a (1 + ~'x) ] + [h a (1 + ~'z) ] ax ~ ~ ap' a [h (l + ~'ox)] + 12 ky ( ~-~ )y=0 (2) = 6nU -~ In dimensionless form the above equations can be written as: a2p -' R 2 a2h -' + (D)2 Kz a2h-' K x ~ + ( k ) a - 7 _ ~ = 0 (3) aft O )~ 0 aft O--'Oa [~a (1 + ~'x) ~ ] + ( L ~ [~a (1 + ~'z) ~-~ ] 0~\" = hs [h (1 + ~ox)] +/3 ( ~-y)Y=O (4) Pressure in the clearance space of the bearing is obtained by the simultaneous solution of Eqs (3) and (4) with the appropriate boundary conditions, namely, for porous bushing: p ' ( O , - 1 , ~-) = 1 p ' (0,y, -+1) = 0 (5) aft' (0, y, o) = 0 a~- Coefficient of friction Since the oil film cavitates beyond 0 = 02, forming a discontinuous mixture of oil, vapour, air etc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003900_bfb0042539-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003900_bfb0042539-Figure3-1.png",
        "caption": "Figure 3, The TH8 Robot.",
        "texts": [
            " In this case the error of this parameter will be forced to zero and the corresponding error will be calculated and calibrated through the errors on the other parameters. There is no proposed general method to determine these parameters till now, they can be obtained on a case by ease basis by detecting the linear independence of the different columns of the jacobian matrix. Numerical procedure like those proposed by sheu and Walker for the inertial parameters [12] can be used. 4- Exper imenta t ion The experimental results are carded out on a french robot TH8-ACMA, which is a six degree of freedom robot figure 3. The tool is a cylinder along the z6 axis. The classification of the identifiable parameters and the eliminated parameters, on which the error parameters cannot be calculated, for the TH8 robot are given in table 1. The linear relations between the columns of the jacobian matrix are given in the appendix. 4.1 Measurement of Cartesian position 4.1.1 Instrumentation The instrumentation must be able to determine with precision the cartesian position of the tool point of the robot. So, the measurement system is based on the use of two theodolites and a cylindrical target fixed on the robot terminal link"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003344_03093247v191009-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003344_03093247v191009-Figure2-1.png",
        "caption": "Fig. 2. Geometry ofcontact arrangement",
        "texts": [
            "00 at University of Birmingham on May 31, 2015sdj.sagepub.comDownloaded from stress must be less than the yield stress in pure shear. These are shown in Fig. 1, which is a view of the yield surfaces looking down the hydrostatic axis, and may be expressed mathematically, together with von-Mises\u2019 criterion as max ( - Cjj I ) < 27,; (Tresca) (4) s.. I J * s.. I J < 2r2; (von-Mises) ( 5 ) max ( I Sii I ) < r ; (Hill) where sjj = ajj - okk 6ij/3 and 13ii and Sii are the principal complete and deviatoric stress components respectively. Figure 2 shows the general arrangement of the zone of contact and resulting pressure distribution when two bodies are pressed together. If one body is slid over the other, as indicated, an additional shear stress, o13, is imposed at the surface whose magnitude is proportional to the local contact pressure. In the absence of this second boundary load, the severest state of stress always occurs on the axis of loading (x = y = 0) and, if vonMises\u2019 criterion is assumed, with u = 0.3, it occurs at a depth of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003507_jsen.2006.881421-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003507_jsen.2006.881421-Figure3-1.png",
        "caption": "Fig. 3. Bearing test bed with hydraulic load application and speed-control capability.",
        "texts": [
            " The position of structural defects located in the inner raceway of a bearing varies with the rotation of the bearing. As a result, interactions between a rolling element and the defect can take place at any angular position, making the exact preferable location for placing a vibration sensor difficult to determine intuitively. Therefore, a ball bearing with a seeded inner raceway defect (0.1-mm diameter hole) was assumed in this paper to illustrate the sensor-placement optimization procedure based on the EfI method. As shown in Fig. 3, such a bearing was housed in a rectangular housing plate (item 7 in Fig. 3), which also provided a physical platform for placing accelerometers for bearing vibration measurement. Three pockets were machined on the housing plate to accommodate the sensors. The inner raceway rotates with the shaft driven by a dc motor. A static preload was applied to the bearing through a hydraulic cylinder. Using the FE software package ANSYS, a geometry-true FE model of the bearing with surrounding support structure (e.g., housing plate, shaft, and two supporting pillow blocks) was constructed, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003301_s00216-006-0836-0-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003301_s00216-006-0836-0-Figure1-1.png",
        "caption": "Fig. 1 Scheme for the PMME device [32]",
        "texts": [
            "8 wt%), and the initiator AIBN (2 mg, 1 wt% of monomer and crosslinker), was mixed and degassed to remove oxygen by ultrasonication for 10 min. Subsequently, the mixture solution was filled into the pretreated capillary. The capillary was sealed immediately with silicon rubber, and then the heat-initiated polymerization was performed at 60 \u00b0C for 18 h. The capillary was washed with methanol to remove the unreacted component and porogenic solvent after the polymerization was finished. Derivatization\u2013PMME procedure The extraction device is composed of an extraction pinhead and the syringe barrel, as shown in Fig. 1. The original metallic needle of the pinhead was replaced by a 3 cm-long monolithic capillary. The extraction device could be used after the capillary was fixed in the pinhead by the adhesive [32]. Considering the configuration of the extraction device and the reagent characteristics, Asp and Glu were first derivatized and then extracted for the final determination. As seen in Fig. 2, the solution derivatization procedure was performed as follows: the desired amount of mixed amino acid solution, 20 \u03bcl of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000114_s0956-5663(97)00011-0-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000114_s0956-5663(97)00011-0-Figure1-1.png",
        "caption": "Fig. 1. Sensor, and position in F1A chamber. (A) Relationship of sensor components. AUX: auxiliary electrode; REF: reference electrode; WEI: working electrode with enzyme; WE2: working electrode without enzyme. The parts within the dotted circle lie within the O-ring (id = lOmm) of the chamber. (B) Cross section of perspex FIA chamber. The inlet stream was directed to the centre of the reference electrode, the outlet streams being placed",
        "texts": [
            " Flow injection analysis offers convenience arising from automation, but perhaps more importantly, a higher precision and accuracy than is easy to achieve from batch analyses through the higher degree of control and constancy of conditions implicit in the technique. In this paper a description is given of estimations of the lactate concentration in buttermilk and yoghurt using screenprinted sensors mounted in a flow injection analyser. EXPERIMENTAL Sensor construct ion Sensors, in which the lactate is detected by lactate oxidase and hydrogen peroxide oxidised by a layer of platinised carbon, were produced as in Collier et al. (1996) with the exception of the sensor design and outer membrane. The sensor components (Fig. 1A) were re-aligned so that the reference electrode was centrally placed with the working electrodes on either side. This design is similar to that of Urban et al. (1991). One electrode, WE1, contained enzyme; the other, WE2, did not. The latter was used to estimate nonspecific oxidation currents. The outer membrane consisted of polyurethane (SG80A; Thermedics Inc., USA) applied as a 2% solution in 98% tetrahydrofuran: 2% dimethylformamide from an airbrush (Hart et al., 1996b). Sensors were stored over silica gel in a refrigerator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002332_s0263574700010638-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002332_s0263574700010638-Figure1-1.png",
        "caption": "Fig. 1. Generalized representation of a multi-legged walking machine on rough terrain indicating arbitrary orientation of surface normals at points of contact.",
        "texts": [
            " Three representative tasks are defined and an example is specified which is based on the Adaptive Suspension Vehicle which has been developed at The Ohio State University.1 Nonlinear optimization techniques are used to solve for the force distribution which minimizes the maximum ratio of tangential to normal forces and the points of foot contact. These optimal force distributions are then studied and an alternate computation technique is proposed which yields force distributions which have many of the desirable characteristics of the optimal solution while being more computationally efficient. II. FORMULATION OF THE WALKING PROBLEM Figure 1 depicts a generalization of the walking problem for n-legs in 3-dimensional space. It is assumed that the system is on rough terrain, i.e. the surface normals at the points of contact do not necessarily align with the body 2-axis. The relationship between the desired forces expressed in the body frame and the foot reaction forces is easily constructed. If the foot reaction forces are resolved into components which are parallel to the body-fixed axis, the relationship is shown as described in ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001327_s0003-2670(02)01521-0-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001327_s0003-2670(02)01521-0-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the cell injector: (1) Plexiglas cube; (2) round hole; (3) microscope slide; (4) metal tubing; (5) separation capillary; (6) injection capillary; (7) trumpet-shaped glass tube of injecting cells; (8) buffer reservoir; (9) anode and (10) Pt wire.",
        "texts": [
            " It consisted of a carbon fiber microdisk electrode (about 30 carbon fibers with 6 m diameter) as the working electrode, a saturated calomel electrode (SCE) as the reference electrode, and a coiled Pt wire (0.5 mm diameter, 4 cm in length) placed at the bottom of the cell as the auxiliary electrode. The Pt wire also served as a ground for the separation potential. The arrangement of the electrochemical detection cell was illustrated in [20] in detail. The carbon fiber microdisk bundle electrodes used here were described previously [21]. Fig. 1 shows the cell injector. A Plexiglas cube (1) (2 cm\u00d71.5 cm\u00d73 mm) with a round hole (2) of 2.5 mm diameter was placed on a microscope slide (3). The cube had been machined to contain a small groove (around the hole) just the right size to accommodate a metal tubing (4) (400 m i.d., 680 m o.d.). A hole was machined through the metal tubing with a diameter of 400 m. Since both the hole of the metal tubing and the hole of the Plexiglas cube were concentric, the hole of the metal tubing can be observed under a microscope",
            "5 ml centrifuge tube. The supernatant was adjusted to pH 9.48 by adding 10 l of 10 mol/l NaOH. This was the extract of amino acids from lymphocytes. The cell injector was placed on the inverted microscope (Chongqing Optical Instrument Factory, Chongqing, China) with a magnification of 640\u00d7. The separation capillary, injection capillary and the buffer reservoir with an anode were filled with electrophoresis buffer. The other end of the separation capillary was inserted into a buffer reservoir (not shown in Fig. 1) with a cathode. The lymphocyte suspension was transferred into the glass tube of injecting cells. When a cell appeared between the separation capillary and the injection capillary under the field of vision of the microscope, an injection voltage of 2.0 kV was applied to transport the whole cell into the separation capillary tip. Once one cell was injected into the separation capillary tip, the anode was manipulated up, out of the buffer reservoir. The entire process of cell injection typically took 3\u20134 min"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002009_2003-01-1076-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002009_2003-01-1076-Figure2-1.png",
        "caption": "Figure 2. Heat sources and thermal interactions inside the passenger compartment in a hot climate.",
        "texts": [
            " Glare is difficult to measure, but there are reports that solar-control window films reduce glare by as much as 80% [33]. The same source reports that reducing glare by 40% or more improves driving comfort, vision, and safety. Reducing glare is particularly important for improving safety when driving in strong sun and snow. THERMAL INTERACTIONS INSIDE THE Thermal interactions between the environment and the vehicle, its shell, and the passenger compartment in a hot climate are very complex. The diagram above (Figure 2) illustrates the most important heat flows and thermal properties of the vehicle skin and interior components. These interactions must be considered in optimizing thermal management strategies. For example, components that help reduce the load on the HVAC system under operating conditions can have adverse effects on thermal loads when the vehicle is parked in the sun on a hot day. Sources of thermal loads are discussed below. Strategies and technologies that can minimize these loads are described in the following two sections"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000507_027836499501400207-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000507_027836499501400207-Figure7-1.png",
        "caption": "Fig. 7. Exrxmple pushing problem.",
        "texts": [
            " the velocity cone (Mason 1986) to be a constraint on the possible velocity directions of the slider contact point. Each force inside the contact friction cone is mapped by the limit curve to a corresponding rod endpoint velocity angle 0~. These velocity angles sweep out the velocity cone. Note that the convexity of the limit curve implies that the velocity angle 8s increases monotonically with the force angle 0. Now it is rather easy to see how pulling is possible. Coulomb\u2019s law is satisfied only by forces applied into the slider, but there is no similar requirement on velocities. Figure 7, for example, shows the velocity cone for I = 2 and p = 2, which includes velocities away from the slider. The pusher must perform work to move the slider, so the quantity f - vs must be positive. The force angle 0 and the velocity angle 0, can vary by any amount less than 90 degrees. Because of this, it is possible to construct problems with pulling solutions for any nonzero coefficient of friction at the pushing contact. Pulling is always impossible when the contact is frictionless. 3.3. Slip With Infinite Fiction An infinite coefficient of friction results in a friction cone spanning 180 degrees, consisting of exactly those forces directed into the slider"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002398_978-1-4615-0085-8-Figure2.1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002398_978-1-4615-0085-8-Figure2.1-1.png",
        "caption": "Figure 2.1 Pressure ring infiltrometer (Matula and Kozakova, 1997): 1. piston valve to open {close the water outlet, 2. moveable air tube of Mariotte bottle to set the water level (8) inside the infiltrometer ring, 3. Mariotte bottle, 5. infiltrometer ring, 6. bulb full offield saturated soil, 7. wetting front, 8. wetting zone",
        "texts": [
            " Angulo-Jaramillo et al (2000) divided the infiltrometers into: - Tension disc infiltrometers - Pressure ring infiltrometers (Matula and Kozakova, 1997) was applied in situ. The pressure ring infiltrometer (Matula and Kozakova, 1997) consists of a Mariotte bottle, mounted on the top of a single iron infiltration ring of 0.15 m inner diameter, driven to a short distance (0.10 m) into the soil top layer. A wide range of steady water pressure can be applied to the soil surface inside the infiltration ring using a moveable air tube within the Mariotte bottle. The schematic diagram of the pressure ring infiltrometer (Matula and Kozakova, 1997) is shown on Fig. 2.1. The field experimental work was conducted in 1997 and repeated in 2000 again at the experimental field of the Research Institute of Plant Production (RIPP), Praha - Ruzyne on a Hapludalfs (US Classification) / Orthic luvisol (F AO). The whole experimental site was separated into 4 tillage treatment areas (ITA4, ITAl, ITA2, ITA3) in 1997-1999 and 4 ITA in 1999 - 2000 (ITAOl, ITA02, ITA03, ITA04), that where maintained using different tillage treatments (see Fig. 2.2). The ITA were segregated mechanically (paths) and marked from each other with an application of chemical spray (Gramoxon)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001915_pcc.2002.998568-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001915_pcc.2002.998568-Figure11-1.png",
        "caption": "Figure 11. Configulation of the experimental WTG system",
        "texts": [],
        "surrounding_texts": [
            "Fig.6 shows the comparison between generated power with flywheel PI and ggnerated power without flywheel P2 in the case of V, = 6.0 m/s, AV, = 3.0 m/s and T = 10 s. From Fig.6, it became clear that rotation speed of WTG is almost adjusted to the wind speed fluctuations with flywheel, but it's not adjusted without flywheel when the wind speed is increasing. Therefore power coefficient C, without flywheel is low values when the wind speed is increasing. As a result, PI, P2 and power ratio PllP2 amounts to 38.9 kW, 26.8 kW and 1.45, that is, more energy is extracted from the wind energy by using a flywheel.\nWe also calculated the power ratio P1/P2 in the case of various wind speed model. Fig.7 and Fig.8 shows the relation between normalized period -and power ratio in the case of average wind speed V, = 7.0 m/s and amplitude of wind fluctuation V, = 3.0 m/s respectively. Normalized period means T/Ts , where T, = E,/P : energy time constant (s), E, : stored energy of WTG (rated speed) ( J ) , P : rated power of WTG (W).\nFrom Fig7 and Fig.8, it became clear that power ratio Pl/P2 has the optimum point in the case of normalized period T / r S around 4.5 at every average wind speed and amplitude of wind speed fluctuations. For example, the period, which has the optimum power ratio, is around 10 s in the case of 275kW WTG in Tappi-zaki. But Pump Up operation with a flywheel must use a bilateral frequency converter. From Fig.9, it became clear that the energy time constant of WTG tends to be almost proportional to the rated power of WTG. And the period of the largest scale of commercial WTG (rated power is 2.5 MW), which has a maximum power ratio, can also expect to be around 45 s because the energy time constant of this WTG is 10 s (Fig.9). As a result, it\nbecame clear that the effect of Pump Up operation is increasing in proportion to the scale of WTG.\n3.2.2 Tappi-zaki wind speed model\nFig.10 shows the comparison between fixed speed rotation and MPPT in Tappi-zaki WTG system. Fig.lO(a) shows the wind speed model in Tappi-zaki, which is used the simulation. Average wind speed is around 6.2 m/s. From Fig.10 (b) and (c), it became clear that the value of C, is around 0.395 (it's a maximum value.) by adjusting the rotation\n- 325 -",
            "speed to wind speed in the case of MPPT operation. But in the case of fixed speed rotation, rotation speed is constant in spite of the wind speed, so that value of C, is always small in comparison with MPPT operation. As a result, generated power of MPPT P G ~ and generated power of fixed speed rotation P G ~ amount to 16.8 kW, 35.8 kW, that is, the generated power increase up to 2 times has been obtained for MPPT operation. But from Fig.10 (d), we can obtain the result that the power fluctuations of WTG increases in comparison with fixed speed rotation operation. Therefore it became clear that flywheel is necessary for MPPT operation to compensate the power fluctuations of WTG for the utility. Rated power Rotor diameter Cut-in wind Rated wind\n400 W Type 3-blades 1.24 m Inertia 23.8 gm2 3.0 m/s Cut-out 20 m/s 12.5 m/s Rated meed 1000 min-'\nRated power Current Pole Reactance\n150 W Voltage 38.8 V 2.31 A Turn 312 1.78 R Resistance 2.03 R 6 type PM-Syn\nbe calculated from Eq.(lO) and Eq.(l l) .\ndue P, = Jewed t\nc, = 5 (11) Paw\nwhere Je : inertia of the experimental WTG, we : angular velocity of the experimental WTG. From Fig.12, it became clear that the peak value of C, is 0.329 in the case of TSR = 10.2. As a result, we can realize the Maximum Power Point Tracking for WTG by adjusting the blade's speed to wind speed such that TSR is 10.2.\n4.2 Experimental Result\n4.2.1 Characteristic of C, Fig.12 shows the relationship between TSR and C, of the experimental WTG system. Characteristic of C,, was determined by measuring the change of blade's rotated speed at the constant wind speed.\nCaptured power Pw and power coefficient C,, can\n- 326 -",
            "4.2.2 MPPT operation\nFig. 13 shows the comparison between the calculated values and the experimental values in the case of MPPT operation. The experimental value is measured by changing the resistance loads at every constant wind speed. And from Fig.12 and Eq.(2), the calculated values is obtained. From Fig.13, it became clear that these experimental values agree well with the calculated values.\nFig. 14 shows the comparison between fixed speed rotation and MPPT. From Fig.14, it became clear that these experimental values agree well with the calculated values.\nAnd from Fig.13 and 14, we can prove the Maximum Power Point Tracking for WTG by using the small WTG system. From Fig.14, it became clear that more energy can be extracted from the wind energy by MPPT in comparison with fixed speed rotation at the low wind speed region. As a result, it became clear that the usable area of WTG can be spread and efficiency of WTGs can be increased by Maximum power point tracking.\n5 Conclusion This paper is proposed the Maximum Power Point Tracking for WTG using a flywheel. Firstly we explained the relation between power coefficient C, and tip speed ratio TSR, that is, we can realize the Maximum Power Point Tracking for WTG by using the Rotary Phase Shifter, which adjusted the blade's speed of WTG to wind speed. In particular, the inertia of WTG is a problem for MPPT because scale of WTG is increasing now. But the inertia of WTG can be canceled by flywheel, so that blade's speed can be almost adjusted to the wind speed when wind speed is increasing rapidly. And we proved that MPPT operation caused the more power fluctuations of WTG in comparison with fixed speed rotation by simulation. Therefore flywheel must be used for MPPT to compensate the power fluctuations. As a result, flywheel generator plays two important roles for WTG. And we can evaluate MPPT operation with the experimental studies by using the small WTG system.\nFrom now on, we intend to evaluate the relation between MPPT operation and fixed speed rotation at changing the wind speed by using the small WTG system, the Rotary Phase Shifter and Flywheel generator. And we intend to examine the power interchange between a WTG and other WTGs to realize the Maximum Power Point Tracking for WTG without flywheel.\nReferences\nA.Koyanagi et a1 : \"Maximum Power Point Tracking of Wind Turbine Generator Using a Flywheel\", Proceedings of the 2001 Japan Industry Application Society Conference,vol.l ,p395398 (2001)\nM.Molinas, H.Nakamura and A.Koyanagi : \"Analytical and Experimental Study of a Rotary Phase Shifter for Power System Applications\", The Transactions of The Institute of Electrical Engineers of Japan, vol.120-B, No.10 (2000)\nH.Chikaraishi, RShimada et al : \"Fast Response Power Stabilizer using the AC-Excited Flywheel Generator\", The The Transactions of The Institute of Electrical Engineers of Japan,vol.llSB,No.ll (1993)\nAjisman, K.Yamagata et al : \"Study of Cooling Gases for Windage Loss Reduction\", The Transactions of The Institute of Electrical Engineers of Japan,vol.l2O-B,No.3 (2000)\nK.Tsuchiya and T.Matsuzaka : \"Simulation of Operating Characteristics of a Wind Energy Conversion System\", The Transactions of The Institute of Electrical Engineers of Japan,vol.ll3-B,No.7 (1993)\nIsaac Van der Hoven : \"Power spectrum of horizontal wind speed in the frequency range from 0.0007 to 900 cycles per hour\", J.Meteorology, V.14,~160-164 (1957)\n- 327 -"
        ]
    },
    {
        "image_filename": "designv11_11_0001836_0375-9601(93)91161-w-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001836_0375-9601(93)91161-w-Figure1-1.png",
        "caption": "Fig. 1. A simple pendulum. Symbols as defined in the text.",
        "texts": [
            "~ 4ka~Y-to2enq~bend(to) Nx/TYI (8) toSm 2mgl \" Consider now the violin modes of the suspension wires. For these to occur, it is necessary for the wires to be slightly extensible. Thus we have the situation where at the pendulum frequency the suspension wires are assumed to be inextensible, whereas when resonant in their violin modes, the wires behave extensibly. In order to see how this changeover takes place, consider the extension of a wire as characterised by the vertical oscillations of the simple pendulum depicted in fig. 1. The equations of motion for the test mass in terms of a horizontal drive at the top, assuming for simplicity that no damping is present, are given by to2 v 2 --O')pen (Xg--Xrn) 2 , (9) Ym +to2vYm = 21 xm -- to gen (X~ --Xm) + higher order cross coupling term, ( 1 O) where Ym denotes the vertical displacement of the mass, x 8 the horizontal displacement of the ground, Xm the horizontal displacement of the mass, tov is the angular vertical resonant frequency of the pendulum suspension and topen is the angular pendulum resonant frequency. If the horizontal driving force is assumed to be harmonic, combining eqs. (9) and (10) yields (0) 2 -- (J)2en) O) 4X2 Ym = 2l(to2v 2 2 __to2)2\" (11) - t o )(tope. From eq. ( 1 1 ) it is observed that for tope, << to << tov, Ym =xZJ2l and hence, from consideration of fig. 1, the suspension wire appears to be inextensible and the mass moves on the arc of a circle centred on the suspension point, i.e. the mass has vertical movement. Note also that the vertical displacement of the mass occurs at twice the frequency of the horizontal drive since xg is harmonic. For to >> tov, Ym ~ 0, and hence for frequencies greater than the vertical resonant frequency of the system, the suspension wire appears to be extensible with the mass having little vertical movement. Thus above their vertical resonance, the suspension wires behave as simple extensible strings",
            " For low frequencies (co << 2 n ( 2 n - 1 )u/41) the imaginary part of ZL behaves as a pure capacitor of value Cx and thus for LLI<< Lpen, i.e. mass of wire much less than mass of pendulum bob, the frequency of the circuit is given by COpe n ~ ~ (15) This is not surprising since at frequencies very much lower than the violin modes the real part of the restoring force which acts on the pendulum through the suspension wires is the same, to first order, above and below the vertical resonance. This is easily shown to be the case by considering the horizontal restoring force applied to the mass of fig. 1 when the pendulum moves by a small distance Xo at frequencies very much lower than the violin modes. Above the vertical resonant frequency, the wire will stretch as discussed in section 4.1, however to first order the change in the tension T of the wire would be small. Hence the horizontal restoring force may be shown to be of the form F~= -mgxo/l . At frequencies below the vertical resonance, the mass would change its vertical position but this change to first order would be small and once again it may be shown that F,=-mgxo/ l "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002630_bf02844131-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002630_bf02844131-Figure1-1.png",
        "caption": "Figure 1 Conventions for foot angle (\u03a8), ankle angle (\u03b8) and knee angle (\u03c6). The foot angle is defined such that a negative foot angle corresponds to a positve inclination to the horizontal (as illustrated).",
        "texts": [
            " In addition, a runway of the surface under study was constructed using slabs of material of the same thickness as that placed on the force plate, and dimensions 800 mm 700 mm. An approach of eight metres in length was provided prior to contact with the force plate. Active markers were placed on the left of each subject\u2019s body at the hip, knee, ankle and metatarsalphalangeal (MTP) joint centres, and at a point on the heel. The locations of the heel and MTP markers were chosen so that a straight line joining these two markers was parallel to the ground during standing. Sagittal plane joint angles were defined as illustrated in Fig. 1. The foot angle was defined as the angle between the foot segment and the horizontal, such that a positive inclination (as illustrated) provided an angle with negative sign. Each subject performed 10 running trials under each of the two surface conditions, with the order of conditions randomised between subjects. The use of 10 trials was justified following a pilot study in which it was demonstrated that beyond 10 trials no gain in the stability of impact force data was obtained (Appendix A1). A running speed of 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003399_j.ijmecsci.2005.04.003-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003399_j.ijmecsci.2005.04.003-Figure12-1.png",
        "caption": "Fig. 12. A cantilever helical rod and dynamic load.",
        "texts": [
            " 10 and 11 including the ratios D=d \u00bc 5 and D=d \u00bc 10 with different number of active turns. As shown in Figs. 10 and 11, as the number of active turns and D=d ratio increase, both displacement amplitude and vibration period increases as expected. On the other hand, as D=d ratio increases, the rigidity of helix decreases. Example 2. A cantilever helical rod consisting of three layers is considered \u00f00 =0 =0 \u00de. It is assumed that each layer has the same thickness. Geometrical properties are d \u00bc 12 cm, a \u00bc 25:52 ; a \u00bc 200 cm (Fig. 12). The material properties for the isotropic layer are E \u00bc 2:06 1011 N=m2; r \u00bc 7850kg=m3 and n \u00bc 0:3. The properties of transversely isotropic material are given in Table 1. Layers are arranged symmetrically with respect to x2 axis (Fig. 13). Free vibration frequencies calculated using the present computer program are given in Table 4. A step load with the amplitude P0 \u00bc 1N is applied vertically at the free end of the rod. For four different cases shown in Fig. 13, forced vibration analysis is carried out"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002155_05698190490440911-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002155_05698190490440911-Figure2-1.png",
        "caption": "Fig. 2\u2014The rotor-bearing system in the test rig.",
        "texts": [
            " The foil element wraps in the reverse direction around the rotation of the shaft for one circumference with its pin inserted into a pinhole of the housing. MoS2 is adopted as the lubricant to achieve better durability. It seems to possess better performance because of its uniform surface stiffness and favorable elastic foundation and to be more convenient for manufacture and installation. The performance of a rotor-bearing system was investigated on a high-speed test rig. The rotor of the test rig is driven by a reaction wheel with the diameter of 22.0 mm, shown in Fig. 2. A pair of this new type of foil journal bearings is used to support the rotor and externally pressurized gas thrust bearings with the inherent compensated restrictor used to equalize the axial force. The material and the dimensions of the shaft are as follows: material: 3Cr13Ni, diameter: 16.99 mm, length: 174.00 mm, and mass: 0.320 Kg. The radial motion of the rotor is measured via two eddy current\u2013type displacement probes mounted on the bearing 308 D ow nl oa de d by [ U N A M C iu da d U ni ve rs ita ri a] a t 0 1: 56 2 1 D ec em be r 20 14 Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002143_bf00374763-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002143_bf00374763-Figure2-1.png",
        "caption": "Fig. 2. [After PARDIES].",
        "texts": [
            " 3a We will now consider in detail two analyses by PARDIES in which rigidification plays an essential role: the first, which is ingenious and correct, is his treatment of a heavy body suspended from a massless thread strung over two frictionless pulleys, which yields a parallelogram decomposition of the weight of the body; the second, which is courageous but incorrect, is his p roof that the tension in a flexible rope is tangential. 33 Problem I (PARDIES [24: w167 LXVI-LXVII ] ) . Consider a weight e suspended f rom an inextensible string which passes over two pulleys a, A and carries two weights d, D (Fig. 2). Continue the line eB to intersect aA perpendicularly at F, and drop the perpendicular AC onto aB extended. Draw FG, Fg parallel to aB, AB, respectively. PARDIES wants to show that e BF e BF (5.1) D BG' d Bg ' which will allow him to deduce immediately that D BG - - ( 5 . 2 ) d Bg He supposes that the cord AB is rigidified (\"is stiff like a bar of iron\"), but still free to pivot about A. The weights e and d pull on the bot tom of the rigid bar, with directions Be and Ba, respectively. PARDIES \"measures\" these forces by the lengths AF and AC, respectively",
            " In his fundamental paper [31] of 1755 on the equilibrium of fluids, he regards the pressure p as the force per unit area exerted by one portion of a fluid on another portion separated from the first by an immaterial diaphragm 6~ He argued that this force is everywhere perpendicular to the diaphragm. promises to shed much light on their interconnections. 5 8 D'ALEMBERT'S objection, which appears in w 18 of [30], will be discussed in Section 17, and a revised form of Statement (B) that meets the objection will be presented there. TRUESDELL [5: p. XI, fn. 1] was aware of d'ALEMBERT'S criticism of the principle of solidification when he stated (B). s9 See Theorem V, in w 27, of [30]; compare also d'ALEMBERT'S Theorems VIII (w 59) and IX (w 61). 60 See Sects. 9-14 and Fig. 2 of [31]; see also TRUESDELL'S summary of this paper as well as his comments on it, on pp. LXXV-LXXXIII of [6]. at equilibrium for a fluid of density 61 ~ which is subjected to external body forces (\"forces acc616ratrices\"). Relative to a set of rectangular Cartesian coordinates, the components of the body force per unit mass acting at the point whose coordinates are x, y, z are denoted by P, Q, R. EULER considers an infinitesimal rectangular parallelepiped of fluid, the edges of which are parallel to the coordinate axes and have lengths dx, dy, dz",
            " He conceives of this general force in the following way: 69 I f in a solid body, elastic or nonelastic, one happens to make rigid and invariable a small element of volume bounded by arbitrary faces, this small element will experience on its different faces, and at each point of them, a definite pressure or tension. This pressure or tension will be similar to the pressure which a fluid exerts against an element of the boundary of a solid body, with this one difference, that the pressure exerted by a fluid at rest against the surface of a solid body, is directed (Ca 1) perpendicularly to this surface from the outside towards the fluid by body and surface forces. He did not actually draw these forces in his figure of the parallelepiped (Fig. 3 of [31]), but he could easily have done so. (In Fig. 2 of [31], EtlLER did draw two pressure forces.) 6s EIJL~R also succeeded in treating the dynamics of inviscid fluids (see [5]). 66 The history of the concept of stress has been traced by TRUESDELL in [3 : Chap. IV], and more extensively in [4, 5]. A modern mathematical discussion of stress can be found in Chap. D of TRUESDELL & TOUPIN [1]. 67 A full treatment of the subject, including dynamical aspects, was eventually published (see the series of papers [33-39]). 68 Here CAUC\u2022V refers to an unpublished memoir [40] by NAVIER"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003346_j.jsg.2004.07.005-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003346_j.jsg.2004.07.005-Figure9-1.png",
        "caption": "Fig. 9. Velocity field associated with the development of a curvilinear faultbend anticline. Particle trajectories are characterised by straight segments parallel to the thrust and by parabolic segments. The latter develop above the upward convex thrust bend.",
        "texts": [
            " This means that the role of the transient configuration can be neglected for the commonly observed ramp cutoff angles. However, an exact analytical solution of round-shaped fault-bend folding can be easily provided only for constantly dipping panels, i.e. when C2 is stratigraphically higher than C3 and the variable cutoff panel is confined to the foreland (Fig. 8d). The velocity field associated with curvilinear fault-bend folding predicts that particles have trajectories that are either parallel to the thrust surfaces or curvilinear (Fig. 9). Fold sectors where particle paths are parallel to the fault traces are named translational sectors, while parabolic or circular trajectories characterise rototranslational sectors. Translational sectors do not include the possibility for particles to modify their distance from the corresponding fault segment. Conversely, particles moving through rototranslational sectors can change their distance from the fault (Fig. 2a). A primary difference between velocity properties characterising translational and rototranslational sectors, respectively, is that layer dip remains constant in the former sectors, whereas it gradually changes in the latter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001396_s0022-5096(01)00130-2-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001396_s0022-5096(01)00130-2-Figure1-1.png",
        "caption": "Fig. 1. An elastic rod clamped at both ends. We experimentally control the distance d(AB) by sliding the point A along \u2018, and the end-rotation R by turning the end of the rod at A around the axis \u2018.",
        "texts": [
            " \u2217 Corresponding author. Tel.: +41-21-693-29-06; fax: +41-21-693-42-50. E-mail address: s.neukirch@ucl.ac.uk (S. Neukirch). 0022-5096/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S0022 -5096(01)00130 -2 We (rst recall the equilibrium equations of an unshearable, inextensible rod with symmetric cross-section and linear constitutive relations, namely an elastica. Then our goal is to examine static con(gurations (and their stability) of a rod clamped at both ends (see Fig. 1). The force and moment balance equations for an in(nitesimal cross-section element of the rod are given by Antman (1995) F \u2032 = 0; (1) M \u2032 + R\u2032 \u00d7 F = 0; (2) where ( )\u2032 def= d=dS, S denoting arclength along the rod. Let {d1; d2; d3} be a right-handed rod-centered orthonormal co-ordinate frame with d3 the local tangent to the rod and d1 and d2 two vectors in the normal cross-section that enable us to follow the twist as we travel along the rod. In the case of an inextensible, unshearable rod we have R\u2032 = d3 (3) while the evolution of the co-ordinate frame di along the rod is governed by the equation d \u2032i = u \u00d7 di ; i = 1; 2; 3: (4) Here u is the strain vector whose components in the moving frame are the curvatures and the twist",
            " We will consider rods with symmetrical cross-section i.e. I1 = I2 = I . We have then 7 unknown vector functions F ; M(S); R(S); d1(S); d2(S); d3(S); u(S) and 6 vectorial ordinary di4erential equations (1)\u2013(4) and a set of three algebraic equations (5) relating them. A static con(guration will be locally stable if it represents a local minimum of the potential energy with regard to all adjacent admissible virtual con(gurations satisfying the boundary conditions. The clamped boundary conditions used here (see Fig. 1) can be written as d3(A) = d3(B); (6) R(B)\u2212 R(A) = d3(B) with \u2208R: (7) We will call end-rotation R the total angle by which the end A is turned around the axis \u2018. We will call end-shortening D the di4erence between the length of the rod and the signed distance AB (see Eq. (9) for a precise de(nition). We are interested in two types of experiments: \u2022 Fixed-R experiment: we start with a twisted straight rod in which we have put a certain number of turns, then we gradually move the two ends in without turning them"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000453_s0925-4005(98)00276-7-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000453_s0925-4005(98)00276-7-Figure1-1.png",
        "caption": "Fig. 1. Schematic drawing of the thick-film three electrode amperometric glucose biosensor strip.",
        "texts": [
            " A polyurethane squeegee was used for the printing process of the three different electrode pastes. These materials were sequentially printed on glass fibre circuit boards each of them containing seven arrays of three copper lines developed by a photolithographic process. Finally the copper lines were covered by a layer of epoxyacrylate (Ebecryl 600, UCB Chemicals) and exposed under UV through a mask. Thus leaving for each array both biocomposite and silver electrode areas of 12 mm2, an auxiliary electrode area of 18 mm2 and the contact pads (Fig. 1). The biosensors were stored dry at 4\u00b0C. Finally, the pseudo-reference electrode area was modified by electrochemical potentiostatic chlorination of the screen-printed silver paste at +1 V (versus SCE) in KCl 1.0 M during 1 min. The working electrode had to be activated electrochemically. This step was carried out by applying cyclic potentials at 50 mV/s between \u22120.25 and +1.6 V versus SCE as described earlier [1]. 3. Results and discussion 3.1. Pseudo-reference electrode The stability of the Ag/AgCl reference electrodes depends highly on the AgCl growth mechanism, which is influenced by the electroactive solution, the current density (or potential) and the duration of the electrochemical treatment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002768_978-3-642-50995-7_7-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002768_978-3-642-50995-7_7-Figure1-1.png",
        "caption": "Figure 1. Linkage.",
        "texts": [
            " AUTOLEV produces complete, fully formatted, ready-to-compile-and-run FORTRAN simulation programs in which, to minimize computation time, repeated strings of symbols have been replaced automatically with new, individual symbols. In addition, each program can incorporate provisions for checking the correctness of the equations of motion under consideration. To explain how one works with AUTOLEV to produce multibody simulations, we shall describe in detail the process employed to generate response curves for the linkage system shown in Figure 1. Readers interested in learning more about AUTOLEV are referred to (2). W. Schiehlen (ed.), Multibody Systems Handbook \u00a9 Springer-Verlag Berlin Heidelberg 1990 'ole begin by typing DOF(1,7) This tells AUTO LEV that the system to be analyzed possess one degree of freedom, and that its motion is characterized by seven generalized speeds (see [1], p. 40), which AUTO LEV names internally as U1, ..\u2022 , U7. Next we tell AUTO LEV the names of all the reference frames (rigid bodies) making up the linkage (see Figure 1): FRAMES(K1,K2,K3,K4,KS,K6,K7) For each frame listed in the FRAMES command, AUTO LEV assigns names to various items of interest associated with the frame. For example, a dextral set of mutually perpendicular unit vectors Kl1, K12, and K13 is designated as fixed in K1, and the mass center of Kl is denoted KISTAR. Similar names are automatically introduced in connection with K2,. ., K7. A Newtonian reference frame N is defined internally when AUTOLEV is activated, and a dextral set of mutually perpendicular unit vectors NI, N2, and N3 is fixed in N. The points of interest on the linkage are listed in a POINTS command: POINTS(0,A,B,C,Pl,P22,P23,P24,P26,P3,P4,PS) Points 0, A, B, C, P1, P3, P4, and PS can be found in Figure 1, and P2i denotes that point of Ki located at P2 (i = 2, 3, 4, 6) (see Figure 1 for P2). Since these points are identified for purely kinematical purposes, but do not correspond to particles, we tell this to AUTO LEV by typing MASSLESS(0,A,B,C,P1,P22,P23,P24,P26,P3,P4,PS) The given angles 13, y, 5, and E (see Figure 1) are designated as variables, as are 92' 94' and 96' angles characterizing the orientations of K2, K4, and K6, respectively, in N: VAR(BETA,GAMMA, DELTA, EPSILON,THETA2,THETA4,THETA6) Similarly, given constants are designated in CONST commands. The distances constant, LO the natural length of the spring, and TORQKl is the (constant) value of the K13 measure number of the torque of the driving couple. 'ole type CONST(D,DA,E,EA,ZF,FA,R,RA,S,SA,SB,SC,SD,ZT,TA,TB,UX,UA,UB) CONST(XB,YB,XC,YC,SIGMA,LO,TORQK1) The HASS command is used to assign names to the masses of K1, \u2022\u2022\u2022 , K7",
            " Having defined TORO in this .anner, we can have the best of two worlds in connection with the FORTRAN simulation program. For the problem at hand, the constant value of TOROK1 will be read from a data file and assigned to TOROK1, and then, in turn, to TORO. Vhen TORO is not a constant, we can edit the aforementioned subroutine, replacing TOROK1, on the right-hand side of this equation, with any desired function. To take into account the spring force, we must first determine the position vector PPsC from Ps to C (see Figure 1). To this end, we input the position vectors POB and POC, from 0 to Band C, respectively, POB=XB*N1+YB*N2 POC=XC*N1+YC*N2 and then use the ADD command to form the position vector PBC from B to C: PBC=ADD(POC,-POB) -> (369) PBC=(-XB+XC)*N1+(-YB+YC)*N2 while the position vector PBPs from B to PS is given by PBPs=SD*K31-SC*K32 so that the ADD command can be used to obtain PPsC, the desired result, as PPsC=ADD(PBC,-PBPs) -> (372) ppsC=(-XB+XC)*N1+(-YB+YC)*N2-SD*K31+SC*K32 The determination of the magnitude of PPsC is accomplished by dot multiplying PPsC with itself, which leads to the square of the magnitude of PPsC, HAGPPsC2=DOT(PPsC,PPsC) -> (374) HAGPPsC2~(-XB+XC)*(-XB+XC)-2*(-XB+XC)*COS(GAHHA)*SD-2*( -XB+XC)*SC*SIN(GAHHA)+(-YB+YC)*(-YB+YC)+2*(-YB+YC)*COS(GAHHA) *SC-2*(-YB+YC)*SD*SIN(GAHHA)+SC*SC+SD*SD whereupon the RIGHT command is used to raise the right-hand side of the equation in line (374) to the ",
            "5*(-Z146)\"2*SIGMA To cause AUTO LEV to write a computer program for the simulation of motions of the linkage, we issue the command (428) CODE(LINKAGE,ENERGY,CONTROLS) This yields a FORTRAN program called LINKAGE. FOR, containing a subroutine ENERGY for computing the total energy of the linkage, as well as a subroutine CNTRL in which TORQ is computed. A portion of the FORTRAN program is shown in Figure 2. Here one can see that AUTOLEV has produced a ready-to-compile-and-run program, complete with DIMENSION statements, COMMON blocks, READ and VRITE statements, and so forth. Vhen the initial values of ~, y, &, and \u20ac (see Figure 1) are given, those of 92' 94' and 96 can be determined easily. In general, however, any one, but no more than one, of these seven initial values can be specified independently, and the remaining six must be found by solving a system of six coupled transcendental equations. Indeed, the determination of initial values of angles is a major obstacle that must be overcome whenever one is dealing wi th closed loops of bodies, and it is not handled easily by conventional multibody programs. To show how AUTO LEV can be used to come to grips effectively with this dilemma, we determine expressions for the sine and cosine of each of 92' 94' and 96' completely in terms of known quantities",
            " Use of these expressions in conjunction with the FORTRAN function DATAN2 permits one to obtain ini tial values of the three angles. Moreover, these six relations are precisely the ones needed to determine the values of any six of the linkage angles when the value of the seventh is available. The strategy we employ to find the relationships of interest is to obtain closed loop conditions for each of three such loops in the linkage. By picking these loops in such a way that each involves at most one of K2, K4, and K6, we can obtain a separate expression for each of 92' 94' and 96. Ve make use of the fact that (see Figure 1) the position vector from Pl to P2 is equal to the sum of the position vectors from Pl to 0, from o to B, and from B to P2; the position vector from P3 to P2 is equal to the sum of the position vectors from P3 to A, from A to B, and from B to P2; and the position vector from P4 to P2 is equal to the sum of the posi tion vectors from P4 to A, from A to B, and from B to P2. Ve first input the position vector POA from 0 to A, in terms of the given quantities XA and YA, so that we can form the position vector PBA from B to A by means of the ADD command, in conjunction with the position vector POB from 0 to B, which is already in the workspace: POA=XA*Nl+YA*N2 PBA=ADD(POA,-POB) -> (435) PBA=(XA-XB)*Nl+(YA-YB)*N2 Now all of the position vectors needed for the computations at hand are in the workspace"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000618_s0020-7462(97)00052-8-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000618_s0020-7462(97)00052-8-Figure1-1.png",
        "caption": "Fig. 1. Inverted pendulum model.",
        "texts": [
            " In Section 3, the robustness of the control system with respect to the physical parameters and measurement uncertainties in the base point accelerations is evaluated. In Section 4, the discontinuous terms in the control strategy are replaced with smooth functions. We trade off the stronger stability against the generation of the high-frequency chattering in the control torques. The precise nature of this trade-off is also studied. Section 5 presents some simulation results and is followed by concluding remarks. 2 . METHODOLOGY 2.1. Derivation of the model The inverted pendulum model is shown in Fig. 1. OX\u00bdZ is the inertial coordinate system with X in the horizontal direction, \u00bd in the vertical direction and Z forming a right-handed orthogonal coordinate system. The body coordinate system is denoted by oxyz and is attached to the center of mass o. It is oriented along three principal axes of the inverted pendulum. OX\u00bdZ and oxyz coincide at the initial time. The rotations are described by the ZX\u00bd type of Euler angles [19]. The displacements of the base point are shown as fI (t), gJ (t) and hI (t) described in the inertial coordinate system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000967_icsyse.1990.203156-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000967_icsyse.1990.203156-Figure3-1.png",
        "caption": "Figure 3: Comparison of the minimum distance to the obstacles for solutions with and without the secondary constraints.",
        "texts": [],
        "surrounding_texts": [
            "Th1-h~ = [ 0 ;] (1) = Bna . . . Bo A0 . . . A,, where A; represents the homogeneous transformation from coordinate frame i - 1 to i of the first robot which has nl joints and B , is the inverse of the transformation between coordinate frames i- 1 and i of the second robot which has nz joints. During the calculation of (l), the transformation between the ith joint coordinate frame and the coordinate frame of the second robot\u2019s end effector, denoted by Ui, can be obtained from 300 CH2872-0/90/0000-0300 0 $1.00 1990 IEEE The columns of the relative Jacobian, which are composed of relative linear and angular velocity vectors due to the ith joint are closely related to the third and fourth columns of the above U matrices. In particular, it is easy to show that the relative linear velocity, U;, is given by the cross product of the third and fourth column of U; and that the relative angular velocity, U;, is given by the third column of U; (see Figure 1). The relative Jacobian, denoted J R , is therefore given by (3) where the upper 3 X 3 rotation R h l t h a from ( I ) , is required in order to express the relative velocity with respect to the first hand's coordinate frame. The composite Jacobian, denoted J c , represents the set of secondary constraints which consist of obstacle avoidance, joint limit avoidance, and absolute position and orientation requirements. The obstacle avoidance criteria is represented by an obstacle avoidance Jacobian which relates the joint rates to the absolute linear velocity of those links that contain proximity sensors. It is obvious that the absolute Cartesian motion of a link possessing a sensor can only be affected by joints which are closer to the base. Thus the obstacle Jacobian, denoted Jo, for a sensor which is mounted on the sth link of the second robot is given by the 3 x (nl + n2) matrix robot1 robot2 The Jacobian used to specify the mechanical joint limit constraints is trivial because there is no need to transform from joint space to Cartesian space, i.e. the only joint which affects the motion of the ith joint is the ith joint. Thus the general form for the 1 x (nl + n 2 ) joint limit Jacobian, denoted J L , is The third type of Jacobian considered is an absolute constraint Jacobian which relates the joint rates of the system to the absolute motion of the end effector. As in the obstacle avoidance Jacobian, none of the joints of the opposite robot affect the absolute motion of the end effector and their corresponding columns in the absolute Jacobian are zero. The remaining columns of an absolute Jacobian are obtained by inserting the full 6 x n standard Jacobian. For the absolute constraints on the second robot the 6 x (nl + n2) absolute Jacobian denoted J ~ A is r o b o t 1 robot2 (6) The composite Jacobian is formed by combining the three types of Jacobians described in (4), (5), and (6) to (7) [\\?;!I iJ2A1 where each subscript indicates the type of Jacobian and na and nl are the number of sensors and joints with limits respectively. The dimension of J c is (3na + nl + 12) x (nl + n2). 111. Specifying Secondary Constraints The secondary constraints of obstacle avoidance, joint limit avoidance, and absolute end effector locations are described by the equation JcO = i (8) where i is of the form iL[iOl ... io,, i L 1 a . . iL,, i l A i 2 A ] (9) and i o is the desired velocity of a link possessing a sensor, i~ is the desired velocity of a joint approaching a limit, and i~ is the desired absolute velocity of the end effector. The velocity i o is a 3 element vector given by i o = cY(do)fi (10) where A is a vector pointing away from the obstacles, d o is the distance to the obstacles, and CY is a scalar function that is inversely proportional to d o . The velocity i~ for the ith joint is given by where emid, is the joint value midway between the two joint limits and dL is given by dL = min(Omazi - O i , 0; - Omin,). (12) where Om,,, and Omin, are the maximum and minimum joint limits for the ith joint. The velocity . i ~ is composed of both linear and rotational velocities so that in general It is assumed that the absolute constraints on the end effectors are specified in world coordinates so that the 3 element linear velocity is given by where p d is the desired position for the end effector and p c is the current position of the end effector. The 3 element rotational velocity is obtained in an analogous manner based on the difference between the desired and current orientations. IV. Calculating Solutions If the desired relative velocity required to complete an assembly task is denoted by k~ then the solution for the joint velocity that achieves this velocity and simultaneously comes closest to satisfying the secondary constraints specified by (8) is given by [5,6] where + denotes the pseudoinverse. The first term J i k ~ represents the minimum joint velocity required to achieve the primary task. The term [Jc(l- J ~ J R ] + is the projection of the composite Jacobian onto the null space of the relative Jacobian which is required to keep the secondary constraints from affecting the relative motion specified as the primary constraint. The vector J c J i k ~ must be subtracted from the desired secondary constraint velocity i in order to account for the velocities induced by the pseudoinverse solution of the primary constraint. The solution given by (15) gives equal weight to all of the secondary criteria, i.e. it minimizes the quantity Ili - Jc01I2 . In practice a weighted least squares solution is desirable in order to assign a dynamic priority to the secondary constraints. This is performed by specifying a diagonal positive semi-definite matrix Q and then minimizing the quantity llQ(i - Jc0)l12. In addition to specifying relative priorities, Q provides a convenient method of completely removing any of the secondary constraints by setting the corresponding element to zero. V. Results The trajectory generation program was tested for a workcell consisting of two seven link robots, the Cybotech and CESARM manipulators. The robots are specified to start in an awkward initial configuration with one arm over the other (see Figure 2-a) and are then commanded to follow a relative end effector trajectory which ends with the two end effectors facing each other. The joint trajectories to achieve the desired relative trajectory are first calculated using only the minimum norm solution. Next, the secondary criteria of obstacle and joint limit avoidance are added and the resulting motions are compared to the minimum norm case. A quantitative comparison of the three cases is presented in Figures 3 and 4 which graphically present the minimum distance to obstacles and joint limits throughout the trajectory. The application of only the minimum norm solution rapidly results in a collision between the two arms (see Figure 2-b). When the obstacle avoidance constraint is added to the trajectory generation, however, the manipulators reorient themselves so that there is no collision at the point where the minimum norm solution collides (see Figure 2-c) or throughout the remainder of the trajectory (see Figures 2-d and 3). Unfortunately, the reorientation used to avoid the obstacles results in a violation of the joint limit constraint on the sixth joint of the Cybotech manipulator (see Figure 4). This can be remedied by using the formulation which includes both the obstacle avoidance and the joint limit avoidance constraints. A comparison of Figures 3 and 4 illustrates how the proposed algorithm uses the weighting parameters to allocate the available redundancy to the more critical of the secondary constraints. As a result, the manipulators are able to complete the assigned task without violating any of the constraints. VI. Summary The algorithm presented generates joint trajectories for two robots cooperating to perform an assembly task specified by a trajectory expressed in the coordinates of one of the parts. The robots are considered as a single redundant system with secondary criteria such as obstacle and joint limit avoidance, as well as absolute constraints being satisfied while performing the assembly task. The Jacobian relating the joint rates of the entire system to the relative motion of one of the hands with respect to the other is used to generate the relative motion satisfying the cooperative task. Motion satisfying the secondary criteria is generated by a composite Jacobian equation whose solution is constrained to be in the null space of the relative Jacobian. References A. Hemami, \u201cKinematics of two-arm robots,\u201d IEEE J. Robotics Auto., vol. RA-2, no. 4, pp. 225-228, 1986. K. Laroussi, H. Hemami, and R. E. Goddard, \u201cCoordination of two planar robots in lifting,\u2019 IEEE J. Robotics Auto., vol. RA-4, no. 1, pp. 77-85, 1988. S. Lee, \u201cDual redundant arm configuration optimization with task-oriented dual arm manipulability,\u201d IEEE Trans. Robotics Auto., vol. RA-5, no. 1, pp. 78- 97, 1989. J. Y. S. Luh and Y. F. Zheng, \u201cConstrained relations between two coordinated industrial robots for motion control,\u201d Int. J. Robotics Res., vol. 6, no. 3, pp. 60- 70,1987. A. A. Maciejewski and C. A. Klein, \u201cObstacle avoidance for kinematically redundant manipulators in dynamically varying environments,\u201d Int. J. Robotics Res., vol. 4, no. 3, pp. 109-117, 1985. Y. Nakamura, H. Hanafusa, and T. Yoshikawa, \u201cTaskpriority based redundancy control of robot manipulators,\u201d Int. J. Robotics Res., vol. 6, no. 2, pp. 3-15, Summer 1987. H. Seraji, \u201cAdaptive force and position control of manipulators,\u201d J. Robotic Systems, vol. 4, no. 4, pp. 52- 71, 1987. H. Suh and K. G. Shin, \u201cCoordination of dual robot arms using kinematic redundancy,\u201d Proc. 1988 Int. Coni. Robotics Auto., pp. 504-509, 1988. R. Zapata, A. Fournier, and P. Dauchez, \u201cTrue cooperation of robots in multi-arms tasks,\u201d Proc. 1987 Int. Conj. Robotics Auto., pp. 1255-1260, 1987. 300000 225000 VI a\u2019 a\u2019 150000 5 a\u2019 U L m U1 R 075000 0 0 0 0 0 0 1 D i s t a n c e t o Nearest Obs tac le ~ Min Norm Obs tac le Avoidance J o i n t L i m i t & Ob Av _ _ _ _ _ _ 26 00 51 00 76 00 I Time 0"
        ]
    },
    {
        "image_filename": "designv11_11_0001120_304-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001120_304-Figure1-1.png",
        "caption": "Figure 1. Coordinates and computational domain used for the plasma plume simulation.",
        "texts": [
            " In addition, Kim and Farson (2001) could not get a quasi-steady solution, and the radiation energy loss from the plasma plume was not included in their two-dimensional model. As a result, their twodimensional modelling results could not well represent actual laser welding processes. This paper presents a more generalized three-dimensional modelling approach to study the plasma plume characteristics. The plasma plume parameters including the spatial distributions of temperature and vapour concentration and the flow field will be investigated in some detail. Laser absorption and refraction are then evaluated based on these modelling results. Figure 1 shows the coordinate system used in this study, which is taken to be fixed with the laser beam. The assumptions employed in the modelling include: (a) the welding process and the plasma plume are steady; (b) the flow is laminar; (c) the plasma is in the local thermodynamic equilibrium (LTE) state; (d) the plasma plume absorbs part of the laser energy through the inverse Bremsstrahlung and radiates energy to the surroundings; (e) pure iron is used as the workpiece, the coaxially injected shielding gas and the laterally injected assisting gas (if any) are pure argon, whereas the plasma plume consists of a mixture of argon and iron vapour",
            " In equation (5), the source terms Ur is the temperature- and concentrationdependent radiation power per unit volume of plasma, and the data presented by Menart and Malik (2002) and Essoltani et al (1994) are used in the calculation. I is the local laser intensity, whereas \u03b1 is the laser absorption coefficient. For the case of the CO2 laser, the absorption coefficient is calculated as (Ready 1971) \u03b1 = 1.63 \u00d7 10\u221242 N2 e T 1/2 e \u00d7 [ 1 \u2212 exp (\u22121.36 \u00d7 103 Te )] (m\u22121) (7) in which Ne is the electron number density, whereas Te is the electron temperature. The computational domain used in the modelling of the laser-induced plasma plume is the cube denoted as ABCDEFGH in figure 1. The dimensions of the computation domain are 10 mm \u00d7 10 mm \u00d7 10 mm, the radius of the laser spot at the centre of the workpiece surface is 0.15 mm, whereas the light beam divergence is taken to be 1.7 mrad. Boundary conditions are as follows. Metal vapour with fixed temperature (Tva) and upward velocity (Uva) enters into the plasma plume from the small circular areaSva (light spot) on the bottom boundary shown in figure 1, and thus the boundary conditions at Sva are u = Uva, v = 0, w = 0, T = Tva and f = 1. For the other part of the workpiece surface except for the small circular area Sva, u = 0, v = 0, w = 0, T = Tf and f = 0 are used, where Tf is the ambient gas temperature (i.e. 300 K). At the eastern boundary BCGF, \u2202u/\u2202y = 0, \u2202v/\u2202y = 0, \u2202w/\u2202y = 0, \u2202T /\u2202y = 0 and \u2202f/\u2202y = 0 are employed. For the case including the effect of laterally injected assisting gas on the plasma plume, the argon gas is assumed to be injected from the region IJKL on the western boundary with a fixed velocity Uas at the inclination angle of 45\u02da, and thus u = \u2212Uas/ \u221a 2, v = Uas/ \u221a 2, w = 0, T = Tf and f = 0 are employed",
            " It is obvious that for the cases studied in sections 3.1\u20133.3 (without including the laterally injected assisting gas), the plasma plume will be axisymmetrical and one can use a twodimensional modelling approach and cylindrical coordinates for the study of those cases. However, in order to facilitate the comparison of the computed results for the cases without including the laterally injected assisting gas to those with the lateral injection of the assisting gas, this paper employs the same three-dimensional computational domain (as shown in figure 1), the same mesh (as shown in figure 2) and the same three-dimensional modelling approach for all the case studies in sections 3.1\u20133.4. For the axisymmetrical cases, we have also conducted some two-dimensional modelling study using cylindrical coordinates. It is found that the two-dimensional modelling results concerning the temperature and flow fields within the plasma plume are consistent with their counterparts obtained from the present three-dimensional modelling, although those two-dimensional results will not be presented here as separate figures",
            " Uva) at Sva is taken to be 100 m s\u22121, whereas the velocity of the coaxial shielding gas (Ush) is taken to be 5 m s\u22121. The vapour temperature Tva is treated as a parameter and taken to be 4000, 6000, 8000 or 10 000 K in the computation. Typical calculated results are shown in figures 3\u20135 concerning the effect of the vapour temperatures Tva on the plasma plume characteristics. Figures 3(a)\u2013(d) show the computed isotherms within the plasma plume on the middle vertical section (i.e. on the x\u2013y plane with z = 5 mm in figure 1) for the four different vapour temperatures. It is found that the computed maximum temperatures in the plasma plume are always about 13 900 K. The corresponding computed velocity vector fields (denoted with uniform vector length for clarity) and iron vapour concentration contours are shown in figures 4(a)\u2013(d) and figures 5(a)\u2013(d), respectively. It is clearly seen from figures 4(a)\u2013(d) that there always exist recirculation vortices in the computed flow fields and the vortex locations vary with the variation of the vapour temperature Tva"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000955_robot.2001.932978-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000955_robot.2001.932978-Figure3-1.png",
        "caption": "Fig. 3 . Parameters used in the calculation of Go-To-Target.",
        "texts": [
            " The Scan motor scheina is parameterized by X , the number of degrees to rotate in each direction. The niat1iematica.l formulation for t,liis schema is as follows: I/,,,, = current hea,tling +/- X-degrees I ~ K c a n ~ ~ = 1.0 A.2 Go-To-Ta.rget The Go-To-Target motor schema is impleniented as a linear attraction. The magnitude of the attraction varies with distance to the target; 1.0 outside of a controlled zone, decreasing linearly from 1.0 to 0.0 at the dead zone\u2019s boundary, axid finitlly 0.0 within the dead zone. The parameters C1 and D1 (shown in Figure 3) are used to specify the radii of the controlled and dead zones respectively. Ma.thematically : Vgo-to-target = vector from center of robot to target object 1 for r > C1 0 for r 5 D1 for D1 < 7\u2019 5 C1 r - D L Jlr\u2019go-to-targetll = A. 3 S wirl-Obst acles At a.ll times the robot is avoiding obstacles. Avoidance is implemented using circumnavigation or \u201dswirling\u201d around each obstacle (Figure 4). The a.ppropriate direction for circumnavigation depends on whether the robot is attempting to r e x h the target (acquire) or the goal location (deliver) [B]",
            " The SwirlObstacles iiiotor schema creates a vector perpendicular to the line from the robot to each obstacle it detects in the a.ppropria.te direction. The magnitude of each of these vectors is zero beyond a controlled zone and infinite within a dead zone. Hetween the two it increases linearly until it reachers a maximuni value at the dead zone boundary. The vectors corresponding to each obstacle are then summed to form the output of this schema. The parameters for the Swirl-Obstacles schema are C? and Da, the controlled and dead zone radii (defined similarly to C1 and D1 as shown in Figure 3) . The mathematical forniulation for Swirl-Obstacles is: A.4 Dock The Dock motor schema is used to lead the robot a.round the target and into the appropriate position and orientation for pushing. This behavior is critical to ensure proper alignment of the robot and trailer for our non-holononiic vehicle. Dock constructs a vector that varies in direction from directly towards the target object to perpendicular for circumnavigation. Outside of a wedge-shaped controlled zoiie, Dock returns only the perpendicuhr vector component, while within the controlled zone it returns a linear combination of the two vectors",
            " In between these distances, the outputs of the two scheinas are 1inea.rl-y combined. Dock is weighted higher as the robot gets closer to the target. In addition to the alignment vectors, the Acquire behaviord asseinlhge also includes the SwirlObstacles motor schema,. This schema is included to help prevent collisions with obstacles. The alignment phase of the Acquire behavioral assemblage is parameterized by Cq and Dq, the radii of the controlled and dead zones, defined similarly to C1 and Dl as shown in Figure 3. Mathematically, with T defined as for the Go-To-Target schema: Valigninent = PVgo-to-target + (1 - P)Vdock 1 for T > C, 0 for T < 0 4 p = { g;?G4 for D4 5 r 5 cq B.3 Deliver The Deliver behavioral assemblage, activated when the robot has acquired the target object, is used to move this object froni its original locat,ion to the goal location. This assemblage combines the Push and Swirl-Obstacles motor schema,; in order to allow the robot to accomplish its task while avoiding obstacles. Two types of pushing tasks were investigated: box pushing and ball dribbling during a soccer game"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002804_j.mechmachtheory.2005.07.008-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002804_j.mechmachtheory.2005.07.008-Figure1-1.png",
        "caption": "Fig. 1. Mating surfaces in the fixed space E3 f .",
        "texts": [
            " Let k1, k2, (e1,v1) and (e2,v2) be the eigenvalues and eigenvectors of the matrix A \u00bc a11 a12 a21 a22 \u00bc E F F G 1 L M M N \u00f024\u00de Then we have ke1 \u00bc k1 ke2 \u00bc k2 \u00f025\u00de and ge1 \u00bc e1pe;n \u00fe v1pe;h je1pe;n \u00fe v1pe;hj ge2 \u00bc e2pe;n \u00fe v2pe;h je2pe;n \u00fe v2pe;hj \u00f026\u00de Therefore, once obtained at a given point on Re the principal directions ge 1 and ge2 and the corresponding principal curvatures ke1 and ke2, we may write te\u00f0se\u00de \u00bc cos bge1 \u00fe sin bge 2 \u00f027\u00de and, employing Rodrigues formula, mu e;se \u00bc \u00f0ke1 cos bge1 \u00fe ke2 sin bg e 2\u00de \u00bc \u00f0ke1\u00f0te ge1\u00dege1 \u00fe ke2\u00f0te ge2\u00dege 2\u00de \u00f028\u00de where b is the angle, in the tangent plane, between ge1 and te, positive if a counterclockwise rotation around mu e aligns ge1 onto te (we remind that ge1 ge2 \u00bc mu e). Moreover the normal curvature and the geodesic torsion defined in Eqs. (22) and (23) can be calculated by means of Euler s and Bertrand s formulas, respectively [2, p. 132 and 159]: ken \u00bc ke1cos 2b\u00fe ke2sin 2b \u00f029\u00de se \u00bc 1 2 ken;b \u00bc \u00f0ke2 ke1\u00de sin b cos b \u00f030\u00de Let us consider another Euclidean space E3 f . As shown in Fig. 1, in this new space we define a first translating axis a by means of one of its (moving) points Oa(/) and a fixed unit vector a, and a second translating axis b again by means of one of its points Ob(/) and a fixed unit vector b. In practical terms they are the two axes (i.e., directed straight lines) of the gear pair under investigation (the generating tool and to be generated gear). The dependance of Oa and Ob on the parameter of motion / shows that in the following treatment the two axes a and b are allowed to translate with respect to each other, while their directions remain fixed, that is a and b are constant unit vectors",
            " Denoting by P\u0302 \u00f0n; h;/\u00de the generic point of R\u0302\u00f0/\u00de, its position vector p\u0302a with respect to the moving point Oa(/) is given by the following expression which employs the compact notation introduced in (1) p\u0302a\u00f0n; h;/\u00de \u00bc P\u0302 \u00f0n; h;/\u00de Oa\u00f0/\u00de \u00bc R\u00f0pe\u00f0n; h\u00de; a;w\u00f0/\u00de\u00de \u00f031\u00de and where pe(n,h) was defined in Eq. (13). Of course, it is equally possible to relate P\u0302\u00f0n; h;/\u00de to the position vector p\u0302b\u00f0n; h;/\u00de with respect to the moving point Ob(/) p\u0302b\u00f0n; h;/\u00de \u00bc P\u0302 \u00f0n; h;/\u00de Ob\u00f0/\u00de \u00bc p\u0302a\u00f0n; h;/\u00de d\u00f0/\u00de \u00f032\u00de where (Fig. 1) d\u00f0/\u00de \u00bc Ob\u00f0/\u00de Oa\u00f0/\u00de \u00f033\u00de is a variable vector depending arbitrarily on /. It should be noted that the relationship between pe and p\u0302b is a rotation plus a translation, i.e. a general affine transformation. Both position vectors p\u0302a\u00f0n; h;/\u00de and p\u0302b\u00f0n; h;/\u00de of R3 are related to the same family of surfaces Uf of E 3 f . As a consequence of Eqs. (31) and (32), along with the general properties (9) and (10), we have the following derivatives p\u0302a;n \u00bc p\u0302b;n \u00bc R\u00f0pe;n; a;w\u00f0/\u00de\u00de p\u0302a;h \u00bc p\u0302b;h \u00bc R\u00f0pe;h; a;w\u00f0/\u00de\u00de \u00f034\u00de p\u0302a;/ \u00bc w0a p\u0302a \u00bc w0a R\u00f0pe; a;w\u00f0/\u00de\u00de \u00bc R\u00f0w0a pe; a;w\u00f0/\u00de\u00de \u00f035\u00de p\u0302b;/ \u00bc p\u0302a;/ d 0 \u00f036\u00de By definition the normal vector m\u0302 to each regular surface R\u0302\u00f0/\u00de of the family (hence for fixed /) is given by m\u0302\u00f0n; h;/\u00de \u00bc p\u0302a;n p\u0302a;h \u00bc p\u0302b;n p\u0302b;h \u00bc R\u00f0me\u00f0n; h\u00de; a;w\u00f0/\u00de\u00de 6\u00bc 0 \u00f037\u00de where Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000204_0022-0728(95)04027-l-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000204_0022-0728(95)04027-l-Figure1-1.png",
        "caption": "Fig. 1. A schematic diagram of the Clark dual 0 2 Jr- C O 2 sensor, enclosing the Koslow 10/zm diameter Au microdisc electrode in a PTFE body, and with a 12 /zm thick PTFE membrane covering the electrode surface.",
        "texts": [
            " Experimental purity, Fluka AG) in Spectrosol DMSO supplied by BDH Chemicals Ltd. A 12 /xm thick PTFE membrane (supplied by Radiometer A / S , Denmark) was fitted to the end of the electrode holder, and was held in place by an O-ring. The glass rod holding the gold microdisc working electrode was pushed tightly against the Teflon membrane, trapping a thin layer of electrolyte between the microcathode and the membrane surface [7]. The PTFE sensor holder also housed a silver wire quasi-reference electrode, as shown in Fig. 1. For the 0 2 and CO 2 gas concentration studies, the sensor was held vertically in an Adams tonometer [12,13], which was thermostatted at 37\u00b0C (normal human body temperature). The gas inlet to the tonometer was connected to a W6sthoff (Bochum, Germany) triple gas mixing pump (model 2M 302/a-F), which produced tertiary gas mixtures of 0 2, CO 2, and N 2 which were accurate to _ 1% relative of the selected ratio. The concentrations of the test gases applied to the sensor were also measured with a respiratory gas monitor (Hewlett Packard model M1025A, Bracknell, UK), which measured the O 2 concentration with a fast response paramagnetic analyser, and the CO 2 concentration with a photoacoustic IR CO 2 analyser",
            " The tertiary gas mixtures with CO 2 concentrations varying between 3% and 15% v / v , and 0 2 varying between 5% and 30% v / v , with the balance N2, were supplied via the W6sthoff gas mixing pump to the membrane-covered sensors in order to test (a) their output current-gas concentration linearity, and (b) for any presence or absence of cross-interference from the concomitant 0 2 and CO 2 reduction processes occurring at the microelectrode surface [8]. All studies were conducted with a sensor constructed like an ordinary Clark oxygen electrode [1,7], as shown in Fig. 1. The working electrode was either a 10 /xm gold microdisc electrode sealed in a glass rod (Koslow Corporation, Edgewater, N J) or else a gold microdisc electrode (diameter 3.4 /xm, ascertained by the oxidation of ferrocene in acetronitrile [8]), again sealed in a glass rod and fabricated at La Trobe University, Australia [11]. The electrode was housed in a polytetrafluoroethylene (PTFE) machined holder, designed to hold a few microlitres of the working electrolyte. The electrolyte was 0.2 mol dm -3 tetraethylammonium perchlorate (TEAP, greater than 99% Figs",
            " Caution must be employed when making exact quantitative comparisons between these two figures, since the sensor was dismantled and then reassembled between the studies, in order to obtain the two sets of 6%, (c) 9%, (d) 12%, and (e) 15% v/v respectively, at a constant 02 concentration of 15% v/v, when 5% v/v H20 had been added to the DMSO solvent. results sequentially. Since the exact magnitude of the sensor limiting currents is a function of the membrane and electrolyte layer thicknesses, as well as the 02 and CO e gas concentrations, and since the PTFE membrane material inevitably stretches to a different extent each time it is applied to the sensor body (Fig. 1), then the limiting currents might be expected to vary somewhat between the two studies, even when the same prevailing 02 and CO 2 concentrations pertain. However, inspection of the I L for 02 on both Figs. 10 and 11 shows that they are essentially the same, within measurement error, when either 5% or 10% v / v H 2 0 is added to the DMSO solvent. The only apparent change is in the magnitude of the CO 2 reduction wave, with the CO 2 limiting currents being decreased on average by about 17% (relative to those currents obtained with 5% v / v H20) , when 10% v / v HeO was added to the solvent"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002222_1.1576425-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002222_1.1576425-Figure1-1.png",
        "caption": "Fig. 1 Schematic diagram of eccentric-tappet pair: \u201ea\u2026 original; \u201eb\u2026 equivalent.",
        "texts": [
            " Their solution also explained a part of the abnormal surface dimple phenomena observed by Kaneta et al. @10,11#. Evidently, the technique could also be applied to the TEHL of cam-tappet pair. However, the arc transition of typical cams results in mathematical difficulties in kinematic and dynamic analysis and temperature computation. Therefore, in this work, the TEHL problem of an eccentric-tappet pair is solved numerically. Kinematic and Dynamic Equations of Eccentric-Tappet Pair. A schematic diagram of the eccentric-tappet pair is shown in Fig. 1~a!, where the eccentric-wheel is assumed as solid ~a! and the tappet solid ~b!. A dynamic coordinate system xoz is built as shown in the figure with the origin set at the nominal contact point o. In the process of the work, the coordinate system is always moving with the follower so that the velocity components of both the eccentric-wheel and the faced tappet in the z-direction are zero. It is well known that in lubrication theory the velocities components ua , ub , in x-direction are referred to as the relative velocities of the surfaces relative to the dynamic coordinate system. Therefore, after dynamic analysis they could be written as H ua5Rv ub5ev cos vt (1) where vt is the turning angle of the eccentric-wheel and R and e are the radius and the eccentricity of the eccentric-wheel, respectively. Thus, Fig. 1~a! is equivalent to Fig. 1~b! from the elastohydrodynamic viewpoint. The lift of the tappet is s~ t !5e~12cos vt !. (2) 2003 by ASME Transactions of the ASME s of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: http://tr In order to facilitate the presentation of results, the entraining velocity is defined as ue5~ua1ub~ t !!/2 (3) When the velocities of the solids have the same magnitudes and opposite senses, zero entraining velocity occurs. Following the work of Ai and Yu @6#, the load carried by the eccentric-wheel and tappet is taken to be the resultant of the inertia force F j and the spring force Fs ",
            ", (4) where F j(t)5(ms/31mT1mv)(d2s(t)/dt2), Fs(t)5F01s(t) \u2022ks , ms , mT , and mv are the masses of spring, tappet and valve train, F0 is the initial load, and ks is the stiffness coefficient. Supposing the length of eccentric-wheel is L, the total load per unit length can be written as w load~ t !5 F~ t ! L 5S F01s~ t !\u2022ks1S 1 3 ms1mT1mvD d2s~ t ! dt2 D Y L , (5) where w05F0 /L is the initial load per unit length. Reynolds Equation. Yang and Wen @12# have presented a generalized Reynolds equation for both Newtonian and some nonNewtonian models. For the present transient line contact Newtonian problem in the xoz coordinate system shown in Fig. 1~b!, considering the possible zero entraining velocity in a working cycle @9#, this equation can be rewritten as ] ]x F ~r/h!eh3 ]p ]x G56ua ]~ r\u0303ah ! ]x 16ub ]~ r\u0303bh ! ]x 112 ]~reh ! ]t , (6) where (r/h)e , r\u0303a , r\u0303b are equivalent quantities concerning viscosity h and density r of the lubricant, defined as: ~r/h!e512~here8/he82re9!, r\u0303a52~re2re8he!, r\u0303b52re8he , re5~1/h !*0 hrdz , re85~1/h2!*0 hr*0 z 1/hdz8dz , re95~1/h3!*0 hr*0 z z8/hdz8dz , he5h/*0 h1/hdz , he85h2/*0 hz/hdz . Equation ~6! is subjected to the boundary conditions as follows Tribology ibology"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003346_j.jsg.2004.07.005-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003346_j.jsg.2004.07.005-Figure2-1.png",
        "caption": "Fig. 2. Comparison between kink-style and circular sector hinges: (a) in the two constructions, motion above the same fault geometry produces different particle trajectories, different fold geometries and different time evolution of bedding dip. The resulting cumulative layer-parallel slip distribution (b), and growth stratal geometries (c), strongly differs in the two hinge styles.",
        "texts": [
            " Suppe, 1983; Jamison and Pope, 1996; Medwedeff and Suppe, 1997). The application of kink-style models to many natural anticlines worldwide supports the geometrical validity of this assumption. A satisfactory geometrical fit, however, does not necessarily imply that fold kinematics is unequivocally constrained. Identical fold geometries can be obtained via different kinematic pathways (e.g. Storti and Poblet, 1997). Comparison between a kink-style hinge and a circular sector highlights remarkably different particle paths (Fig. 2a). A kink axial surface imposes an instantaneous transition from the unfolded state to the final attitude of the folded multilayer. The corresponding particle path consists of two straight segments (e.g. Hardy, 1995). On the other hand, a circular hinge sector produces the progressive variation of layer dip up to its final folded attitude. The corresponding particle path is curvilinear. Different particle paths imply (1) different partitioning of layer-parallel slip in flexural-slip folding and (2) different growth stratal geometries when syntectonic sedimentation occurs during folding. (1) With a kink axial surface, the total amount of layer-parallel slip required by parallel folding is instantaneously acquired in the entire folded multilayer (Fig. 2b). Conversely, progressive folding within a circular hinge sector implies the occurrence of infinitesimal increments of layer-parallel slip until the final layer dip is attained. The upward broadening geometry of circular hinge sectors causes a vertically inhomogeneous distribution of layer-parallel slip increments (Fig. 2b). (2) The instantaneous acquisition of final layer dip past a kink axial surface produces growth strata geometries consisting of uniformly dipping rock panels paralleling the top of the pre-growth strata (Suppe et al., 1992). On the other hand, progressive rotation of the substratum during sediment deposition produces wedge-like geometries (e.g. Hardy and Poblet, 1994) (Fig. 2c). Differences illustrated in Fig. 2 remark how the proper modelling of natural fold geometry cannot be restricted to a mere geometric criterion, suitable to provide multiple solutions. Instead, it includes the choice of the most appropriate fold kinematics, according to the basic milestones of cross-section balancing (e.g. Elliott, 1983). Our major purpose for implementing circular hinge sectors in the classical, kink-style model of Suppe (1983) was to provide an additional kinematic pathway to compressional faultbend folding (Fig",
            " The velocity field associated with curvilinear fault-bend folding predicts that particles have trajectories that are either parallel to the thrust surfaces or curvilinear (Fig. 9). Fold sectors where particle paths are parallel to the fault traces are named translational sectors, while parabolic or circular trajectories characterise rototranslational sectors. Translational sectors do not include the possibility for particles to modify their distance from the corresponding fault segment. Conversely, particles moving through rototranslational sectors can change their distance from the fault (Fig. 2a). A primary difference between velocity properties characterising translational and rototranslational sectors, respectively, is that layer dip remains constant in the former sectors, whereas it gradually changes in the latter. The velocity field of a curvilinear fault-bend anticline in the post-transient configuration includes one rototranslational sector. In step I (Fig. 10a and b), HL, BP, BP 0, CP, FP and FL are translational sectors and FP 0 is the rototranslational sector. In step II (Fig. 10d), BP 00 becomes a rototranslational sector while FP 00 becomes a translational sector",
            " It is worth noting, however, that the expected displacement and size of thrusting and folding induced by the predicted forelandward shear are far below the resolution of regional balanced cross-sections. Analogously, the predicted amount of layer-parallel shortening (Fig. 17d) is expected to be significantly lower than that observed in \u2018undeformed\u2019 foreland, which can exceed 20% (e.g. Casas et al., 1996). Different partitioning of bending and layer-parallel slip in the kink bands and circular hinge sectors, respectively (Fig. 2) suggests different expectations for rock fabric evolution in the various fault-bend folding models. Neglecting the role of mechanical stratigraphy, the assumption of a relationship between bending angle and deformation intensity may provide a crude approximation for predicting folding-related deformation intensity in kinkstyle folding (e.g. Storti and Salvini, 1996). Application of this approach to fault-bend folding (Fig. 18a) produces a deformation pattern that can be conveniently described in terms of deformation panels and deformation domains (Salvini and Storti, 2004)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002026_3-540-44842-x_74-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002026_3-540-44842-x_74-Figure1-1.png",
        "caption": "Fig. 1. Existing test parts (length x width)",
        "texts": [
            "  Springer-Verlag Berlin Heidelberg 2003 Studies related to RP processes tend to focus on many aspects, including benchmarking the capability of the system and quality assurance. For benchmarking, a test part is usually required, and many studies have developed test parts prior to this study. The project funded by the European Community reported to determine the levels of dimensional accuracy and surface finish achievable with various layer-manufacturing processes. The test part geometry, shown in Fig.1(a), has planar surfaces that include various angles in the x, y and z directions. The surfaces are disposed to facilitate measurement. However, it is impossible to evaluate various geometric characteristics since it includes no features other than angles [1,2]. The Intelligent Manufacturing Systems (IMS) project reported the capabilities of RP systems, including build time, build volume, system cost and accuracy expectation, through IMS test parts built by many companies. Although the two IMS test parts shown in Fig.1(b) were created to provide a variety of geometrical features, it is difficult to quickly acquire measurement data to evaluate geometric characteristics or dimensional accuracies on the account that they have many freeform shapes and fillets or rounded features that are not easily measured by a coordinate measuring machine (CMM) [3]. Juster et al. proposed a new benchmark part (Fig.1(c)) for evaluating the differences in the accuracy of major machines. Using this part, which includes various features, it is possible to evaluate the geometric and dimensional characteristics according to features of different sizes. However, the base plane is so big that curling of the base surface, which then affects the measurement, can occur. Since it also has freeform features like the IMS parts, it is not simple to obtain and estimate the measurement data rapidly. The essential primitives, such as a sphere and a large cylinder, were excluded as well [4]. The standard part proposed by 3D Systems (Fig.1(d)) was designed to facilitate measurement since features on the base surface are almost aligned symmetrically right and left. Due to the lack of necessary features to satisfy various evaluation lists, however, evaluation is very restrained, and measurement data in each of the x, y and z directions cannot be obtained because most of the features are arranged in one direction. Ippolito et al. compared the accuracy and surface roughness of major RP techniques by using this part [5]. Zhou et al. developed a standard sample (Fig.1(e)) to provide for the benchmarking of some features. Even though the sample part has the essential primitives for the evaluation of features dimensional accuracy, since their dimensions are so small and the axes of all the features are aligned in one direction, dimensional characteristics based on features of different sizes and measurement data in other directions cannot be acquired. Besides, the distance between features is very small, which makes it difficult to obtain measurements by a CMM [6]. Nakagawa et al. developed the benchmark part in Fig.1(f) to evaluate the performance of commercial RP systems. Unlike other conventional test parts, small features, such as walls and holes, were included in the benchmark part to assess the ability of the RP systems to make fine details. However, the walls and holes are aligned along one axis and the benchmark part consists of only several simple features, and most of all, its size and features size are so small that we cannot acquire data with respect to differences in their size [7]. The drawbacks of existing test parts used for respective studies can be summarized as follows"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002568_1.1864114-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002568_1.1864114-Figure2-1.png",
        "caption": "Fig. 2 Geometry of the base plane triangle",
        "texts": [
            " Third, the projections of B1, B2, B3 on plane xy are recorded as B1 , B2 , B3 , respectively. Accordingly, the formulation is founded very simply on the geometry of eight 2006 by ASME Transactions of the ASME 3 Terms of Use: http://asme.org/terms t p Downloaded F planes of interest, namely A1A2A3, A1B1A2, A2B2A3, A3B3A1, B1H1B1 , B2H2B2 , B3H3B3 , and B1B2B3 with particular attention on the intersections A1H1, B1H1, H1B1 , A2H2, B2H2, H2B2 , A3H3, B3H3, H3B3 . With reference to the geometry of base xy plane triangle A1A2A3, Fig. 2, the following expressions can be deduced using Cosine Law, taking into account angular relationships and isosceles triangles 1 = cos\u22121 a2 2 + a3 2 \u2212 a1 2 ; 2 = cos\u22121 a3 2 + a1 2 \u2212 a2 2 ; 2a2a3 2a3a1 Journal of Mechanical Design rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 10/04/201 3 = cos\u22121 a1 2 + a2 2 \u2212 a3 2 2a1a2 1 1 = 1 + 2 \u2212 3 2 ; 2 = 2 + 3 \u2212 1 2 ; 3 = 3 + 1 \u2212 2 2 2 R = a3 2 cos 1 = a1 2 cos 2 = a2 2 cos 3 3 Angles A2A1B1= 1, A3A2B2= 2, and A1A3B3= 3 are then computed by applying Cosine Law to triangles A1A2B1, A2A3B2 and A3A1B3, respectively, as follows: 1 = cos\u22121 L1 2 + a3 2 \u2212 L2 2 2L1a3 ; 2 = cos\u22121 L3 2 + a1 2 \u2212 L2 2 2L3a1 ; 3 = cos\u22121 L5 2 + a2 2 \u2212 L6 2 2L5a2 4 Designating the angles between the base plane and side triangular planes, namely B1H1B1 , B2H2B2 , B3H3B3 by 1 , 2 , 3, respectively, the coordinates of the points B1 B1x ,B1y ,B1z , B2 B2x ,B2y ,B2z and B3 B3x ,B3y ,B3z can now be expressed in the following way, Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003507_jsen.2006.881421-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003507_jsen.2006.881421-Figure9-1.png",
        "caption": "Fig. 9. Sensor locations used for the experimental evaluation.",
        "texts": [
            " 8, it is evident that, as a candidate sensor location is removed from the candidate set, the individual EfI values associated with the remaining locations may vary accordingly. Thus, only one sensor location is allowed to be removed at a time in order to guarantee that no critical sensor locations would be eliminated incorrectly. To experimentally evaluate the sensor-location optimization approach, four accelerometers (model U352B10) with a package footprint of approximately 10 mm were installed to measure vibrations from a ball bearing with a seeded outer raceway defect and experimentally evaluate the simulation results (Fig. 9). Three accelerometers, which are denoted as sensors 1\u20133, were placed on the selected optimal locations: sensor 1 on node 612 at the top of the housing plate, sensor 2 on top of the bearing corresponding to nodes 1995/2074, and sensor 3 to the right side of the bearing corresponding to nodes 2071/2076, respectively. The fourth accelerometer, which is denoted as sensor 4, was placed on the bottom of the bearing, which is symmetrical to the sensor 2 location but not recommended by the optimization procedure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003206_j.mechmachtheory.2003.12.003-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003206_j.mechmachtheory.2003.12.003-Figure2-1.png",
        "caption": "Fig. 2. Six-link mechanism composed of seven revolute pairs.",
        "texts": [
            " a1 sin h1 a2 sin h2 a3 sin h3 0 a1 cos h1 a2 cos h2 a3 cos h3 0 0 a4 sin\u00f0h2 \u00fe a1\u00de a3 sin h3 a5 sin h5 0 a4 cos\u00f0h2 \u00fe a1\u00de a3 cos h3 a5 cos h5 2 664 3 775 dh1=ds dh2=ds dh3=ds dh5=ds 2 664 3 775 \u00bc 0 0 cos a2 sin a2 2 664 3 775 \u00f05\u00de The determinant of its coefficient matrix (the Jacobian matrix) of the left hand side of Eq. (5) becomes as follows. d\u00f0s\u00de \u00bc a2a3 sin\u00f0h5 h3\u00de sin\u00f0h1 h2\u00de a3a4 sin\u00f0h1 h3\u00de sin\u00f0h5 h2 a1\u00de \u00f06\u00de Generally, the sign of the value of the determinant d\u00f0s\u00de changes at limit positions of the driving link, that is, at stationary configurations. Letting the kinematic constants and the angular displacements of moving links be lengths and angles as shown in Fig. 2, the set of closed loop equations of the Stephenson-3 six-link mechanism becomes following four equations. a0 \u00fe a1 cos h1 \u00bc a2 cos h2 \u00fe a3 cos h3 \u00f07\u00de a1 sin h1 \u00bc a2 sin h2 \u00fe a3 sin h3 \u00f08\u00de a3 cos h3 \u00fe a4 cos\u00f0h2 \u00fe a1\u00de \u00bc a5 cos h5 \u00fe a6 cos h6 \u00fe a7 \u00f09\u00de a3 sin h3 \u00fe a4 sin\u00f0h2 \u00fe a1\u00de \u00bc a5 sin h5 \u00fe a6 sin h6 \u00fe a8 \u00f010\u00de If a value of the angular displacement h6 (the input variable) of the driving crank is given, Eqs. (7)\u2013(10) become the set of non-linear simultaneous equation with four unknowns h1, h2, h3 and h5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000808_20.582604-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000808_20.582604-Figure1-1.png",
        "caption": "Fig. 1 Computation model",
        "texts": [
            " Y e stray load 10-s and the mechanical loss are given as typical values in many small size motors from the textbook[9]. Stator and rotor copper loss is W, = 3 IiR,, W, == 3 IiRZ , respectively. The core loss is calculated from B-Loss curve. Il . NUMERICAL RESULTS Fig.l is our computation model. It shows one pole of the 3.7kW 4 pole motor. In heat conduction problem, Neumann boundary cundilion is applied to the left side and to the righit side of the model. Mixed boundary condition is given to the upper side i.e. fin surface in Fig.1. The model has three equivalent layers. First, there is an equivalent contact layer with 1 [mml thickness between stator core and stator 1720 and b=0.6. F'ig.2 shows FE mesh of the model. Number of elements is 9747. Most of the elements lie in near the rotor bar. Fig.3 shows the heat source distribution. 'The values at several points in the motor are shown in Table IJI. Fig.4 shows equithermal line distribution. Most of the lines lo on rotor bar gap, air gap and stator insulation. This tells us that temperature decades down very suddenly at these regions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000615_rnc.4590050410-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000615_rnc.4590050410-Figure2-1.png",
        "caption": "Figure 2. A multi-trailer system with n (passive) trailers and m (active) steering wheels, with a virtual extension of nj-, virtual trailers in front of each steering wheel",
        "texts": [
            " However, the general multisteering system can be transformed into Goursat normal form after prolongation. Consider the following theorem. Theorem 8. Converting the n-trailer, m-steering system into Goursat form2' The n-trailer, m-steering system can always be put into extended Goursat normal form, for any n, m and for any configuration of steerable cars and passive trailers, using a prolongation of degree n , + ... + nm-l. Proof. Consider the n-trailer, m-steering system with virtual extension as shown in Figure 2. That is, in front of each steerable axle, imagine that there are nj-' virtual axles, and that only the front axle in each virtual chain is steerable. Note that with this virtual axle formulation, the actual steerable axles within the multi-trailer chain are no longer assumed to be directly steerable, but rather are controlled through the virtual steering axles and the chains of virtual trailers. The angle if the jth virtual steering axle is represented by @{ where the subscript 'v' stands for virtual"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000507_027836499501400207-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000507_027836499501400207-Figure4-1.png",
        "caption": "Fig. 4. Quasistatic pulling.",
        "texts": [
            " The support frictional force at each support point directly opposes the motion of the support point, and the integral of these differential forces over the support yields the total support frictional force. Consider Figure 3, for example. For the velocity center shown, the frictional support force acting on the slider is precisely balanced by the pusher force f passing through the contact. For a pusher velocity vp equal to the rod endpoint velocity vs, and a large enough coefficient of friction 11, we have a solution. There is nothing unusual about this solution. Because the pusher velocity v~ is directed into the slider, we have pushing, not pulling. But consider the example of Figure 4, where the applied force passes closely on the other side of the ring center. Here a solution is obtained for a pusher velocity vp equal to the slider velocity v~ but directed away from the slider: pulling. (Because the motion of the pusher is specified, pulling is defined as a velocity away from the slider, not a force.) Note that another solution is that the slider simply breaks contact and does not move. This at The University of Iowa Libraries on June 8, 2015ijr.sagepub.comDownloaded from 176 problem is ambiguous"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001948_aic.690490222-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001948_aic.690490222-Figure3-1.png",
        "caption": "Figure 3. Parameters characterizing a concave crystal in a conical-shaped cavity.",
        "texts": [
            " This is possible if the free energy of the system has a minimum above the liquidus temperature, in particular at the temperatures reached during regeneration. Second, we show that a stable crystal contained in a small crack does not grow out of the cavity in the subcooled solution unless the disk is flexed. We begin with an illustration of a conical-shaped crack and determine the conditions under which sodium acetate trihydrate crystals can be harbored in it. The parameters defining the size and shape of the crystal are shown in bold in Figure 3. These are the maximum horizontal radius of the crystal, r , the contact angle between the solution and the crystal, , and the half-angle at the apex of the cavity, . For the crystal with a concave surface in Figure 3, r 0, 0 180 , and 0 90 . Two additional parameters are useful and can be derived from the preceding three primary parameters: the \u017d .radius of curvature of the concave or convex, not shown surface of the crystal, z, and the half-angle of the segment of the sphere formed by this concave surface, , where s y y90 1\u017d . and r zs 2\u017d . sin For a concave surface of the crystal, and z are positive, while for a convex surface they are negative. Consider the growth of a crystal in the conical-shaped cavity illustrated in Figure 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003909_icsmc.2005.1571491-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003909_icsmc.2005.1571491-Figure1-1.png",
        "caption": "Figure 1. An illustration of the geometry of the tracking-navigation problem",
        "texts": [
            " Smart motion: The orientation angle of the prey is timevarying but in a smart way in order to escape to the predators. Smart preys require more elaborated strategies. We have the following assumptions 1. Each robot has a sensory system which allows to detect obstacles, and estimate the position of the prey with respect to the robot. 2. The robots\u2019 velocities satisfy vi > vp, for i = 1, ..., N . 3. The robots and the prey move with constant speed. 4. The path traveled by the prey is continuous. Figure 1 represents a scenario with three predator robots and the prey. The lines of sight are the imaginary straight lines that start from each robot and are directed towards the target. These lines are called L1, L2 and L3 in figure 1. The angles formed by the positive x-axis and the lines of sight are called the angles of the lines of sight. These angles are denoted by \u03b21, \u03b22 and \u03b23 in figure 1. The relative velocity in the Cartesian frame of reference between robot Ri and the prey is given by the following system x\u0307pi = vp cos \u03b8p \u2212 vi cos \u03b8i y\u0307pi = vp sin \u03b8p \u2212 vi sin \u03b8i i = 1, ..., N (3) This model can be written in polar coordinates as follows r\u0307pi = vp cos (\u03b8p \u2212 \u03b2p) \u2212 vi cos (\u03b8i \u2212 \u03b2i) rpi\u03b2\u0307pi = vp sin (\u03b8p \u2212 \u03b2p) \u2212 vi sin (\u03b8i \u2212 \u03b2i) i = 1, ...N (4) Systems (3) and (4) give the relative motion of the prey as seen by robot Ri. The first component in equation (4) represents the relative velocity along the lines of sight, the second component represents the relative velocity across the lines of sight Li"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000667_s0026-265x(02)00042-5-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000667_s0026-265x(02)00042-5-Figure1-1.png",
        "caption": "Fig. 1. Cyclic voltammograms of 1.0=10 M CoTAPc in 0.10 M TEAP in DMSO during polymerization on glassy carbony3 electrodes. Scan rate: 200 mV s . (a) 25 cycles of electropolymerization using the q0.800 to y2.000 V potential window, peaky1 numbering follows the assignment indicated in the text. (b) Cycle No 1 using the y0.200 to q1.000 V potential window, indicating the oxidation peak responsible for the start of electrochemical polymerization (i.e. the subtraction of one electron from the \u2013NH2 groups on the 4,9,16,23-tetraaminophthalocyanine). Potential started at y0.200 V.",
        "texts": [
            " Electrical connection to the modified ITO surface was made via a spring clip. The spacing between the cell and modified ITO surface was 0.50 mm. The auxiliary and reference electrodes were positioned away from the light path and kept in place by a specially prepared septum fitted on the top of the cell. For the spectroelectrochemical studies, applied potential of q1.000, q0.800, q0.500, 0.000, y 0.500 and y1.000 V was used. Difference spectra were obtained with respect to the corresponding polymeric film on ITO in an open circuit. Fig. 1a shows cyclic voltammograms corresponding to 25 cycles of electropolymerization, with one cycle in Fig. 1b. Three redox couples can be identified and are represented by the following equations: 3q 2y qw xCo ,Pc 1 y 2q 2y o9w xqe | Co ,Pc E s0.327 V 2 2q 2yw xCo ,Pc 3 y q 2y o9yw xqe | Co ,Pc E sy0.550 V 4 q 2y yw xCo ,Pc 5 y q 3y o92yw xqe | Co ,Pc E sy1.650 V 6 These peak assignments are consistent with what is known about the electrochemical behavior of metal\u2013phthalocyanine complexes and films derived from them w6,9x. The formal redox potentials, E 9, taken as the average of the anodic ando cathodic peak potential, are listed by the equations of the corresponding processes. Fig. 1b, depicting the first cycle of electropolymerization, shows two anodic peaks and one cathodic peak. The anodic peak appearing at the most electropositive potential, and without the corresponding cathodic process, is due to the oxidation of the amino groups in the ligand moiety. This peak can be observed during the first two or three cycles, but is overlapped by the growth of the anodic peak corresponding to 2 in Fig. 1a. The other two peaks correspond to the redox processes identified as involving the Co(III)yCo(II) couple. The oxidation of the \u2013NH group is considered2 to be the initial step in the polymerization process w9x. This oxidation occurs near 0.625 V, a potential more negative than that observed for the same process in the electropolymerization of Cu(IIyI)\u2013 4,9,16,23-tetraaminophthalocyanine w9x. Plots of peak current as a function of the square root of the scan rate from 50 to 200 mV s were linear,y1 indicating diffusion-controlled mass transport during electropolymerization. As shown in Fig. 1b, circumscribing the scanned potential from 1.000 to y0.200 V, the only peaks observed are peaks 1 and 2 corresponding to the Co(III)yCo(II) redox couple. A slight increase in the separation of these peaks was observed with increasing cycles. This insinuates slower charge transfer through the film due to the increased thickness of the film as the electropolymerization progresses. Plots of anodic and cathodic peak current as a function of the number of electropo- lymerization cycles were linear, at least up to 45 cycles",
            " Because of these characteristics of the electropolymerization, the peak for amino oxidation can be observed in the cyclic voltammogram for the zinc complex, but is unobservable in the cyclic voltammogram for the cobalt complex. Glassy carbon surfaces covered with films of CoTAPc take on a blue color, particularly dark when the film is thick. When these surfaces are used as working electrodes immersed in solutions of supporting electrolyte, characterization via cyclic voltammetry yields similar information collected during electropolymerization. The same redox couples illustrated in Fig. 1 are observed, but values for E 9 are slightly different. For peakso 1y2 E 9 is q0.368, for peaks 3y4 E 9 is y0.459o o and for peaks 5y6 E 9 is y1.541 V. Fig. 4a,bo shows peaks 1y2 of the voltammetric characterization of films corresponding to 15 and 20 cycles of electropolymerization when the potential window is circumscribed from q1.000 to y0.200 V. The anodic peak due to \u2013NH oxidation, observed2 during the first cycles of polymerization, was evident in characterization runs (ca. q0.900 V) of relatively thicker films (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001215_1.1286520-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001215_1.1286520-Figure7-1.png",
        "caption": "Fig. 7 Precision linear motor system",
        "texts": [
            " These two methods can be summarized and compared as follows; ~i! u\u0304*,ux : This is the case when there is no saturation. ~ii! u\u0304*>ux : This is the case when the input magnitude of Q becomes ux . 538 \u00d5 Vol. 122, SEPTEMBER 2000 rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 11/03/201 Thus, we can sequentially deduce from Table 1 that all the signals in the systems are equivalent. 4.1 Precision Control Test Bed. The system we are dealing with is the one axis precision linear motor system as shown in Fig. 7. Figure 8 shows the hardware configuration of the precision control test bed. The host computer computes the control input every 1 msec. Then, the control input is converted by 12-bit D/A converter and applied to linear servo-motor ~ANORAD, LEB-S2-S-NC! through DC Servo Amplifier ~ANORAD, AM-4-BLMS-S!. The position measured by encoder ~RSF Elektronik, MS 44! which has 2 mm resolution, is fed back through counter board ~ADVANTECH, PCL-833! to main computer. We will use the double integrator as the nominal linear model of the system to apply PTOS directly, and leave unmodeled system dynamics as a part of equivalent disturbance, since it is expected that DOB can cancel out equivalent disturbance",
            "15 second, and the maximum position error including overshoot is within about 620 mm. From the simulation results, we can observe that the proposed system performs high-speed motion by using maximum control input of PTOS, and the linear controller of PTOS with DOB also performs high-accuracy motion under equivalent disturbances. 4.4 Experimental Results. The proposed servo-algorithms are implemented and tested on the precision linear motor system Transactions of the ASME 3 Terms of Use: http://asme.org/terms Downloaded F of Fig. 7. The nominal model of system, the parameters of PTOS, and the parameter of Q-filter are all the same to the simulation. But, artificial disturbances are not injected to our system. However, the control input is saturated by the sum of control input signal due to PTOS and estimated equivalent disturbance signal including frictions and modeling uncertainties from DOB. Figure 15 shows the result of instability of the system with conventional DOB. Figures 16~a!, ~b!, ~c!, and ~d!, respectively, show the position response, the reference velocity and the real velocity, the control input signal ( u\u0302), and the position error, where DOB with ASE is employed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000750_niox.2000.0273-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000750_niox.2000.0273-Figure1-1.png",
        "caption": "FIG. 1. Test electrodes. Uniform disk electrodes were constructed of metal or graphite slugs that were wrapped with 30 AWG Cu wire (the electrical lead), and then encapsulated in shrink-melt fluoropolymer tubing.",
        "texts": [
            " Ru was supplied by Englehard Corporation, and because Ru cannot be drawn or shaped by conventional methods, it was ground abrasively from a larger billet. Electrode materials were round, solid cylinders (nominally 0.5 mm in diameter) except for iridium, which was supplied as a solid square cylinder, 0.5 mm on a side. Electrodes were prepared by wrapping 1 cm of an 8-cm length of solid copper wire (30 AWG ) tightly around one end of each electrode slug. This assembly was inserted into a 6-cm length of shrink-melt tubing (Small Parts Co.) and then heated to approximately 350\u00b0C with a heat gun until the tubing sealed around the electrode (Fig. 1). After encapsulation, a disk of the electrode material was exposed by cutting through the tubing, and the tip was polished first on 600-grit silicon carbide abrasive paper (Buehler) in water and then on felt , AND COURY pads in aqueous slurries of successively finer grits of powered alumina abrasive (Buehler) of 0.5-, 0.3-, s of reproduction in any form reserved. c e c w t M v c t t e a r c d w m c p a w a d C a f m t P i a f m h 2 ALS F \u2022 0.1-, and 0.05-mm particle size. Electrodes were leaned ultrasonically in deionized water following ach polishing step and then given a final ultrasonic leaning in methanol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002371_s0043-1648(03)00371-5-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002371_s0043-1648(03)00371-5-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the configuration of the precision stage positioning system.",
        "texts": [
            " In the mild wear mode, it is reported that the surface becomes relatively smooth, and a low wear amount of less than 10\u22126 mm3/N m is obtained even though the friction coefficient is not small [8]. Therefore, Al2O3 ceramics were selected as drive tip and driven rail in this investigation and the method to keep the wear mode of them in mild wear mode is necessary. In this paper, we propose the selecting method of the optimum preload of USM and the optimum gains of PID controller to control wear mode of Al2O3 drive tip into mild wear mode for stable precision positioning. Fig. 1 shows schematic diagram of the configuration of the precision stage positioning system used in this investigation. The stage system consists of one tip type USM (Naomotion Ltd.) [9], a linear stage with cross roller guide, a PID controller, a motor driver, a glass scale and a linear encoder. The curvature radius of drive tip is 7 mm. Al2O3 is selected for drive tip and driven rail. Material properties of Al2O3 used in this investigation are shown in Table 1. Fig. 2 shows schematic diagram of the stage driving principle with ultrasonic motor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001016_robot.1993.292205-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001016_robot.1993.292205-Figure3-1.png",
        "caption": "Fig. 3. 3-D cost map and GP method cost curves",
        "texts": [
            " Since a higher value of this performance Criterion represents proximity to the joint limits, we refer to it as \"cost\" which needs to be minimized. The \"End-effector Trajectory\" axis represents the moving distance of the endeffector. The \"Self motion\" axis indicates the self motion of the manipulator. On these maps, we use joint 1 value for self motion since it has a one-to-one correspondence with the self motion along the end-effector trajectory. The curves along the end-effector trajectory direction on the 3-D map in Fig. 3 are referred to as \"cost curves.'' Separate cost curves are obtained for different initial configurations. The cost curves in Fig. 3 are for the joint trajectories obtained using the GPM to minimize the \"cost.\" The same scalar constant \"k\" is used in the second part of (9) to compute these joint trajectories. It may be noted that for the starting configurations close to the \"local maximum\" (peak in the middle), the curves change the direction to the \"lower cost area\" much later compared to the curves starting away from the local maximum. If the starting configuration is too close to the local maximum, the curves do not deviate much from the LN trajectory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003190_s10544-005-6071-1-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003190_s10544-005-6071-1-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of a flat-chip microsensor used for a flow-injection system (units in mm).",
        "texts": [
            " In addition, the flow rate of the sample solution was experimentally optimised by comparing the relationship between flow rate of the flat-chip sensor and the detected current. In the optimal conditions adopted by these evaluations, a calibration curve of the flat-chip sensor was determined and excellent precision of analysis of salivary amylase activity was demonstrated. The flat-chip sensor used for analysis of amylase activity consisted of a pre-column and a flat-enzyme electrode in a flow cell (Figure 1). In order to miniaturize the flow cell (25.7 ml volume), two enzymatic membranes were immobilised on the same planar surface. Maltose phosphorylase (MP, 5.0 U, Kikkoman Co, Japan) immobilized with PVA-SbQ (CAS No. 229-47-5, Toyo Gosei Kogyo Co., Ltd, Japan) (Harrison et al., 1988) on the pre-column (MP membrane) and a flow path (volume of 60 mm3) were deposited over a MP membrane. A working electrode (WE, platinum, 2.54 mm2 area, 0.4 \u00b5m thickness), a counter electrode (CE, platinum, 0.4 \u00b5m thickness) and a reference electrode (RE, Ag, 1 \u00b5m thickness) were fabricated concentrically on the same planar surface by sputtering to make the flat-enzyme electrode (Figure 2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000817_jsvi.1997.1051-Figure15-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000817_jsvi.1997.1051-Figure15-1.png",
        "caption": "Figure 15. Rotating and translating beam model.",
        "texts": [
            " In the preceding section, only the case of a rotating beam is considered. In this and the following sections one considers the case of a rotating and translating beam and examines the effect of the longitudinal displacement due to bending on the stability of the rigid body modes. First the equations that govern the rigid body motion are summarized. In the analysis presented in this section, the beam is assumed to rotate with a constant angular velocity about an axis passing through one of its end points as shown in Figure 15. It is also assumed that the beam can have an arbitrary planar rigid body translation. In the case of rigid body motion, the position vector of an arbitrary point on the beam center line can be written as r=R+Au\u0304o , where R=[Rx Ry ]T is the position vector of the reference point, A is the planar transformation matrix defined as A=$cos u sin u \u2212sin u cos u % (90) and u\u0304o =[x 0]T is the position vector of the arbitrary point. The velocity and acceleration vectors of an arbitrary point can be written as r\u0307=R + u Au u\u0304o , r\u0308=R \u2212 u 2Au\u0304o , where Au = 1A/1u",
            " (91) It is clear from the displacement equations that the motion in the x direction is oscillatory, while the motion in the y direction increases with time. The results obtained in this section for the simple rigid body model will be used to provide an explanation for some of the results obtained using the flexible body model. In this section, the effect of the displacement due to bending on the dynamic equations of the rotating and translating flexible beam is examined. To this end, the planar beam model shown in Figure 15 is used. The beam is assumed to rotate with an angular velocity u and can have an arbitrary rigid body base translation. The global position vector of an arbitrary point on the beam can be written as r=R+Au\u0304, (92) where R=[Rx Ry ]T is the global position vector of the reference point, A is the planar transformation matrix defined by equation (90), and u\u0304 is the local position vector of the T     1 C en tr if ug al st iff ne ss co effi ci en ts fo r di ff er en t m od e sh ap es M od e sh ap e St iff ne ss co effi ci en t S im pl y su pp or te d (M l) j + (G 1l ) j = \u2212 (m (C ss ) j /2 )[ (n 2 Jl 2 / 3 \u2212 1) S j = (C ss ) j si n n j x \u2212 1 4 co s 2n jl + (5 /8 n j l) si n 2n jl] w he re (C ss ) j is an ar bi tr ar y co ns ta nt an d n j = jp /l C an ti le ve r be am (M l) 1 + (G 1l ) 1 = \u2212 0\u00b7 35 88 m (C cl )2 1 S j = (C cl ) j [s in n j x \u2212 si nh n j x + D j( co s n j x \u2212 co sh n j x )] (M l) 2 + (G 1l ) 2 = \u2212 5\u00b7 28 12 m (C cl )2 2 w he re D j = (c os n j l+ co sh n j l) /( si n n j l\u2212 si nh n j l) (M l) 3 + (G 1l ) 3 = \u2212 16 \u00b78 86 8m (C cl )2 3 n 1 = 1\u00b7 87 5/ l, n 2 = 4\u00b7 69 4/ l, n 3 = 7\u00b7 85 5/ l, n 4 = 10 \u00b79 96 /l (M l) 4 + (G 1l ) 4 = \u2212 35 \u00b70 56 2m (C cl )2 4 F re e en ds (M l) 2 + (G 1l ) 2 = \u2212 14 \u00b79 37 9m (C fe )2 2 S j = (C fe ) j [s in n j x + si nh n j x + D j( co s n j x + co sh n j x )] (M l) 3 + (G 1l ) 3 = \u2212 32 \u00b75 76 2m (C fe )2 4 w he re D j = \u2212 (s in h n j l\u2212 si n n j l) /( co sh n j l\u2212 co s n j l) (M l) 4 + (G 1l ) 4 = \u2212 13 6\u00b7 28 41 m (C fe )2 4 n 1 = 0, n 2 = 4\u00b7 73 2/ l, n 2 = 7\u00b7 85 3/ l, n 4 = 10 \u00b79 95 /l , n 4 = 14 \u00b71 37 /l (M l) 5 + (G 1l ) 5 = \u2212 21 9\u00b7 94 43 m (C fe )2 5 F ix ed en ds (M l) 1 + (G 1l ) 1 = \u2212 0\u00b7 06 39 m (C ff )2 1 S j = (C ff ) j [s in n j x \u2212 si nh n j x + D j( co s n j x \u2212 co sh n j x )] (M l) 2 + (G 1l ) 2 = \u2212 3\u00b7 16 62 m (C ff )2 2 w he re D j = \u2212 (s in n j l\u2212 si nh n j l) /( co s n j l\u2212 co sh n j l) (M l) 3 + (G 1l ) 3 = \u2212 14 \u00b78 93 0m (C ff )2 2 n 1 = 1\u00b7 87 5/ l, n 2 = 4\u00b7 69 4/ l, n 3 = 7\u00b7 85 5/ l, n 4 = 10 \u00b79 96 /l (M l) 4 + (G 1l ) 4 = \u2212 33 \u00b70 55 4m (C ff )2 4 arbitrary point on the beam center line defined in the beam co-ordinate system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001509_imtc.2002.1006860-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001509_imtc.2002.1006860-Figure1-1.png",
        "caption": "Figure 1. Load distribution in a ball bearing",
        "texts": [],
        "surrounding_texts": [
            "The short-time Fourier transform (STFT) addresses non-stationary signals by breaking a signal into a set of data subset with a fixed window width (T,,,) along the time axis, and then performing Fourier transform on each data subset, instead of on the whole signal set. Under the generalized transformation frame, STFT has a measure that is constant over each time window but different for different time windows. Hence, it maintains temporal location information of each data subset, with the time resolution being T,. However, STFT cannot resolve a signal feature when the time interval of the feature is longer than the window width T,. Thus, the efficiency of STFT for signal feature extraction is limited especially when the feature interval is unknown.\nAs a time-scale domain analysis technique, the wavelet transform utilizes template functions of different time resolutions at different scales to extract nonstationary \u201cdisturbance\u201d features in a signal. Thus, the temporal information of the signal features is maintained in the decomposition results. Furthermore, if the \u201cdisturbance\u201d signal repeats with a fundamental frequency coo at a scale, the measure function C(s, U) or C@, m) will also repeat itself along the time axis at the frequency 0,. As a result, the fundamental frequency of the disturbance feature is also maintained in the wavelet transform, although not explicitly expressed. Through variation of the scales of the template function, nonstationary or transient \u201cdisturbance\u201d features within a signal can be extracted more effectively than by using the Fourier transform.\nThe time resolution of the wavelet transform increases linearly with the logarithm of the scale, enabling signal features to be extracted at different resolutions. The frequency resolution of wavelet transform is IDm which is higher at higher scale levels (corresponding to a slow-changing signal) than at lower scales (corresponding to fast-changing signal). This is in contrast to the Fourier transform, which maintains a constant frequency resolution over the entire spectrum, as its time resolution is defined by the signal duration.\nAs an example of feature extraction using the wavelet transform, an FSK (frequency shifted keying) signal is considered, Such a signal is commonly used for data modulation, and is expressed as:\n(8) square (Wt) for message \u20181\u201d square (W2t) for messuge \u201c0\u201d\nwhere square(2@) is a periodical square wave with unit amplitude. Choose the Harr wavelet [8-91 as the mother wavelet for analysis, because of its square-shaped function that matches the FSK signal form. Given that the wavelet has a support of L = 1 second, the measure C(s, m) is calculated to be at time t = msl and scale\nsl=l/fi, for a message \u201c1\u201d. The measure C(sl, m) is zero for a message \u201c0\u201d. At scale s2=l/fz, Cfi2, m) is & at time t = ms2 for a message \u201c0\u201d , and zero for a message \u201c1 \u201d. Thus, the Harr wavelet locates the time instant of the message 1 or 0 at scale SI and s2, and expresses the FSK signal f(t) as a single-form expression:\nm\nIn contrast, if the Fourier transform is applied, it would not be able to express at which time which message (1 or 0) is transmitted. The sine and cosine template functions in the Fourier transform do not match the FSK signal shape, and consequently, the frequency component of the FSK signal will be spread out in a broad spectrum, especially when the message \u201c0\u201d and \u201c1\u201d are randomly transmitted.\nTo achieve improved signal feature extraction, spectral analysis is performed on the data subset obtained from the wavelet transforms. The final data set is expressed as:\nThis indicates that the Fourier transform of the wavelet decomposed data set can be viewed as the Fourier transform of the original signal f(t) passing through an anti-aliasing low-pass filter with the cutoff frequency at\n2k I @ k , O ( f ) l 2 . If the template function Wk,O(t) correlates well with a certain feature of the signal f(t), then its\nFourier transform wk,,(f) will also contain the spectral information of that feature. As a result, the filter 1 @ k , O ( f ) l 2 will extract the features from the original signal f(9 at the scale k. Due to a lower degree of correlation between this filter and the other constituent components in the signal, other components will be attenuated during the process.\n- f q . The filter is represented by the transfer function\nN\nIll. DEFECT SIGNAL MODEL\nTo verify the effectiveness of the proposed technique, vibration signals from a conventional ball bearing with a seeded localized point defect was investigated. Vibration measurement has been shown as an effective method to monitor the bearing operating condition. Material fatigue, faulty installation, or inappropriate lubrication will cause the bearing raceway or the rolling balls to crack, spall, or pit. Every time when a rolling element rolls over such a defect within the bearing structure, an\n\u2018317",
            "impulsive vibration signal will be generated due to the component interaction. The impact magnitude will depend on the defect dimension and the bearing load distribution, which is illustrated in Figure for a ball bearing under radial load. The symbol Qp denotes the load at a position given by angle p, and QmM is the maximum load carried by the ball at the lowest position (p = 0). The radial load vector is pointed downwards, through the center of the bearing. Applying the load distribution function [ 121, Qp is defined as:\nLo otherwise\n1 where cosh, =pd and E =--(i-cosp,). The symbol\nrepresents the angular extent of the load zone, E is the load distribution factor (n =1.5 for ball bearing), 6, is the shaft radial shift in the load direction, and Pd is the diametral clearance of the bearing. The load distribution curve ploted is based on &=0.43 (assuming Pd=2pn and &=lOpn), and the load zone is calculated to be k PI = f82.8\". For zero clearance (Pd =O), pI=9@. The impact caused by the ball contact with defects when the bearing is rotaing will be propotionally modulated by the load distribution. Because of the bearing clearance, there will be no impact generated outside the load zone. At the location with maximum load, the impact will be the strongest.\n2 4 2\nIf the specific location as well as the number of the structural defects vary, then the impact repeating rate, or defect frequency &, will change accordingly. This indicates that the frequency information will be useful to identifjmg defective features in the bearing. Several characteristic bearing defect frequencies are calculated and shown in Table 2, assuming that there is no sliding between the rolling elements and the raceway. The symbol d, denotes the bearing pitch diameter, D is the diameter of the rolling balls, Z is the number of balls in the bearing, and& is the bearing rotating frequency.\nThe experimental study utilized a ball bearing with 10 balls (Z=lO), each having a diameter D=24mm. The pitch diameter dm=140mm. The impact frequencies produced by a single defect on the inner raceway, outer raceway and within a ball, have been calculated to be 5.86f,, 4.14&, and 5.66f,, respectively, withf, being the shaft frequency.\nThe impact from the localized bearing defect causes the bearing, the housing, and the shaft to vibrate. Approximating the structure as a second-order massspring-damp vibration system, the displacement resulting from the structural vibration due to the impact can be simulated as:\nd(t) = ae-500' sin(wdt -9) (12) where a is the gain factor, cp is the initial phase associated with the initial conditions, 8 o=O indicates a zero initial condition, oo is the undamped natural frequency of the structure, cod = moo , and 5 is the damping ratio. The corresponding acceleration of the structure is expressed as:\n&t) = awie+ot sin(wdt -e, - 20) (13) Using an accelerometer, the impulse response of the bearing structure was measured and shown in Figure 2. The plot indicates strong damping, with the lowest resonant frequency located at about 180 Hz.\nMagnitude (B)\n1 .o - 0.0-\n-1 .o -\n0 ' O i l 0.b Od3 Oi4\nTime (5)\nMagnitude ( d z e d ) '\"iF\"-;l 02- OD -\n0 100 ZOO 300 4m 500 6m 700 800 XI0 1000\nFrequency(Hz)\nFigure 2. Bearing structure impulse response\n318",
            "Based on the load distribution function in Eq. (1 1) with ~ = 0 . 4 3 and the impulse response model in Eq. (13) where (Or28)=O, (=0.9, wd=150Hz, and a bearing rotating speed of 600 rpm, the vibration experiment shown in Figure 2 was simulated, with the result plotted in Figure 3. The load distribution in Eq. (11) and amplitude factor am; in Eq. (1 3) have been normalized. The continuous thin line shows the bearing load distribution, and the dotted line represents the repetitive impulse responses caused by a localized inner raceway defect (0.25 mm). The thick line represents the modulated signal by the bearing load distribution. Because of the bearing load modulation, there exist intervals where no impulse responses are visible. In the frequency domain, the modulation spectrum shown as a lobe of line spectrum is repeated every 58.6 Hz, corresponding to the analytically calculated defect frequency on the inner raceway (5.86fJ.\nThe modeling result was validated through experimental studies, for which a through-hole of diameter 0.25\" was drilled in the inner raceway to simulate a localized bearing defect. A controlled radial load of 10 kN was applied to the bearing. In Figure 4, the two dominant frequency components identified at fspFol = 4 1 Hz (4. Ifs> and fm = 20 Hz (2jJ relate to the unbalance and bearing misalignment, respectively. However, defects characteristic frequency at fBpF1148.6 Hz (calculated), i.e. the impulse response resulting from the defect impact\non the bearing inner raceway, which is of major interest to bearing fault diagnosis, is nearly invisible in the frequency domain. Furthermore, as seen from Figure 3, the signals are spread out in a broad spectrum, posing difficulty to the spectral analysis technique to extract feature components.\nFigure 5 shows the result of defect feature extraction for the experimental data shown in Figure 4, using wavelet transform with subsequent Fourier transform. The mother wavelet used was a fifth-order Daubechies wavelet The upper portion of Figure 5 (a) shows the mother wavelet Wl,~( t ) with support on [0, L). Details of the data reconstructed at scale 26 is shown in the middle section (b). Subsequently, Fourier transform is applied to the wavelet-extracted signal, and the corresponding frequency spectrum is shown in Figure 5 (c). A large peak is clearly shown at frequency of 58 Hz, indicating the existence of a localized defect in the inner raceway.\nComparing the results shown in Figure 4 and Figure 5, the advantage of the combined wavelet and spectral analysis technique becomes obvious. Although the defect impact signal is weak in magnitude, the wavelet transform was still effective in extracting the defect. This indicates that the wavelet analysis method may be applied to effectively detect bearing defects in the incipient stage. On the other hand, the wavelet information in the time domain alone does not reveal any frequency information of the defects. The scale information can only tell that the defect signal has good correlation with the template function, at that particular scale. Without the aid of Fourier transform, it is difficult to tell if a signal component at the defect frequency& (58.6 Hz) indeed exists."
        ]
    },
    {
        "image_filename": "designv11_11_0002548_ac00137a009-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002548_ac00137a009-Figure5-1.png",
        "caption": "Figure 5. CV curves of BCG transfer across the interface with different solvents (W, 0.01 M LiCl + 0.4 mM BCG, pH 4.95 B-R buffer: 0, 0.01 M TBATPB): 1, NB; 2, 1,P-DCE. Scan rate, 40 mV/s; Aowp vs. TBA+ I SE.",
        "texts": [
            " 10, MAY 15, 1987 data of BCG transfer a t the W/NB interface for different kinds of supporting electrolytes in W phase, listed in Table 11, show that LiCl, MgS04, Na2S04, and NaF can be used as supporting electrolytes in W phase, but not CuSO, because of its interference in the transfer of BCG. Supporting Electrolytes in 0 Phase. The peak potential of BCG transfer shifts negatively with increasing concentration of TBATPB in the 0 phase. The relationship between kw(ppa and CTBATpB(0) can be represented by the following empirical equation: Aowppa = 278.1 - 37.1 log CTBAT~B(O) = -0.9945 (12) where y is a correlation coefficient. Effect of the Solvent of the 0 Phase on Transfer of BCG. Figure 5 shows the CV curves of BCG transfer across the interfaces with different solvents. The transfer potential of BCG at W/1,2-DCE is more negative than at W/NB due to the effect of solvent polarity. At the interface of W/(NB + CB), the transfer potential shifts negatively with the increasing ratio of CB in 0 phase. Furthermore, we can get the experimental relationship between peak potential and dielectric constant of 0 phase as Aowp1,2 (mV) = 356.8 - 15'88 X lo2 y = -0.9780 (13) This means that the transfer potential shifts linearly toward the negative with an increasing reciprocal of the dielectric constant of the 0 phase and suggests that dye ions with negative charge are less stable in low t organic phase"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001624_robot.1996.506582-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001624_robot.1996.506582-Figure1-1.png",
        "caption": "Figure 1: Regrasp primitives",
        "texts": [
            " R ~ ( w ( c r ~ , k ) , e ~ ( c r ~ , k ) ) as seen from the object frame, does not change no matter where the rotation axis is. Thus the rotation axis can be arbitrary. Step 3) The union is the region of the axis A for which the third finger can rotate the object at orientation angle P k . The intersection of the regions U ( p k ) between k = 0 and k = Mp is the region for A where the third finger can rotate the object between those angles. If this is empty, the axis A needs to be repositioned during pivoting (or Primitive C in Fig.1 is used). The calculation for taking the union in Eq.(6) requires computational efforts. A reasonable alternative is to use only large regions among i = 1,. . . , L. Let E%, be the edge such that E ~ ( W ( a i ~ , k ) , Ei, (cui , , k ) ) is the j th largest. Define the union of up to the Kth largest regions as K ) = U RA(W(ai3 ,k) ,e i , ( a i J , k ) ) (8) j=l, ..., K and First calculate V ( 1). If V ( 1) is not empty, the problem is solved. Otherwise, calculate V(2) and so on, until V ( K ) is not empty"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000179_1.2893956-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000179_1.2893956-Figure7-1.png",
        "caption": "Fig. 7 Calculation system with definition of unbalances and amplitude margins",
        "texts": [
            " The calculation model of the turboset has 37 nodes of lateral and torsional vibrations and 5 nodes for the axial directions. Thus, they have 200 degrees of freedom in all. The dynamic coefiicients of the seals and bear ings with respect to speed and load are calculated for all static equilibrium conditions which mean a steady state operating point for a given speed and loading condition. The data of unbalances are assumed as the maximum value for the turbine rotor and generator rotor, which is recommended by the com pany. The actual values are given in Fig. 7. We first calculate the amplitude of vibrations and the dynamic gear force due to unbalances. The results of the unbalance re sponse are shown in Fig. 8 assuming a turbine unbalance and in Fig. 9 for an unbalance in the generator rotor. The abscissa was split into an interval of increasing speed from 0 to 1, mean ing 100 percent operational speed, and into a load portion from 0 percent to 100 percent load, exactly as the turbine is actually Transactions of the ASME Downloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use operated. All calculation results are about the vibrations at the midspan of each component as shown in Fig. 7. From the results of Fig. 8 we see that the coupled effects due to the turbine unbalances are just slightly visible by amplitudes of the rotors being away from the turbine. This means that the amplitudes due to a turbine unbalance are nearly zero in the generator. The dynamic gear forces will only amount to 0.4 percent of the static value in this case. A high generator unbalance which is assumed in Fig. 9 may cause small lateral vibration amplitudes of the turbine. The dynamic gear forces reach a value of 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000238_306-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000238_306-Figure1-1.png",
        "caption": "Figure 1. Piston and cylinder with jaws.",
        "texts": [
            " As the process is quasi-static, the changes in kinetic energy are zero and E = U . Thus the energy balances for the three systems S1, S2 and S3 are U1 = W31 +W21 (10a) U2 = W12 (10b) U3 = W13 +Q3. (10c) For the system S \u2032 = S1 + S2 U \u2032 = W31. (11) Moreover, U1 + U2 gives U1 + U2 = W31 +W21 +W12. (12) Since U \u2032 = U1 + U2, W21 +W12 = 0 also applies, obviously, as the situation involves the works of two opposite forces with the same displacement. Situation B. The cylinder can slide with friction on two external jaws kept at rest (figure 1). With a clamp it is possible to tighten the jaws, and thus change the frictional force. We consider three systems: the cylinder S1, the jaws S2, and the gas S3. The pressure of the gas in the cylinder is kept much higher than the pressure outside, so most of the force opposed to the motion of the cylinder is provided by the frictional force and one can neglect the work W1 of the air outside on the cylinder (at any rate, taking this work into account hardly changes the situation; one need only replace the term W31 by W31 + W1)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003909_icsmc.2005.1571491-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003909_icsmc.2005.1571491-Figure3-1.png",
        "caption": "Figure 3. Two robots in a collision course",
        "texts": [
            " In this case, a collision cone is built, and the collision is avoided by deviation of R\u2217 i from its nominal path. The control law using the deviated pursuit is disactivated during this phase, and re-activated after the collision danger is averted. The control law for the orientation angle of R\u2217 i is given by \u03b8\u0307i = \u2212k2 ( \u03b8i \u2212 \u03b8des i ) (13) where \u03b8des i is the desired orientation angle, and k2 is a real positive constant. The collision cone is built around the estimated point of collision, where this point becomes the center of a circle of radius 2d (as shown in figure 3) upon which the cone is constructed. The orientation angle for R\u2217 i is calculated so that the velocity vector of R\u2217 i is outside the cone. R\u2217 i can perform a right or left deviation (towards point A or B). We suggest that R\u2217 i turns towards the closest point to the other robot, which is point A in figure 4\u2013b. This is the final navigation mode, where the aim of the robots is to enclose the prey. Circle formation as well as other geometric forms formation was addressed in [10] based on geometrical rules"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002290_j.ijadhadh.2003.10.004-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002290_j.ijadhadh.2003.10.004-Figure2-1.png",
        "caption": "Fig. 2. Shell/solid finite element model for a DLS specimen; the substrate is elements.",
        "texts": [
            " Using the same practice, we will define rigid links across the width of the coupon along a line through the center point of the overlap. The solution corresponding to this case is obtained as: Du \u00bc 3Fl1 2btE 1 \u00fe l3 2l1 \u00f03\u00de for l1= l2. The shell/solid model was chosen as the baseline FE model. Shell elements are preferred when thin walled structures such as vehicles are modeled. Shells are superior to a single layer of solid elements in modeling the out-ofplane bending behavior. In the shell/solid model, the substrates were modeled by shell elements and the adhesive was represented by solid elements, as shown in Fig. 2. The nodes at the end of double legs were fully constrained and uniform displacement was applied at the nodes at the end of single leg. For LS-DYNA analysis, the displacement at the moving end of the DLS specimen was applied at a constant velocity of 0.1 mm/ms. Simulations were carried out for SRIM/LESA DLS specimen series S13 (25.4/1.3, 25.4 mm overlap with an adhesive thickness of 1.3 mm). Fig. 3 plots the experimental results for three specimens. Also shown in Fig. 3 are a plot of the analytical prediction by Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000286_0956-5663(96)87663-9-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000286_0956-5663(96)87663-9-Figure1-1.png",
        "caption": "Fig. 1. Diagram showing relationship of screen-printed sensor components. A UX, auxiliary electrode; IS, insulation shroud; REF, reference electrode; WE1, working electrode with enzyme; WE2, working electrode without enzyme.",
        "texts": [
            " The construction of a lactate sensor, consisting of an electrochemical cell, enzyme layer and outer membrane, completely by screen-printing methods and its ability to measure, in batch mode, L-lactate in yoghurt and buttermilk are described in this paper. A DEK 245 printer (DEK Printing Machines Ltd., UK) was used to produce sensors in the form of a planar, three-electrode electrochemical cell, in which the working electrode is split into two. The arrangement of the components is indicated in Fig. 1. Sensors were screen-printed in groups of 10 onto clear polyvinyl chloride. The conducting tracks and auxiliary electrodes consisted of silverloaded ink (Electrodag 427SS, Acheson). The reference electrodes were made by applying a crescent consisting of silver-loaded ink mixed with finely ground silver chloride (Materials Characterization & Analysis Services, UK) in the ratio 0.12 g AgC1 per gram of ink, onto the end of a conducting track. The working electrode was divided into two, so that one side could be left without enzyme to estimate any spurious oxidation currents arising from interferents"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002819_027836498900800505-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002819_027836498900800505-Figure1-1.png",
        "caption": "Fig. 1. Coordinate frames for the Rhino XR-2. Reprinted by permission. Pradeep, et al. C Copyright",
        "texts": [
            " This clustering of joint variables, illustrated by the example in Section 5, is an important phenomenon to recognize when one sets out to do inverse kinematics. The clumping of joint variables at Bobst Library, New York University on May 19, 2015ijr.sagepub.comDownloaded from 64 plays an important role also in the analysis of crippled motion in robots (Pradeep and Yoder 1986; Pradeep et al. 1988). 5. An Example: The Rhino XR-2 This section uses the notation of dual-matrix exponen tials to derive the direct kinematic equations for the Rhino XR-2. As may be noted from Figure 1, this instructional robot is kinematically similar to a number of popular industrial manipulators. The joint and link parameters of the Rhino XR-2 are given in the table below (Schilling 1988). Substituting the parameters 6&dquo; and an from the table into the arm equation (56), one obtains In light of (35), the real part of this transform consists of a proper orthogonal matrix A that describes the net rotation from the base to the hand, while its dual part gives the product [t]A, where t denotes the translation vector connecting these two frames (Hsia and Yang 1981)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002332_s0263574700010638-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002332_s0263574700010638-Figure4-1.png",
        "caption": "Fig. 4. Walking Machine Crossing Crest.",
        "texts": [
            " Task 1: Compute the force distribution throughout a stride for straight-line walking on smooth terrain at a constant acceleration of 0.3 g. Note that this task is equivalent to straight-line walking up an incline of 16.7\u00b0 in which the body is kept parallel to the ground at zero acceleration. Task 2: Compute the force distribution for a straight-line stride and a constant acceleration of 0.3 g - J 1.52m |*\u2014 I J4 3.05 m\u2014J\\ 1.2 m vehicle mass: 3200 kg for the situation in which the walking machine is astride the crest of a small hill. This situation is shown in Figure 4. The radius of the hill is taken such that the surface normals at the points of contact for legs 1 and 3 are rotated 45\u00b0 forward and backward from the body z-axis, respectively. Task 3: Compute the force distribution for straightline walking and a constant acceleration of 0.3 g along the crest of a hill. This situation is depicted in Figure 5. The radius of the hill is taken such that the surface normals of all feet are rotated laterally from the gravitational direction by 45\u00b0. As a point of comparison, we will compute the force distribution for all three tasks using the Moore-Penrose pseudo-inverse"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001366_pime_proc_1992_206_183_02-Figure18-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001366_pime_proc_1992_206_183_02-Figure18-1.png",
        "caption": "Fig. 18 Lengthwise section of the bearing friction simulator (47)",
        "texts": [
            " Mass inertia is also accounted for in the non-linear equations of motion and non-circular profiles are also considered, obtaining some differences compared with earlier published results. Some experimental apparatus are developed to measure friction in engine crankshafts. The crankshaft @ IMechE 1992 bearing friction is measured in an actual engine block by Gauthier and Constans (47). The friction due to other parts of the engine are eliminated: auxiliary components are disconnected and piston strokes are reduced to zero using, instead of the real crankshaft, a straight shaft with all bearings along the same axis (Fig. 18). The effects of compression, combustion and inertia forces acting in the real engine are calculated and applied to the pistons with hydraulic servojacks. Figure 19 shows the measured friction torque and sum of the friction losses from each individual bearing, for different static loads (constant compression applied on pistons) and for the dynamic load. Results obtained from a theoretical analysis seem to be in agreement with the experimental ones. In reference (48) both friction and film thickness are measured in a firing engine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003211_j.jbiomech.2005.02.020-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003211_j.jbiomech.2005.02.020-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of baseball and baseball bat, showing finite element mesh and initial conditions imposed on the proximal and distal extremities of the bat, and the baseball.",
        "texts": [
            " 3-D models of two baseball bats were developed using ANSYS/LS-DYNA FEA software (version 6.1; LSTC, Livermore, CA.). Geometry was obtained from one aluminium alloy bat (Easton BE-811) and one wooden bat (Easton Redline Pro Stix 271) of similar length and mass (Table 1). Data from calliper measurements made of the internal and external geometry at 168 intervals along the bat length were input as Cartesian (x; y; z) coordinates in LSDYNA. The shapes were generated using spline functions to avoid discontinuities resulting from stepped cross-sectional properties (see Fig. 1). The wooden bat was modelled as a homogeneous solid, discretised into 9800 eight-node SOLID-164 hexahedral elements. These elements were used to prevent meshing and hourglassing problems in the contact region, and improve the accuracy of the solution (ANSYS/LSDYNA Theoretical Manual, 2002). The metal bat was sed as the basis for this mathematical model of bat\u2013ball impact ARTICLE IN PRESS R.L. Nicholls et al. / Journal of Biomechanics 39 (2006) 1001\u20131009 1003 represented as a hollow tube meshed with 12,974 hexahedral elements to accommodate the variation in wall thickness along its length (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000534_s1474-6670(17)47309-5-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000534_s1474-6670(17)47309-5-Figure3-1.png",
        "caption": "Fig. 3. Showing the velocity relationships between two bodies when the rear body is an active car .",
        "texts": [
            " If the linear velocity of the last body is v~m' then the derivatives of x and y are the projections of this velocity, y x (1) (2) Now , let vf represent the the linear velocity of the axle with angle B{. Consider first the case of a pas sive trailer; refer to Figure 2. The linear velocities of body i-I has two perpendicular components: one in the direction of the linear velocity of the ith body, J = cos((J{ 1 - (J{)J 1 , s , 1-) and the other in the direction of the angular ve locity of the ith body, Li iJi = sin((}i 1 - (}i)J 1. (3) S , 1 ' ,- When the rear body is an active car instead of a passive trailer (see Figure 3), the relationship between the two linear velocities has the form \u00b7+1 \u00b7+1 . . . . t?,.. . cos((}~ . -4l)=t?,.. . cos((}~ . -4l), J J '] and the angular velocity vector ~ . 4>i J has two components, i .. _ Lnj+l 4l - sin((}~+1 - <Pi)~+1 J . . J - sin((}~ . - 4l)~ . . J J The derivatives of the steering wheel the inputs (4) angles are ei = wi . (5) nj_l The kinematic equations for the multi-steering trailer system are completely given by (1-5). Now that kinematic behavior of the multi-steering system has been described , the transformation to multi-input chained form can be found "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001655_elan.200390088-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001655_elan.200390088-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the long-optical thin-layer spectroelectrochemical cell used in the experimental section. A) 3D view: a) platinum sheet electrode; b) Ag/AgCl/KCl reference electrode; c) spacers; d) epoxy piece containing the platinum working electrode; e) inert epoxy wall. B) Side view: f) platinum wire counter electrode.",
        "texts": [
            "50/0 bedbelowwere introduced. Themain features of the cell are its effortless assembling, easy cleaning and, of course, perfect planarity of the working electrode. The dimensions of the cell permit its use in conventional cuvettes (10 10 mm) employed with commercial instruments. The light beam crossing the solution in a parallel direction to the working electrode surface allows us to monitor the processes taking place in the diffusion space. Our long-optical-pathway thin-layer spectroelectrochemical cell is outlined in Figure 1. The cell body was machined from an opaque inert epoxy resin. It consists of two plane walls (d and e) placed face to face in the spectrophotometric cuvette separated a known distance by two standard styrene spacers (c), (3 5 mm,) whose thickness was previously calibrated with a Mitutoyo Digimatic Indicator (0.001 mm of resolution). The use of different thickness spacers enables us to work not only under thin-layer but also under semiinfinite diffusion conditions. The working electrode was placed in the rectangular epoxy piece (34.4 9.3 4.7 mm) marked as d) in Figure 1. It consists of a platinum sheet soldered on the backside to a copper wire to assure good electric contact. Two different platinum sheets (11.2 7.2 mm and 11.2 3.0 mm) were used throughout the experiments. The platinum sheet (a) and the copperwirewere embedded into an epoxy resin by a hot-high-pressure process, resulting in a compact structure that was cut and polished later. The second part of the body cell was an inert epoxy wallpiece (30 9.3 4.7 mm) denoted as (e) in Figure 1. This element limits the diffusion space for the species into the solution. The light beam samples the whole diffusion space between the epoxy pieces. Prior to use, the platinum electrode was prepared by mechanical and electrochemical processing. The mechanical treatment consisted of two steps: a pre-polishing with silicon carbide sheets (Struers 1000 and 4000) and a polishing with 1 m alumina paste. Then the electrode was sonicated for 10 minutes in deionized water. An electrochemical conditioning of several voltammetric cycles at 2 Vs 1 between 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003477_s0263574705001694-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003477_s0263574705001694-Figure1-1.png",
        "caption": "Fig. 1. Two-degree-freedom planar robot in Cartesian space.",
        "texts": [
            " He defined objective functions in both Cartesian space and joint space, and combined them to optimize the robot trajectory. In this paper, we first outline the problem of the placement of a robot base for a given path of its end-effector. We analyze the reachable workspace and derive a condition for singularity avoidance. Then, we apply a GA method to search for the optimal location of the robot base. An example simulation of a two degree-of-freedom robot is provided to demonstrate the effectiveness of the proposed method. In this work, we consider a robot which has two joints and two links as shown in Figure 1. The end-effector moves on the XY plane. Let the length of Link 1 and 2 be L1 and L2, respectively. Let the angles between Link 1 and positive X axis, and between Link 2 and extended Link 1 be \u03b81 and \u03b82, respectively. Ps(xs, ys) and Pt (xt , yt ) are the starting and terminal points of the end-effector of the robot which moves along PsPt \u2212\u2192 . Let Pb(xb, yb) be coordinate of the robot base, and the starting point Ps(xs, ys) be located at the origin of XY frame. Our objective is to search for the optimal location of the robot base, so that the end-effector of the manipulator moves from the starting point Ps to the terminal point Pt in a minimum joint distance subject to additional constraints",
            " Pamanes and Zeghloul10,11 briefly described these criteria. For a serially connected nonredundant manipulator, when the end-effector passes close to a singular position, the determinant of the Jacobian matrix approaches zero, which results in excessive joint velocities and torques. To prevent this, it is natural to use the manipulability measure as a criterion for the optimal placement of the robot base. http://journals.cambridge.org Downloaded: 11 Mar 2015 IP address: 128.218.248.200 As shown in Figure 1, the kinematic formulation for the two degree-of-freedom (dof) revolute-joint robot is as follows. The x and y coordinates of the end-effector can be expressed in terms of the input joint angles and link lengths as: xe = xb + L1 cos \u03b81 + L2 cos(\u03b81 + \u03b82) (3a) ye = yb + L1 sin \u03b81 + L2 sin(\u03b81 + \u03b82) (3b) where xb and yb refer to the location of the base frame, L1 and L2 denote the link lengths, and \u03b81 and \u03b82 the joint angles. The Jacobian matrix for the robot is J (q) = [\u2212L1 sin \u03b81 \u2212 L2 sin \u03b82 \u2212L2 sin(\u03b81 + \u03b82) L1 cos \u03b81 + L2 cos \u03b82 L2 cos(\u03b81 + \u03b82) ] (4) where q is the vector of joint coordinates, q ={\u03b81, \u03b82}, and \u03b82 = cos\u22121 ( [(xe \u2212 xb)2 + (ye \u2212 yb)2] \u2212 ( L2 1 + L2 2 ) 2L1L2 ) or \u03b82 = \u2212cos\u22121 ( [(xe \u2212 xb)2 + (ye \u2212 yb)2] \u2212 ( L2 1 + L2 2 ) 2L1L2 ) \u03b81 can be obtained from Equation (3)",
            " Once two chromosomes are selected, the GA will perform a crossover operation by swapping portions of their binary strings according to given crossover rate. The final step is that the GA generates random mutations by flipping a small percentage of bits in the whole population. After these operations, a new generation will be created, and the GA will be ready to evaluate it and proceed to the next generation. The evolutionary process will continue until it satisfies some conditions, such as the given number of generations. A workcell of a 2 dof planar robot is shown in Figure 1. In our calculations, the length for Link 1 and Link 2 are 0.5 m and 0.5 m, respectively. The first joint can rotate freely while the second joint is limited to \u2212150\u25e6 <\u03b82 < 150\u25e6 without loss of generality. The desired path is a straight line that starts at the origin Ps(0.0, 0.0), and terminates at Pt (\u22120.5, 0.15). The feasible area for the placement of the robot base is shown in Figure 4. We select the minimum total rotation of joint 1 and 2 as the fitness function. When the velocities of joint 1 and 2 are constant, the smaller the total rotation angle the less time it takes for one cycle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000534_s1474-6670(17)47309-5-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000534_s1474-6670(17)47309-5-Figure5-1.png",
        "caption": "Fig. 5. A unicycle with a \"virtual\" extension, inter preted as another axle added in front of the original robot.",
        "texts": [
            " (8) Since the system is drift-free, the relative degree1 of any choice of outputs will be equal to one. In particular, the relative degree of the body angle 0 with respect to the steering input is equal to one. Consider adding a new state ~ = a, and a feed back w = tan( l/> - 0) v . The extended system (x, y , 0, l/\u00bb now satisfies the equations x cos 0 v y sin 0 v (9) 0 tan(l/>-O) v l/> a, and the added state l/> can be interpreted as the angle of another axle in front of the original steer ing wheel, and the new input a as the steering ve locity of this \"virtual\" wheel (see Figure 5) . The relative degree of the body angle 0 with respect to the (virtual) steering input is two. Remark. Any trajectory 'Y = (x, y, 0, <p) of (9) can be projected down to give a trajectory 7r(r) = ( = (x, y, 0) of (8) . Also, for any trajectory ( of (8) for which 0 is Cl and for which B = 0 whenever x = if = 0, there exists a trajectory 'Y of (9) such that 7r(r) = (. Trajectories where the unicycle spins about its axis without moving either forwards or backwards cannot be realized with the extended model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000976_20.728299-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000976_20.728299-Figure5-1.png",
        "caption": "Fig. 5. Sample rotors.",
        "texts": [
            " Decrement of this torque is represented with the following expression derived from (7) and (11) of [3] taking constant : (2) Accordingly, in cases where the space higher harmonic flux exists, the synchronous pull-out torque is represented with the following: (3) In short, in order to reduce the influence of space higher harmonic flux, it is desirable that is greater [3]. From Figs. 3 and 4, it is apparent that constants , , , and of Fe\u2013Cr\u2013Co magnetic material are larger than those of Alnico 5 in the actual driving range It can therefore be predicted that of motor characteristics of the output power, efficiency and the power factor of the Fe\u2013Cr\u2013Co magnetic material are greater than those of Alnico 5, while the stator current of Fe\u2013Cr\u2013Co magnetic material becomes smaller than that of the Alnico 5. Fig. 5 shows sample rotors. Different types of motors were produced by changing five factors such as 1) number of poles, 2) rotor ring material, 3) ring thickness, 4) ring supporting material, and 5) gap length. 1) First, concerning the number of poles, although a motor usually uses less than four poles, we adopted three different pole types: two poles, four poles, and 12 poles since magnetic material with large coercive force (such as Fe\u2013Cr\u2013Co magnet) is suitable for multipolar motors. 2) As to rotor ring material (Fig. 1), we adopted three types of magnetic material: anisotropic Fe\u2013Cr\u2013Co magnet [Fig. 5(a)], isotropic Alnico 5 having nearly the same loop area as that of anisotropic Fe\u2013Cr\u2013Co magnet [Fig. 5(b)], and semihard Alnico T, kA/m, Fig. 5(b)] most popularly used in motors due to its optimum magnetic characteristics. 3) Thickness (although is actually length as shown in Fig. 1, it is hereafter represented with of the rotor ring made of semihard Alnico material, which is usually used, is less than When semihard Alnico material is used with its greater , it is necessary to make smaller due to the limited magnetomotive force of the stator. Here, in this study, we selected three types of thickness as mm), 1.21 mm), and 1.36 mm). 4) The ring support is made of two types of material, aluminum (for CF-type motor) and pure iron (for RFtype motor)",
            " 5) Lastly, since of the ring is greater, gap length is limited to a small range due to the magnetomotive force of the stator. In this study, was chosen to two values as 0.1 and 0.2 mm. In this study, we measured the motor characteristics of a total of 108 different types of motors produced by variously combining the above factors (1)\u2013(5). Additionally, separate from these motors, we produced and examined a number of RF-type motor samples of two different types using Fe\u2013Cr\u2013Co magnetic material; one having radial anisotropy [Fig. 5(c)] and the other having isotropy. OF Fe\u2013Cr\u2013Co MOTORS, ALNICO 5 MOTORS, AND SEMIHARD ALNICO MOTORS In this section, we compare and discuss characteristics of motors made of anisotropic Fe\u2013Cr\u2013Co magnetic material, isotropic Alnico 5 magnetic material, and the most widely used semihard Alnico kA/m) magnetic material. We quantitatively made clear that a motor using anisotropic Fe\u2013Cr\u2013Co magnetic material is far superior to others. In this section, we deal with Fe\u2013Cr\u2013Co magnetic material having only diametral magnetic anisotropy [Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002756_012-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002756_012-Figure2-1.png",
        "caption": "Figure 2: We encounter three different types of gluonic pole matrix elements (GPME\u2019s): the quark-GPME \u03a6G=(\u03a6G)a rs(t a)sr=Tr[\u03a6a Gta] and the two gluon-GPME\u2019s \u0393 (f) G =\u0393abc G (ta)cb=\u0393abc G ifabc and \u0393 (d) G =\u0393abc G dabc. The dabc and fabc are the symmetric and antisymmetric structure constants of SU(3): tatb=TF N \u03b4ab+1 2 ( dabc+ifabc ) tc.",
        "texts": [
            " Due to the presence of two gauge-links (in the matrix representation), rather than one, as was the case in quark distribution, there are two different types of gluonic pole matrix elements: those with soft gluons arising from the gauge-link U or U \u2032, respectively. This complicates the occurrence of T -odd effects in gluon distributions somewhat. Since the correlator is colortraced, it is convenient to consider the commutator and anticommutator combinations of \u2013 7 \u2013 J H E P 0 2 ( 2 0 0 7 ) 0 2 9 gluon fields in the matrix elements. These involve the symmetric and the antisymmetric structure constants of SU(3) color (figure 2). Taking the first moment of the gluon correlator (A.3a) it follows that \u0393 [UU \u2032]\u03b1 \u2202 (x) = \u0393\u0303\u03b1 \u2202 (x) + C (f) G \u03c0\u0393 (f) G \u03b1(x, x) + C (d) G \u03c0\u0393 (d) G \u03b1(x, x) , (3.5) where the gluonic pole strengths C (f/d) G involve sums and differences of contributions arising from the two different gauge-links. The matrix element \u0393\u0303\u2202 (which is purely T -even in the case of gluon distribution) only involves a color commutator (cf. (A.8e) and (A.6f)). The definitions of the different matrix elements appearing in this expression are given in appendix A",
            " Note that the T -odd quark and gluon distribution (fragmentation) functions that appear in the parametrizations of the gluonic pole matrix elements are different from quark-quark or gluon-gluon matrix elements. They contain an additional zero-momentum gluon (the gluonic pole). Therefore, it is not obvious if such T -odd functions can be interpreted as probability distributions. The emergence of two (the f and the d) T -odd gluon distribution (or fragmentation) functions is simply the consequence of the two possible orderings of the three gluons in the matrix element \u0393G in figure 2. From symmetry relations it follows that G (f/d) T (1)(x) can be written as the x-even and x-odd combinations of a single gluon distribution function, i.e. G (f/d) T (1)(x)=1 2 ( G (1) T (x)\u00b1G (1) T (\u2212x) ) and similarly for \u2206H (f/d) T (1)(x). As seen in equation (3.5) the x-even and x-odd combinations of gluon distribution functions can appear with different prefactors. Hence, the description of the gluon contribution to T -odd effects involves two different gluonic pole cross sections, one containing the gluonic pole factors C (d) G and one containing the factors C (f) G "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003256_j.jsv.2004.06.029-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003256_j.jsv.2004.06.029-Figure2-1.png",
        "caption": "Fig. 2. Ball bearing with strong nonlinearity in spring characteristics [2].",
        "texts": [
            " Therefore, the practical transition is comparatively smooth and the spring characteristics can be approximated by a power series of low order. Hence, the setup shown in Fig. 1 is generally assumed to have a weak nonlinearity. Some machine elements cause strong nonlinearity in the system. For example, since ball or roller bearings have little damping effect, aircraft gas turbine engines generally adopt squeeze film damper bearings for some of their bearings. A simplified model of such a bearing is shown in Fig. 2. Damper oil is supplied between the bearing holder A and the casing B. Holder A is supported by a weak spring S and is kept at the center of the casing B. When the shaft vibrates, element A moves relative to element B, and therefore the oil dampens the vibration. When this type of bearing is used in the rotor system, the relationship between the rotor radial deflection r and the restoring force F shows strong nonlinearity with a deadband as indicated [2]. Fuzzy set theory was initiated by Zadeh [8] and developed by many other researchers, including Kaufmann and Gupta [9]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003834_j.snb.2005.02.013-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003834_j.snb.2005.02.013-Figure1-1.png",
        "caption": "Fig. 1. Schematics of the cylinder configuration of the CRE.",
        "texts": [
            " The results obtained with his system are compared to those obtained with an Orion 00200 Ag/AgCl commercial electrode having double liquid unction. A Felisa oven was used to aid consolidation of the omposite electrodes. .3. Fabrication of a CRE: cylindrical and tubular onfigurations The mix to elaborate the composite CRE was based on 4.22% graphite, 5.78% AgCl, 5.78% silver dag and 44.31% poxy resin (17.1% corresponded to the H.R. and 27.21% raldit). To prepare the cylinder configuration, the composite ix was introduced into a PVC tube provided with a copper ar serving as electric contact, as schematically shown in Fig. 1. The composite was left to consolidate for 72 h at 50 \u25e6C in an oven. To produce a tubular configuration, a methacrylate support was required such as shown in Fig. 2. The hollow is filled up with the composite and left to harden just as with the previous configuration. Once the resin had hardened, the ends were insulated with the epoxy resin, then a 0.7 mm diameter bore hole was drilled at the centre of the composite. 2.4. Characterisation of the CRE The CRE\u2019s response was characterised as indicating electrode for the chloride ion using the cylinder configuration and comparing the response with that of a SCE"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002471_10255840310001637266-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002471_10255840310001637266-Figure3-1.png",
        "caption": "FIGURE 3 (a) The assumed barrel shape of the ligament before stretching with e \u00bc 0:5 mm: (b) Ligament shape when fibre are straight (the longitudinal section is shown in Fig. 1).",
        "texts": [
            " Using trial and error the minimum value was obtained. The osmotic pressure was taken to be constant during an analysis although the osmotic pressure is expected to change with the change in the total volume of the ligament and the amount of fluid inside the ligament. Mechanism 1 Comparing the volumes of parabolic edged barrels and cylinders having equal edge lengths showed that the volume of a barrel is higher than that of the cylinder. This leads us to the conclusion that straightening of initially parabolic fibres (Fig. 3) leads to an initial reduction in the volume of the ligament as the fibres straighten (Fig. 4). The relationship between the engineering volumetric strain and the engineering longitudinal strain is shown in Fig. 4. The curves show that initially for very small longitudinal strains (as the fibres straighten) there is a relatively large reduction in the volume of the ligament (Fig. 4b). As the length increases, the volume starts to increase again until it reaches the initial volume of the ligament at higher longitudinal strains"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001696_s004540010017-Figure23-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001696_s004540010017-Figure23-1.png",
        "caption": "Fig. 23. Moving a leaf in a lumpy tree.",
        "texts": [
            " To see this, note that if A is pointy, the subtree of the spine above x has negative weight, and the sum of those weights must be greater than \u22121, since adding the weight of x gives a positive number. Similarly, if A is convex, the subtrees have positive weight with sum less than 1, since adding the (positive) weight of x produces a valid weight. In both cases, there can be only one subtree of the spine above x\u2014rotations at the root combine all the original subtrees. A symmetric claim holds if B is convex or pointy. If A is lumpy, we distinguish between two cases, shown in Fig. 23. Let e be the top-level edge joining A to B, and let f be the second-level edge at A. Inside the microstructure disk at A, f is the finite edge; it joins the turns represented by the children of the root of A. Denote the left and right subtrees of A by AL and AR . In case (1), f points toward e; in terms of tree weights, the weight at AR is negative. In this case we translate f away from the polygon interior, so that the microstructure containing x slides toward B. See Fig. 23(1). When the microstructure gets sufficiently close to B, we can enclose it along with B in a higher-level microstructure disk. In tree Morphing Simple Polygons 31 terms, we remove AR from A and join it to the old tree B as its left sibling. Because AR has negative weight and B has positive weight, the new tree is valid. In case (2), f points away from e (the weight of AR is positive). Let g be the finite edge inside the microstructure disk for AR , and let ARL and AR R be the left and right subtrees of AR . By construction, the sum of the weights of AL and ARL is greater than one, and so the weight of AR R is negative. That is, g points toward e. We translate g away from the polygon interior, so that the microstructure for AR R slides toward B. See Fig. 23(2). As in case (1), we make AR R into the left sibling of B. We are left with a (possibly nonconvex) quadrilateral as the top-level structure, with the four angles represented by 32 L. Guibas, J. Hershberger, and S. Suri AL , ARL , AR R + B, and C (the original third angle of the triangle). One more parallel translation reduces the polygon to a triangle (unless the quadrilateral happens to be a parallelogram). If B is lumpy, the same construction can be used symmetrically. Now suppose that A is pointy, while B is convex (or symmetrically B is pointy and A is convex)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001541_ias.1997.643017-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001541_ias.1997.643017-Figure11-1.png",
        "caption": "Fig. 11. Representation of a skewed rotor bar",
        "texts": [],
        "surrounding_texts": [
            "which is twice supply-frequency. This Variation is due to the rotation of the axis of saturation in the stator. When the axis of saturation is aligned with the axis of the winding it is difficult for the winding to produce flux and so the inductance is relatively low. As the saturation pattern rotates, the self inductance increases until it is at a maximum value when the axis of saturation and the axis of the winding are orthogonal.\nB. Mutual inductance between stator phases\nThe mutual inductances between stator phases calculated for an unsaturated motor are shown in Fig. 5 and those calculated for a saturated motor are shown in Fig. 6. The stator mutual inductances are affected by rotor slotting in the same way as the self inductance. When the motor is saturated there is the same periodic variation in the inductance at twice supply-frequency and the mean value of mutual inductance reduces by 14.6% from the unsaturated value. As expected, the mutual inductances are\nnegative and a phase difference of 60\" between the values of M12 and MI3 can clearly be seen in Fig. 6.\n-326 I I\npeak\n-338 1 -340 ' I\n0.0 90.0 lxo.o Angular displacement of rotor (degrees)\nat rotor speed with a phase difference of 90\" between them. This agrees with the variation assumed in equation 9.\nThe effect of saturatiorl on M I , and MI^ can be observed in Fig. 8. The sinusoidal variation at rotor speed is still evident, however the amplitudes of the mutual inductances are modulated at a frequency of 2 Hz, which is twice slipfrequency. This modulation is similar to that see in the self inductance of a stator phase and is due to the rotation of the axis of saturation in the rotor at slip-frequency . The a-axis and p-axis current distributions are orthogonal so that when the axis of saturation in the rotor is aligned with the a-axis distribution h f 1 , has its minimum value and hfla has its maximum value.\nD. Self inductance seen by the rotor current distribution\ndistributions, obtained from the linear model, are shown in Fig. 9. Both current distributions see the same constant value of self inductance. When the self inductance\nto rotor slotting was observed. However, there is no such variation due to stator slotting present in the self inductance seen by a rotor current distribution. The stator slotting produces a current distribution in the rotor which has a different spatial variation from that of the fundamental\nThe self inductances seen by the a-axis and p-axis current\nof a stator winding was examined a periodic variation due",
            "a-axis and @-axis current distributions and so has no effect on the self inductance seen by these distributions.\nThe effect of saturation on the self inductance seen by a rotor current distribution is clearly visible in Fig. 10. There is a periodic variation in inductance at a frequency of 2 Hz about a mean value. This variation at twice slipfrequency is due to the rotation of the axis of saturation in the rotor. There is a 180\" phase difference between the variation of La and Lp because the a-axis and ,&axis current distributions are orthogonal.\nIv. THE EFFECT OF SKEW ON INDUCTANCES\nNow that the effect of saturation on the inductances L1, M,, MsT and L, is understood the effect of skew on these inductances will be examined.\nA . Representation of skew in the model Williamson, Flack and Volschenk have demonstrated that the time-stepping, finite-element model described in Section I1 can be extended to include skew [5 ] . In this extended model the skewed rotor bar of Fig. l l a is represented by a number of straight segments as shown in Fig. l l b . As the number of straight segments is increased the accuracy with which the model represents a skewed bar improves. The skewed motor may now be represented by a\nnumber of 2-D finite-element slices each at a different axial position in the machine. The mutual inductances are calculated for each slice independently and then summed to give the mutual inductance matrix at each time-step.\nThe 22kW, 4 pole motor modelled in Section I11 with an unskewed motor has actually got a rotor skew of 1.5 rotor bars. The multi-slice, finite-element model described above has been used to simulate this motor using 5, 2-D slices to represent the skewed machine. As for the unskewed case, the motor was excited from a balanced 415V, 50 Hz supply and simulated at a full-load slip of 0.02. Results were obtained for both an unsaturated and a saturated motor.\nB. Linear Model\nA linear simulation of the skewed motor was initially carried out to examine the effect of skew on inductance if saturation is ignored. The self inductance of a stator phase, calculated for each of the 5 slices in the model, is plotted in Fig. 12. The only effect of skew in the linear model is to al-\n785 , i\nter the phase of the periodic variation due to rotor slotting between slices. The magnitude of this variation and the mean value of inductance remains the same in each slice. The self inductance for the skewed motor is the sum of the self inductances calculated for each slice. This is plotted as a heavy line in Fig. 12. A periodic variation due to rotor slotting is still present but, as expected, the magnitude of",
            "this variation is much less than in an unskewed motor. In an unsaturated motor the mutual inductance between stator phases, Ads, is affected by skew in a similar way to L1 and the self inductance of a rotor current distribution, L,, is unaffected by skew.\nThe mutual inductances between a stator phase and the a-axis and ,&axis distributions are plotted in Fig. 13. The\nmagnitude of the mutual inductance is the same in all slices with a difference in phase between slices arising from the angular displacement between the rotor cages in each slice.\nC. Non-linear model\nThe presence of skew in an induction motor produces an axial redistribution of air-gap flux which results in an axial variation in the saturation in the motor. The authors have verified elsewhere that the multi-slice model is capable of predicting this variation [6]. As an indication of the degree of flux redistribution due to skew in the simulated motor, the predicted axial variation of flux-density in one stator tooth is shown in Fig. 14, together with the flux-density for the unskewed motor. There is clearly a reduction of\nthe flux-density at one end of the machine and a corresponding increase at the other end. The effect of this axial variation in saturation on the self inductance of a stator phase may be seen in Fig. 15. In slice 1, where the satura-\ntion is lowest, the periodic variation due to rotor slotting is apparent but there is very little variation due to saturation at twice supply-frequency. In moving along the machine from slice 1 to slice 5 the motor becomes increasingly saturated and this is reflected in the self inductance; the mean value of inductance in a slice becomes progressively lower and the magnitude of the twice supply-frequency variation increases. A similar progressive change in the mutual inductance between stator phases and in the self inductance seen by the a-axis and p-axis rotor current distribution will also occur.\nThe effect of skew on the mutual inductances between a stator phase and the a-axis and ,@axis current distributions is shown in Fig. 16. In each slice there is still a phase\ndifference of 90' between M l a and MI0 and, as with the linear model, the phase of the mutual inductance is different in each slice. Examination of Fig. 16 appears to reveal that the magnitude of MI0 is more affected by the axial variation in saturation than that of Mia. In addition to being altered by the axial variation in saturation due to skew, the magnitudes of the mutual inductances will also be modulated by the rotation of the axis of saturation in the rotor. Over the time period of Fig. 16 the axis of saturation is aligned with the p-axis and is orthogonal to the a-axis . The axial variation in saturation due to skew will have a greater effect on inductance values when the mo-"
        ]
    },
    {
        "image_filename": "designv11_11_0000480_tia.1994.350317-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000480_tia.1994.350317-Figure5-1.png",
        "caption": "Fig. 5. Magnetic field inside a PM machine with a deformed stator",
        "texts": [
            " The advantage of (44) is the fact that it describes only the interaction between the high-frequency currents and the fundamental field. If the mode shape k is known, (55) can be evaluated easily using the finite element method. When the vector potential is used in the calculation, flux linkages can be obtained readily [lo], [111 and accurately. The derivative can only be obtained by making several calculations in which the stators deformation factor differs. From these results, the differentiation can be done fairly accurate. Fig. 5 shows an example of the field with a deformed stator. As a 2 example, Fig. 6 represents the orbit plot of the vector r, for a theoretical mode shape having eight nodes in a four-pole machine. According to (33), this should equal zero. In practice, this is not true because of the nonlinear behavior of the magnetic circuit and the nonsinusoidal behavior of the fundamental field. IX. CONCLUSIONS Using the modal analysis concept for calculating the vibrational level of an electrical machine stator, the de- VERDYCK AND BELMANS: ACOUSTIC MODEL FOR PERMANENT MA signer is freed from calculating real magnetic forces, being normally difficult and inaccurate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003823_icar.2005.1507430-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003823_icar.2005.1507430-Figure12-1.png",
        "caption": "Fig. 12. The path the robot traverses when the ball always appears in region 2.",
        "texts": [
            " The path that the robot found is not exactly the one in Figure 10, since for example the robot does not always go to the exact grid-cell of point A. Rather, to visit region 1, it goes to one of the grid-cells close to A. The exact motion of the robot is visible in our on-line videos. This initial experiment verifies that our greedy algorithm can produce the optimal solution in the most benign case. 2) Always in One Region Distribution: As a second test, we created a distribution such that the ball only appeared in region 2. The path that the robot finds is approximately the one shown in Figure 12. It took the robot only one pass through the field to approximately follow the path in Figure 12. On average, every ball is noticed 47\u00b1 1.3 seconds after its appearance. In the experiment 100 balls were shown to the robot. Of course, the optimum solution here is for the robot to stay close to region 2 and visit the balls right after it appears, but our algorithm enforces the constraint that the robot should continually visit the whole environment at least periodically in case new events occur. With the condition that we want to visit the whole environment continually, 47 seconds is reasonable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000454_12.403738-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000454_12.403738-Figure1-1.png",
        "caption": "Figure 1. A PolyBot segment showing a connection port. A node is made of 6 ports in a cube shape.",
        "texts": [
            " introduced CONRO,12 a self-su\u00c6cient unit-modular recon gurable system. Yim introduced Polypod19 showing a variety of locomotion modes. The PolyBot system, Polypod's successor, currently has up to 24 modules in simple con gurations, however in 2001 it is expected to have hundreds of modules with a large number of possible con gurations. The PolyBot system is composed of two types of modules. These systems will be used as examples throughout the paper. PolyBot has a one degree of freedom module called a segment which has two connection ports and is shown in Figure 1, and a zero degree of freedom cube-shaped module called a node which has six connection ports. Two modules mate by joining at their connection ports. The ports on PolyBot are hermaphroditic however, in general ports may have a gender. Since segments have only two connection ports, a robot consisting of segments alone could only be connected to form chains. By adding nodes, PolyBot can approximate a much larger variety of shapes. Figure 2 shows photos of the system recon guring between a loop, a snake and a 4 legged spider"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000336_s0045-7825(99)00371-0-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000336_s0045-7825(99)00371-0-Figure12-1.png",
        "caption": "Fig. 12.",
        "texts": [
            " In this section, a few of numerical examples of circular and annular plates, as shown in Figs. 12 and 13, are calculated to demonstrate further the capability and accuracy of the DQEM as well as to provide some detailed results for the axisymmetric bending of thick Mindlin plates. It should be noted that all the examples treated in this section cannot be solved directly by the DQM due to the discontinuity of loading conditions, geometry or material. And two-element discretization is adopted for all the plates except one subject to a uniformly distributed load from r o to r~ shown in Fig. 12 (Case 6), for which three-element discretization is required. Six different cases of circular plates as shown in Fig. 12 are investigated. The converged results up to five significant digits are tabulated in Tables 3 and 4. The first three examples in the figure are the circular plates subject to different types of loading: (a) a uniformly distributed load from r 0 to the edge; (b) a uniform annular line load at r o, and (c) a uniform annular Numerical examples of circular plates analyzed by the DQEM. line moment at r o. The DQEM results of these three examples are presented in Table 3 with the corresponding thin plate exact solutions [32] for the purpose of comparison"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000810_s0924-0136(02)00356-4-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000810_s0924-0136(02)00356-4-Figure5-1.png",
        "caption": "Fig. 5. Effective strain rate distribution during tyre rolling.",
        "texts": [
            " No modification to the basic model was required for this purpose. The mesh configuration of material and rollers used in the tyre simulation together with the plane of boundary condition nodes is illustrated in Fig. 4. Two 308 dense mesh regions were employed for this simulation. These are located in the two roll gap regions so as to adequately represent the deformation in those most rapidly deforming areas. The effectiveness of the dense regions in covering the areas of greatest strain rate can be seen in Fig. 5, in which the effective strain rate distribution during the process is shown. The resulting mesh was made up of 1620 nodes. The process took place over 40 revolutions at a variable feed rate, this required 4800 deformation increments and took approximately 3 weeks runtime. The wheel rolling process differs from conventional ring rolling due to the lack of a central mandrel, the use of profiled axial rolls, and the presence of idle pressure rolls. The configuration is illustrated in Fig. 6. These differences meant that a modified version of the rolling simulation program was required"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001024_978-1-4757-5070-6_3-Figure3.13-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001024_978-1-4757-5070-6_3-Figure3.13-1.png",
        "caption": "FIGURE 3.13. The separation of electric (Galvani) potentials 4> of conductors Mel and Me2 into potential drops across the surface dipoles X and the Volta potentials \",. Only the Volta-potential difference 11\", = (\",Mel - \",Me2) is measurable.",
        "texts": [
            " This has indeed also been shown with other techniques.(17,67) Introducing the N-sulfopropyl groups (results B) leads to the behavior of a cation exchanger, as expected from the composition of the modified polymer (see Fig. 3.2). Electrodes The electric (Galvani) potential of a conducting phase (e.g., Me) cpMe can be divided into two portions: (1) the surface dipole potential XMe and (2) the Volta (outer) potential I{IMe.(68,69) The situation is illustrated in 398 KARL DOBLHOFER AND MIKHAIL VOROTYNTSEV Fig. 3.13 for two conductors (Mel, Me2) at different potentials. The Volta-potential difference between Mel and Me2, fl.\", = \",Mel - \",Me2, is a measurable quantity, e.g., with Kelvin's method of the vibrating capacitor plate. (7~72) As discussed in the preceding section, the electrode potential E defines (4)Me - 4>S), i.e., the Galvani-potential difference between the electrode and the bulk electrolyte. We now consider experiments in which the electrolyte concentration is changed while the electrode potential E is held constant (by a potentiostatic arrangement)",
            " The electrode is mounted vertically in a holder that enables it to be moved down (immersion into the electrolyte for electrochemical equilibration) and up (removal from the electrolyte and positioning in front of the Kelvin vibrator). The fl.\", measurements are conducted in an atmosphere of nitrogen saturated with water. The water-saturated atmosphere is neces sary to keep the state of the polymer the same as in the electrolyte, and oxygen must be excluded to avoid electrode reactions that can change the value of (~Me - ql'0ly) in the withdrawn (emersed) state. The reference conductor (Kelvin vibrator) for the 111/1 measurements should have a constant XMe value to give reproducible 111/1 results (see Fig. 3.13). This condition is difficult to fulfill, because in the water-saturated atmosphere, uncontrolled adsorption processes may take place on its surface. It is therefore necessary to calibrate the vibrator regularly. This is done by determining 111/1 between the Kelvin vibrator and a stable reference. It turns out that the surface of a polarized electrolyte can act 400 KARL DOBLHOFER AND MIKHAIL VOROTYNTSEV as a stable, convenient reference for the Volta-potential measurements.(74-76) The approach is illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003817_rsta.2006.1897-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003817_rsta.2006.1897-Figure1-1.png",
        "caption": "Figure 1. (a) The active solution with motor centres and entanglement points. (b) The \u2018tube\u2019 encircling the polymer and the directed motion vm. We show the lengths x, Le and De.",
        "texts": [
            " We model the ATP-induced activity of actin clusters by stochastic forces on the polymers, parallel to the filament contour (transverse motion is constrained by entanglements), which always act in the same direction with respect to the polarity of the filaments. The effect of the motor activity is (i) to increase the amplitude of the longitudinal fluctuations along the contour of the filaments, giving rise to a higher effective temperature T/TCTact for the tangential motion, and (ii) to give the filaments a non-zero curvilinear drift velocity in their tubes, vm. Increasing/decreasing activity leads to an increase/ decrease in Tact and vm. A cartoon of the system is shown in figure 1. Effective temperatures for non-equilibrium systems have been used to model noise in foams and other driven systems (Langer & Liu 2000). The linear viscoelastic response of such an active polymer solution can be derived, assuming that its structure is not perturbed by the activity of the motor clusters. Despite this crude assumption, one uncovers rich physical behaviour, as the \u2018activity\u2019 modifies the already subtle dynamics of passive semiflexible polymer solutions (MacKintosh et al. 1995; Isambert & Maggs 1996; Gittes & MacKintosh 1998; Morse 1998a,b)",
            " The Hamiltonian of a worm-like chain is given by Hwlc\u00bdR\u00f0s\u00de;L\u00f0s\u00de Z k 2 \u00f0L 0 dsjv2sRj2C \u00f0L 0 dsL\u00f0s\u00de\u00f0jvsRj2K1\u00de; \u00f05:1\u00de where vxAhvA/vx; and an instantaneous local tension, L(s), is induced by the incompressibility of the chain. The persistence length LpZk/kBT is the lengthscale over which the chain loses memory of its orientation (see figure 2). The filaments are confined to a \u2018tube\u2019 (Doi & Edwards 1986) of diameter DewLp(x/Lp) 6/5. We define an entanglement (deflection) length (Odijk 1983; Semenov 1986) LewLp(x/Lp) 4/5, as the distance between successive collisions of Phil. Trans. R. Soc. A (2006) the filament with its tube (figure 1b). The hierarchy of length-scales is L, Lp[Le[a. On length-scales [!Le, the relaxation is due to the dynamics of \u2018free\u2019 chains (Doi & Edwards 1986), while for [OLe, it is due to diffusive directed motion of the polar filaments in their tubes. For [!Le (and consequently [!Lp), the chain conformation is anisotropic and can be described by weak undulations about a rigid rod. Owing to the rod-like nature of the polymer segment, the coupling to the shear flow is anisotropic. For short filaments L!Lp, the rotational diffusion of a rod of length L determines the dynamics of u\u0302\u00f0t\u00de, which is much slower than that of rs, rt"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001659_s0094-114x(02)00003-4-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001659_s0094-114x(02)00003-4-Figure3-1.png",
        "caption": "Fig. 3. End-crossed profile of dressing gear.",
        "texts": [
            " The drive ratio i21 may be determined by considering that the velocity v1 equals to v2 on the direction perpendicular to the helical line. Then, we obtain i21 \u00bc x2 x1 \u00bc r1 \u00f0a r1\u00de tan b1 ; \u00f01\u00de a \u00bc mnz2 2 cos b2 \u00fe mnz1 2 cos b1 ; \u00f02\u00de where mn is the normal module, z1 and z2 are the tooth numbers of the gear and the TI worm, respectively, and r1 is the gear pitch radius. To perform TCA on the worm-gear set, the following analyses are based on the hypothesis: the gear tooth surface RI is known, while the TI worm tooth surface RII is to be derived. As shown in Fig. 3, the gear tooth surface RI is actually an involute helical surface, and the equation of rI can be represented in coordinate system S1 as follows: x1 \u00bc rb cos s \u00fe rbk sin s; y1 \u00bc rb sin s rbk cos s; z1 \u00bc p1\u00f0s r0 k\u00de; \u00f03\u00de where s and k are the two variable parameters of surface RI, rb is the radius of the base circle, p1 is the lead-per-radian revolution of surface RI, and r0 is the half-angle of tooth groove on the base circle. In the meshing process of the worm-gear set (or finishing the TI worm using a diamond dressing gear), the tooth surfaces of the gear and the TI worm are in continuous tangency at every instant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002282_0263-8231(91)90037-j-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002282_0263-8231(91)90037-j-Figure1-1.png",
        "caption": "Fig. 1. Example of open thin-walled beam cross-section: geometric centre G (centroid of section): principal axes r 1 and ( through G; shear centre 0; axes y and z through 0 in parallel to 17 and (.",
        "texts": [
            " In this paper, the twelve order static governing equations are solved exactly in the absence of body force. The displacement functions (1I, Z, ~ ) are not independent due to the coupling of the axial force. Using the exact solutions as shape functions, finite element matrices are developed in terms of the twelve generalized coordinates: I1, Z, ~ and their first derivatives at the two ends. Since the element is statically exact, it converges rapidly in dynamic and stability problems. 2 EQUATIONS A uniform beam with an open thin-walled cross-section of the type shown in Fig. 1 is considered. If no distributed external load acts along the beam element and if a central static axial load P is applied to the beam ends, one has EI.o~ .... - p l o g 6 \" + P ( w \" + YG0\") + m(bJ + YG~) = 0 EIcv .... - pI~iJ\" + P ( v \" + ZGq~\") + m(i~ + ZG~) = 0 (1) EIw(P . . . . - p l w ~ \" - GI, dp\" + p ( r 2 0 '' + yGW\" -- Z~V\") + JoO + m(yG6J + ZG i)) = 0 Primes and dots mean differentiation with respect to position x and time t, respectively. Equations (1) were derived by Vlasov. ~ Shear deformation is not considered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002591_0094-114x(85)90040-0-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002591_0094-114x(85)90040-0-Figure2-1.png",
        "caption": "Fig. 2. Involute generation.",
        "texts": [
            " The vector location of the cutting surface normal, n, is now used to determine the location of the cutting points, P and Q, on the rack form as a function of the gear blank rotation, 02. The locations of these cutting points in the gear blank coordinate frame are then found by a coordinate transforma- Rack-generated spur gears tion. The locus of these cutting points define the gear tooth and fillet shape. INVOLUTE GENERATION The section of the rack form which generates the involute portion of the tooth is the straight side [5]. As shown in Fig. 2, this cutting point will lie on the line of action of the involute mesh between the rack form and the gear. As seen in Fig. 2, the involute is 353 cut for both positive and negative rotations of the gear blank from the initial position. The normal to the rack surface, n, is directed along this line of action and can be expressed as n = - s in 611 + cos 6.1, (2) in the rack coordinate frame, where \u00a2b is the pitch circle pressure angle of the tooth. The location of the cutting point, P, on the rack surface, as shown 354 in Fig. 3, can be written as B. HEFENG et al. rl = - u cos &il - u sin dPjl, (3) where u is the distance along the rack surface from the pitch point, O~, to P"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000184_70.631235-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000184_70.631235-Figure3-1.png",
        "caption": "Fig. 3. A planar 4R manipulator. (a) The manipulator with the singular configuration. (b) A trajectory on the self-motion manifold.",
        "texts": [
            ") Traversing each loop corresponds to a self motion that rotates the third (outermost) link through one complete revolution, and changes the \u201cposture\u201d of the first two links by changing the sign of and Indeed, the first two links can be considered to be a 2R manipulator tracing out a circular path [3]. The projection of the self motion path onto the plane shown in Fig. 2(c) should be compared to the first example. The self motions of a four link planar manipulator starting at a singular point are studied in this example. [Fig. 3(a)]. Since the degree of redundancy is two, the self motion manifold is 2-D and looks like a pair of cones in joint space near the singular point (the common vertex of the two cones.) In Fig. 3(b) we have attempted to display a portion of this manifold by finding a self-motion that \u201cspirals around\u201d the cone. The 4-D joint space has been projected down to three dimensions by ignoring the first joint angle To further aid visualization of the 3-D figure, the projection of the path onto the plane is also shown. At each time step in the integration, was adjusted so as to have constant length, to satisfy the constraint and to point at a fixed angle away from the singularity. The error in this calculation (movement of the end effector) is less than 10 In this example we study a singularity of codimension 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000907_s0956-5663(01)00205-6-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000907_s0956-5663(01)00205-6-Figure4-1.png",
        "caption": "Fig. 4. Schematic drawing of the wall-free droplet cell integrated within a SECM. The gold plate is mounted via double-faced adhesive tape on the cell holder of the SECM, allowing movements in all directions via high-precision step motors having a nominal resolution of 10 nm/microstep (not shown). A droplet of 100 l is placed surrounding the micro-electrode and the gold plate. Two clamps mounted on magnets and either holding a AgCl-coated silver wire or a platinum wire are positioned on a metal plate, so that the ends of both wires are inside the droplet.",
        "texts": [
            " The volumes of these measuring cells are generally in the lower milliliter range, and the sample is usually located at the bottom of the cell, preventing an easy optical control of the position of the micro-electrode above the sample. For fast spot-finding purposes, however, an optical control of the position of the micro-electrode is indispensable. By means of a wall-free droplet (typical volume of 10\u201350 l), in which the micro-electrode is inserted from the top, the time for the integration of the enzymemodified surfaces into the SECM and a first coarse positioning of the micro-electrode could be significantly decreased. In Fig. 4, a photograph of the set-up for SECM measurements in a wall-free droplet clearly shows the good visual accessibility of the sample. The Au-modified wafer segment is mounted on the cell holder of the SECM. The micro-electrode is perpendicularly approached to the Au-surface until a distance of about 1 mm between the electrode tip and Au-surface is attained. Afterwards, the micro-electrode is roughly pre-positioned in the x, y-plane in close proximity to the enzyme structures on the sample surface in order to allow the enzyme structures to be in the area, which will be investigated in the subsequent scanning process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002491_s0022-460x(88)80114-7-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002491_s0022-460x(88)80114-7-Figure2-1.png",
        "caption": "Figure 2. Internal and applied forces.",
        "texts": [
            " In the following we review the governing equations for generally curved and twisted rods and then we develop the stiffness and mass matrices as well as the load vector for an arbitrarily curved and twisted rod element. Finally, we illustrate our formulation by a number of examples. Consider a spatially curved and twisted rod as shown in Figure 1. Let the internal force and moment vectors in the rod be denoted by Q and M respectively. Also let the applied force and moment vectors per unit length be F and I~, respectively. Now, using the sign convention of elasticity, one may write the equilibrium equations for a bar of finite length as follows (see Figure 2): for translational equilibrium, I/ Q 2 - Q t + F(s) ds = ~ nlfi ds, (1) I 1 where m is the mass per unit length and u is the displacement vector; for rotational equilibrium, M~-M,+(r2xQ2)-( r , xQ,)+ , ( r x F + G ) d s = d , mrx~ids+d['2dt J,, ibds, (~) where j is the dyadic of the moments of inertia per unit length and 0 is the vector of rotations. One may express equation (2) in the following alternative form: x (j~lx m rx~) ds. (3) I I Now, since the rod under consideration is of arbitrary length, it follows that the satisfaction of equation (3) requires that dsd M + d r x o + r x d - ~ Q + r x F + G = d ( j 0 + m r x 6 ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003784_1.1829070-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003784_1.1829070-Figure4-1.png",
        "caption": "Fig. 4 \u201ea\u2026 The indeterminate ten-bar linkage. \u201eb\u2026 The secondary instant centers obtained from the Aronhold\u2013Kennedy theorem. \u201ec\u2026 The first arbitrary choice of the instant center I19 . \u201ed\u2026 The second arbitrary choice of the instant center I19 . \u201ee\u2026 The secondary instant centers I49 and I19 .",
        "texts": [
            " It is interesting to note that all three examples belong to the class of nonsingle-input-dyadic ~NSID! linkages, as defined by Ref. @16#. Note that the first two examples have four-bar loops, but are still regarded as NSID according to the definitions presented in that paper. MARCH 2005, Vol. 127 \u00d5 251 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use 252 \u00d5 Vol. 127, M Downloaded From: http://mechanic Example 1. A Ten-Bar Linkage With all Revolute Joints Consider the indeterminate ten-bar linkage shown in Fig. 4~a!. The focus of this example is to locate the instant center for coupler link 9; i.e., I19 . Given the 13 primary instant centers, the four secondary instant centers I13 , I24 , I16 , and I57 can be obtained directly from the Aronhold\u2013Kennedy theorem, see Fig. 4~b!. The instant center for coupler link 9 must lie on the line connecting the instant centers I16 and I69 ~referred to here as the locus of I19). However, there is not sufficient information to find the unique location of this instant center from the Aronhold\u2013Kennedy theorem. The first of the two methods, presented in the Sec. 3, will be used to find the location of the instant center I49 . Then it will be possible to use the Aronhold\u2013Kennedy theorem and locate the instant center for link the coupler link 9. First, remove link 8, which results in the two-degree-offreedom linkage shown in Fig. 4~c!. For this linkage, the instant center I19 can lie anywhere on the line connecting I16 and I69 . Therefore, this linkage can be reduced a single-degree-of-freedom ARCH 2005 aldesign.asmedigitalcollection.asme.org/ on 02/26/20 linkage by choosing I19 arbitrarily on this line ~denoted here as I19 1 ), see Fig. 4~c!. Note that this arbitrary choice of I19 1 is justified in Sec. 3, and is not related to the location of I19 for the original ten-bar linkage. The procedure to locate the instant center I49 1 is: ~i! locate I39 1 at the intersection of the two lines I19 1 I13 and I3-10I9-10 ; and ~ii! locate I49 1 at the intersection of the two lines I19 1 I14 and I39 1 I34 . Now choose another point on the line I16I69 as a second arbitrary location for I19 , denoted here as I19 2 , see Fig. 4~d!, and locate the instant center I49 2 using a similar procedure. Finally, draw a line through the two instant centers I49 1 and I49 2 , see Fig. 4~e!. This line represents the locus of the secondary instant center I49 . Finally, replace link 8 to restore the original ten-bar linkage, as shown in Fig. 4~e!. The exact location of the instant center I49 is the point of intersection of the locus of I49 with the line drawn through I48I89 , as shown in the figure. The Aronhold\u2013Kennedy Transactions of the ASME 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: http://mechanic nical Design MARCH 2005, Vol. 127 \u00d5 253 aldesign.asmedigitalcollection.asme.org/ on 02/26/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use 254 \u00d5 Vol. 127, Downloaded From: http://mechan theorem can now be used to determine the unique location of the instant center I19 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003743_j.elecom.2006.09.032-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003743_j.elecom.2006.09.032-Figure1-1.png",
        "caption": "Fig. 1. Photo of the electrochemical cell used (a) and the measurement scheme (b). WE \u2013 microcylindrical working electrode, RE \u2013 reference electrode, CE \u2013 counter electrode, CA \u2013 capillary. A dispensed nitrobenzene drop is seen in the centre of the cell.",
        "texts": [
            " We dispense an oil drop of required size from a capillary into the aqueous phase and insert a platinum or gold microwire into the drop. This approach should enable easy change of the drop and renewal of the initial electrochemical conditions. It also leads to the exposition of the organic phase. Voltammetric measurements were performed in the three-electrode system using an AUTOLAB PGSTAT 30 (Eco-Chemie, Utrecht, Netherlands) potentiostat. A special voltammetric cell has been constructed. A photo of the cell and the measurement scheme are shown in Fig. 1a and b. Platinum cylindrical electrodes of 50, 100 and 300 lm in diameter served as the working electrodes. A silver/silver chloride/saturated KCl (E = 0.199 V versus SHE) was used as the reference electrode and a platinum wire served as the auxiliary electrode. The organic phase in the form of a drop was dispensed from a capillary with a help of a precision dispenser (Fig. 1b). This way of dispensing a drop of oil resembles clearly the construction of the hanging mercury drop electrode by Kemula and Kublik. Another micrometer screw was used to control the approach of the wire to the drop. In this way a possible (but sporadic) formation of the meniscus at the three-phase boundary could be compensated. The cell was enclosed in a Faraday cage in order to minimise electrical interferences. Typical instrumental parameters for square-wave voltammetry (if not specified otherwise) were the following: SW frequency of the potential modulation, f: 10 Hz; SW height of the potential pulses, ESW: 50 mV; and potential step of the staircase ramp, dE: 1 mV"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001068_bf01573694-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001068_bf01573694-Figure1-1.png",
        "caption": "Fig. 1. Schematic cross-section of electrical machine with a nonuniform air-gap",
        "texts": [
            " The considerations have been limited to the determination of the mutual inductance of two arbitrary windings coupled by the main flux. However, an expression for the self inductance can be obtained when assuming that these two windings are identical and located at the same place. In order to illustrate how to use the relationships presented in this paper, the algorithm of derivation will be described in detail. 2 D e t e r m i n a t i o n o f w i n d i n g i n d u c t a n c e s Let us consider two windings which, for the sake of analysis, are located in the machine air-gap as shown schematically in Fig. 1. We assume that their MMFs are produced by the currents perpendicular to the planar cross-section and can be expanded into the following Fourier series 0, i, 2 Waka (v) = - - - c o s v ( x - Xa) (1 a ) TC v=l 1) Ob = ib 2 W b k b (o) - - - cos ~o(x - xb) (1 b) ~Q=i 0 or in the form of exponential functions O~ = ia 1 ~ w l~le~V(,_xo ~ (2a) v~0 0b = ib l~ ~ o = - - c o ~ o ~ 0 (2b) where ~alVl -- Waka Ivl iv I (3a) Wble[ -- Wbkb bl 101 (3 b) Such a form of MMFs can be written for the windings with symmetry axes at arbitrary positions xa and Xb",
            " The function A is derived from the representation of a real magnetic field distribution correlated to the air-gap geometry. For the purpose of its quantitative determination, the calculation of the machine air-gap field distribution is required. Omitting, however, quantitative considerations, let us confine ourselves to the statement, that for rotating electrical machines the air-gap permeance can be written in the general form: m = --co n = - - o o = ~ ~ A.,..eJm'e j<~+\")<~ (5) m = - - o o n = - o 0 Now, we can return to our case of two windings \"a\" and \"b\" of Fig. 1. The properties of the windings are defined by: - harmonic number sets JK and @, where ~#, ~ _ Z - {0} (set of whole numbers excluding 0) v e ~A/', ~oe~ - coefficients ka I~1, kb IQI referred to the windings. T. J. Sobczyk and R Drozdowski: Inductances of electrical machine windings with a nonuniform air-gap 215 The properties of the function A are correspondingly defined: - sets M and N where M, N ~ Z (set of whole numbers), r n ~ M , h e N - coefficients Am,~ of Fourier series. In order to determine the mutual inductance of these two windings, it is necessary to define the magnetic flux density created by one of these windings and to calculate the flux linkage of the other one"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002737_cdc.2004.1429361-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002737_cdc.2004.1429361-Figure1-1.png",
        "caption": "Fig. 1. View of the motorcycle model. The roll angle \u03d5 shown in the figure is positive.",
        "texts": [
            " In section V, we analyze a successive approximation scheme for finding a bounded roll trajectory consistent with a given lateral acceleration profile (equivalently, a given plane trajectory). Getz [5], [6] provides a simple model for a nonholonomic bicycle, suitable for use in motorcycle trajectory exploration. (In fact, such a model has been used effectively in the development of a smart motorcycle driver [7].) The motorcycle model we use may be viewed as a plane that is allowed to slide and roll on the ground. The coordinates of interest include (see Figure 1) J. Hauser is with the Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO 80309-0425, USA, hauser@colorado.edu A. Saccon and R. Frezza are with the Dipartimento di Ingegneria dell\u2019Informazione, Universita\u0300 di Padova, 35131 Padova, Italy, {asaccon,frezza}@dei.unipd.it \u2022 \u03d5 is the roll (or lean) angle \u2022 \u03c8 is the yaw (or heading) angle \u2022 x is the x coordinate of the point of contact of rear wheel \u2022 y is the y coordinate of the point of contact of the rear wheel \u2022 \u03b4 is the steer angle For the sake of consistency, the inertial x-y-z coordinate system is taken as North-East-Down with angles oriented by the right hand rule so that, for example, the heading angle \u03c8 is measured from North with East being \u03c0/2 radians"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000308_s0020-7462(98)00001-8-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000308_s0020-7462(98)00001-8-Figure4-1.png",
        "caption": "Fig. 4. The functions h )0. and h )%5 for different values of b. The sketch of the different phase portraits in each zone is also reported.",
        "texts": [
            " (20b) In the space of parameters ('/c, ac/f ), the functions h )0. ('/c, b ) and h )%5 ('/c, b ) separate the non-chaotic zones (above) from the possibly chaotic regions (below). They depend only on the parameter b, defined in Eq. (16), which is a function of the load p and of the parameters k i . Actually, the function b (p, k i ) is surjective on the interval ]!1, 1[, so that it makes sense to study the functions h )0. and h )%5 for every b3]!1, 1[. For different values of b, these functions are shown in Fig. 4, where the associated phase portrait is also sketched in each region. All the critical curves have the classical bell shape which gives a single chaotic resonance '1 [18]. They decrease exponentially fast to zero when ' increases. This means that, for sufficiently small periods of excitation, the system is not chaotically excited. At the same time, the curves approach zero when 'P0, so that the system is also chaotically protected from very large periods of excitation. The maximum value h )0. ('1 ) of h )0. is an increasing function of b, which tends to 0 for bP!1 and which goes to infinity when bP1; furthermore, h )0. ('1 ) increases very rapidly with b, and for positive values of b, even a very small amplitude of the excitation causes a homoclinic bifurcation. The maximum value of h )%5 , on the other hand, is a decreasing function of b such that limb?~1 h )%5 ('1 ):1.055/c and limb?1 h )%5 ('1 )\"0. It decreases very slowly, and for b(0 it is almost constant (Fig. 4). For sufficiently large values of b, h )0. 'h )%5 for every ' [Fig 4a]. This means that for small values of f no intersections occur [region (A) of Fig. 4a]. When f crosses its first critical value, homoclinic bifurcation takes place, so that a hyperbolic Cantor set appears in a neighborhood of the saddles [region (B) of Fig. 4a]. The dynamics should therefore be chaotic only for \u2018\u2018large\u2019\u2019 values of the displacement. After the second global bifurcation [region (C) of Fig. 4a], the region where the chaotic effects are observable enlarges. Initially, the three centers are again stable and only fractal basin boundaries and chaotic transients are observed (cf. Section 4). When f further increases, a transition to a chaotic attractor is feasible. The global bifurcations analytically detected by Eqs. (20a) and (20b) can therefore be considered as the starting point for this route to completely chaotic dynamics. This means that ac/ f'maxMh )0. , h )%5 N (ac/ f'h )0. in this particular instance) is a safety criterion to prevent chaos, even if in some cases it may be conservative, because the Cantor set initially does not influence all the phase space but just a part. We can roughly resume the previous scenario by saying that, for these values of b and for growing values of f, chaos initially appears in the outer region of the phase space and then approaches the central part until all the dynamics becomes chaotic. When b is less than !0.691, a fourth region appears [labelled (D) in Fig. 4b], where heteroclinic but not homoclinic bifurcation occurs. In this case, a value '\u00aa [which can be considered as the chaotic resonance of the region (C) (Fig. 4b)] exists for which h )0. (h )%5 for '('\u00aa and h )0. 'h )%5 for '''\u00aa . In this latter case, no qualitative difference exists with respect to the case of Fig. 4a. In the former case, on the other hand, a different succession of events occurs when the amplitude of excitation increases. It is now the heteroclinic bifurcation that initially takes place, so that we can say that in this range chaos should emerge in the middle of the phase space and then \u2018\u2018propagate\u2019\u2019 toward the exterior. 3.2. The case p'p #3 When the load is slightly greater than the critical value, chaos may occur as a consequence of homoclinic bifurcation [see Fig. 3c]. This scenario is substantially similar to that of a Duffing\u2019s equation with cubic non-linearities, which has been thoroughly studied [6, 7] and which is quite well understood [14, Section 4",
            " The examined region of the initial conditions (D b D)0.6 and D bQ D)0.6 in this particular instance) is subdivided into basic cells corresponding to graphic resolution of the PC. The trajectory starting from a single cell is followed until it approaches (after a transient of 2000]\u00b9 ) an attractor, and every box touched is labelled accordingly. The procedure is repeated for all the non-previously labelled cells, until the whole region is examined. e f\"0.01 is chosen as being representative of the non chaotic zone [region (A) of Fig. 4a], namely, a/ f\"5 (Fig. 7). The three centers of the unperturbed equation now become three asymptotically stable attracting centers. No manifolds intersection occurs, and the basins have the classical shape of tongues spiralling toward the attractors. They are separated by curves which are the stable manifolds of the two saddles. When f crosses h )0. we enter the region (B) [Fig. 4a], where the outer stable and unstable manifolds intersect. In this case, the basin boundaries become fractal, at least locally in some parts of the phase space. An example is shown in Fig. 8, which corresponds to e f\"0.05 and a/ f\"1. The three attractors were not destroyed by the homoclinic bifurcation, but the separation between their basins is no longer given only by curves. In the case of Fig. 8, the fractal nature of the basins, which is their main qualitative property, is not very accentuated and it is partially concealed by the graphic approximation. After the heteroclinic bifurcation [region (C) of Fig. 4a], the transverse intersection of the other stable and unstable manifolds further contributes to the fractalization of the boundaries. For e f\"0.30, i.e. a/ f\"0.167, the basins of attraction are illustrated in Fig. 9. The fractals are now well recognizable and are distributed over the whole phase space. One of the consequences of this scenario is the sensitivity to the initial conditions, which can also be observed by direct integration: a very small change in the initial conditions will cause remarkably different time histories, even if the same attractor is ultimately approached"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002962_s0022112087001022-FigureI-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002962_s0022112087001022-FigureI-1.png",
        "caption": "FIGURE I. Circular motion of an appendage near a rigid plane boundary. The direction of the current is indicated by the large white arrow.",
        "texts": [],
        "surrounding_texts": [
            "The feeding appendages of many small animals (such as planktonic arthropods) are stalk-like appendages from which emerge long slender filaments, called \u2018setae \u2019. As a first approximation to this geometry we might take any such appendage to be a single rigid straight stalk with the possibility of some variation in friction coefficient. Of independent interest is the waving of a slender, flexible filament as a model for a flagellum or a cilium. In the present discussion we shall adopt the classical Gray-Hancock theory (Lighthill 1975). This approach, modified to include the interactions between waving appendages, was used by Blake (1972) to study ciliated surfaces. It was also used by Pironneau & Katz (1974) to study optimal movements of a single flagellum. 426 S. Childress, M. A . R. Koehl and M . Miksis The hydrodynamics of flagellar motions with application to the feeding of sessile organisms has been discussed by Lunec (1975) and, in a series of papers, by Higdon (1979u-c). In the latter work the role of boundary and body is partially accounted for through the Green function for a spherical body above a rigid plane. Using slender-body theory, Higdon considers a flagellum oriented normal to the plane and attached to the outermost point of the sphere, extending outward into a half-space of fluid. The flow set up by waves of a given form is determined numerically, and optimization is done numerically over the geometry of and the parameters of the wave. In the classification of the present paper Higdon thus studies a first-order scanning system, and it can be compared with other systems involving artificially tethered organisms (see $9). In the present section our object is briefly to describe some results for elongated appendages obtained in simple models of the kind we have used above. We first formulate the problem for an arbitrary continuous linear stalk attached to the origin in an infinite expanse of fluid. We denote the locus of points on the appendage by x(s, t ) , where s,O 2 s 2 L, is the arc length. Assuming that the leg or flagellum is inextensible, s becomes a Lagrangian coordinate for linear position which is a variable independent oft. The condition of inextensibility is then According to Gray-Hancock theory, the force per unit length experienced by a waving linear appendage thin in cross-section compared to a typical radius of curvature along its axis, is given by two resistance coefficients C,, by In general the resistance coefficients will be time-dependent since the geometry of filaments, bristles, etc. might be subject to variation over an orbit. Our problem is then to minimize W = 1; k*M*idsdt . 0 In an unbounded fluid the scanning is first-order, and if the Stokeslet field is oriented along the 2,-axis we will fix rT f L 4 ds dt (Problem 1). f = ! o ! o If the appendage is regarded as situated above the rigid plane x3 = 0, then from $7 we have g = ST S L x3 4 ds dt (Problem 2) (71) as our measure of scanning amplitude. Note that for a rigid straight stalk with constant C , problem 1 becomes equivalent to the motion of a sphere on a spherical surface; we know from 52 that there is then no radial scanning current to any order. If C, is allowed to vary, the problem is equivalent to a three-dimensional version of the sphere problem of $4, to which must be added the constraint that the motion be on a spherical surface. If the stalk is flexible and attached to the plane boundary, our problem is similar to that of fluid transport by cilia (Blake 1972). The observed movement of a cilium involves an almost stalk-like \u2018effective\u2019 stroke, followed by a return stroke nearer 0 Scanning currents in StokesJlow and the feeding of small organisms 427 the wall. The effective stroke tends to emphasize C,, while the return stroke involves, in some instances, largely tangential motion and a force determined by the somewhat smaller coefficient C,. A beating movement of this kind can cause points along the appendage to move on closed orbits resembling ellipses or circles, so such points might be compared to the sphere moving near a boundary, as discussed in the preceding section. This raises the question of whether boundary interaction of this kind is largely determining on optimal movements, or whether both the boundary effect and distinct friction coefficients are involved. A good candidate for optimality in either (70) or (71)) which is suggested by the form of the observed effective and return strokes noted above, is shown in figure 8(a, c ) . In problem 1 with C , > C, > 0, there is some countercurrent created by the return stroke. In problem 2 the return stroke creates no countercurrent but the value assigned to C, should include the effect of wall interference. We show in figure 8 (b) another candidate for an optimal effective stroke, suggested to us by Pironneau, which arises in a related problem of optimal swimming (Pironneau & Katz 1974). In the following we consider the four combinations involving either (70) or (71) and with effective strokes (a) or (b) in figure 8, which we indicate by appropriate sub and superscripts. As noted by a referee, there are physical restrictions on the bending of actual cilia which would necessarily modify these optima away from the completely flexible movements. (72) (Lf 9 9) If we define efficiencies (71972) = F\u2019 then it is not difficult to calculate 7pp b, corresponding to the two motions shown in figure 8. We obtain, with p = C,/C,, 428 S. Childress, M . A . R. Koehl and M . Miksis FIQURE 9. A jointed appendage consisting of two straight stalks of lengths B(t) and 1 -B(t) . I n these computations we have repeatedly used the constancy of the optimal rate of dissipation. We also note that hydrodynamic interactions between different points on the stalk have been neglected, even though in a motion such as the return stroke these would be appreciable. For the case without boundary, (73a) shows that motion ( b ) (by which we mean the effective stroke in figure 8 b together with the return stroke of figure 8 c ) is preferred for all p, and for the typical value p = 0.7 we have qp) = 0.035, qlb) = 0.050. In the case of a plane boundary, motion ( a ) is preferred provided that p > 0.2. With p = 0.7 we have qp) = 0.061,qib) = 0.056. For p = 1 , q!f) = 0.053,r]ib) = 0.047. Thus there is a very weak effect of p, which suggests that boundary effects are more important to the scanning strategy than the intrinsic hydrodynamics of a stalk. If we take p = 1 , the points on the stalk behave essentially like spherical bodies and so the theory is a continuous version of the scanning problem considered in $7. The fact that biological appendages are attached to boundaries and sometimes have motions resembling (a) could imply that the comparably modest improvement in efficiency over motion ( b ) may be of consequence to the organism. However any hinged appendage swung from the base by muscles would more readily do (a) than ( b ) , and so be a consequence of morphology rather than hydrodynamic performance. The solution of the constrained minimization problem (67)-(69) with (70) or (71) is not an easy matter for general flexible filaments. Perhaps the simplest geometry which is capable of describing a family of realistic movements is that shown in figure 9. The appendage consists of two straight stalks joined a t the point P. By allowing the point P to move as a function of time, the two motions of figure 8 can be realized, along with a large family of intermediate cases. We shall not pursue this line of investigation here, but will summarize some results for small perturbations of a uniformly rotating stalk when the point P is not allowed to move, as would be the case for an anthropod appendage with one joint. Let the two segments of the stalk have, in suitable units, lengths /3 and ( 1 -p). The system is hinged a t 0 and P and we assumc the appendage remains in the (q, s,)-plane. The angles 0 and $ are defined in figure 9. If, using (69) and (70) we seek extrema of W+Af in this problem, we observe that e, = +, = --+227Ct (74) Scanning currents in Stokes $ow and the feeding of small organisms 429 are solutions of the Euler equations, with f = 0. If we seek nearby extremals by perturbing in an amplitude parameter E , there results 8 = B0 + EA cos 2 ~ t , (754 9 = $,,+EB C O S ~ K ~ , (75b) where A and B are functions of p = C,/C, and p. We can then calculate an efficiency using (72), and then an optimal p for given p (p = 0.48 for p = 0.5). A similar analysis is possible for a filament rotating above a plane wall (/3 = 0.75 for p = 0.5). These solutions are, however, far from the motions shown in figure 8, which depend very much upon the motion of the point P. Ideally, the two-stalk system with variable P might provide an effective cilium model provided that wall-dependent C, and C, were used, but this leads to a difficult minimization problem, about which little is known. For 0 < p < 1 in the absence of a wall, we conjecture that ( b ) , ( c ) of figure 8 is the optimal scanning movement in the two-stalk model, as determined from the efficiency (72)."
        ]
    },
    {
        "image_filename": "designv11_11_0001891_20.312541-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001891_20.312541-Figure3-1.png",
        "caption": "Fig. 3 - Transformed domain",
        "texts": [
            " For the second region, we take: r = [ (RI /d) - R(R, - R)/d\u2019 ] x, s = [ (RI /d) - R(R, - R)/d\u2019 ] y, t = z . For the third region: And for the fourth region: r = [ (RI /d) - R(R, - R)/d\u2019 ] x, r = x , s = y , t = ZI+(Z,(Z,-ZI)/Z) s = [ (R, /d) - R(R, - R)/d\u2019 ] y, t = ZI + (Z,(Z, - Zi )/Z) where d = (x\u2019 + y\u2019 > R , RI > R , Z, * 0. It is easy to see that for d +=CO we have, D = ( r\u2018 + sz )In = RI, and for z+ 03 , t = Z,. Thus, with this mapping it is not necessary to shorten the domain at an arbitrary distance where the electric potential is known to be negligible. Figure 3 shows a view for this mapping. FINITE ELEMENT MODELLING The governing equation of the system is: V. ( a V V) = 0 in the x, y, z coordinate system (1) with the usual Dirichlet and Neumann boundary conrlltions. The integral equation obtained by Weighted Residual Method applied to each element in this coordinate system is given by: Defining the o erator; We can rewrite [2] as: In the (r,s,t) coordinate system, the analogous operator is: Drst = [%%%I Which, after some algebraic manipulation results in: D, = JDrst (4) and &dy& = IS\u2019 brhdt ( 5 ) where J is the Jacobian matrix of this mapping"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000090_s0967-0661(98)00082-3-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000090_s0967-0661(98)00082-3-Figure6-1.png",
        "caption": "Fig. 6. General diagram of the measurement system.",
        "texts": [
            " General guidelines for the selection of good weighting functions can be found in Beaven et al. (1996) and McFarlane and Glover (1990). The control experiments were carried out with a physical model of a tanker on the Silm Lake, at the Ship Handling, Research and Training Center in I\"awa, Poland. The model is a replica of the 145000 DWT tanker m/t \u2018Zawrat\u2019 and it has been built on a 1:24 scale (Fig. 7). The hull contour displacement is 12.18 tons, while the main dimensions are \u00b8 pp \"12.21 m, B\"2.0 m, H\"0.85 m, and the maximum speed is 1.62 m/s. Fig. 6 presents a general diagram of the measurement system. A computer (PC) installed on the model collects the data, which are transmitted to it through a number of serial interfaces and a radio modem. The position of the model is determined by a photo-optical positioning system, composed of two revolving optical telescopes installed at the two ends of the base AB, of length 72 m. On the model, a source of an infra-red light of circular radiation is installed. The telescopes are controlled by microprocessors which send the actual values of the bearings through cable lines to a computer located in the control room on the shore"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000179_1.2893956-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000179_1.2893956-Figure4-1.png",
        "caption": "Fig. 4 Schematic diagram of a gear pair",
        "texts": [
            " A lumped mass modeling is used for the analysis of axial vibrations. Then the equations of motion of a typical rotor bearing system can be written as, [M]{q] + ( [ C ] - I a [ G , ] ) { q } + [K]lq} = ( f ) (1) where the global displacement vector {q} and the force vector { f ) , based on the nodal coordinates system as shown in Fig. 3, are represented by f 1 = (2) 3.3 Gear Modeling. The gear pair is modeled by rigid disks and linearly distributed springs along the contact lines. The gear pair used for analytical modeling is shown in Fig. 4, where a and /? are transverse pressure angle and helical angle respectively. The displacement vector of the contact points can be written as a function of .j, which is a local coordinate to the axial direction. Si(s) = (Xi + rAi)e, + (y, + se,t)e, + {z, - r,9, - ,s^\u201e.)e, Sj{s) = {Xj - rjB^j)e, + {yj + s9,j)ey + {Zj + rjdj j)e\\ (3 ) Then the normal displacements of the contact points can be obtained by using of following vector calculations. S,\u201e = (5, \u2022 e\u201e)e\u201e, Sj\u201e = (Sj- e\u201e)e\u201e (4) where, e\u201e is a unit normal vector of the contact point defined as e\u201e = sin /3e^ + sin a cos Piy + cos a cos pe, (5) Using Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000706_s0956-5663(02)00091-x-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000706_s0956-5663(02)00091-x-Figure1-1.png",
        "caption": "Fig. 1. Cyclic voltammograms of 0.5 mM Q0 at the E. coli -modifed carbon paste electrode in a buffer solution (pH 6.5) containing 20 mM glucose (A) in the absence and (B) presence of 4 mM PQQ and 10 mM MgSO4. Scan rate: 5 mV s 1.",
        "texts": [
            " The electrochemical measurements were carried out with a three-electrode system using a BAS CV50W voltammetric analyzer (BAS Inc.), in which a saturated Ag j AgCl electrode and a platinum disk were used as the reference and counter electrodes, respectively. The measurements were made at 25 8C in a buffer solution of pH 6.5 unless otherwise stated. The solution was stirred with a stirring bar when a current was measured at a fixed potential. The buffer solution was prepared with NaH2PO4 and Na2HPO4 and the ionic strength was adjusted to 0.3mol dm 3 with NaCl. 3. Results and discussion 3.1. Cyclic voltammogram Fig. 1 shows cyclic voltammograms of 0.5 mM Q0 at the E. coli -modified carbon paste electrode in a solution containing 20 mM glucose in (A) the absence and (B) presence of 4 mM PQQ and 10 mM MgSO4. Although the voltammogram of Q0 at the electrode is distorted and shows irreversible nature, it is evident that the cathodic current is greatly decreased and the anodic current is increased by the addition of PQQ and Mg2 . This indicates that E. coli has the catalytic activity for oxidizing glucose with Q0 as an electron acceptor to produce the catalytic anodic current only when PQQ and Mg2 are present in solution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001310_s0043-1648(96)07337-1-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001310_s0043-1648(96)07337-1-Figure1-1.png",
        "caption": "Fig. 1. Types of basic misalignment in a journal bearing.",
        "texts": [
            " The fluid film bearings, although well designed, seldom operate under perfectly aligned conditions. Misalignment of these bearings is generally caused by assembling or manufacturing errors, off-centric loads, shaft deflection due to elastic and thermal distortions or externally imposedmisaligning moments. Any angular misalignment occurs with a couple, and either may be considered as the cause of or result of the other.Misalignment in the bearing generally occurs as a combination of two basic types (Fig. 1). These two basic types are: c axial or vertical misalignment, measured as the angle, b v , between the axis of the journal and the bearing in the axial plane. The plane containing the line of action of the radial central-bearing load and the bearing axis is called the axial plane (YOZ plane); c twisting or horizontal misalignment, measured as the angle, b h , between the axis of the journal and the bearing in the plane (XOZ plane) perpendicular to the axial plane. 2. Literature review Pinkus and Bupara [1] have studied the effect of misalignment on load capacity, oil flow and friction and presented charts which bring out some salient features of misaligned grooved bearings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000507_027836499501400207-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000507_027836499501400207-Figure2-1.png",
        "caption": "Fig. 2. Schematic view of\u2019 the pusher and slider, viewed from above.",
        "texts": [],
        "surrounding_texts": [
            "174\nWhen one rigid object (the pusher) pushes another (the slider) across a horizontal support plane, Coulomb\u2019s law of friction admits some surprising phenomena. First, it is possible to move the slider by moving the pusher away from the slider: pulling. Second, even with an infinite coefficient of friction, it is possible to obtain slip between the two objects as the pusher moves into the slider. This contradicts the common conception that infinite friction always prevents slip. The perfectly rough contact of classical mechanics is not realized by an infinite coefficient of friction. This article shows examples of the phenomena with both quasistatic and dynamic analyses.\n1. Introduction\nIn our work on planning manipulator pushing operations, it seemed reasonable to make use of the following two conjectures:\n1. A pusher can move an object only by moving into it.\n2. If the pusher moves into the object and there is an infinite coefficient of friction at the pushing contact, then the contact will not slip.\nIt was with considerable surprise that we discovered that these two seemingly obvious statements are incorrect. We explain why and discuss the implications for rigidbody mechanics with friction.\nConsider two rigid objects in frictional contact, supported by a horizontal planar surface, with gravity acting along the vertical. The motion of one object, the pusher, is given. The motion of the other object, the slider, is subject to Newton\u2019s laws. Frictional forces are governed by Coulomb\u2019s law. This article constructs examples exhibiting two counterintuitive phenomena:\n1. Pulling. The slider may maintain contact with the pusher, even when the pusher moves in a direction away from the slider. 2. Slip with infinite friction. Even with an infinite coefficient of friction, slip can occur between the pusher and the slider when the pusher moves into the slider.\nThis second phenomenon has implications for the concept of perfectly rough contact. Usually a perfectly rough contact is defined as a contact that does not permit slip. Some treatments erroneously assume that this is equivalent to an infinite coefficient of friction p. For example, Rutherford (1951, p. 41 ) states\nIn the second case in which 11 = oo no sliding is possible and the surfaces are said to be perfectly rough.\nIntuitively this seems correct, but we now see that the two concepts are not equivalent.\nThese phenomena have several practical implications. In manipulation planning, a frequently used simplifying assumption is that the coefficient of friction at a forceapplying contact is sufficiently large to prevent slip. As we show, however, even an infinite coefficient of friction\nmay be insufficient to prevent slip. Further, rigid-body simulations may fail to find valid solutions if we adopt a definition of infinite friction that disallows slip. Finally, simulations that disregard pulling solutions and implement perfectly rough surfaces embrace assumptions outside the laws of rigid-body mechanics with Coulomb friction. The article begins with a review of the general method for solving frictional contact problems. Then we construct examples exhibiting the two phenomena. First we apply a quasistatic analysis, where forces of acceleration are assumed negligible, and then we follow with a full dynamic analysis. Finally, we discuss alternative definitions of infinite friction and the relation to perfectly rough surfaces.\nat The University of Iowa Libraries on June 8, 2015ijr.sagepub.comDownloaded from",
            "175\n2. Determining the Motion of a Pushed Object\nThe solution of frictional rigid-body contact problems presents some unusual difficulties. Under Coulomb\u2019s law, the force at a point contacting a surface must satisfy\nwhere ft is the tangential frictional component, in is the normal component, and , is the coefficient of friction. During sliding contact,\nand the frictional force is directed opposite the direction of sliding. (For simplicity, static and kinetic coefficients of friction are assumed equal.) Thus, Coulomb\u2019s law does not directly specify contact forces. Rather, it imposes constraints that vary with the contact mode: whether the contact is being maintained, and whether the contact is sliding. Frictional contact problems are solved by case analysis. For each contact mode, we determine whether forces and accelerations exist satisfying the simultaneous constraints of Coulomb\u2019s law, Newton\u2019s second law, and whatever kinematic constraints may be present. Each consistent set of forces and accelerations is deemed a solution to the problem. Problems with multiple solutions are ambiguous. Problems with no solutions are inconsistent. More detailed descriptions are given in L6tstedt (1981), Erdmann (1984, 1994), Rajan et al. (1987), Brost and Mason (1989), Dupont (1992), Trinkle and Zeng (1992), Wang et al. (1992), and Baraff (1993).\n3. Quasistatic Pushing and Pulling All of the examples in this article are of the form illustrated in Figures I and 2. The pusher is a straight fence. The slider is a ring of unit radius and unit mass. The support force is distributed evenly about the ring, and the coefficient of support friction is uniform. Attached to the the ring is a massless rod that extends radially a distance I from the center of the ring. The rod does not contact the support surface, and the slider is pushed at the free end of the rod. The rod makes an angle of 45 degrees with the fence. The coefficient of friction at the contact is p. The force f applied by the pusher passes through the contact at an angle ~. The linear pusher velocity is denoted vp, at an angle of 0,. The slider velocity at the rod endpoint is vs, at an angle of 6S. All angles are measured with respect to the fence. All variables are nondimensionalized through division or multiplication, as needed, by a reference mass (the mass of the slider), a reference length (the radius of the ring), and a reference time. We will say that a vector is directed into the slider if it has a nonnegative component along the outward-pointing\nnormal of the fence, that is, if the angle is in the closed interval [0\u00b0, 180\u00b0]. Otherwise we will say that it is directed away from the slider. Force vectors are drawn with filled arrowheads and velocity and acceleration vectors are drawn with open arrowheads.\nSlider velocities will sometimes be represented as velocity centers. The velocity center is the point in the plane about which the motion is a pure rotation. Similarly, slider accelerations from rest will sometimes be represented as acceleration centers. Now suppose that the slider motion is slow enough that inertial forces are negligible compared with support friction. Then a solution obtains whenever the pushing force is exactly balanced by the support frictional force. The support frictional force at each support point directly opposes the motion of the support point, and the integral of these differential forces over the support yields the total support frictional force. Consider Figure 3, for example. For the velocity center shown, the frictional support force acting on the slider is precisely balanced by the pusher force f passing through the contact. For a pusher velocity vp equal to the rod endpoint velocity vs, and a large enough coefficient of friction 11, we have a solution. There is nothing unusual about this solution. Because the pusher velocity v~ is directed into the slider, we have pushing, not pulling.\nBut consider the example of Figure 4, where the applied force passes closely on the other side of the ring center. Here a solution is obtained for a pusher velocity vp equal to the slider velocity v~ but directed away from the slider: pulling. (Because the motion of the pusher is specified, pulling is defined as a velocity away from the slider, not a force.) Note that another solution is that the slider simply breaks contact and does not move. This\nat The University of Iowa Libraries on June 8, 2015ijr.sagepub.comDownloaded from",
            "176\nproblem is ambiguous. In fact, there is a third solution involving pulling with slip at the contact point, but we will concentrate on pulling with sticking contact. To show that the solutions shown in Figures 3 and 4 really are solutions, we integrate the support frictional forces around the ring and show that the total frictional force the slider applies to the support equals the pushing force f. We use two coordinate systems (Figure 5), one system .x-y aligned with the pusher, and a primed system x\u2019-y\u2019 aligned with the applied force but centered on the ring of the slider.\nWith some modifications, Goyal (1989) gives the following expressions for frictional force and torque applied by the ring to the support surface in the primed system:\nwhere T~TI is the slider weight multiplied by the support friction coefficient, c,~ is the slider angular velocity, and v is the velocity of the slider center along the y\u2019-axis. (The velocity of the slider center along the 3/-axis is zero. The velocity center will fall a directed distance -vjw along the x\u2019-axis.) The integrals are elliptic integrals that could be reduced to normal form as in Goyal (1989). The frictional force and torque measured in the un-\nprimed system are:\nFor quasistatic balance the torque about the contact point must be zero:\nEq. (7) implicitly defines a velocity center as a function of the force angle 0. In principle, we could solve eq. (7) for lJ.-\u2019/v as a function of 0. The quantity -v/c.~ gives the velocity center location on the x\u2019 -axis and the sign of To, gives the rotation sense. In practice, the relation of the pusher force to the slider motion can be obtained numerically. The next section describes a convenient geometric interpretation of this relation.\n3.1. Limit Surfaces\nTo visualize the relation between the pusher force and the slider motion, we can employ the limit surface of Goyal, Ruina, and Papadopoulos (1991). The limit surface is the locus of generalized forces (fx, fy,T) arising from support friction during all possible slider motions. It is a closed, convex, two-dimensional surface enclosing the origin. If a slider motion (v~, vy, cv) causes the slider to apply a force (/.r,./~,T) to the support, then (v~, v., w) is parallel to the outward-pointing normal of the limit surface at ( f~, fy, T).\nat The University of Iowa Libraries on June 8, 2015ijr.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv11_11_0000245_1.2889764-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000245_1.2889764-Figure3-1.png",
        "caption": "Fig. 3 Position of a point in thie reference system",
        "texts": [
            " (8) allows the dis placement to be expressed as a function of the nodal elastic coordinates for the element: ml = 4 I Vi(e'f' 'H'^t'\") (10) where matrix H L is a special case of matrix H''' in which the integral is extended to the whole element length, and hence becomes a constant matrix, pressed as As a rule, matrix H'L can be ex- Hi': = \u00b1 CO 2 a?* dx\" dx\" (11) where the plus or minus sign is used depending on whether the element is scanned in the positive or negative direction of the X\"' axis, respectively. 2.2 Position Vector. The position of an arbitrary point in the overall reference system can be defined as (Fig. 3) r\u00bb = R' + A'iui + uf) (12) where R' is the position vector for the origin of the system X T ' ; A' is the matrix transforming a vector of the body coordi nate system to the overall reference system and hence dependent on the angle 6' between the two systems; uH denotes the position of the point relative to the X T ' system in the undeformed state; and uji is the deformation-induced displacement vector. Both Uu and Of are expressed in the reference system for body (. The nomenclature adopted here uses u\" and w\" to denote the same quantity, so the representation system employed is the sole difference"
        ],
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    },
    {
        "image_filename": "designv11_11_0001310_s0043-1648(96)07337-1-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001310_s0043-1648(96)07337-1-Figure2-1.png",
        "caption": "Fig. 2. Configuration of misaligned journal bearing.",
        "texts": [
            " [12] discussed different excitation techniques and have concluded that the sweep frequency rotating force perturbation method used by Muszynska et al. [13] has an excellent signal to noise ratio. The authors [12] have presented an algorithm for identifying eight linearized oil film coefficients, applicable for the identification of dynamic coefficients of cylindrical and tilting pad bearings. The same method is used here for the identification of stiffness and damping coefficients of themisaligned 3-lobe bearing. Fig. 2 shows the configuration of a misaligned journal bearing. The severity of misalignment has been represented by a parameter, D m , degree of misalignment, as discussed in refs [5,14]. The misalignment ratio, l, is defined as [14] ls\"2bz/C p , where C p is the radial clearance. Let l m be the maximum possible misalignment ratio, l e be the misalignment ratio at the bearing end, e 0 be the eccentricity ratio at the mid-plane, f be the attitude angle under the aligned condition and c be the angle between the plane of misalignment and the axial plane containing the load vector"
        ],
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    },
    {
        "image_filename": "designv11_11_0000810_s0924-0136(02)00356-4-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000810_s0924-0136(02)00356-4-Figure7-1.png",
        "caption": "Fig. 7. Mesh configuration for wheel rolling simulation.",
        "texts": [
            "2, it was considered best to determine pressure roll velocities in the same way as was used for mandrel speed, and apply a full friction model at each interface. In addition, the presence of the pressure rolls meant that the dense mesh region on that side of the wheel needed to be extended to cover the entire region in close proximity to the pressure and edge rollers. This meant that a 908 dense region was used on that side of the wheel, and a 308 dense region used in the proximity of the drive roll as illustrated in Fig. 7. This clearly has resulted in an increased problem size, a situation that was partially reduced by excluding the boss section of the wheel from the model. Historical observations of the process has lead to the general assumption that the boss section is unaffected by the rolling process. This assumption suggests that the inner radius of the meshed region, the boundary with the boss can be assumed to be fixed during the process. Hence velocity boundary conditions have been applied in all directions to the inner ring of nodes in the mesh"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003047_iros.2003.1249198-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003047_iros.2003.1249198-Figure2-1.png",
        "caption": "Figure 2: Single arm supparted by a vehicle.",
        "texts": [
            "j-k$) (13) Finally note that, in order to be comprehensive of the overall cases fi 5 f i ~ , while avoiding any possibility of chattering in the vicinity of the threshold value po, it is practically convenient to adopt the following expression for i, automatically guaranteeing a smooth transition between the two different cases: where a ( p ) is a continuous scalar function of p, which is unitary for p I po and hell-shaped, tending to zero within a finite support, for p > f i ~ . 3 Control of a Single Arm Non-Holonomic Mobile Manipulator The case of an arm of the same type of Fig. 1, now mounted on a 3D moving base as in Fig. 2, is now considered. The vehicle is assumed to be a non-holonomic one, in the sense that it allows a linear velocity vector only directed along its principal axis, and an angular velocity vector Q only lying on a plane passing through a known point of such principal axis, and orthogonal to it. The arm and the ve- hicle are regarded as two separate \u201cbasic robotic units\u201d, whose motions however needs to be suitably coordinated to obtain the accomplishment of the assigned common task in a cooperative way"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002297_robot.1998.680701-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002297_robot.1998.680701-Figure3-1.png",
        "caption": "Fig. 3: 2 object system iisetl in numerical exaiiiplc",
        "texts": [
            " Tlie sairiC condit ioii is lioltl for another contact poiiits. This holds tlie tlieorein. 0 We note that the vector z is included in the matrices B j k ( z , U ) and Bot(z , U ) . Moreover: although tlie matrices B J k ( z , U ) and Bot(z , U ) are cornposed of the matrix X ( z . a,). it, is generally h r d t,o olitairi X(Z, U ) syrnbolically sirice tlic clinierision of Xjz, U ) is large. 5 Numerical Example To confirm Theorem 1, we show a numerical example. Suppose that two cylindrical objects are enveloped by two planar fingers, as shown in Fig.3, where the finger 1 contacts with object 1 with two different points and finger 2 contacts with object 2 at one contact point. The constraint condition (13) is described as follows: = 0. (25) wliere 81 = 0~21\". o2 = [ez1 & * I T . p , , = [ X B ~ y ~ ~ ] ~ and p B 2 = [xB2 yn2]'. Tlie matrix of eq.(25) corresponds to O ( Z , U ) in eq.(13). Since d imQ(z ,u ) = 8 x 10 and rankO(z,u) = 8: cy = 2 in cq.(20) arid the contiit,ioii of eq.(15) is satisfied. Iii 2 . only the two elements can be independently chosen"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003206_j.mechmachtheory.2003.12.003-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003206_j.mechmachtheory.2003.12.003-Figure11-1.png",
        "caption": "Fig. 11. Identified motion domains of the driving link in Example 4.",
        "texts": [
            " The result of identification does not contradict with the whole input and output relationship in Fig. 10(b). Example 4. We identify the domains of motion of the Stephenson-3 six-link mechanism composed of seven revolute pairs whose kinematic constants are as follows. a0 \u00bc 25; a1 \u00bc 40; a2 \u00bc 40; a3 \u00bc 35; a4 \u00bc 50; a5 \u00bc 30; a6 \u00bc 20; a7 \u00bc 30; a8 \u00bc 35 \u00bdmm a \u00bc 70 \u00bddeg The constituent four-bar linkage is the double crank mechanism and one of two closed curves of the coupler curve is the curve that the number of the node is one and the number of rotation is two as shown in Fig. 11(a). In this case, four limit points and four turning points are obtained respectively as shown in Fig. 11(a). Then, the relationship between angular displacements of the driving link FG and the link AB becomes the curve of rotational-oscillating motion and the curve of two reciprorotationaloscillating motion as shown in Fig. 11(b). By using the procedure in Section 5.2, the numbers 1\u20134 are assigned to five domains of motion to be mapped on four number lines as shown in Fig. 11(c). Numbers of circuits and branches are two and four, respectively. In the case of the other closed curve of the coupler curve, the number of domains of motion is two and numbers of circuits and branches are one and two, respectively. Example 5. We identify the domains of motion of the Stephenson six-link mechanism composed of seven revolute pairs whose kinematic constants are as follows. a0 \u00bc 40; a1 \u00bc 40; a2 \u00bc 30; a3 \u00bc 40; a4 \u00bc 4; a5 \u00bc 3; a6 \u00bc 20; a7 \u00bc 20; a8 \u00bc 20 \u00bdmm a \u00bc 70 \u00bddeg The constituent four-bar linkage is the double lever mechanism and one of two closed curves of the coupler curve is similar to the 8 character as shown in Fig"
        ],
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    },
    {
        "image_filename": "designv11_11_0003396_bf02156005-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003396_bf02156005-Figure3-1.png",
        "caption": "Figure 3. d and d' directions.",
        "texts": [
            " For ~ < I22max,tO each value of 12 four or six different real wave lengths correspond; hence, for I2 < ~'~2rnax a harmonic wave of frequency I2 propagates with different wave lengths, of which some are greater than the length of a coil, others are smaller. In addition to what stated so far, and that can be immediately inferred from fig. 2, it is worth pointing out the subsequent further difference between the simple theory results and those achieved by the proposed theory. According to the former, due to the coupling of displacements and rotations of the wire sections, the ~2' values correspond to displacements in the direction d, while the I2\" values correspond to displacements in the direction d' , as shown in figure 3. Moreover directions d and d' result to be independent of the wave length. On the contrary, according to the theory under examination, the values I21 (o.) and I22 (v) correspond to displacement directions which vary depending on the wave number. To prove this fact, denoting by /3 the angle formed by the resulting displacement w(v) direction and the tangent t to the helix (see figure 4), in figure 5 are drawn the functions /310') and /32(o) that correspond to the solutions I21 (o) and I22(=,) calculated for different values of~x 0). The variation of /3 as o varies - shown by figure 5 - is only negligible for very low values of =, 0 ' < 0.2) for which the two values/31 == lr/2 - - 2\u00a2x and /32 ~ - 2\u00a2x correspond to the displacements w respectively in the two directions d and d' shown in figure 3. Figure 5 also shows that for values of o close to 2 cos \u00a2x the displacement directions are practically reversed compared O) For the determination of functions ~(o) see Appendix II. 34 MECCANICA 80 a-5\" 10 (tO 6 0 , 40 30 2 0 10\" ,'.2 ,'~ o:e , 'j ; -10 - - ~ . . \u2022 ~,%Gm.q 2 0 \" ' . . % '~% \u2022% % \u2022 \u2022 30. ~',,.~.-I(Y' \u2022~. 40 SO 60 70 80 gO 100 110 120 %, %% ~%% %%% \"\\ \\ #, - - - - - Figure 5. The functions ~(u). to those corresponding to u ~ 0 . For example, in o ther words, displacements tha t correspond to solutions I21 which, for low , a n d low c~, are practically longitudinal, tend to become rotational for u-+ 2 cos a, i",
            " This last aspect turns out to be particularly interesting in those cases where the spring is part of more complex systems, such as, for example, those of valve mechanisms; in such a case an evident simplification can be obtained by schematizing the springs as lumped systems. Moreover, this simplification supplies natural frequency values more exact than those obtainable by replacing the spring with an equivalent rod. APPENDIX I. According to Wittrick's simple theory, the following decoupled equations of motion can be written: / : d : d at 2 = v 2 as 2 a2 d' ~2 d' at 2 ---- 0'2 aS 2 (I.l) d and d ' being the displacement directions shown in figure 3, and v and v' the propagation velocities of the deformation waves along the wire, given by (I.2) ,ff U r ~ Putting in the (I.l) solutions such as: d = A ei#se itot d' = B ei#S e i~t (I.3) we have: { G0 2 _- U2#2 w '2 = v'2/~2 (1.4) and taking into account the (I.2), (8) and the value of the ratio {t3y/~, ) = 1.3: . - - = - - 0 3 a (I.5) 1.14 - - Finally, taking the (9) into account, we obtain: p 7r I2\" = 1.14 - - (I.6) APPENDIX H. Angle ~ (see figure 4) is defined by: Y = arctg - - z (II.l) where the ratio y/z can be derived from one of the (4)"
        ],
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    },
    {
        "image_filename": "designv11_11_0002143_bf00374763-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002143_bf00374763-Figure6-1.png",
        "caption": "Fig. 6. An arbitrary subset P of a system of particles S is rigidified",
        "texts": [
            " linear and angular m o m e n t u m follow as theorems. 11s This derivation is completely independent o f whether or not the system is rigid. Consequently, in deriving the usual balance principles for a system of particles, one does not need the principle o f rigidification at all. But, because o f this, we are then free to ask whether these balance laws imply either o f Statements (A) or (B) for such a system. To investigate this possibility, consider an n-particle subset P o f a system S of particles (Fig. 6) moving in inertial space. Denote the posit ion vector o f the particle Pi (i---- 1, 2 . . . . . n) in the current configuration o f the body by ri. Let F;j be the force exerted on Pi o f P by another particle Pj o f P. These internal forces are either prescribed by constitutive equations or are due to internal constraints. In any case, because o f assumption (ii), the resultant force and momen t o f the internal forces will vanish. Let F~ be the sum o f the forces exerted on a particle P; o f P by material outside o f S and let FI' be the sum 'of the forces in its configuration at time to to become/~ l~s The strong form of the third law incorporates the collinearity (or centrality) condition, i"
        ],
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    },
    {
        "image_filename": "designv11_11_0002222_1.1576425-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002222_1.1576425-Figure7-1.png",
        "caption": "Fig. 7 Isothermal pressure and film thickness profiles at zero entrainment",
        "texts": [
            " Nevertheless, the pressure profile they obtained was in the traditional form with pressure peak and spike. They explained the dimple occurrence by using the squeeze effect. Messe\u0301 and Lubrecht @7# also showed the dimple phenomena in a working cycle of cam-tappet pair when the two surfaces move in opposite directions and also explained it by the squeeze effect. However, their dimple at zero entraining velocity is not as deep as the one in this work and their pressure and film thickness profiles are not in symmetrical form. Using the present program, Fig. 7 depicts the isothermal pressure and film thickness profiles at zero entrainment. In the figure, there does exist a shallow dimple in the central region of the oil film with very thin film thickness at the entrance but the pressure profile is still in the familiar form. These features roughly reveal that the squeeze effect does play a role in the formation of dimple at zero entrainment but not a deciding factor. Yang et al. @9# investigated the steady line contact TEHL with high slide-roll ratio and explained the dimple phenomenon by temperature-viscosity wedge mechanism"
        ],
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    },
    {
        "image_filename": "designv11_11_0002037_1.1510879-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002037_1.1510879-Figure1-1.png",
        "caption": "Fig. 1 \u201ea\u2026 Front view of brush seal depicting force system exerted by shaft onto bristle tip due to diametral interference, \u201eb\u2026 section view of annular front and back plate that constrain bristle pack, \u201ec\u2026 depiction of hypothetical free-body diagram in x-y plane, and \u201ed\u2026 geometry of deformed bristle illustrating length coordinate and fiber slope in local frame of reference.",
        "texts": [
            " Results are reported for a range of brush seal design parameters in order to provide a better understanding of the role that seal geometry, friction, and bristle flexural rigidity play in generating rotor contact force. @DOI: 10.1115/1.1510879# Recently, engineers that are engaged in the design of turbomachinery for propulsion and electrical power generation have made considerable progress in developing brush seals as a replacement for traditional labyrinth seals. This, in part, has been motivated by the need to improve the efficiency of turbomachinery as well as the need to reduce manufacturing cost and simplify the repair/ refurbishment of machine components. As shown in Fig. 1~a! and 1~b!, a brush seal consists of an array of fibers that are constrained between two annular plates. Fibers having flexural rigidity EI and length L are aligned at lay angle u, and project inward between the front and back plates. The inner diameter of the brush seal D f , is referenced from the undeformed filament tips, and is designed to interfere with the shaft/rotor of diameter Ds (.D f). Thus, when aligned concentrically, the radial interference D*(5(Ds2D f)/2) ensures uniform contact of filament tips along the rotor surface. This interference is an important design parameter for the brush seal and has widespread implications on seal performance including wear rate, resistance to leakage, and overall life of the seal/rotor system. As depicted in Fig. 1~b!, the brush seal is subjected to complex loading during actual operation. That is, the shaft can undergo eccentric rotation, and pressure changes between the successive stages of the turbine can give rise to aerodynamic filament loads, as gases move rapidly through the seal fibrous network. Additional aerodynamic load due to rotor-induced swirl may also occur during operation. At the same time, internal forces arise within the components of the seal due to interfilament contact as well as interaction between the fibers and the constraining surface of the back plate",
            " For illustration purposes, a free-body diagram of an arbitrary fiber located at the interior of the bristle pack is shown in Contributed by the Tribology Division of the THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for presentation at the ASME/STLE Tribology Conference, Cancun, Mexico October 27\u201330, 2002. Manuscript received by the Tribology Division February 14, 2002 revised manuscript received July 2, 2002. Associate Editor: J. A. Tichy. 414 \u00d5 Vol. 125, APRIL 2003 Copyright \u00a9 2 rom: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Term Fig. 1~c!. Thus, the candidate loads depicted in the x2y plane include interfilament contact forces P1 , P2 , . . . , Pn , distributed transverse load q (x2y) , bristle tip/rotor resultant contact force F res , rotor-induced swirl force Fsw , and the internal moment and shear reaction loads M and V , respectively, associated with the cantilever support. Generally, the overall effectiveness of the seal is measured by its ability to thwart leakage between successive stages of the turbine, impart minimal damage to the rotor surface, and meet life expectancy requirements that are consistent with turbine maintenance schedules",
            " At the same time, the precise location at which the bristle tip resides on the surface is unknown, and must be computed as an integral part of the solution. In order to avoid placing unnecessary restrictions upon the magnitude of the bristle tip deflection, the problem will be formulated in terms of nonlinear beam theory. This problem is closely related to previous work reported by Stango et al. @7,8# which examined the constrained deformation of a filament tip in contact with a rigid surface of prescribed geometry. The present contact problem is depicted in Fig. 1~a!, and consists of an initially undeformed bristle of length L oriented at fixed angle u with respect to the centerline of the seal. The shaft diameter Ds exceeds the diameter formed by the undeflected bristle tips D f . Thus, insertion of the shaft gives rise to the radial interference parameter D*, which causes the static normal filament tip force Fn . Subsequent rotation of the shaft gives rise to the shear force mFn at the filament tip due to kinetic friction and, therefore, the resultant force F res is inclined by the friction angle m as shown, and is subject to the condition that the bristle tip must be located on the surface of the shaft. Thus, if coordinate j denotes a point on the shaft surface, then requiring that the bristle tip be located along the shaft surface leads to the following: xj5~Rs1H*2D*!cos u2Rs cosS u1 j Rs D (1a) y j5Rs sinS u1 j Rs D2~Rs1H*2D*!sin u (1b) where Rs is the radius of the rotor, and H* is the radial filament length. As illustrated in Fig. 1~d!, the deformed configuration of the bristle\u2014or elastica\u2014can be readily described by the arc length coordinate s along the fiber, and the corresponding slope angle f, which in turn satisfies the Bernoulli\u2013Euler law: EIk5M (2) with k5 dF ds (3) where k and M refer to the bristle curvature and bending moment, respectively. Thus, based upon the force system shown in Fig. 1~a! the curvature-moment relation is EI df ds 5Fy~L*2x !1Fx~n~L*!2n~x !!. (4) Differentiating the above expression with respect to s, and recognizing that force components Fx and Fy and angle a are given by Fx5F res sin~a2m! (5a) Fy5F res cos~a2m! (5b) 416 \u00d5 Vol. 125, APRIL 2003 rom: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Term a590 deg2S u1 j Rs D (5c) along with dx/ds5cos f, dn/ds5sin f, leads directly to the governing equation for bristle deformation: d2f ds2 52 F res EI cos~a2m2f"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003818_robot.2006.1641883-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003818_robot.2006.1641883-Figure3-1.png",
        "caption": "Fig. 3. (a) maze: solid view, 6-DOF robot, and wire view. (b) walls: environment and serial robot (7 DOF). (c) hook.",
        "texts": [
            " \u2022 Connection pair selection \u2014 Connections were attempted between each node added to the roadmap and the k-closest (k = 10) nodes already there. \u2022 Node visibility (local planner)\u2014 Two nodes are visible if they can be connected by either the straight-line or the rotate-at-s (s=0.5) local planners [27]. We applied the five node generation methods to three different environments. The maze environment is composed of a series of tunnels, some of them are dead ends. The robot is a rigid body with 6 DOFs that has to go from the top to the bottom part of the maze. (Figure 3(a)) The serial walls environment is composed of five chambers divided by walls with small holes in them. The robot is an articulated 2-link manipulator with 7 DOFs. (Figure 3(b)). The hook environment is composed of two walls with narrow holes and the robot is a 6-DOF rigid body that can only traverse the narrow passages using translational and rotational motion. (Figure 3(c)). For each sampling method, nodes were added to the roadmap in an iterative fashion in ten independent runs using different seeds for the random number generator. Section V discusses the results obtained. Node classification. We extracted metrics after each sample was added and connected to the roadmap. In particular, each node was classified as one of the four types described in Section III-B. A node that cannot be connected to an existing roadmap component is a cc-create node. A node that causes a reduction of the number of components in the roadmap is a cc-merge node"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002382_a:1022159318457-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002382_a:1022159318457-Figure2-1.png",
        "caption": "Figure 2. Planar version",
        "texts": [
            " Note that \u03a0 and P can be computed from the total kinetic energy T of the body-fluid system: T = 1 2 (\u2126tJ\u2126+2\u2126tDv+ vtMv), where M and J are respectively the body-fluid mass and inertia matrices. In [5], the Hamiltonian structure of the dynamics of the underwater vehicle is described. We consider a neutrally buoyant, uniformly distributed, ellipsoidal vehicle moving in the vertical inertial plane and we neglect viscous effects. We denote by (x, z) the absolute position of the vehicle, where x is the horizontal position and z the vertical position. Let \u03b8 describe its orientation in this plane, so that q = (x, z, \u03b8), see Fig. 2. Under our assumptions, M and J are diagonal and D = 0 so that for our vehicle restricted to the plane T = 1 2 (I\u21262 + m1v 2 1 + m3v 2 3), where I is the body-fluid moment of inertia in the plane and m1 and m3 are body-fluid mass terms in the body horizontal and vertical directions, respectively. We assume that m1 = m3, i.e., the planar vehicle is not a circle. We choose the state vector to be w = (x, z, \u03b8, v1, v3,\u2126). Here \u2126 is the scalar angular rate in the plane. The equations of motion of this mechanical system are x\u0307 = cos \u03b8v1 + sin \u03b8v3, z\u0307 = cos \u03b8v3 \u2212 sin \u03b8v1, \u03b8\u0307 = \u2126, v\u03071 = \u2212v3\u2126 m3 m1 , v\u03073 = v1\u2126 m1 m3 , \u2126\u0307 = v1v3 m3 \u2212m1 I "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001732_bf01257995-Figure16-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001732_bf01257995-Figure16-1.png",
        "caption": "Fig. 16. Example of environment 2D U2.",
        "texts": [
            " Conclusion Through experimentation, we derive the existence of a critical number of vertices above which a reactualizing is quicker than modeling a new one, but on the contrary, beneath which a modeling proves better because it is quicker. This principle of model updating can be adapted to the robot evolution in a universe whose geometry it will explore and memorize. 2.3. APPLICATION TO 2D 1/2 2.3.1. Principle The displacement of a robot in a complex universe, constituted by plane, horizontal, and inclined surfaces, requires an adapted representation. Here we are still in a universe limited to 2D 1/2 consisting only of polyedral obstacles (for example, Figure 16). The principle of this method lies in decomposing the model into basic surfaces, in separately computing the representation of each of them, and then in reassembling the whole into a minimum amount of final grids. The first operation consists in decomposing our universe into two types of surfaces: - the planes (plane surfaces with a constant height), - the transitions (plane surfaces with a variable height). The eventual passage between plan and transition, or between transitions, depends on the relative and absolute slope of these surfaces. 2.3.2. C o n v e n t i o n s ~rij = 1 if there is a possibility of evolution between the plane i and the transition j (aij = 0 in the contrary case). ~rlj = 1 if there is a possibility of evolution between the transition i and the transition j (crij --- 0 in the contrary case) with i( ) j and 0-ij = ~rji. In the case of Figure 16, we have O'1,1 = 1, erl,2 + 0, 0-2,1 = 1,02, 2 = 1, and 0-12 = 0 - 2 1 = 1, Each decomposed surface will be modeled by the method explained above. Yet, the obtained models must conform to some rules [1]. Now the problem is to 'open' the edges which are likely to be crossed over. Given lij the number of cells representing the edges formed by the intersection of the transition j and the plan i (or transition j) . R u l e : One shows the accessibility of a surface by making the (lij - 2) central cells constituting the border likely to be crossed over",
            " Approach criterions Rx, Ry and Rz, according to relative actual position cell/aim cell will give GRID MODELING OF ROBOTIC CELLS 219 us the grids, lines and columns of our model on which the mask operation has to be made. Given rc(i,j, k), the cell in which the mobile lies and re(u, v, w) the aim cell. The following re(i, j, k) is defined by the criterion of the speediest approach to the aim. Case Approach i, j, k u > i R x = l u < i R x = - 1 i = i + Rx u = i R x - O v > l R y = l v < j R y = -1 j = j + Ry v ~ - j R y = O w > k R z = 1 w < k R z = - I z = z + R z w = k R z = O 220 V. B O S C H I A N A N D A. P R U S K I Example o f application Let us consider the example represented by Figure 16. The modeling procedure will give the two grids below. (P1, P 2, T1,72) are represented on the grid 0, (P3, P4, T3) are represented into the grid 1. mmmmmmmmm W mmnmmmmmnmml \u2022 m [] | \u2022 [] \u2022 [] \u2022 m n i i l i l l mmmmmm [] mmmmmm \u2022 m mmmmmmmmm m 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o : P r x : Pa ~ d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 mid 1 We find the position of the robot (Pr) on column 10, line 9 of grid 0 and the position of the aim (Pa) on column 13, line 6 of the grid 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002284_analsci.19.289-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002284_analsci.19.289-Figure1-1.png",
        "caption": "Fig. 1 Schematic diagram of the chip-based flow cell (a) and top view of the PDMS membrane (b). B, microbeads; F, porous filter; G, optical glass; I, inlet port; M, multistrand bifurcated optical fiber; O, outlet port; P, plexiglass; R, PDMS rubber membrane.",
        "texts": [
            " Both the syringe pump and the distribution valve were controlled by a personal computer using software written in Visual Basic. A Model RF-540 spectrofluorometer (Shimadzu, Kyoto, Japan) was used for recording spectra and measuring fluorescence intensity. A chart recorder (Dahua Instrument Co., Shanghai, China) was used to record the peak traces. The chip-based flow-through cell was a specific modification mode of the sandwich design described in Ref. 23. It was a four-layer structure as shown in Fig. 1a. The top and bottom Plexiglass wafers (60 mm \u00d7 50 mm \u00d7 3 mm) were used to accommodate inlet and outlet ports at the top and to fix the fiber-optical probe at the bottom, respectively. Between the two Plexiglass wafers, a PDMS membrane (30 mm \u00d7 20 mm \u00d7 0.7 mm) with a cut-through channel (10 mm \u00d7 1.8 mm) and a porous filter (pore diameter 20 \u00b5m), and an optical glass wafer (30 mm \u00d7 20 mm \u00d7 1 mm) were held in place (Fig. 1b). Four screws were applied to tighten the four-layer structure so that no leakage would happen when solution or beads suspension was delivered to pass through the cell. With this modification, the flow-through cell was coupled to the fiber-optical probe via the optical glass window, resulting in less stray light and background fluorescence. A multistrand bifurcated optical fiber (Chunhui High Tech. Co., Nanjing, China), composed of 32 fibers (core diameter of 80 \u00b5m) for incident light and 32 fibers for emission light, was used to couple the chip-based flow-through cell to a spectrofluorometer, as described in detail in the section of Method development"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002028_978-1-4613-9030-5_37-Figure37.4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002028_978-1-4613-9030-5_37-Figure37.4-1.png",
        "caption": "Figure 37.4: Raibert's one-legged hopping machine. The length of the leg is about 0.5 m. (From Raibert (1986); reprinted with permission.)",
        "texts": [
            " It was a relaxation oscillator; once it was running, we had no control over it beyond tuming the gas supply on and off. 37. McMahon; Spring-Like Properties of Muscles and Reflexes in Running 581 37.2.2 Raibert's Robots Marc Raibert and his students have built run ning machines with one, two, and four legs, all under computer control, all with pneumatic leg springs enclosing a fixed volume of air (Raibert, 1986). The most extraordinary thing about these machines is that they balance themselves while running. A diagram of Raibert's one-legged hopping machine is reproduced in Figure 37.4. The body of the machine is an aluminum frame containing hydraulic actuators for flexion-extension motions of the hip joint in two planes, air valves, gyro scopes, and computer interface electronics. The large computer that actually controls the machine sits in its own air-conditioned room many feet away; it communicates with the machine via an umbilical cord that dangles from the ceiling. The umbilical also brings in hydraulic power. The driver stands somewhere out of harm's way and controls the machine by moving a joy - stick that commands changes in velocity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001870_s0389-4304(00)00044-8-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001870_s0389-4304(00)00044-8-Figure2-1.png",
        "caption": "Fig. 2. Ring gap position of each ring.",
        "texts": [
            " Standard rings were used as the test top (compression) ring and the second (scraper) ring, while three types of oil control rings were used. Namely, a standard type oil control ring A with 30 N tangential tension and 4 mm width, an oil control ring B with the same shape as the oil control ring A but with a di!erent tangential tension of 15 N, and another oil control ring C with 2 mm width and 30 N tangential tension, as shown in Table 2. A rotation stopper was installed to the piston so that individual ring gaps were positioned as shown in Fig. 2, with the gap of each ring angled about 903 against the OFT measuring point. Grooves for detection of OFT were provided at the upper portion of the piston skirt as shown in Fig. 3. Stepped rings were used for the grooves and the compres- sion/scraper rings in motoring operation for the veri\"cation of OFT. Fig. 4 shows the OFT measured results at individual sensors where the standard piston ring set (with the oil control ring A) was used. The measured data of 10 continuous cycles are superimposed in each diagram"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003889_3-540-29461-9_55-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003889_3-540-29461-9_55-Figure1-1.png",
        "caption": "Fig. 1. The 1-DOF pantograph-leg: (a) a scheme; (b) the built prototype at LARM",
        "texts": [
            " Basic considerations for a leg design can be outlined as follows: the leg should generate an approximately straight-line trajectory for the foot with respect to the body [7\u201311]; the leg should have an easy mechanical design; if it is specifically required it should posses the minimum number of DOFs to ensure the motion capability. Among many different structures, we have considered a leg mechanism that is based on a Chebyshev mechanical design [12, 13]. The proposed leg mechanism is schematically shown in Fig. 1. In particular, its mechanical design is based on the use of a Chebyshev four-bar-linkage, a five-bar linkage, and a pantograph mechanism. For such mechanism, the leg motion can be performed by using 1 DOF. The leg has been designed by considering compactness, modularity, light weight, reduced number of DOF as basic objectives to achieve the walking operation. Furthermore, the mechanical design has been conceived to built a low cost prototype, as shown in Fig. 1. Numerical and experimental results in [15] show that good kinematic features can be obtained when points C and P in Fig. 1 are not coincident. In particular, it has been shown in [14, 15] that better features can be obtained if the transmission angles \u03b31 and \u03b32 have suitable large values. Kinematic and Dynamic analyses have been carried out in order to evaluate and simulate the performance and operation of the leg system. In particular, the mechanical design is based on the Chebyshev design [12, 13]. Three reference systems have been considered, as shown in Fig. 2. The position of point B with respect to CXY frame can be evaluated as a function of the input crank angle \u03b1 as XB = \u2212a+ n cos\u03b1+ (c+ f) cos \u03b8; YB = \u2212n sen\u03b1\u2212 (c+ f) sen \u03b8 (1) where \u03b8 = 2 tan\u22121 sen\u03b1\u2212 (sen2\u03b1+B2 \u2212D2)1/2 B +D (2) Coefficients B, C and D can be derived by the closure equation of the mechanism"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002301_a:1023275502000-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002301_a:1023275502000-Figure1-1.png",
        "caption": "Figure 1. A planar blimp with rotating thruster.",
        "texts": [
            " Given G-invariant X = (g\u03be(r), v(r)) \u2208 D and Y = (g\u03b7(r),w(r)) \u2208 D , the symmetric product associated with \u2207 is \u3008X : Y \u3009 = g ( Asym(\u30085 : 9\u3009I )\u2212 I\u0303\u22121 L\u0303 s +A (\u3008v : w\u30096\u0303 \u2212 6\u0303\u22121 S\u0303 s ) \u3008v : w\u30096\u0303 \u2212 6\u0303\u22121 S\u0303 s ) , (9) where 5 = \u03be +A(r)r\u0307, 9 = \u03b7 +A(r)r\u0307 and L\u0303 s = \u2212D(I 5\u0303)(\u00b7, w)\u2212 \u2212D(I9)(\u00b7, v)+ I (A\u0303v, \u03b3\u00b7w \u2212 [\u00b7, \u03b7])+ I (A\u0303w, \u03b3\u00b7v \u2212 [\u00b7, \u03be ]) \u2208 g D\u2217 S\u0303 s = I (9,B(v, \u00b7))+ I (5,B(w, \u00b7))+ I (A\u0303w,B(v, \u00b7))+ + I (A\u0303v,B(w, \u00b7))\u2212D(I9)(A\u0303\u00b7, v)\u2212D(I5)(A\u0303\u00b7, w)+ +DI (\u00b7)(5+ A\u0303v,9 + A\u0303w)\u2212DI (\u00b7)(A\u0303v, A\u0303w) \u2208 T \u2217M, with \u3008\u00b7 : \u00b7\u30096\u0303 the symmetric product defined by \u22076\u0303. Planar model for a blimp system. Consider a rigid body moving in SE(2) with a thruster to adjust its pose (see Figure 1). The original motivation for this problem is the blimp system developed in [51] restricted to the horizontal plane. The control inputs are the thruster force F 1 and a torque F 2 that actuates its orientation with respect to the body axis. The acting point of the thruster is assumed to be located along the body\u2019s long axis, at a distance h from the center of mass. The configuration of the blimp is given by (x, y, \u03b8, \u03b3 ) \u2208 SE(2) \u00d7 S 1, where (x, y) is the position of the center of mass, \u03b8 is the orientation of the blimp with respect to the fixed basis {Xf , Y f } and \u03b3 is the orientation of the thrust with respect to the body basis {Xb, Y b}"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000265_0022-0728(95)04432-9-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000265_0022-0728(95)04432-9-Figure2-1.png",
        "caption": "Fig. 2. Cyclic voltammograms for a poly MB-laponite-LDH electrode in deareated 0.1 M phosphate buffer solution (pH 7.0) (a) in the absence and (b) in the presence of 1 mM NADH; scan rate 2 mV s- 1.",
        "texts": [
            " The growth of a polymeric MB film within the clay-enzyme material was illustrated by the appearance of new peaks which increased continuously with successive potential scans. However, the exact reaction mechanism of the polymer formation remains to be clarified [ 19]. The cyclic voltammograms of the resulting poly MBlaponite-enzyme electrodes depict an identical electro- chemical behaviour whatever the immobilized dehydrogenase. This behaviour is characterized by two distinct quasi-reversible redox couples at El~ 2 = --220 and - 4 0 mV (Fig. 2). These two redox systems have been observed already and it has been reported that they correspond to monomer-type and polymer redox activities respectively [10]. Recently, it has been suggested that the more negative redox couple could be due to the activity of MB monomers merely adsorbed on the polymer itself [20]. Thus, the redox system observed at - 2 2 0 mV with the poly MB-laponite-enzyme electrodes could be attributed to MB monomers adsorbed strongly within the interlamellar space of the clay film, the MB polymer blocking their desorption",
            " As reported previously for polypyrrole-clay modified electrodes [21,22], the oxidative polymerization of the incorporated MB monomers results in a composite material which is mechanically more stable than the laponite clay coating. This stability increase was corroborated by the absence of release in the aqueous electrolyte of immobilized dehydrogenases. The electrocatalytic properties of the MB-laponite-enzyme electrodes towards NADH oxidation have been investigated by cyclic voltammetry in the absence and presence of 1 mM NADH. In the presence of 1 mM NADH, Fig. 2 shows a marked increase in anodic and a decrease in cathodic currents of the MB polymer redox couple. As expected these effects indicate an electrocatalytic behaviour of the poly MB-laponite-enzyme electrode. Because the MB polymer constitutes an efficient means of NADH oxidation at decreased potentials, the analytical capabilities of the bioelectrodes based on lactate dehydrogenase (LDH) and alcohol dehydrogenase (ADH) have been investigated for the determination of lactate and ethanol respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001686_1.1567749-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001686_1.1567749-Figure2-1.png",
        "caption": "FIG. 2. Views of the control volume ~elementary cell! where balance equation are applied.",
        "texts": [
            " For these steady state conditions, the cutting velocity is given. Local angle of inclination and drilling velocity have therefore to be determined by using a set of coupled equations which have allowed for local mass, pressure, and power balance. In the following sections we will derive each term of all required equations and will point out the fundamental and physical aspects of each equation. Similarly to hydrodynamical issues, we have to determine a control volume where balance equations will be applied ~Fig. 2!. This control volume is an elementary volume of the molten layer. Mass and power transfers will be expressed through it. Regarding mass balance equation we have to take into account every gain and loss of material that the control volume is going to experience. Let us consider the control volume labeled i, located in the middle of the cutting front, the global mass balance equation can be written rsvd~ i ! r\u0304 k~ i !L1rmvmz~ i21 !d~ i21 !rk~ i21 ! 5rmvm~ i !d\u0304~ i !L1rmvmz~ i !d\u0304~ i !rk~ i !1rmvv~ i "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001744_1.1332395-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001744_1.1332395-Figure5-1.png",
        "caption": "Fig. 5 Surface temperature rise at u\u00c41.0\u201et\u00c45.190\u00c310\u00c05 s\u2026, jump start up",
        "texts": [
            "asme.org/about-asme/terms-of-use Downloaded F Jump Start Up. The jump start up process refers to the condition when the rolling speed is increased from zero to the desired speed in one step under full load. For a slide to roll ratio of S 50.2, Fig. 4 shows the temperature rise on the two contacting surfaces for the first time step (u50.2). As the lubricant film is just starting to form at the left, the temperature rise at this moment is mainly due to the friction generated by the solid contact. Figure 5 illustrates the temperature rise at u51.0, when the lubricated contact is formed over about half of the Hertzian contact region. Because the friction coefficient for lubricated contact is much smaller than that for solid contact, the temperature rise in the lubricated contact region is much smaller than the temperature rise in the solid contact region. Figure 6 demonstrates the temperature rise at the last time step before solid contact disappears (u51.8). As the hot region is moving out of the contact area and new hot spot is generated at the solid contact area, a saddle shaped temperature rise distribution is formed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000765_s0043-1648(02)00108-4-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000765_s0043-1648(02)00108-4-Figure1-1.png",
        "caption": "Fig. 1. Main deformations of wheelset: (a) bending deformation; (b) torsinal deformation; (c) oblique bending deformation and (d) torsional deformation.",
        "texts": [
            " In other words, the relations between the elastic deformations and the traction in a contact patch of wheel/rail can be expressed with the formula of Bossinesq and Cerruti in the theories. In practice, when a wheelset is moving on track, the elastic deformations in the contact patch are larger than those calculated with the present theories of rolling contact. It is because the flexibility of wheelset/rail is much larger than that of elastic half space. Structure elastic deformations (SED) of wheelset/rail caused by the corresponding loads are shown in Figs. 1 and 2. The bending deformation of wheelset shown in Fig. 1a is mainly caused by vertical dynamic loads \u2217 Corresponding author. Tel.: +86-28-7600882; fax: +86-28-7600868. E-mail address: xuesongjin@263.net (X. Jin). of vehicle and wheelset/rail. The torsional deformation of wheelset described in Fig. 1b is produced due to the action of longitudinal creep forces between wheels and rails. The oblique bending deformation of wheelset shown in Fig. 1c and the turnover deformation of rail shown in Fig. 2 are mainly caused by lateral dynamic loads of vehicle and wheelset/rail. The torsional deformations with the same direction of rotation around the axle of wheelset (see Fig. 1d), available for locomotive, are mainly caused by traction on the contact patch of wheel/rail and driving torque of motor. Up to now very few published papers have discussions on the effects of the SED on creepages and creep forces between wheelset and track in rolling contact. In fact, the SED of wheelset/rail mentioned above runs low the normal and tangential contact stiffness of wheel/rail. The normal contact stiffness of wheel/rail is mainly lowed by the subsidence of track. The normal contact stiffness lowed doesn\u2019t affect the normal pressure on the contact area much",
            " Finite element method is used to determine the SED of them. According to the relations of the SED and the corresponding loads obtained with FEM, the influence coefficients expressing elastic displacements of the wheelset and rail produced by unit density traction acting on the contact area of wheel/rail are determined. The influence coefficients are used to replace some of the influence coefficients calculated with the formula of Bossinesq and Cerruti in Kalker\u2019s theory. The effect of the bending deformation of wheelset shown in Fig. 1a and the crossed influences among the structure elastic deformations of wheelset and rail are neglected in the study. The numerical results obtained show marked differences between the creep forces of wheelset/rail under two kinds of the conditions that effects of the SED are taken into consideration and neglected. In order to make better understanding of effects of the SED of wheelset/track on rolling contact of wheel/rail it is necessary that we briefly explain the mechanism of reduced contact stiffness increasing the ratio of stick/slip area in a contact area under the condition of unsaturated creep-force",
            " 4b it is known that the tangent traction F1 reaches its maximum F1max at w1 = w\u2032 1 without considering the effect of u0 and F1 reaches its maximum F1max at w1 = w\u2032 1 with considering the effect of u0, and w\u2032 1 < w\u2032\u2032 1 . u0 depends mainly on the SED of the bodies and the traction on the contact area. The large SED causes large u0 and the small contact stiffness between the two bodies in rolling contact. That is why the reduced contact stiffness increases the ratio of stick/slip area of a contact area and decreases the total tangent traction under the condition of the contact area without full-slip. In order to calculate the SED described in Fig. 1b\u2013d, and Fig. 2, discretization of the wheelset and the rail is made. Their schemes of FEM mesh are shown in Figs. 5, 7 and 9. It is assumed that the materials of the wheelset and rail have the same physical properties. Shear modulus: G = 82,000 N/mm2, Poisson ratio: \u00b5 = 0.28. Fig. 5 is used to determine the torsional deformation of the wheelset. Since, it is symmetrical about the center of wheelset (see Fig. 1b), a half of the wheelset is selected for analysis. The cutting cross section of the wheelset is fixed, as shown in Fig. 5a. Loads are applied to the tread of the wheelset in the circumferential direction, on different rolling circles of the wheel. The positions of loading are, respectively, 31.6, 40.8 and 60.0 mm, measured from the inner side of the wheel. Fig. 6 indicates the torsional deformations versus loads in the longitudinal direction. They are all linear with loads, and very close for the different points of loading",
            " The numerical results obtained show the differences of the creep forces of wheelset/rail under two kinds of conditions that effects of structure elastic deformations of wheelset/rail are taken into consideration and neglected. (3) The structure elastic deformations of wheelset and track run low the contact stiffness of wheelset and track, and reduce the creep forces between wheelset and track remarkably under the conditions of unsaturated creep force. Therefore, the situation is advantageous to the reduction of the wear, rolling contact fatigue of wheel and rail. (4) In the study the effect of the bending deformation of wheelset shown in Fig. 1a is neglected, and the crossed influence coefficients AIiJj(i = j ; i, j = 1, 2) are not revised. So, the accuracy of the numerical results obtained is lowed. In addition, when the lateral displacement of center of the wheelset, y > 10 mm, the flange action takes place. In such situation the contact angle is very large and the component of the normal load in the lateral direction is very large. The large lateral force causes track and wheelset to produce large structure deformations, which affect the parameters of contact geometry of wheel/rail and the rigid creepages"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000507_027836499501400207-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000507_027836499501400207-Figure3-1.png",
        "caption": "Fig. 3. Quasistatic pushing. The d~fferential support frictional forces acting at points on the ring are indicated by arrows for the velocity center shown. The integral of these differential frictional forces exactly balances the applied force f.",
        "texts": [
            " Similarly, slider accelerations from rest will sometimes be represented as acceleration centers. Now suppose that the slider motion is slow enough that inertial forces are negligible compared with support friction. Then a solution obtains whenever the pushing force is exactly balanced by the support frictional force. The support frictional force at each support point directly opposes the motion of the support point, and the integral of these differential forces over the support yields the total support frictional force. Consider Figure 3, for example. For the velocity center shown, the frictional support force acting on the slider is precisely balanced by the pusher force f passing through the contact. For a pusher velocity vp equal to the rod endpoint velocity vs, and a large enough coefficient of friction 11, we have a solution. There is nothing unusual about this solution. Because the pusher velocity v~ is directed into the slider, we have pushing, not pulling. But consider the example of Figure 4, where the applied force passes closely on the other side of the ring center"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002365_robot.1994.350994-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002365_robot.1994.350994-Figure3-1.png",
        "caption": "Figure 3: Variation of wc with different camera positions (planar robot).",
        "texts": [
            " For this situation we will analyze how the manipulability and observability vary for different positions of the active camera and the trajectory of the camera. We use the notation introduced earlier and omit the details of the derivation for brevity. z . l2 + 1 il el + i2 cos(el + e2) J , = [ -l1 sin el - l2 sin(O1 + 02) -12 sin(& + 02) The manipulability, Wr = Idet(J,)I = 11121 sin821 The Observability, wv = Idet(J,)I = & For this example we consider only the non-redundant case where both J, and J, are square matrices, thus we simplify Equation 20 to combine the observability and manipulability, giving Fig. 3 shows the variation of wc with the two camera parameters R (varied from 30 to 40 unit distance) and 0 varied from 0 to n/3, for a particular pose of the robot 02 = r/2; I1 = 12 = 10; f = 1). In this simple caae we can see that observability would increase as either R or 8 decreases. A singular position is reached when the 0 = ~ / 2 , or the the axis of the camera lies on the X - Y plane. Fig. 4 shows the variation of the combined manipulability and observability measure we against a variation of the camera parameter 8 (hm 0 to r / 3 , with fixed R = 100) and a circular trajectory of the end effector of the robot as traced by changing 82 @om 0 to T ) , with O1 h e d "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003779_s11044-006-9028-0-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003779_s11044-006-9028-0-Figure5-1.png",
        "caption": "Fig. 5 A spherical 4-bar mechanism",
        "texts": [
            " Multiplication of the matrix L5 and L6 with the respective selector in Table 2 yields two systems of respectively five constraints. Application of the SVD to the matrices C5 and C6 yields a system of, respectively, one and two kinematic constraints U\u03045 P5 L5q\u0307 = 0 U\u03046 P6 L6q\u0307 = 0. This is the overall system of three linear independent kinematic constraints for the gener- alized velocities q\u0307 = (q\u03071, q\u03072, q\u03073, q\u03074). Springer 4.3 Spherical 4-bar mechanism The revolute joint axis of the spherical 4-bar mechanism in Figure 5 intersect in a common point. Any choice of cut-joint imposes the five cut-joint constraints for revolute joints in Table 1. It is now not so obvious that only two of them are independent. Regardless of the chosen cut-joint, the constraint algebra has dimension d = dim clos D\u03b1 = 3. For simplicity, the revolute joints are placed at a unit distance from the center of rotation, i.e., the intersection point of the axes. J4 is selected as cut-joint, so that the FL 4 and the cotree H are as in Figure 5. Then, the Jacobian in Equation (19) is L4 = \u239b\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239d \u2212 1 9 \u221a 2 (1 + 5c3 + \u221a 3s3) \u2212 1 27 \u221a 2 (1 + 5c3 + 9s1s3 + \u221a 3 ((c3 \u2212 4)s1 + s3) + c1(7c3 \u2212 7 \u221a 3s3 \u2212 4)) \u221a 2 3 1 9 ( \u221a 6 (1 \u2212 c3) \u2212 3 \u221a 2s3) 1 27 ( \u221a 6 (1 \u2212 c3 \u2212 c1(4 + 5c3) \u2212 3s1s3) + 3 \u221a 2 (s13 \u2212 4s1 \u2212 s3)) \u2212 \u221a 2 3 1 9 (4c3 \u2212 4 \u221a 3s3 \u2212 1) 1 27 (4c3 \u2212 1 + 4 \u221a 3((1 + 2c3)s1 \u2212 s3) \u2212 4c1(4c3 \u2212 1 + 2 \u221a 3s3)) 1 3( 1 3 \u221a 2 (1 \u2212 c3 \u2212 \u221a 3s3) ) 1 9 \u221a 2 (1 \u2212 4c1 \u2212 4c1\u22123 \u2212 c3 \u2212 c1+3 \u2212 \u221a 3 (4s1 + s3 \u2212 s1+3)) \u2212\u221a 2 1 9 \u221a 2( \u221a 3 (1 + 5c3) + 3s3) 1 27 (3 \u221a 2 ((c3 \u2212 4)s1+(1\u22127c1)s3)+\u221a 6 +(1 + 5c3 + c1(7c3 \u2212 4) + 9s1s3)) \u2212 \u221a 2 3 0 0 0 \u239e\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u23a0 with sa+b := sin (qa + qb), etc",
            " It is not clear by inspection that clos D4 is equivalent to the algebra of spherical motions so (3). Composing C4 from d = 3 independent vectors from the involutive closure, or just using the complete set in Equation (25), and with the selector P4, in Table 2 the SVD yields U\u0304 = ( \u22120.25 0.433013 0.75 0.433013 0.0 0.433013 0.25 0.433013 \u22120.75 0.0 ) . The remaining two kinematic constraints are obtained from Equation (28). These constraints are independent and the mechanism has the DOF 1. The configuration in Figure 5 is singular, and the constraints (28) are redundant (only in the singular configuration) in Springer accordance with the mechanism\u2019s kinematics. An advantage when using the involutive closure basis is that the matrix C4 is well conditioned and its decomposition is numerically stable. 4.4 X-mechanism Also for the X mechanism in Figure 6, the constraint algebra is not obvious. Assume for simplicity the side lengths a = b = \u221a 2. Evaluating D\u03b1 for all four joints shows that always d = dim clos D\u03b1 = 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001624_robot.1996.506582-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001624_robot.1996.506582-Figure11-1.png",
        "caption": "Figure 11: The region for rotation",
        "texts": [
            "269-279, 1989 Conditions (2) and (3) Condition (2): Collision avoidance The distal link is most likely to interfere with the object. This paper considers only its collision with the edge on which it exerts a force. The condition that the distal link does not interfere with the edge is given by If2 - CrLl > n/2 (16) where CYL is the angle of the distal link from the x-axis (see Fig.10). slip is substantially pure rotational. Hence we assume that when 1 > 10 =(given constant), the slip is pure rotational where I is the distance from the axis A to the line of the action of f \u2019. The hatched region in Fig.11 is the region of the fingertip of the third finger where the rotation takes place about the axis A. Let n R and nL be the outer normals of right and left edges of the friction cone, respectively. The hatched region is given by nRTx > 10, or, nLTx > lo B Numerical method for calculating workspace 1. Find a rectangle as small as possible which encloses W . Divide the rectangle into small cells with required precision. 2. For a reference point of each cell, typically center of the cell, check whether it is reachable by solving inverse kinematics and check also the conditions (2) and (3)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002299_027836402761393487-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002299_027836402761393487-Figure2-1.png",
        "caption": "Fig. 2. Model of the system.",
        "texts": [
            " We show that the joint trajectory can be obtained uniquely by assuming quasi-static motion of the object (Assumption 1). In the next step, we plan the trajectory of contact coordinates where they finally converge to the desired values. In this stage, we propose a method for trajectory planning by combining the trajectory of two equilateral triangles as a locus of contact points on the object surface. This method can be applied for a non-spherical object. For a spheroidal object, we show that any contact configurations can be finally achieved within the limit of CSR (Theorem 2). Figure 2 shows the model where an object is put on a plate attached at the tip of a manipulator. We specify the following definitions: R: Coordinate frame fixed at the base. Y : Coordinate frame fixed at the center of gravity of the plate (Y = A) and the object (Y = O). CY : Contact frame of the plate (Y = A) and the object (Y = O) whose origin is always at the point of contact. LY : Local frame fixed relative to Y which coincides with CY at time t where Y = A,O. pY \u2208 R3: position vector of the origin of X with respect to R where Y = A,O"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001499_20.877692-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001499_20.877692-Figure1-1.png",
        "caption": "Fig. 1. 5th harmonic magnetic force vectors applied to the SRM structure.",
        "texts": [
            " After the velocity calculation in different points on the motor surface with the 3D finite element method, the noise emitted by the motor is evaluated. In order to evaluate acoustic noise applying BEM, velocities boundary conditions are generated and applied to a boundary elements mesh which represents the electric machine surface. However, for analytical acoustic noise calculation, a mean value is used. The calculation of noise applying BEM is the main contribution of this paper. Comparison between calculated and measured results are given for a 8/6 poles Switched Reluctance Motor (SRM) shown in Fig. 1. Manuscript received October 25, 1999. C. G. C. Neves, R. Carlson, N. Sadowski, and J. P. A. Bastos is with the GRUCAD/EEL/CTC/UFSC, P. O. Box 476, Florian\u00f3polis, SC, 88040-900 Brazil (e-mail: guilherm@grucad.ufsc.br). N. S. Soeiro is with the DEM/CT/UFPA, Bel\u00e9m, PA, 66000-00 Brazil. S. N. Y. Gerges is with the Vibrations and Acoustic Lab./MEC-CTC/UFSC, Florian\u00f3polis, SC, 88040-900 Brazil. Publisher Item Identifier S 0018-9464(00)06778-9. The Maxwell Stress Tensor is used in this work to calculate the magnetic pressure as follows [1]: (1) where is the permeability of the air, is the vector normal to iron and is the air side magnetic induction. To simplify the problem, the force densities over each stator tooth are integrated and supposed acting concentrated in a point in the center of the inner surface of this tooth. After an harmonic decomposition, the calculated mechanical forces obtained with 2D electromagnetic calculations are applied in the 3D structural representation of the motor, supposing that they act at equidistant plans through the axial direction, as shown in Fig. 1. In the same figure the magnetic force vectors corresponding to the th force harmonic are presented. With the forces and the 3D mechanical model, the forced vibrations are obtained using Modal Superposition Method. In this method the response of a continuous structure to any force can be represented by the superposition of the various responses in their individual modes. These responses can be nodal displacements, velocities and accelerations. This method requires a natural response calculation prior to further solution steps [4]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002375_bf00288431-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002375_bf00288431-Figure2-1.png",
        "caption": "Fig. 2. Sketch of phase plane for (4.5). Note that the condition (2.6c) implies p < l",
        "texts": [
            "2b) with boundary conditions (4.1) where, now, n = n(x) and u = u(x). We can integrate (4.2a) once and use (4.1) to get dn d2u O ~xx +~n~x2 = 0, which gives n = C exp, D dx]' (4.3) where C is such that ~ n dx = no, the total cell number. Substituting this expression for n into (4.2b) we have 1 - ~ C e x p \\ Ddx] l q D ~-~x~J~x2+SU ~xx-1 =0 . (4.4) Setting p = du/dx, (4.4) may be written as a pair of first order differential equations, namely, du dxx = P ' (4.5a) dp su(p - 1) - - = . (4.5b) dx 1 - - z C e -~p/~ 1 + - ~ - ~ p Figure 2 illustrates the phase plane for system (4.5). From this figure we can deduce the possible steady states. For example, the trajectory that starts at A, at x --0 and comes back to A at x = 1 automatically satisfies the boundary conditions because d2u dp u =0 , d x 2 - d x - O and dn 0 dxx-- D~x2 exp ~, Ddx] ' and is therefore a possible steady state. It is sketched in Fig. 3. Clearly, if the trajectory is traversed m times we get m humps for the cell density n(x). These solutions are similar to those computed numerically in [8] for the time dependent problem for a more generalized system than the one we are studying here"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003524_tmag.2005.854863-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003524_tmag.2005.854863-Figure6-1.png",
        "caption": "Fig. 6. SeveralB\u2013H hysteresis loops under excitation with minor loops using loss estimation.",
        "texts": [
            " For the major loop period , we get the value of equivalent to and obtain the losses with the value at two induction points nearest by interpolation from the loss data without any minor loops as in Fig. 4. We estimate from the two loss data by supposing that is proportional to , where is a constant in the narrow induction region as in Fig. 5. is obtained by a similar procedure concerning the minor loop period , and is obtained as the sum of and . Table I shows the experimental and predicted loss values under several excitations as shown in Fig. 6. Less than 4% error has been obtained. The TABLE I EXPERIMENTAL AND PREDICTED LOSSES UNDER SEVERAL EXCITATIONS Fig. 7. Magnetic losses in the minor loop w as a function of the minor loop position b . In this experiment, the absolute value of the induced voltage is constant as shown in (a). cause of errors would be the loss increase due to biased magnetization [4]. The minor loop losses depend on the minor loop position as shown in Fig. 7. We can estimate the losses with some minor loops less than 2% by compensation of the minor loop position as shown in Table I"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001213_s0925-4005(97)00270-0-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001213_s0925-4005(97)00270-0-Figure1-1.png",
        "caption": "Fig. 1. Schematic drawing and cross-sectional view of either the thick-film amperometric transducer or the amperometric GOD biosensor.",
        "texts": [
            " Once homogenized the composite\u2019s viscosity was adjusted with cyclohexanone. Used a polyurethane squeegee, each of the resulting composite pastes were printed onto a glass fibre circuit board on which ten copper lines 1\u00d730 mm were patterned by a conventional photolithographic process. The printed layer was cured for 72 h at 40\u00b0C. Finally the copper lines were covered by a layer of epoxy diacrylate (Ebecryl 600, UCB Chemicals) and exposed through a mask under UV. Thus leaving a graphite-epoxy working area of 12 mm2 and a contact pad (Fig. 1). The transducers were stored dry at room temperature. The same transducer fabrication process explained above was used to glucose biosensor construction. The GOD-graphite-epoxy paste was prepared by simple dispersing graphite powder and GOD in Epo-Tek H77 epoxy resin. Once homogenized the biocomposite be- fore printing, the viscosity was adjusted with cyclohexanone (Table 1). The printed biosensors were stored dry at 4\u00b0C. The resulting glucose biosensor based on the prepared biocomposites was characterized through the selective biocatalytic generation of hydrogen peroxide by the enzyme GOD"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001096_305-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001096_305-Figure2-1.png",
        "caption": "Figure 2. The elementary load on the bearing surface.",
        "texts": [
            " (16) Integrating equation (14) and taking into account the boundary condition (10), one obtains p(x, t) = B(x, t) + [A(x, t) \u2212 Ao](pi \u2212 Bi) \u2212 [A(x, t) \u2212 Ai](po \u2212 Bo) Ai \u2212 Ao (17) where A(x, t) = \u222b dx Rh3f (l, h) At(x, t) = \u222b R \u2202h \u2202t dx D(x, t) = \u222b RR\u2032F(l, h) dx Dt(x, t) = \u222b At(x, t) Rh3f (l, h) dx B(x, t) = 3j\u03c1\u03c92 10 D(x, t) + 13\u00b5Dt(x, t) F (l, h) = g(l, h) f (l, h) \u2212 40 ( l h )2 Bi = B(xi, t) Bo = B(xo, t). (18) For bearings of the synovial joints the rotational inertia may be neglected (j = 0) and the lubricant film is purely squeezed. Therefore the solution of equation (14) satisfying the condition of symmetry: \u2202p \u2202x = 0 for x = 0 (19) is given by the formula p = po + 12\u00b5[Dt(x, t) \u2212 Dto]. (20) The load capacity of the bearing is given by N = \u03c0R2 i pi + 2\u03c0 \u222b xo xi pR cos\u03b2 dx. (21) The sense of the angle \u03b2 arises from figure 2. Let us consider the simulation of the squeeze-film behaviour of a human joint whose geometry is shown in figure 3. The articulation of the joint is modelled as the case of a nonspinning spherical rotor approaching a hemispherical bearing with the velocity \u2202h/\u2202t . Using the nondimensional parameters h\u2217 = h C = 1 \u2212 \u03b5 cos\u03d5 l\u2217 = l C (22) which are h\u2217 = 0 (1), l\u2217 = 0 (10\u22121) we can present the auxiliary function (given by equation (15)) in a simpler form: f (l\u2217, h\u2217) \u2248 1 \u2212 12 ( l\u2217 h\u2217 )2 . (23) This form of f permits us to calculate the pressure distribution and the load capacity which are given by the formulae (for po = 0) p\u2217 = pC2 \u00b5R4 r \u03b5\u0307 = 3 \u03b5 { 1 (1 \u2212 cos\u03d5)2 \u2212 1 + 6l\u2217 \u00d7 [ 1 (1 \u2212 cos\u03d5)4 \u2212 1 ]} (24) N\u2217 = NC2 \u00b5R4 r \u03b5\u0307 = 6\u03c0 \u03b53 { \u03b5 1 \u2212 \u03b5 \u2212 \u03b52 2 + ln(1 \u2212 \u03b5) + 6l\u22172 ( 1 3 [ 1 (1 \u2212 \u03b5)3 \u2212 1 ] \u2212 \u03b52 2 )} "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003146_1-84628-214-4-Figure4.8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003146_1-84628-214-4-Figure4.8-1.png",
        "caption": "Fig. 4.8. Swimbot orientation compared to goal direction modifies genetically determined turning mechanisms.",
        "texts": [
            " If a swimbot has succeeded in reaching a food bit, that swimbot\u2019s energy goes up \u2014 if its energy level is high enough (above hunger threshold), it begins to look for a mate. A successful that which produces an offspring causes the energy level of each parent swimbot to decrease by 50% \u2014 that energy is given to the offspring. Each swimbot has an innate orientation, or heading, determined by the axis of its main body part. While pursuing a goal, the direction from the swimbot to its goal is compared to its orientation at every step, as illustrated in Fig. 4.8. The size and sign of the resulting angle are used to modify the phases and amplitudes of all the part motions. Genetic factors determine the amounts that these phases and amplitudes are modified, per part. No explicit definition of turning is provided \u2014 the solutions are those of a blind watchmaker. Turning solutions are among the more complex emergent behaviors in swimbots and are difficult to describe objectively. 4 GenePool 89 When a swimbot\u2019s mental state switches to looking for a mate, it scans all the swimbots within a specific radius (its \u201cview horizon\u201d) at one instant, with a \u201csnapshot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003509_cca.2005.1507162-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003509_cca.2005.1507162-Figure1-1.png",
        "caption": "Fig. 1. Experimental Testbed",
        "texts": [
            " Thus, as starting point for derivation of the proposed controller, the considered hydraulic system is at first transformed into a suitable canonical form using differential geometric methods [13]. The effectiveness relating to the robustness against considerable parametric uncertainties and to the tracking performance of the presented nonlinear control approach is demonstrated both by simulations and experiments. H 0-7803-9354-6/05/$20.00 \u00a92005 IEEE 422 The hydraulic actuation system under consideration is available as an experimental setup at our Institute Laboratory and depicted in Fig. 1, where the valve\u2013cylinder configuration is extra shown schematically in Fig. 2. Therewith, the considered plant consists mostly of an asymmetric single-rod cylinder (also termed differential cylinder) and a servovalve. For the derivation of the mathematical model of this hydraulic system, some (simplifying) assumptions are made; among other effects of leakage flows and valve hysteresis are negligible. The piston motion equations can be written as: RBBAApg fpApAxm (1) where BAflpg VVmm is the total mass, px the piston position, iA the piston surface area in the chamber i and ip the pressure in the chamber i (with BAi , ), Rf the friction forces",
            " The derived sliding mode control law is now given by both contributions (18) and (26) as follows: )(sat)()()( xxxx s uu eq . (27) Note that stability proof can be ascertained by using the Lyapunov function 2 2 1 sV . However, for guaranteeing that the system trajectories have to reach the prescribed sliding surface in finite time and stay on this, the sliding conditions 0ssV have to be modified to sss as aforementioned. To demonstrate the effectiveness of the derived control law, experiments were carried out on the experimental testbed shown in Fig. 1 as illustrated in the following section. The nominal physical parameter values of the hydraulic servosystem under consideration are: mm63kd , 2mm23117.Ap , 04.2 , mm500H , kg2.604\u02c6 gm , Ns/m5000\u02c6 vF , N50\u02c6 cF , N700\u02c6 hF , m/s0175.0hC , 3 0 cm6.198AV , 3 0 cm8.297BV , 3kg/m870fl , MPa80p , MPa0Tp , MPa1800flmE , 5.01\u0302 , 90\u02c62 , 3\u02c63 , MPa280maxP , l/min150NQ , MPa7NP , Nv N v Px Q B 5.0max . The bounds of uncertainties ranges are given by the following expressions, where minmax,i : %201\u02c6 gig mm , %101\u02c6 jij ( 3,2,1j ), )(,, ijiflifl EE , %FF vv 101\u02c6 , %FF cc 101\u02c6 and %FF hh 101\u02c6 ",
            " These considerable parameter variations serve to demonstrate the robustness of the proposed controller. To determine the sliding surface design parameters 0C , 1C and 3C , while maintaining stabilizing requirements, stable eigenvalues must be suitably selected, namely using pole placement. Thus, these parameters are determined here via assignment of all poles by -80. The width of the boundary layer is selected as 05.0 and the design parameter 1 . To experimentally illustrate the effectiveness of the proposed nonlinear controller, major experiments carried out on the experimental setup in Fig. 1 were performed to verify the excellent simulation results shown in Fig. 3 and Fig. 4, namely under different operating conditions. For lack of place, all the experimental results can not be unfortunately presented, but only a few as shown in Fig. 5 (piston position tracking) and in Fig. 6 (pressures behavior in both cylinder chambers). These experimental results demonstrate that the presented control approach is highly effective, i.e. this control law not only provides improved tracking performance, it also ensures high robustness against considerable parametric uncertainties (especially load variations, changes in fluid compressibility and friction constants)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000438_bf00230653-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000438_bf00230653-Figure1-1.png",
        "caption": "Fig. 1 The positioning of infrared-emitting diodes (1REDs) on the adjustable cuff fixed to the arm and to the frame fixed to the trunk is shown along with the humerus-fixed (XHYHZH) and earth-fixed (laboratory - XYZ) coordinate systems",
        "texts": [
            " Data recording Body segment positions in three-dimensional space were recorded using a three-camera WATSMART system (Northern Digital; Waterloo, Canada). The system was calibrated to an accuracy of less than 2 mm in a volume of approximately 0.6 m (a/p) by 1.1 m (lateral-medial) by 1.4 m high. This procedure permitted a Cartesian coordinate system external to the subject to be set up within the calibrated volume so that the xy, xz, and yz planes were parallel to the horizontal, sagittal and frontal planes of the subject, respectively (Fig. 1). Experimental paradigm The subjects performed an arm angle reproduction task while standing. Vision was occluded by a blindfold. The experimenter first placed the arm and trunk into a position designated as the target orientation (arm orientation relative to the trunk and/or earth was perceived and memorized by the subject). The experimenter then moved the subject's arm (which was kept slightly flexed at the elbow) and trunk to a different position. The subject then moved his/her arm to indicate its perceived target orientation relative to the trunk or the external coordinate system",
            " For example, the experimenter would place the arm horizontal and directed anterior (i.e., perpendicular to the trunk frontal plane) with the trunk in a vertical position. After trunk flexion, matching to the extrinsic coordinate system would involve returning the arm to a horizontal and anterior position (i.e., no longer perpendicular to the trunk frontal plane). In contrast, matching to the intrinsic Infrared light-emitting diodes (IREDs) were placed on devices attached to the trunk and arm for the experiment in which arm angles were measured relative to the trunk (Fig. 1). Six IREDs were placed on an adjustable frame that snugly fitted the subjects about the thoracic region of the trunk. It was assumed that the motions of this trunk frame represented motion of the thoracic region of the trunk and that breathing movements had no effect on measurements of trunk orientation. Three of these IREDs defined a plane parallel to the frontal plane of the trunk, while the other three IREDs defined a parasagittal plane. Each set of three IREDs defined a coordinate system fixed to the trunk with longitudinal (ZT), a/p (XT), and medial/lateral (YT) axes",
            " This transformation matrix was used to transform the coordinate system defined by the parasagittal plane IREDs into one with axes parallel to those of the coordinate system defined by the frontal plane IREDs. That is, if the frontal plane IREDs were not accurately recorded, the parasagittal plane markers were used to define the same coordinate system as would have been defined by the frontal plane IREDs. If both sets of trunk IREDs were recorded accurately on a trial, the set of IREDs with the most accurate recordings as determined from the rms error in distances among the three IREDs was used to compute the trunk coordinate system. An adjustable aluminum cuff (Fig. 1) was attached firmly to the arm so that, with the subject in anatomical position, two sides were parallel to the frontal plane and the other two sides were parallel to the sagittal plane. Because the cuff was attached to the soft tissue overlying the humerus, it would not accurately follow the longitudinal rotation of the humerus through its full range (cf. Darling and Gilchrist 1991). This problem was corrected with two hinge devices consisting of two strips of galvanized steel, with one end of each strip pivoting about a nut and bolt (Fig. 1). These devices were positioned such that one end was held firmly between the two walls of the cuff on the medial and lateral sides and the hinge was placed over the flexion/extension axis of the elbow. The free ends were placed over the medial and lateral sides of the forearm and secured with a velcro strap so that if the elbow was even slightly flexed the hinge device would force the cuff to closely follow humeral rotation while allowing unrestricted elbow motion. Three IREDs were placed on each of the anterior and lateral surfaces of the cuff to represent frontal and sagittal planes of the arm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001452_1.2789019-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001452_1.2789019-Figure1-1.png",
        "caption": "Fig. 1",
        "texts": [
            " Among these, the subspace iteration method suggested by Bathe and Wilson (1976) is employed in the present analysis. In this study, the element stiffness matrix of a typical helical element has been obtained numerically based on the transfer matrix method (Haktamr and Klral, 1993; Yddlrlm, 1995). Element equation is written as {p} = [kl{d} (2) where { p } and { d } are the element vectors containing the end forces and the end displacements, respectively. [k] is the element stiffness matrix. A helical node considered here has the six degrees-of-freedom shown in Fig. 1. Denoting the ends of the element by subscripts i and j , the end quantities of an element are written in open form as {P} = { P l P2 P3 . . . Pl2} r = {{P}i {p}j}r (3a) {d} = {dl d2 d3 . . . d,2} r = {{d}, {d}j} r. (3b) The subscripts 1, 2, 3 and 7, 8, 9 correspond to the end forces in (3a) and the translational displacements in (3b)..The subscripts 4, 5, 6 and 10, 11, 12 represent the end moments in Journal of Applied Mechanics Copyright \u00a9 1998 by ASME MARCH 1998, Vol. 65 / 157 Downloaded From: http://appliedmechanics",
            " In this study considering the axial and shear deformation effects, the element transfer matrix is obtained numerically up to any desired accuracy by the numerical algorithm devised by Ylld~r~m (1995, 1996a-b, 1997a). It is assumed that the centroid of the cross-section coincides with its shear center, normal, and binormal axes are the principal axes, warping is neglected and, further, the bar is made of a linear elastic, homogeneous, and isotropic material. The numerical algorithm is given in the Appendix. The transformation of the element transfer matrix between the local and global coordinates is in the form of (Fig. 1). [ F ( 6 j - qb,)]xrz = [ T ( O j ) ] - ' [ F ( $ j - $ , ) ] , , , b [ T ( q S ~ ) ] (7) where the transformation matrix [ T] consists of four submatrices [A]. 10 k \u2022 . . . . . HYPERBCX.OI DAL \"I'YP ~ k ~ = 5 \u00b0 1 ~ _ R I / R 2 = 0 ' I 0 , 0 1 L \u00b1 ~ 1 _ _ ] _ _ 1 _ _ _ Z Z l . . ~ L _ _ . . L _ Z L ~ _ . t . . . L_ 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 n 1 0 . . . . . . \" i 1 2 = , I - ~ - ~ ~ 0.1 k ~ < ~ . - . _ ~ 0 . 0 1 ~ i \u2022 JI ~ - - - I - A-- - & - - - J - L II I 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 n 0 0",
            "+ _I+ _ J l ~ _ _ L + _ + 3 4 5 6 7 8 9 10 11 12 13 14 15 16 n Fig. 4 The six lowest dimensionless frequencies of conical spring fixed at both ends (n is the number of turns) [A] [0] [0] [0] \"1 [T] = [0] [A] [0] [0] J (8) [0] [0] [a ] [0] [01 [0] [01 [A] The elements of the submatrix [A] are obtained as - - c o s a sin 4, cosacos~b s i n a ' ] [A] = -cos ~b -s in ~b 0 J (9) sin a sin ~b -s in a sin 4, cos c~ where a is the helix pitch angle. The angle ~b is measured from the X-axis in horizontal plane (Fig. 1 ). Mottershead (1980) has given the consistent cylindrical helical element mass matrix in semi-open form, which has been obtained by the finite element method. For the reason of simplicity, the consistent spatial straight element mass matrix given by Craig (1981) is employed in this study (Fig. l (b)) . In the computation of the element mass matrix, the total length of the element L is determined approximately as L = R ( 4 ' ~ ) ( ~ j - 4 ' , ) ( 1 0 ) COS o/ where R is the horizontal radius of the helix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002847_b:tril.0000044500.75134.70-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002847_b:tril.0000044500.75134.70-Figure5-1.png",
        "caption": "Figure 5. The spring loading unit.",
        "texts": [
            " The glass disc and the steel ball are driven by synchronous pulleys and belts separately. Quasi-monochromatic light is obtained by a narrow band interference filter, and then collimated and reflected from the beam splitter inside the microscope. Lastly, the beam is normally projected on the EHL contact region. The resultant interference pattern is magnified by the microscope and captured by a CCD camera. The video microscope system has a focal depth of 3.5 lm and a view field of 627 lm \u00b7 470 lm. The spatial optical resolution is 0.98 lm/pixel. Figure 5 gives some details of the spring-loading unit. The disc is made of crown glass. A chromium layer of 22 nm in thickness is coated on the loaded side of the glass disc as a beam splitter. The chromium side of the glass disc is very smooth and has a roughness of Ra = 4 nm. The roughness of the ball surface is Ra = 11 nm. Both the roughness were measured by a stylus profilometer (Talysurf PGI). Within the contact, the roughness can be largely reduced as the two surfaces elastically conform. In classical monochromatic EHL interferometry, the determination of an absolute film thickness is based on the known order of fringes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003779_s11044-006-9028-0-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003779_s11044-006-9028-0-Figure4-1.png",
        "caption": "Fig. 4 Planar mechanism with DOF 2, from Ref. [18], Section 7.1",
        "texts": [
            " Also, if one or more of the revolute joints are replaced by a spherical or universal joint, the algorithm successfully removes all dependent constraints. In the latter case, a spherical joint serves as a cut-joint, since the motion space of universal joints is not a SE (3) subgroup. The 4-bar mechanism with two or three spherical/universal joints is a nontrivial exceptional mechanism. 4.2 Planar two-loop mechanism The second example is the planar mechanism from Section 7.1 in Ref. [18], shown in Figure 4. It consist of five bodies (including the ground) connected by six joints. There are \u03b3 = 6 \u2212 (5 \u2212 1) = 2 FLs, so that two cut joints must be selected and two constraint algebras are to be determined. Since all joints have a DOF 1, regardless of the used cut-joint, five constraints are imposed for each of the two cut joints. That is, any choice of cut joints yields a system of 10 closure constraints for the remaining four generalized coordinates. These must obviously be redundant. Checking all possible spanning trees reveals that the minimal dimension of the two constraint algebras is achieved for the tree G, and cotree H, Springer respectively, in Figure 4. In accordance with the FLs 5 and 6, the generalized coordinates for the tree topology MBS are q = (q1, q2, q3, q4). The constraint algebra clos D5 is the Lie algebra of the group of planar translations and clos D6 is the Lie algebra of the group of proper planar motions, i.e., dim clos D5 = 2 and dim clos D6 = 3. Multiplication of the matrix L5 and L6 with the respective selector in Table 2 yields two systems of respectively five constraints. Application of the SVD to the matrices C5 and C6 yields a system of, respectively, one and two kinematic constraints U\u03045 P5 L5q\u0307 = 0 U\u03046 P6 L6q\u0307 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001005_0165-0114(94)00225-v-Figure18-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001005_0165-0114(94)00225-v-Figure18-1.png",
        "caption": "Fig. 18. Control surface of a fuzzy controller with fuzzy inputs.",
        "texts": [
            " This example shows that the output set of the controller reflects, to a certain degree, shape and location of the fuzzy input. On the other hand, it is obvious that reduction of a fuzzy input set to its mean value leads to a loss of information about the confidence about the input signal. Control surface: The transfer function (control surface) of a fuzzy controller with fuzzy inputs and crisp outputs cannot be determined in the same easy way as for crisp inputs and outputs because the variety for fuzzy inputs is much higher than for crisp inputs. Fig. 18 shows the transfer function UN =f(~N, ae~) of the fuzzy controller described above for a bell-shaped fuzzy input with different standard deviations tre~. An essential result is that the transfer function becomes flatter the larger the standard deviation of the input signal is going to be. The consequence for the systems behavior is that model uncertainties, unmodelled 328 R. Palm, D. Driankov / Fuzzy Sets and Systems 70 (1995) 315-335 disturbances and parameter fluctuations are stronger filtered than in the case of small deviations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001626_robot.1990.126316-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001626_robot.1990.126316-Figure5-1.png",
        "caption": "Figure 5. A bubble enclosing part of the second link is first swept over range dB, the sweep bubble resulting is swept over range da.",
        "texts": [
            " robot, where the first joint angle may vary between a and atda and the second joint angle between 0 and BtdO. A bubble representing a part of the first link is swept from a to a t d a (da e x) and can easily be enclosed in a sweep bubble: (3) where I$,, b7 and 6 are the centers of the sweep bubble and the bubbles at joint angles a and a tda respectively and where rs and rb are the radii of the sweep bubble and the bubble being swept. Sweep bubbles for other links are calculated by the same procedure (figure 5). The rotation invariance of bubbles facilitates the calculations. Only the centers have to be rotated over the different joint ranges. In fact that is the only reason for using bubbles instead of e.g. boxes aligned with the coordinate system. When a sweep bubble intersects an obstacle bubble (possible collision) one of two actions can be taken. Either we burst the robot bubbles or we divide the block in two smaller blocks. Note that it is not useful to split the joint range of joint n if a bubble representing a part of any of the links 1 to n-1 collides with an obstacle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002491_s0022-460x(88)80114-7-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002491_s0022-460x(88)80114-7-Figure1-1.png",
        "caption": "Figure 1. Global and local frames 9",
        "texts": [
            " Since in this approach displacement shape functions are not used, it is generally not possible to obtain consistent load vectors and mass matrices and one must resort to lumped representations for the applied and inertial loads. In more recent tim.~es, finite element models have been developed for pretwisted, curved and helical rods [4-11]. In the following we review the governing equations for generally curved and twisted rods and then we develop the stiffness and mass matrices as well as the load vector for an arbitrarily curved and twisted rod element. Finally, we illustrate our formulation by a number of examples. Consider a spatially curved and twisted rod as shown in Figure 1. Let the internal force and moment vectors in the rod be denoted by Q and M respectively. Also let the applied force and moment vectors per unit length be F and I~, respectively. Now, using the sign convention of elasticity, one may write the equilibrium equations for a bar of finite length as follows (see Figure 2): for translational equilibrium, I/ Q 2 - Q t + F(s) ds = ~ nlfi ds, (1) I 1 where m is the mass per unit length and u is the displacement vector; for rotational equilibrium, M~-M,+(r2xQ2)-( r , xQ,)+ , ( r x F + G ) d s = d , mrx~ids+d['2dt J,, ibds, (~) where j is the dyadic of the moments of inertia per unit length and 0 is the vector of rotations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002826_1.1896964-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002826_1.1896964-Figure1-1.png",
        "caption": "FIG. 1. The experimental arrangement used for laser welding the AA 2024 samples.",
        "texts": [],
        "surrounding_texts": [
            "A. Influence of laser power density The energy density threshold for keyhole initiation on AA 2024 was initially examined. A test with power increasing linearly from 2 to 3 kW was performed in one welding run. Results showed that when using the 200 mm lens, the keyhole was formed at about 2750 W, and the transition between the melt-in and the keyhole mode was very sudden. To obtain a sound fully penetrated weld on the 3-mmthick AA 2024 sheet, a speed of 20 mm/s was employed when using the 200 mm lens and 3 kW laser power; and a speed of 40 mm/s was employed when using the 150 mm lens with the laser power at the same level. There is a possibility to reduce the power level and travel speed and still maintain full penetration; however, for the purpose of examining the influence of laser power density on the process, laser output at a constant 3 kW was maintained throughout the study for the fully penetrated butt welds. The fully penetrated bead-on-plate welds produced by the two laser energy density levels generated by the different focal length lenses were visually inspected. Photographic images of top and under bead views are shown in Figs. 2 and 3. It can be seen that the bead top surface from the 200 mm lens is wider and smoother than the bead produced by the 150 mm lens. In both cases, however, the bottom surfaces are quite rough. Small metal spherical deposits were found after welding in the bottom of the groove provided for the backing gas. Therefore, the rough bottom surface is thought to be related in part to irregular liquid metal droplets ejected from the keyhole. To further examine the keyhole stability, digital highspeed pictures were made under these welding conditions. Two typical images from the camera showing the top view are presented in Fig. 4 indicating that when using the 200 mm lens, a large weld pool with the keyhole root in the pool center was formed. By contrast, when using the 150 mm lens, a narrower pool with the keyhole root close to the weld pool front edge was formed. By taking the license or copyright; see http://jla.aip.org/about/about_the_journal Downloaded 22 Apr 2013 to 171.67.34.205. Redistribution subject to LIA license or copyright; see http://jla.aip.org/about/about_the_journal pictures at a reduced vertical angle, images show that in both cases the pool surfaces exist in a revised conic shape with the keyhole rooted at the bottom of the cone due to the recoil pressure. Viewing the pictures in a continuous motion, a unique characteristic of the keyhole dynamic was found: the keyhole root did not move stably in the direction of welding, but quickly fluctuated in terms of its position and its Downloaded 22 Apr 2013 to 171.67.34.205. Redistribution subject to LIA radiation intensity. These fluctuations appeared to be completely random, and the position changes included both transverse and longitudinal variations with changes occurring over a very short time scale, typically faster than the framing rate of 7100 Hz. The phenomena observed indicate that the keyhole root position fluctuation is consistent with the effect of changes in multiple laser beam hole position fluctuations inside weld pool when using a 150 mm focal lens g key reflections at the keyhole wall surface. As already noted, the license or copyright; see http://jla.aip.org/about/about_the_journal keyhole energy density threshold is high in this alloy and the laser beam energy propagates down to the keyhole root by multiple surface reflections on the conically shaped wall surface. Therefore the keyhole behavior is strongly dependent on the curvature of the pool surface. It was found from the high-speed video that the keyhole root was more stable with the large, smooth conical shape produced by the 200 mm lens. The fluctuation of position Downloaded 22 Apr 2013 to 171.67.34.205. Redistribution subject to LIA and radiation had much higher amplitude when using the 150 mm lens. Representative images of keyhole root position fluctuations from the high-speed film are shown in Figs. 5 and 6. In the case of the 150 mm lens, the keyhole was formed very close to the front edge of pool. The sharp, vertical wall surface tended to reflect the beam around the curvature of le position inside weld pool when using a 200 mm lens sexposure time each keyho pool, which did not favor the smooth propagation of the license or copyright; see http://jla.aip.org/about/about_the_journal Downloaded 22 Apr 2013 to 171.67.34.205. Redistribution subject to LIA license or copyright; see http://jla.aip.org/about/about_the_journal beam into one position at the root. It can also be found in the pictures that part of the laser beam was likely to directly FIG. 12. Thermal cycle measured by a thermocouple at the plate surface clo at a welding speed of 20 mm/sd. Downloaded 22 Apr 2013 to 171.67.34.205. Redistribution subject to LIA impinge on the solid sheet surface due to a much thinner liquid layer at the keyhole front edge. As can be seen in Figs. 5 and 6, the diameters of the keyholes in the case of the 150 mm lens are slightly narrower than in the case of the 200 mm lens. The force due to surface tension of the keyhole in the former case is therefore higher than in the latter due to the smaller radius of curvature. The difference of surface tension force also plays a role in the keyhole fluctuation. The lower the force due to surface tension, the more stable the keyhole is against closure and against pore generation. However, it should be noted that keyhole closure was rarely observed in the high-speed video in either case. The fluctuation of the keyhole root position was accompanied by a fluctuation of the plasma plume intensity in the keyhole, the recoil force generated was therefore also subject to a strong fluctuation. The liquid in the weld pool appeared to be pushed from the keyhole boundary toward the rear of the pool by the fluctuating force, with a return flow after contacting the solid boundary. The liquid in the weld pool was therefore in an oscillatory or wave-like motion. The frequency of the movement was difficult to determine due to the chaotic nature of the movement; however, the amplitude of the movement in the case of 150 mm lens was found to be much higher than that in the case of 200 mm lens. The wave-like liquid pool subsequently solidified with rough ripples on both top and bottom surfaces of the bead as shown previously in Fig. 3. B. Influence of shielding gas Argon and helium shielding gases for weld pool top surface protection were compared in the experiments. Both are commonly used inert gases for laser welding, but they have different physical properties. Helium has a higher heat conductivity and also a much higher ionization potential than argon. It was found from the experiments that plume generation from the keyhole is quite different when using different gases. Argon shielding gas produced brighter and larger the fusion line s150 mm lens at a welding speed of 40 mm/s, 200 mm lens se to license or copyright; see http://jla.aip.org/about/about_the_journal plumes from the keyhole. Helium shielding gas generated a much lower light intensity and a smaller plume. In both cases, however, plume generation was subject to fluctuations. Experimental results indicate that helium led to a better process stability than argon. Visual inspection of the bead surfaces show that in terms of the top surface both gases produced similar appearance, whereas on the under side helium gave a smoother under bead than argon. It was also noted that the large plumes occasionally generated when using argon were often accompanied by the ejection of large liquid spatter droplets, which severely disturbed the keyhole stability. Images of plume generation, accompanied by spatter when using argon and helium shielding gases are shown in Fig. 7. The evaporated metal atoms in a gaseous state form the plume. The temperature of the upper side of the keyhole when using helium could be cooler than when using argon due to the differences in heat conductivity and ionization potential of the two gases. Since the evaporation pressure in the keyhole is a function of temperature, using helium to form a srelativelyd lower and more uniform pressure could be the reason for the better process stability. By varying the shielding gas flow rate and tube diameter of the shielding gas si.e., the gas velocityd, it was found that the gas pressure could have a significant influence on the weld bead profile. For example when using a tube with an inner diameter of 15 mm and with an argon flow rate of Downloaded 22 Apr 2013 to 171.67.34.205. Redistribution subject to LIA 10\u201320 l /min, the weld under bead always contained irregular humps or cavities as shown previously in Figs. 2 and 3. When increasing the gas pressure by using a tube of 6 mm inner diameter sat the same gas flow rated it was observed that the gas pressure depressed the liquid in the weld pool and resulted in a slightly depressed top surface and a smooth under bead surface. Results showing the bead appearance for bead-on-plate welds and butt joint welds are shown in Figs. 8\u201311. The irregular root and undercut of the weld bead has a significant influence on the weld mechanical properties as well as the cosmetic appearance;13,14 therefore for optimal results, a somewhat higher gas flow pressure was provided. The resultant geometry was acceptable. The slightly depressed top surface coupled with the enhanced root reinforcement as shown in Fig. 11 is within the stringent quality category according to the ISO Standard 13919-2; i.e., excessive penetration on the lower surface is less than or equal to 0.65 mm s0.2 mm+0.153 thicknessd and the sagging on top surface is less than or equal to 0.75 mm s0.1 mm+lower surface excessive penetrationd.15 The mechanisms by which the high shielding gas pressure improves the surface roughness are not yet completely understood. The rough lower surface is in part related to irregular liquid metal droplet ejection from the keyhole. It is believed that in general when a high shielding weld made with the 150 mm lens sad and columnar dendrites and partially m the bd. gas pressure is applied at the weld pool top surface, the force license or copyright; see http://jla.aip.org/about/about_the_journal from the gas presses the liquid in the weld pool downwards. The liquid therefore is forced to form an excessive penetration at the lower surface and fill in the cavity left by the irregular liquid ejection, which smoothes the surface prior to solidification. Another possible contributory mechanism is that weld pool oscillation is suppressed, either directly as a result of the high shield gas pressure or through alteration of the plasma plume and hence reaction forces acting on the weld pool skeyholed surface."
        ]
    },
    {
        "image_filename": "designv11_11_0003823_icar.2005.1507430-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003823_icar.2005.1507430-Figure11-1.png",
        "caption": "Fig. 11. The path that the robot finds when there is several appearances of the ball in region 1 and 3",
        "texts": [
            " Region 1 Region 2 Region 3 Region 4 Fig. 8. Representation of configuration II Before the appearance of the balls, the path that the robot finds is very similar to the path shown in Figure 10, which is the minimal path for the uniform appearance of the balls. Because of the noise in the environment, the robot does not exactly follow that path, but the path is very close to that one. After showing the ball for several times in regions 1 and 3, the path that the robot finds is close to the one shown in Figure 11. 5 As is apparent from the path, because of the higher probability of appearance of the balls in region 1 and 3, those regions are visited more frequently. The robot experiments verify that our approach can run in real time on a computationally limited platform, and that the robot can operate using the same algorithm in multiple environments. The robot is made aware of the locations of the walls, but given that information is able to recompute its actions from scratch. However, due to the time-consuming nature of running experiments in the real world, we further validate our approach in simulation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002568_1.1864114-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002568_1.1864114-Figure1-1.png",
        "caption": "Fig. 1 3-3 Stewar",
        "texts": [
            " The motivation behind this work is the direct application of the results to medical practice. Contribution of this study is to be seen in the simplified formulation and solution methodology in the handling of the direct kinematics of several type Stewart platforms, the results of which are already reported in the literature 16\u201318 . Formulation of the Problem The Stewart platform mechanism considered here consists of two platforms, base A1A2A3 at the top, and moving B1B2B3 at the bottom, shown in Fig. 1. Two platforms are connected to each other by six legs, the lengths L1\u2013L6 of which are changeable through six prismatic pairs. Each leg has either spherical joints at both ends or one spherical and one universal joint at each end. Effective degree of freedom of the closed-loop chain is 6, indicating to the control of the relative positions of the platform by means of six linear actuators imbedded in the legs. Rotatibility of each leg around its length axis has no effect on positions of platforms. By the rigidity requirements of A1A2A3 and B1B2B3 platforms, sides of the triangles A1A2=a3, A2A3=a1, A3A1=a2, B1B2=b3, B2B3=b1, B3B1=b2 are already known, Fig. 1. The basic problem here is to determine the coordinates of points B1, B2, B3 with respect to a reference frame fixed to the base, when the leg lengths A1B1=L1, A2B1=L2, A2B2=L3, A3B2=L4, A3B3=L5, A1B3=L6 are specified. To formulate the problem, first a reference frame xyz is selected at point G of the base in such a way that G is the center of the circle circumscribing A1A2A3 with radius R=A1G=A2G=A3G, and that the x axis passes through A1 and xy plane coincides with A1A2A3. Second, perpendicular lines B1H1, B2H2, B3H3 to the sides of A1A2A3 triangle are drawn on planes A1B1A2, A2B2A3, A3B3A1 respectively, Fig. 1. Third, the projections of B1, B2, B3 on plane xy are recorded as B1 , B2 , B3 , respectively. Accordingly, the formulation is founded very simply on the geometry of eight 2006 by ASME Transactions of the ASME 3 Terms of Use: http://asme.org/terms t p Downloaded F planes of interest, namely A1A2A3, A1B1A2, A2B2A3, A3B3A1, B1H1B1 , B2H2B2 , B3H3B3 , and B1B2B3 with particular attention on the intersections A1H1, B1H1, H1B1 , A2H2, B2H2, H2B2 , A3H3, B3H3, H3B3 . With reference to the geometry of base xy plane triangle A1A2A3, Fig",
            "org/ on 10/04/201 3 = cos\u22121 a1 2 + a2 2 \u2212 a3 2 2a1a2 1 1 = 1 + 2 \u2212 3 2 ; 2 = 2 + 3 \u2212 1 2 ; 3 = 3 + 1 \u2212 2 2 2 R = a3 2 cos 1 = a1 2 cos 2 = a2 2 cos 3 3 Angles A2A1B1= 1, A3A2B2= 2, and A1A3B3= 3 are then computed by applying Cosine Law to triangles A1A2B1, A2A3B2 and A3A1B3, respectively, as follows: 1 = cos\u22121 L1 2 + a3 2 \u2212 L2 2 2L1a3 ; 2 = cos\u22121 L3 2 + a1 2 \u2212 L2 2 2L3a1 ; 3 = cos\u22121 L5 2 + a2 2 \u2212 L6 2 2L5a2 4 Designating the angles between the base plane and side triangular planes, namely B1H1B1 , B2H2B2 , B3H3B3 by 1 , 2 , 3, respectively, the coordinates of the points B1 B1x ,B1y ,B1z , B2 B2x ,B2y ,B2z and B3 B3x ,B3y ,B3z can now be expressed in the following way, Fig. 1: B1x = R \u2212 L1 cos 1 cos 1 \u2212 L1 sin 1 sin 1 cos 1 B1y = L1 cos 1 sin 1 \u2212 L1 sin 1 cos 1 cos 1 5 latform geometry B1z = L1 sin 1 sin 1 B2x = \u2212 R cos 2 1 + L3 cos 2 cos 2 + 1 + L3 sin 2 sin 2 + 1 cos 2 B2y = R sin 2 1 \u2212 L3 cos 2 sin 2 + 1 + L3 sin 2 cos 2 + 1 cos 2 B2z = L3 sin 2 sin 2 6 B3x = \u2212 R cos 2 3 + L5 cos 3 cos 3 \u2212 L5 sin 3 sin 3 cos 3 B3y = \u2212 R sin 2 3 + L5 cos 3 sin 3 + L5 sin 3 cos 3 cos 3 B3z = L5 sin 3 sin 3 7 Requiring that the distances between points B1, B2, and B3 remain constant during the movement of the platform B1B2B3 will yield the following equations: B2x \u2212 B3x 2 + B2y \u2212 B3y 2 + B2z \u2212 B3z 2 = b1 2 8 B3x \u2212 B1x 2 + B3y \u2212 B1y 2 + B3z \u2212 B1z 2 = b2 2 9 B1x \u2212 B2x 2 + B1y \u2212 B2y 2 + B1z \u2212 B2z 2 = b3 2 10 If 5 \u2013 7 are substituted into 8 \u2013 10 , half-angle trigonometric identities are utilized, and rearrangements are made, then equation JANUARY 2006, Vol",
            " By this way, originally given C1B1C2C3B2C4B3C1 platform is to be transformed into the standard 3-3 type A1B1A2B2A3B3A1 platform for which developed theory will be directly applicable. An interesting case which requires special attention is the one where 4-3 Stewart platform has a rectangular base. Then, with the notation established in Fig. 3, k1=k3, k2=k4, 1= 2= 3= 4=90\u00b0 will hold, signifying to fact that A2 of Fig. 5, will be at infinity thus making the calculations of L3 ,L4 in terms of L3 ,L4 impossible. In that situation, given rectangle C1C2C3C4 will be converted into a triangle A1A2A3 of the general theory, Fig. 1, in the way depicted in Fig. 6, to render the following results: R = k1 2 + k2 2,a1 = 2 k1 2 + k2 2,a2 = 2k2,a3 = 2k1 1 = 2, 2 = 0, 3 = 3, 1 = 90 \u00b0 , 2 = cos\u22121 k1 k1 2 + k2 2 , 3 = 90 \u00b0 \u2212 2 38 Furthermore, by comparison it is clear that L1 = L1 ; L2 2 = 2L2 2 + 2k1 2 \u2212 L1 2; L6 = L6 ; L5 2 = 2L5 2 + 2k2 2 \u2212 L6 2 39 The only differing point between the theories of 3-3 Stewart platform and of 4-3 type with rectangular base is that the angle 2 of A A B plane with respect to the base A A A , is to be replaced by the angle 2 between C3C4B2 triangular plane and the base C1C2C3C4, understanding that angles 3 of plane A1B3A3 and 3 of plane C1B3C4 as well as 1 of plane A1B1A2 and 1 of plane C1B1C2 remain unchanged, i"
        ],
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    },
    {
        "image_filename": "designv11_11_0003335_0020-7403(81)90025-4-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003335_0020-7403(81)90025-4-Figure3-1.png",
        "caption": "FIG. 3. Trilateral figure. The internal velocity in A B C is prescribed as parallel to A B .",
        "texts": [
            " The second method (the difference is not immediately evident) is more useful for calculation in solutions for the more complex three-dimensional cases. If a multilateral figure is considered, its rigid internal velocity is fully known, when the normal components of the external velocities (equal to the corresponding internal components), are known on two adjacent or non-adjacent sides. The absence of one of these pieces of information can be overcome if the direction of the internal motion is prescribed. The following cases are of interest: side A C , see Fig. 3. The direction of the internal velocity vector is obviously parallel to A B and hence the problem is the same as that given in Example I. The external velocity vectors e, and e~ are given on the sides A B and BC, see Fig. 4. The flux of material through the sides A B and BC is respectively given by: Analysis of plastic deformation according to the SERR method 131 The internal velocity i, must simultaneously meet the continuity conditions across A B and B C If the two sides A B and B C in Fig. 4 are displaced parallel to themselves, by quantifies respectively equal to the normal components of the vectors et and e2 (i.e. equal to PZ and P S ) , then their intersection P determines, together with the point B, the internal velocity i. We obtain, P Z = P B \u2022 sin y; P S = P B \u2022 Sin and Hence, A H A B C H B C B C siny sinO\" sin8 = s i n ( * r - O ) =s inO\" A H A B . sin y C H B C . sin S\" Further we see that, A H A B \u2022 sin y A C A B \u2022 sin y + B C \u2022 sin 8' and hence, from equations (1), we obtain, From Fig. 3 we have, and hence, A H ~ A C d,, + d,: e~ cos cr. sin y\" e :cosB sin8 e ~ ' c o s a sin-r e2\"cos8 sinS' A n = .~,, = _ 4,__, AC ck~ + $: e~' in which d~ is the flux of material through A C 132 F. GAa~ro and A. GIARDA The above given case, can be solved graphically in a.very simple way; let us consider the vectors e,. e., applied to the common vertex B of the sides AB and BC, see Fig. 5. From the end of each vector draw a line parallel to the corresponding side of the figure. The point of intersection of such parallel lines, together with the point B, determines the vector i of the internal rigid motion of the figure"
        ],
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    },
    {
        "image_filename": "designv11_11_0003036_icef2005-1333-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003036_icef2005-1333-Figure3-1.png",
        "caption": "Fig. 3: Appropriate rough surface patch size for flow factor",
        "texts": [
            " In addition to inputting the rough surface profile, the program user must specify the pressure gradient across the patch, the relative sliding velocity between the two surfaces, the fluid viscosity, and the separation between the mean of the rough surface and the smooth surface. It is important to choose dimensions of the rough surface patch carefully. The patch must be large enough to include a large number of asperities. The patch must still be small relative to the total contact area between the ring and liner so that large scale effects, such as surface geometry, do not affect the results. A diagram displaying some key parameters pertinent to selecting the patch size between the ring and liner is shown in Fig. 3. analysis In Fig. 3, Lx and Ly are the patch lengths in the axial and circumferential directions, respectively, g is the perpendicular distance between honing marks, and \u03b8 is the honing cross hatch angle. For the ring-to-liner interaction being considered, the axial patch length was chosen as one fortieth of a typical ring width in the axial direction of the cylinder bore, , 40 )1( BxnLx =\u0394\u2212= (13) where n is the number of nodes in the x-direction and B is the ring axial width. This is the same nodal distance used when solving the Reynolds equation between the ring and liner within MIT\u2019s ring pack program"
        ],
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    },
    {
        "image_filename": "designv11_11_0001532_s0022-460x(03)00283-9-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001532_s0022-460x(03)00283-9-Figure4-1.png",
        "caption": "Fig. 4. Diagrammatic representation of connecting the two platforms.",
        "texts": [
            ", strokes for the six actuators so that the displacement xb \u00bc #rb %rb of the stabilized platform from its ideal position %rb is under the given root-meansquare specification ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E\u00bdxbi\u00f0t\u00dexbi\u00f0t\u00de p pdi; \u00f01\u00de where i \u00bc 1; 2;y; 6 indicate the six components of xb: In Fig. 3, the top operator \u2018\u2018 V \u2019\u2019 gives observed state, and \u2018\u2018 \u2019\u2019 gives predicated valuable or ideal position. In this section, the dynamic modelling of the multi-body system of the plant is carried out in terms of the Newton\u2013Euler equations with Lagrange multipliers. The multi-body dynamics model of the Gough\u2013Stewart platform mechanism shown in Fig. 2 includes 14 rigid bodies. Two of which represent the base and stabilized platforms, and every leg is composed of two rigid bodies. Fig. 4 illustrates the base platform, stabilized platform and the ith leg of the Gough\u2013Stewart platform. In the following equations, the subscript \u2018\u2018a\u2019\u2019 denotes the base platform, \u2018\u2018b\u2019\u2019 denotes the stabilized platform, \u2018\u2018Ui\u2019\u2019 denotes the upper part of the ith leg and \u2018\u2018Li\u2019\u2019 denotes the low part of the ith leg (i \u00bc 1; 2;y; 6). Let X 0 kY 0 kZ0 k be the corresponding local reference frame, let rk denote the position vector of center of mass of body k; and pk be the Euler parameter orientation co-ordinates of the kth rigid body with reference to the global reference frame XYZ: Let s0ai and s0bi; respectively, denote the position vector of point Pai in the frame X 0 aY 0 aZ0 a; and that of point Pbi in X 0 bY 0 bZ0 b: To further simplify the notation, define r \u00bc rTa ; r T b ; r T U1; r T L1;y; rTU6; r T L6 ; p \u00bc pT a ; p T b ; p T U1; p T L1;y; pT U6; p T L6 ; G \u00bc diag \u00f0Ga;Gb;GU1;GL1;y;GU6;GL6\u00de; J0 \u00bc diag\u00f0J0a;J 0 b; J 0 U1;J 0 L1;y;J0U6;J 0 L6\u00de; FA \u00bc FAT a ;FAT b ;FAT U1;F AT L1 ;y;FAT U6;F AT L6 ; n0A \u00bc n0AT a ; n0AT b ; n0AT U1 ; n 0AT L1 ;y; n0AT U6 ; n 0AT L6 : \u00f02\u00de where mk is the mass of the kth body",
            " Thus, in term of Euler parameters of the general constrained force acted on the base platform is given by Faj n0aj \" # \u00bc fj lij dij 2GT a *s 0 aiA T a dij \" # : \u00f014\u00de The general control force vectors acting on the base platform by the 12 cables are Fa n0a \" # \u00bc P12 i\u00bc1 FajP12 i\u00bc1 n 0 aj \" # : \u00f015\u00de Due to the large inertia of the base platform, the motion of the base platform can be predicted in short time with the current states. Let T be the sample interval in seconds, x\u00f0k\u00de be the value of x at kT (k is an integer). The position of the base platform %ra\u00f0k \u00fe 1\u00de can be predicted in the next T with %ra\u00f0k \u00fe 1\u00de \u00bc #ra\u00f0k\u00de \u00fe #va\u00f0k\u00deT \u00fe 0:5#aa\u00f0k\u00deT2 \u00f016\u00de Here, #ra\u00f0k\u00de; #va\u00f0k\u00de and #aa\u00f0k\u00de are, respectively, the current observed position vector, the velocity vector and acceleration vector of the base platform. So the predicted position %rP ai\u00f0k \u00fe 1\u00de of the upper mounting point of the ith actuator Pai (see Fig. 4) is %rP ai\u00f0k \u00fe 1\u00de \u00bc %ra\u00f0k \u00fe 1\u00de \u00fe Aa\u00f0k \u00fe 1\u00des0ai: \u00f017\u00de Take the predicted position of the base platform as reference signals, a control for the next T is: adjust the lengths of the legs making the stabilized platform at the ideal position while the base platform at the predicted position. It is illustrated in Fig. 6, where %li\u00f0k \u00fe 1\u00de and li\u00f0k\u00de are, respectively, the predicted and current length of the ith actuator strut. As shown in Fig. 4, denote %rP bi \u00bc %rb \u00fe Abs 0 bi the ideal position vectors of point Pai of the stabilized platform in the global reference frame. The predicted lengths of the legs can be expressed as %li\u00f0k \u00fe 1\u00de \u00bc jj%rP ai\u00f0k \u00fe 1\u00de %rP bi\u00f0k \u00fe 1\u00dejj \u00f0i \u00bc 1;y; 6\u00de: \u00f018\u00de By the same method of obtaining Eq. (11), the sliding velocities of the ith leg are %\u2019li\u00f0k \u00fe 1\u00de \u00bc \u00f0%rP ai\u00f0k \u00fe 1\u00de %rP bi\u00f0k \u00fe 1\u00de\u00deT %li\u00f0k \u00fe 1\u00de \u00f0#va\u00f0k\u00de \u00fe \u2019Aas 0 ai %vb\u00f0k\u00de \u2019Abs0bi\u00de; \u00f019\u00de where %vb is the ideal velocity of the stabilized platform. The position vector of the base platform can be sampled: ra\u00f0k\u00de; ra\u00f0k 1\u00de; ra\u00f0k 2\u00de;y : \u00f020\u00de As the three-dimensional velocities and the accelerations of the base platform are difficult to measure in such low frequency (about 0",
            " The base point co-ordinates of the centroidal body-fixed reference frame of ith body in the global frame are denoted by ri \u00bc \u00f0xi yi zi\u00de T: \u00f0A:1\u00de The Euler parameters for the ith body are denoted by pi \u00bc \u00f0e0 i e1 i e2 i e3 i \u00de T: \u00f0A:2\u00de The normalization condition is Up i \u00bc pT i pi 1 \u00bc 0: \u00f0A:3\u00de Two 3 4 matrix Ei and Gi is defined as Ei \u00bc e1 i e0 i e3 i e2 i e2 i e3 i e0 i e1 i e3 i e2 i e1 i e0 i 2 64 3 75; \u00f0A:4\u00de Gi \u00bc e1 i e0 i e3 i e2 i e2 i e3 i e0 i e1 i e3 i e2 i e1 i e0 i 2 64 3 75: \u00f0A:5\u00de The transformation matrix A \u00bc EGT: \u00f0A:6\u00de The details of the Stewart parallel mechanism used in this application are given as follow: Base platform (in the base platform frame): Pai \u00bc 4:9 cos \u00f02\u00f0i 1\u00dep=37p=12\u00de 4:9 sin \u00f02\u00f0i 1\u00dep=37p=12\u00de 0 T ; i \u00bc 1; 2; 3: Stabilized platform (in the stabilized frame): Pbi \u00bc 1:8 cos \u00f07ip=3\u00de 1:8 sin\u00f07ip=3\u00de 0 T ; i \u00bc 1; 2; 3: The upper and lower mounting point Pai and Pbi in their local frame X 0 UiY 0 UiZ 0 Ui and X 0 LiY 0 LiZ 0 Li are (see Fig. 4) Pi ai \u00bc 0 0 2 T ; i \u00bc 1; 2;y; 6 and Pi bi \u00bc 0 0 0:2 T ; i \u00bc 1; 2;y; 6: The inertia parameters of the system and initial positions of the platforms are listed, respectively, in Tables 2 and 3. (The initial velocities and accelerations of the two platforms are zero.) [1] D. Stewart, Aplatform with six degrees of freedom, Proceedings of the Institution of Mechanical Engineers 180 (5) (1965) 371\u2013386. [2] Li Hui, China hopes to move FAST on largest telescope, Science 281(5378) (1998) 771\u2013773. [3] Hong Wang, Yanlin Guo, Gexue Ren, Yingjie Lu and Guibin Lin, Experimental Study and Theoretical Analysis of the Structure for Supporting the Deed Cabin of the FAST, Journal of Building Structures (in Chinese), 23 (3) (2002) 63\u201368"
        ],
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    },
    {
        "image_filename": "designv11_11_0001964_robot.1997.614291-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001964_robot.1997.614291-Figure8-1.png",
        "caption": "Figure 8: Robot at Goal Location",
        "texts": [],
        "surrounding_texts": [
            "In this section, the MMF method is bricfly summarizcd. While conventional potential field methods are derived from principles of electrostatics, the Modified Magnetic Field method is derived from electrodynamical considerations. The obstacle forces are obtained from a current based formalism. This distinction and the methods of their computation are briefly summarized in this section and shown in greater detail in [ 5 ] . The conventional attractive potential field form is used to represent the field setup by the attractor: where -kattr is some positive constant used to represent the intensity of the force field and x is the location of the operating point with respect to the goal location Xd. A damping force is used to damp out oscillations that accrue from the specification of the above attractive field and is given in the following form. where x represents the velocity of the robot. The damping field force is a non-conservative force that tends to oppose the motion of the system. The definition of the obstacle field and force is the key innovation of the MMF method. The basis of the MMF is a set of virtual closed current loops enclosing the obstacle. These virtual current loops generate virtual forces that are termed the Modified Magnetic Field . The obstacle force and field are defined by the following relations: Fobs = X x B (3) (4) where B represents the obstacle field, the MMF , and Fobs represents the obstacle force due to this field. Again, x represents the robot velocity, x the unit velocity vector, l represents the direction of the current loop enclosing the obstacle face and p represents the magnitude of the perpendicular distance of the robot from the given obstacle face. The obstacle field definition is similar in structure to the conventional electro-magnetic Magnetic field, however, the structure of the M M F is somewhat different from that of the classical Magnetic field. Using the redefined Eq. 4 B improves the behavior of the control law, resulting in less convoluted paths, than the classical form. This is shown in Fig. 2. Rather than spiral endlessly, the M M F field has some preferred directions such that motions in those directions remain unaffected while others are turned into those directions. 3 Domain Extension of the MMP The form introduced for the obstacle force has been delineated in terms of the vector cross product operation. To address planning in higher dimensional spaces such as configuration or task spaces, the definition needs to be extended to consistently and exactly address force generation. Towards this end, we use the tensor notation to compute the B = B x . = C,(l,x)X) x . (5) term so that the computation of the corresponding obstacle force Fobs becomes a tensor reduction operation with the robot velocity, as Fobs = -BX. In this section, we briefly recount the computation of B for any given obstacle surface and robot velocity given that the form selected for the MMF was given by B = We also discuss the computation of the obstacle forces and torques applied to a robotic link. Previously, we presented control forces that applied to a point robot - whether operating in Cartesian or in joint space. Here we extend the definition of the obstacle force to apply to linked manipulators. The method of computing the B tensor is briefly summarized for its relevance to the next section. Let the n-dimensional obstacle surface be characterized by a minimal set of n orthonormal vectors: 1 surface normal and (n-1) surface vectors. The B tensor matrix is then computed from these vectors. Given that Fobs = x x B or Fobs = -Bx using new notation, it follows that x.(Bx) = 0 from the scalar triple product result. Now this must be true for all x, including those velocity directions that are parallel to the eigenvectors of B. $ in Eq. 4. P For x = [,[ E [EV set ofB] . 1 1 [ 1 1 2 = o (6) To satisfy this requirement, either X g = 0 or llE112 = 0. Skew-symmetric matrices meet these criteria since the roots of skew-symmetric matrices are either zero or strictly imaginary. Now, if X g = 0, then Fobs = AB . = 0 which is exactly the desired behavior if the robot velocity runs parallel to the surface. However, if the robot velocity runs along the surface normal the 1 1 [ 1 1 2 = 0 solution is used, which corresponds to an imaginary root. To choose a real 13 with 2 complex conjugate pairs (to ensure realness of a), select any (n - 2) of the surface vectors as the B eigenvectors with eigenvalues of 0, and choose f~ as the two remaining eigenvalues. Eigenvectors for these last two values are constrained to lie in the plane of the surface normal direction and the last (n-1)th surface vector. Now select any 2-d skew-symmetric matrix with eigenvalues f i , find its eigenvectors and the last two eigenvectors of our MMF matrix is now known in terms of the 2 known basis vectors scaled by the components of the 2-d eigenvectors just found for the known 2-d matrix. Now, the eigenvalues and the eigenvectors are known and the computation of B may be computed. 4 Computing the Obstacle Fields and Forces for a Linked Manipulator An outline of the computation of the obstacle forces for a linked manipulator navigating in a Cartesian or task space are presented herein. Consider the situation shown in Fig. 3. The joint space obstacle forces are generated in joint space and joint limit avoidance is performed by treating each limit or singularity as an obstacle and computing the resulting set of forces as described earlier. Subsequently, task space motion planning is performed whereby the obstacle forces and torques are computed for the task space obstacles. These task space forces and torques are then transformed back to joint space through the manipulator Jacobian, where they are integrated with the previously obtained jointspace forces. Collectively, these forces serve as input control torques in the robot dynamic relation where final force resolution is performed. The joint space obstacle avoidance is performed as shown in the previous section and detailed in [5]. In task space, the obstacle force on the link is formulated in two parts, one generates the task-space force and the other the torque for the given link. To compute the link force component, the link is abstracted to its center of mass and the obstacle force for the center of mass is then computed in Cartesian space, as has been done for the point robot. The obs- tacle force is then computed as: Next, the obstacle torque is computed. This torque, the Modified Magnetic Torque is computed in a somewhat analogous fashion through the following relation: where w represents the angular velocity of the link, s represents the link axis, U the linear velocity due to the orientational component, and I' denotes the Modified Magnetic Torque Field, the angular analog of the MMF . The M M T F and the obstacle torque has similar electro-dynamic connotation as the MMF , however, in implementation, we have yet again, departed from the classical electro-magnetic mathematical definitions. Rather than visualizing the robot link as a point charge, as has been done in classical potential field methods and earlier in this paper in the development of the M M F , here the link is treated as a dipole and derivations of r o b s derive from the interaction of the dipole moment with the obstacle torque field. Eq. 8 constitutes a contraction mapping of the tensor I?. The cross product terms in Eq. 9 may be computed as outlined in Sec. 3. While the tensor form is necessarily important for higher dimensional spaces, the cross product form may be retained for classical Cartesian space development. The rationale for the above mathematical structure will be briefly outlined. The considerations governing the M M T F equations here are similar to those that went into formulating the MMF forces. Ideally, we would like to preserve link configurations in which the link lies parallel to the obstacle surface (i. e. where r o b s = sTn = 0) and reorient those in which the link lies along the surface normal. Towards that end, the sTn term is important in that this term is zero for every link configuration that lies along the surface and is only non-zero when the link axis is oriented towards the surface. Additionally, a torque expression that ensures that the work done by that torque will always be zero is desired i.e. r such that W = w.7 = 0, as will be shown to be important in the brief outline of the Lyapunov Energy analysis perform in the next paragraph. The (U x (li x s ) ) x w term in the definition of I' ensures that this requirement on the obstacle torque is met. Multiplying the dyads in Eq. 9 by the vector s causes the contraction of the tensor B, and yields the above vector, (li x s ) x w. The presence of the . x w term, this term is guaranteed to be orthogonal to U, and hence ensures that the work done by this obstacle torque is zero. To show that this choice of the obstacle torque preserves the convergence properties of this method (see [ 5 ] ) a Lyapunov candidate function of the form V = p X M T x + U ( x ) , or more verbosely, $ (XTXl + qTq) + U(x). The state velocity vector has been decomposed into the linear and angular components. The state vector x = [xl,4] where xl denotes the linear position vector, and q, the angular position quaternion. Furthermore, using the unit rotation quaternion representation, q = -($ @ q) and q = @ q + $ @ ($ @ q), where $ = [w,O] is the vector quaternion form of w and 8 represents the quaternion product, the convergence analysis is performed in this generalized position-orientation space. Further detail on the quaternion analysis may be found in [6]. The time derivative of the Lyapunov function yields 9 = M (XTxl + q'q) + VUTx, + VUTq. The rate of change of Lyapunov energy can be represented as i, = x:(-vU(xi) - k2Xl - BXl) + qT(-vU(q) - k 2 q f ( T o b s @ q - $ @ ($ 8 9))) + vU(Xl)Txi + vU(q)Tq (10) where Tabs is the quaternion form of r o b s , given by Tabs = [ r o b s , 01. Since r o b s is defined to be either zero (when s I n) or else normal to w , and may be given by the relation r o b s = (Q x w ) when not zero, the time rate of change of the Lyapunov function, upon resolution of the quaternion relations, becomes simply i, = -k2X?Xl - k2qTq 5 0 which is inherently negative semi-definite. Using the LaSalle Invariance Principle, strict negative definiteness can be shown. 5 Result of Dynamic Control on Puma560 using MMF Methods The governing robot dynamic equation is given by the relation: M ( 0 ) 8 +C(6,0)6 +k(O) = r (11) where M represents the mass matrix, C , the matrix of Coriolis and centripetal forces, k, the gravity vector and 0 the vector of joint angles, r is the applied joint force. The M M F control scheme outlined in this paper generates the set of r that will be applied to the dynamic control equation. The resulting joint positions and velocities represents the motion of the robot. In this section, an example of a robot navigating in the space of obstacles - both task space obstacles as well as Cartesian space obstacles - and required to obtain a certain goal configuration, is presented. The planner control is effected in the following fashion. The joint space obstacles (joint limits) are generated thus: upper joint limit 1 corresponds to a surface at [&,O, . . .O] and with surface normal [--I, 0 , . . .O]. Correspondingly, the surface vectors for this surface are setup as [O, 1,O.. .O], [O, 0,1, . . .O] , . . . [O, 0 . . . I] with accurate assignments for the sign of the surface vectors to ensure closed loops around the joint space boundary. This done, the joint space forces are computed using the relations Fattr = -kl(O - Od) (12) Fdamp = -m) (13) = -azo (14) Next the Cartesian space obstacle forces are computed. The Cartesian space force and torque are computed for each of the N-links of the robot. F:::t = Xzo(X:om x B:om) (15) ,xart - T T N obs - ( Xz=O(n(v (lz .)) (16) Now the generalized force vector is obtained by stacking the force and torque terms: (17) which is transformed through the generalized Jacobian matrix into joint space yielding the resultant relation: 7- = Faitr + Fdamp + FZS + JTFS,Er (18) Now by appending gravity compensation to this T , it is applied as the control to Eq. 11 Although parameter adjustment and tuning are not mandatory for convergence, the robot motion plan will be correlated with the parameters used for the control inputs. The parameters used affect the inertia in the control system. For instance, the larger the proportional gain in the attractive force, the steeper a potential well it sets up and hence the robot slides down it with correspondingly greater energy. A shallow well, on the other hand results in very straight lined paths, where the robot heads straight for the goal, but navigation around the obstacle becomes very exaggerated. The resulting task space paths are shown in the associated figures. In this problem, the objective or the desired configuration was stipulated at @, = [67.5, -45,176.4, -35.5,33,200]. The joint limits were the standard joint limits of a Puma560. and the initial configuration was given by 00 = [-75.6, -15,91.5,143, -59.7,112.3]. Task space obstacles were vertical walls located at: Wall config. Centroid Normal Vertical [0.05,0.4,0.6] [0, -1,Ol Horizontal [0.55,0.025,1.25] [O,O, -11 The robot starts with its tip very close to both, the vertical wall in X and the Joint4 joint limit. To get to the goal, without colliding with the walls or going through its limit, the robot, increases its elbow angle (dropping the forearm) but lifting the shoulder joint. To navigate the facing wall, the robot lifts its entire arm to the tool, curving up to avoid the wall, lifting the shoulder a t the same time. The presence of the short ceiling flattens the trajectory, leaving the robot having to pull out from the ceiling before it can adequately pull up to cross the second enclosing wall to the goal. The robot approaches the second vertical wall but has to approach very close to it to avoid both, its Joint3 singularity as well as the first vertical wall. Small \u201cbobbles\u201d are seen in the elbow and tip paths as the action of the M M F manifests its self strongly at this point due to the proximity of the robot to the obstacle surfaces. Removing the horizontal wall results in a much smoother and natural looking trajectory, whereby the robot tip first falls toward the floor as the forearm falls and the robot base turns toward the goal; the elbow and tip then smoothly curve up and over the second vertical wall. The corresponding joint space trajectory during this navigation are shown in Fig. 9 Joint 1 is most encumbered in this move. The robot starts off fairly close to its joint1 lower limit and has to further approach it to navigate the walls. In nearing the goal, it approaches very close to its other limit and the characteristic \u201cbobble\u201d is seen in the joint space trajectory at the highest points in the joint path arc. Vertical [0.75,0.0,0.85] [ - l , O , O ] 6 Conclusions In this paper, we reviewed the concept of the Modified Magnetic Field to robot motion planning and control in an obstacle field. The treatments in both Cartesian space and configuration space were highlighted. The fundamental idea is based on the electrodynamic principle, where a magnetic component originates from the presence of fictitious current elements wrapped around each obstacle. Extension of the planning algorithm to a linked manipulator was then presented where the objective was to navigate both joint space and Cartesian space constraints. The al- gorithm was successfully able to negotiate the constraints. Since the forces generated by the MMF can be analytically computed, the algorithm has also been implemented as a real-time feedback controller. References [I] J.C.Latombe, Robot Motion Planning. 101 Philip Drive, Assinippi Park, Norwell, MA 02061: Kluwer Academic Publishers, 1991. [2] 0. Khatib, \u201cReal-time obstacle avoidance for manipulators and mobile robots,\u201d Proc. of the IEEE Internat? Conf. on Robotics and Automation, pp. 500-505, 1985. [3] D. E. Koditschek, \u201cExact robot navigation by means of potential functions: Some topologi- cal considerations,\u2019\u2019 Proc. of the IEEE Intemat \u2019I Conf. on Robotics and Automation, pp. 1-6, 1987. [4] K. J.O. and K. P.K., \u201cReal-time obstacle avoidance using harmonic potential functions,\u2019\u2019 IEEE Ransuctions of Robotics and Automation, vol. 8, pp. 338-349, Jun. 1992. [5] L. Singh and H. Stephanou, \u201cA collision-free, realtime motion planning with guaranteed convergence using analytical circulation fields,\u201d Submitted IEEE Int? Conf. on Robotics and Automation, 1996. [6] L. Singh and H. Stephanou, \u201cTask-based servoing in vector-quaternion space,\u201d Proc. of the IEEE Internat? Conf. on Robotics and Automation, vol. 25, pp. 100-110, May 1995."
        ]
    },
    {
        "image_filename": "designv11_11_0000615_rnc.4590050410-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000615_rnc.4590050410-Figure4-1.png",
        "caption": "Figure 4. A five-axle trailer system with the first and fourth axles steerable",
        "texts": [
            " The exception is m = 2, two steerable axles, two passive axles, alternating. That is, the first and third axles are steerable, and the second and fourth axles are passive. This situation would arise if a car were towing another car and both of the cars had drivers at the steering wheels. This example satisfies Proposition 10, and thus can be converted into Goursat form without prolongation. The five-axle system with two steering wheels is the lowest-dimensional case where interesting things begin to happen. Example 2 . Five-axle, one-four steering Figure 4. First consider the five-axle system with the first and fourth axles steerable, as sketched in The constraints are that each axle rolls without slipping: w'=sin O'dx'-cos 8 ' dy ' i = 1 , 2 , 3 a'=sin q9dxi-cos @'dyl, j = 1 , 2 The Pfaffian system is thus I = {a ' , w l , w2, a', w 3 ) and a complement to this system is: { d$', d@*, dx2). This basis is adapted to the derived flag, I = {a', w ' , w2 , a', 03) I (1) = { w ' , w 2 , w3) 1'2) = 1 ' 3 ) = { w21 (01 and it can be checked that each { I ( ' ) , dx2) is integrable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001625_robot.1994.351105-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001625_robot.1994.351105-Figure6-1.png",
        "caption": "Fig. 6: Point contact between A's vertex and B's face",
        "texts": [
            " Let us consider the example whose initial configuration is shown in Fig.S(a) and final one in (b). The initial configuration is on C5face-Type-B and the final one on C5face-Type-C. First, the topological path is determined by the algorithm presented in Sec.3. The obtained path is (C5face-Type-B, C4face-TypeB, C5face-Type-C, C4face-Type-B, C5face-Type-C), which is illustrated in Fig.4. The first motion makes the diagonal line VA~VA, parallel to the face F B ~ while keeping the positions of V A ~ and VA, (See Fig.6). The motion is specified by QVA, Qt + X = Vil , Q(VA, - VA,)Q~ = Vi, - Vi 1 ' (17) (18) where Vil and Vi, are the position of V A ~ and VA, respectively where A is at the initial configuration. Equation (17) keeps the position of VA, and Eq.(18) the orientation of the edge VA,VA~. We can have x = vi, - QVA,Q+, (19) from Eq.(17). Therefore, the total equations can be solved by substituting the solution of Eq.(18) to Eq.(19). That is, we can have the desired curve in the configuration space by solving the quadratic equations with three variables because the number of variables in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002011_ecc.2003.7086519-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002011_ecc.2003.7086519-Figure1-1.png",
        "caption": "Figure 1: The 4 rotors rotorcraft.",
        "texts": [
            " Helicopters are of the most complex flying machines. Its complexity is due to the versatility and manoeuvrability to perform many types of tasks. The classical helicopter is conventionally equipped of a main rotor and a tail rotor. However other type of helicopters exist including the twin rotor (or tandem helicopter) and the co-axial rotor helicopter. In this paper we are particularly interested in controlling a mini-rotorcraft having four rotors. Four-rotor rotorcraft, like the one shown in figure 1, have some advantages over conventional helicopters. Given that the front and rear motors rotate counter clockwise while the other two rotate clockwise, gyroscopic effects and aerodynamic torques tend to cancel in trimmed flight. This four rotor rotorcraft does not have a swashplate. In fact it does not need any blade pitch control. The collective input (or throttle input) is the sum of the thrusts of each motor. Pitch movement is obtained by increasing (reducing) the speed of the rear motor while reducing (increasing) the speed of the front motor. The roll movement is obtained similarly using the lateral motors. The yawmovement is obtained by increasing (decreasing) the speed of the front and rear motors while decreasing (increasing) the speed of the lateral motors. This should be done while keeping the total thrust constant. In view of its configurations, the four-rotor rotorcraft in figure 1 has some similarities with PVTOL (Planar Vertical Take Off and Landing) aircraft problem. Indeed, if the roll and yaw angles are set to zero, the four-rotor rotorcraft reduces to a PVTOL. In a way the 4-rotor rotorcraft can be seen as two PVTOL aircraft connected such that their axes are orthogonal. In this paper we present the model of a four-rotor rotorcraft whose dynamical model is obtained via a Lagrange approach. A control strategy is proposed having in mind that the four rotor rotorcraft can be seen as the interconnection of two PVTOL aircraft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003606_detc2005-85337-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003606_detc2005-85337-Figure8-1.png",
        "caption": "Fig. 8 Mobility analysis of 4-RARAR1R1RA PKC: (a) The original kinematic chain and The kinematic chain with an equivalent serial kinematic chain added.",
        "texts": [
            " The number of overconstraints of this 3-legged PKC is \u2206 = 3\u2211 i=1 ci \u2212 c = 3\u2212 1 = 2. Following the procedure for the full-cycle mobility inspection, we have Step 1 Since \u2206 = 2 6= 0, go to the next step. Step 2 For this PKC, there are no inactive joints. Step 3 It can be found that the PKC has full-cycle equivalent serial kinematic chain. The full-cycle equivalent serial kinematic chain can be represented by leg 1. Thus, the PKC has full-cycle mobility. Example 3 Consider the 4-RARAR1R1RA PKC shown in Fig. 8(a) [11]. In this PKC, the axes of all the RA joints are parallel, while the axes of the R1 joints within the same leg are parallel. The mobility analysis of this PKC can be performed as follows. Instantaneous mobility analysis The wrench system of each leg is a 1-\u03b6\u221e-system in which the base wrench can be a \u03b6\u221e whose axis is perpendicular to the 7 nloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/07/2016 Ter axes of all the R joints within the leg. The wrench system of the PKC is a 2-\u03b6\u221e-system, which is composed of all the \u03b6\u221e whose axes are perpendicular to the axes of the RA joints",
            " (4), (7) and (8), we obtain C = 6\u2212 2 = 4 and F = C + 4\u2211 i=1 Ri = 4. The number of overconstraints of this 4-legged PKC is \u2206 = 4\u2211 i=1 ci \u2212 c = 4\u2212 2 = 2. Following the procedure for the full-cycle mobility inspection, we have Step 1 Since \u2206 = 2 6= 0, go to the next step. Step 2 For this PKC, there are no inactive joints. Step 3 It can be found that the PKC has full-cycle equivalent serial kinematic chain. The full-cycle equivalent serial kinematic chain is a PPPR serial kinematic chain in which the axis of the R joint is parallel to the axes of the RA joints [Fig. 8(b)]. Thus, the PKC has full-cycle mobility. Example 4 Consider the 2-RARARARa-R\u03b1R1R1R1R\u03b1 PKC shown in Fig. 9(a) [12]. In this PKC, the axes of all the RA joints are parallel, the axes of the Ra joints are coaxial, the axes of the R\u03b1 are parallel to the axes of the Ra joints, while the axes of the R1 joints within a same leg are parallel. The mobility analysis of this PKC can be performed as follows. Instantaneous mobility analysis Copyright  2005 by ASME ms of Use: http://www.asme.org/about-asme/terms-of-use Dow The wrench system of each RARARARa leg is a 1-\u03b60-1\u03b6\u221e-system, whose base can be represented by a \u03b6\u221e whose axis is perpendicular to the axes of all the R joints and a \u03b60 whose axis intersects the axes of the Ra joint and is parallel to the axes of the RA joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002378_robot.1998.680881-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002378_robot.1998.680881-Figure4-1.png",
        "caption": "Figure 4. Considered displacements.",
        "texts": [
            " This displacement can be written as a function of the arm joint parameters 0,, e, ..., 0, at time t. So, at any time t+dt, the position of depends on the previous position of the vehicle Mv(,, and the current joint values of the arm 0=[0,(t+dt), e,(t+dt), ..., O,(t+dt)lT. x\",\",l = Om 'p\",\",, = Odeg %l\",t = Odeg in the world reference frame F =Om Therefore, after n displacements, the position of the end-effector in the world reference frame is given by the displacement FDe(,n, which is the composition of FDv(init), VDv(l,l for i=l..n, and as shown in figure 4. So, FDe(,nl is written as a function of every joint parameters [(si)i=l,,n, (Vi)i=l..n, (0i)i=l.,6] . (si, vi),=, ..,, are respectively the n curvatures (inverse of the steering radius) and the n velocities of the vehicle involved in the n displacements (YDv~li))i=l,,n, and (0i)l=l,,6 are the six joint parameters of the arm involved in the last displacement vDe(lt,l. The desired position of the end-effector in the world reference frame F is represented by the displacement FDe(des). Then, we have to compute the 2n+6 joint variables [(Si)i=l,,n ,(vi)i =,.. ,(Oili =,,, 6 ) which make the feasible displacement FDe(ln) equal to the desired displacement FDe(des). Figure 5 shows how we have implemented this method for our simulations. 4. Simulations The algorithm implemented for the simulations is the following (figure 5 ) , where <<OD denotes the composition of two transformations, and v, is an average velocity desired for the vehicle. We can use any representation for the displacements depicted in figure 4 and 5. In this section, we develop the trajectory generation method and give some simulation results with two representations: homogeneous matrices [7] and dual quaternions [e]. 4.1. Using homogeneous matrices In this first example, the displacements shown in figures 3 and 4 and used in figure 5 are represented using homogeneous transformations. Therefore, we can write displacement tiDv,inil) with the matrix: 0 Every elementary displacement vDv(tl) can be written thanks to the matrix: [cos(d$,i) -sin(d$,i) 0 dx,,] 0 with, if the vehicle is moving in a circular way: d4L = Si",
            " For the vehicle that we consider, the maximum values are: SmaX=0.5 m-', v,,,=5 m/s and dt=0.2 s. So, the maximum value for dQy is 0.5x5x0.2=0.5 radians. The maximum error that we make in linearising equation (3) is 4% in approximising sin(d@,,) and 0.3% in approximising At any time, the displacement \"De can be represented by matrix YTe=VTb.bTe, where 'T, is the matrix representing the displacement between Mv and the arm base referential Mb and bTe is the homogeneous matrix obtained with the PUMA direct kinematics. So, the total displacement represented in figure 4 is 'De, represented by matrix cos(d$,,>. This matrix represents the feasible displacement within n iterations for the global system. The problem is to place the end-effector referential Me on a desired position and orientation given by referential Medes. We can represent the desired displacement from F to Medes with matrix FTe(des). Then, we can compute the 2n+6 joint variables {(Si)i=l,,,l ( ~ i ) ~ = , , , ~ , ,(tli)i=l,,6} by minimizing the criterion C,, = 11 T, -F Tedes 11 under the constraints (ISil< S /Si( < d S max , , lvil< v max ,0i < lei1 < 0i hi1 < dv,,, } 4",
            " The eight components of a dual quaternion are defined by the Plucker coordinates of the screw axis associated to this displacement and the rotation and translation around and along this axis. More precisely, if we write 2= (:) a dual quaternion, Z =(Z, Z, Z , Z4)T is called the cc real part D of 2. Its four components are defined thanks to the Euler parameters of the corresponding rotation around the screw axis. And Zo = Zlo Z: Z: is called the (( dual part n of 2. Its four components are defined thanks to the relation Zo = - D . 2 where D is the corresponding translation along the screw axis. Displacements of figure 4 can also be represented using dual quaternions. In this section, we express the displacement FDv(,,,l,, with dual quaternion: ( 1 2 f 0 I 0 0 For a circular motion of the vehicle (using equation 3), displacement YDV(ll) can be written thanks to the dual quaternion of equation (8). For a rectilinear motion of the vehicle (using equation 4), displacement YDV(tl) can be written thanks to the dual quaternion of equation (9). ( 0 1 i ~ , dQvi ,. = 1 sin(+] I 1 '-'dQvi = vi.dt (9) 2 0 0 0 ( 0 , .os(+) (8) Ri",
            "sin( +) 0 l : l dual quaternion product G C3 Z = [ (z:,,) represents the displacement FD, from frame F to frame Mz. This product can be written: with: So, at any time t, the displacement \"De (figure 3 and 5 ) can be represented with the dual quaternion v Q e = v Q b \u20ac 3 b Q e , where \"Q,, is the dual quaternion representing the displacement between Mv and the arm base referential Mb and b Q e is the dual quaternion representing the PUMA direct kinematics. Therefore, the total displacement represented in figure 4 and 5 is FD-, represented by the dual quaternion : Qe=FQy(init) [ ii-' dQvi)@' Qectn) (1 1) This dual quaternion represents the feasible displacement within n iterations for the global system. We can represent the desired displacement from F to Medes with dual quaternion F A Q e(des). Then, we can compute the 2n+6 joint variables {(Si)i=l,,n ,(vi)i=l,,n ,(0i)i=l,,6} by minimizing the criterion of figure 5 written as C,, = I I F Qe-FQe(des) 1) under the constraints: {IS~I < s m a x > Ivi~ < v m a x , eimin < IeiI < 0imaX > < ds,,, > bil< dv,ax } 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001325_s0094-114x(02)00118-0-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001325_s0094-114x(02)00118-0-Figure1-1.png",
        "caption": "Fig. 1. Five-bar equivalent mechanism with a virtual ground link, lvg, as an equivalent of a manipulator.",
        "texts": [
            " A serial-connected manipulator can be analysed in the form of an equivalent mechanism by a virtual joint located between an end-effector and a virtual ground link connecting the end-effector to the origin. The link length and direction of this virtual ground link are dependent on the position of the end-effector. It is in effect associated with a reachable workspace and the virtual angle between the virtual link and the end-effector link is associated with the orientation workspace of the end-effector. Fig. 1 gives a planar four-link manipulator with the virtual adjustable ground link which converts the manipulator into a five-bar mechanism. Introducing a virtual coupler link, lvc, which connects joints B and D, the mechanism is converted into a hypothetical four-bar mechanism. The study of the orientation capability can then be conducted in the form of that of the rotatability of the end-effector link with respect to the virtual ground link, which can be described as the angle of the virtual joint. The virtual joint angle which indicates the orientation capability of the end-effector link is represented by a rotation angle hv",
            " Hence, there are no limited angle ranges, the virtual joint of the end-effector link with respect to the virtual ground link has a full rotation. As a result, a full dexterous workspace exists for the manipulator at the point at which the virtual joint is located. The following produces the analysis of the conditions which produces the complex virtual angle at the point at which the end-effector reaches. It hence gives the region of a full dexterous workspace. The study starts from a four-link manipulator as in Fig. 1. To obtain the full dexterous workspace, it is to confine the virtual angle to a complex solution. First restrict the first solution, cos hva, outside the f 1; 1g range, two conditions are produced. They are \u00f0l1 \u00fe lvc\u00de2 < \u00f0lvg le\u00de2, and \u00f0l1 \u00fe lvc\u00de2 > \u00f0lvg \u00fe le\u00de2. From the first condition, l1 \u00fe lvc < lvg le when lvg > le, the boundary, lvg, can be expressed as l1 \u00fe lvc \u00fe le < lvg. This violates the condition set for formation of lvg. Similarly when lvg < le. Hence the first condition is invalid. From the second condition, l1 \u00fe lvc > lvg \u00fe le, the upper boundary which produces the complex number can be expressed in terms of lvg as lvg < l1 \u00fe lvc le: \u00f08\u00de When le is the shortest link and the end-effector reaches the region which makes lvg as the longest link, this is the Grashof s first condition [13,15] in which the shortest link le has a full rotation",
            " To illustrate the use of the orientation capability map, concentric circles a0, b0, c0 and d 0 adjacent to the critical values are used to identify the orientation ranges. The dexterous workspace is then represented in the range of f100; 360g in Fig. 4. This can also be proved from [7] and further proved by applying the finite twist mapping [5,16] which produces the range as in Fig. 5. In Fig. 5, the outer profile is the reachable workspace while the inner region is the full dexterous workspace. The region with the mesh is partial dexterous workspace. In the above, the orientation capability map has been given by either mapping the graphical representation in Fig. 1 or obtaining the results from the generalised discriminant in (1) and (2). It can be seen from both Figs. 3 and 4 that the two orientation boundary loci define the orientation ranges of a manipulator and distinguish the dexterous workspace from a partial dexterous workspace. Suppose the radius of the lower orientation boundary locus is rol and the offset between the origin of the locus and the coordinate origin is s0 as in Fig. 6, the polar equation of the boundary locus can be given as cos h \u00bc 1 r r2ol s0 2s0 r 1 2s0 : \u00f010\u00de Similarly, the upper orientation boundary locus of radius rou can be given as cos h \u00bc 1 r r2ou s0 2s0 r 1 2s0 : \u00f011\u00de From the analysis, the offset value is s0 \u00bc le and the following is given rou \u00bc l1 \u00fe lvc; \u00f012\u00de rol \u00bc jl1 lvcj: \u00f013\u00de The intersection between the workspace loci which is centred at the coordinate origin and the two boundary loci give the orientation capability of a manipulator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003833_maes.2006.1684262-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003833_maes.2006.1684262-Figure1-1.png",
        "caption": "Fig. 1. Smart VA V",
        "texts": [
            " With consideration of economical efficiency, accessibility, and purchasability, the TeAS IT is chosen for a collision avoidance device for UAVs in this paper, then, components, aural and visual annunciation, advisories, modes, functions, and interfaces of the TeAS II will be examined later. ON\ufffdBOARD REQUIREMENTS I\ufffd\ufffdI I Fig. 2. Classification of Collision A voidance Sensor On-board requirements for a UA V (The Korea Aerospace Research Institute is developing rhe UA V named \"Smart UAV\" currently and a collision avoidance device will be installed in the UA V) are in Figure 1. Maximum velocity for this VA V is 500 krnIh without a payload, 440 kmIh with a payload (a maximum weight of this payload is 40 kg.). The weight and power consumption of a collision avoidance sensor are limited to 25 kg and 250 W, respectively . A space for this device is allowed 62 (W) x 42 (H) x 30 (D) em so that a loading sensor should be small, light-weight, and low-power consumption. TYPES OF COLLISION AVOIDANCE SENSORS Generally the detection sensors are classified by purposes of missions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003047_iros.2003.1249198-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003047_iros.2003.1249198-Figure5-1.png",
        "caption": "Figure 5: Object manipulated by the system",
        "texts": [
            " Obviously enough, the assigned grasping task (being an impossible one) will therefore not be at all accomplished. Finally note that for the same reasons mentioned in the previous section, also in this case 8 should be generated via the smooth form where now (43) - a = (El ,&) with E l , E2 having the same shape as Gin Fig.3. 5 Object Manipulation via Dual Arm, NonHolonomic mobile manipulator The results obtained in the previous section will be now very easily extended to the case of an object manipulated by a dual arm mobile non-holonomic system (Fig.5). The manipulated (lightweight) object is assumed to be firmly grasped by the end-effector of dual arm system. The object itself is characterized by its own fixed body frame <b which is asked to be asymptotically convergent toward an assigned goal frame <g>. By denoting with el the generalized enor (position and orientation) of frame <I> with respect to <g>, let us define as (44) the velocity reference signal that, once applied to 42 , would guarantee <b itself to be asymptotically convergent to <g>"
        ],
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    },
    {
        "image_filename": "designv11_11_0001964_robot.1997.614291-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001964_robot.1997.614291-Figure6-1.png",
        "caption": "Figure 6: Forerm flattens to fit under ceiling",
        "texts": [],
        "surrounding_texts": [
            "In this section, the MMF method is bricfly summarizcd. While conventional potential field methods are derived from principles of electrostatics, the Modified Magnetic Field method is derived from electrodynamical considerations. The obstacle forces are obtained from a current based formalism. This distinction and the methods of their computation are briefly summarized in this section and shown in greater detail in [ 5 ] . The conventional attractive potential field form is used to represent the field setup by the attractor: where -kattr is some positive constant used to represent the intensity of the force field and x is the location of the operating point with respect to the goal location Xd. A damping force is used to damp out oscillations that accrue from the specification of the above attractive field and is given in the following form. where x represents the velocity of the robot. The damping field force is a non-conservative force that tends to oppose the motion of the system. The definition of the obstacle field and force is the key innovation of the MMF method. The basis of the MMF is a set of virtual closed current loops enclosing the obstacle. These virtual current loops generate virtual forces that are termed the Modified Magnetic Field . The obstacle force and field are defined by the following relations: Fobs = X x B (3) (4) where B represents the obstacle field, the MMF , and Fobs represents the obstacle force due to this field. Again, x represents the robot velocity, x the unit velocity vector, l represents the direction of the current loop enclosing the obstacle face and p represents the magnitude of the perpendicular distance of the robot from the given obstacle face. The obstacle field definition is similar in structure to the conventional electro-magnetic Magnetic field, however, the structure of the M M F is somewhat different from that of the classical Magnetic field. Using the redefined Eq. 4 B improves the behavior of the control law, resulting in less convoluted paths, than the classical form. This is shown in Fig. 2. Rather than spiral endlessly, the M M F field has some preferred directions such that motions in those directions remain unaffected while others are turned into those directions. 3 Domain Extension of the MMP The form introduced for the obstacle force has been delineated in terms of the vector cross product operation. To address planning in higher dimensional spaces such as configuration or task spaces, the definition needs to be extended to consistently and exactly address force generation. Towards this end, we use the tensor notation to compute the B = B x . = C,(l,x)X) x . (5) term so that the computation of the corresponding obstacle force Fobs becomes a tensor reduction operation with the robot velocity, as Fobs = -BX. In this section, we briefly recount the computation of B for any given obstacle surface and robot velocity given that the form selected for the MMF was given by B = We also discuss the computation of the obstacle forces and torques applied to a robotic link. Previously, we presented control forces that applied to a point robot - whether operating in Cartesian or in joint space. Here we extend the definition of the obstacle force to apply to linked manipulators. The method of computing the B tensor is briefly summarized for its relevance to the next section. Let the n-dimensional obstacle surface be characterized by a minimal set of n orthonormal vectors: 1 surface normal and (n-1) surface vectors. The B tensor matrix is then computed from these vectors. Given that Fobs = x x B or Fobs = -Bx using new notation, it follows that x.(Bx) = 0 from the scalar triple product result. Now this must be true for all x, including those velocity directions that are parallel to the eigenvectors of B. $ in Eq. 4. P For x = [,[ E [EV set ofB] . 1 1 [ 1 1 2 = o (6) To satisfy this requirement, either X g = 0 or llE112 = 0. Skew-symmetric matrices meet these criteria since the roots of skew-symmetric matrices are either zero or strictly imaginary. Now, if X g = 0, then Fobs = AB . = 0 which is exactly the desired behavior if the robot velocity runs parallel to the surface. However, if the robot velocity runs along the surface normal the 1 1 [ 1 1 2 = 0 solution is used, which corresponds to an imaginary root. To choose a real 13 with 2 complex conjugate pairs (to ensure realness of a), select any (n - 2) of the surface vectors as the B eigenvectors with eigenvalues of 0, and choose f~ as the two remaining eigenvalues. Eigenvectors for these last two values are constrained to lie in the plane of the surface normal direction and the last (n-1)th surface vector. Now select any 2-d skew-symmetric matrix with eigenvalues f i , find its eigenvectors and the last two eigenvectors of our MMF matrix is now known in terms of the 2 known basis vectors scaled by the components of the 2-d eigenvectors just found for the known 2-d matrix. Now, the eigenvalues and the eigenvectors are known and the computation of B may be computed. 4 Computing the Obstacle Fields and Forces for a Linked Manipulator An outline of the computation of the obstacle forces for a linked manipulator navigating in a Cartesian or task space are presented herein. Consider the situation shown in Fig. 3. The joint space obstacle forces are generated in joint space and joint limit avoidance is performed by treating each limit or singularity as an obstacle and computing the resulting set of forces as described earlier. Subsequently, task space motion planning is performed whereby the obstacle forces and torques are computed for the task space obstacles. These task space forces and torques are then transformed back to joint space through the manipulator Jacobian, where they are integrated with the previously obtained jointspace forces. Collectively, these forces serve as input control torques in the robot dynamic relation where final force resolution is performed. The joint space obstacle avoidance is performed as shown in the previous section and detailed in [5]. In task space, the obstacle force on the link is formulated in two parts, one generates the task-space force and the other the torque for the given link. To compute the link force component, the link is abstracted to its center of mass and the obstacle force for the center of mass is then computed in Cartesian space, as has been done for the point robot. The obs- tacle force is then computed as: Next, the obstacle torque is computed. This torque, the Modified Magnetic Torque is computed in a somewhat analogous fashion through the following relation: where w represents the angular velocity of the link, s represents the link axis, U the linear velocity due to the orientational component, and I' denotes the Modified Magnetic Torque Field, the angular analog of the MMF . The M M T F and the obstacle torque has similar electro-dynamic connotation as the MMF , however, in implementation, we have yet again, departed from the classical electro-magnetic mathematical definitions. Rather than visualizing the robot link as a point charge, as has been done in classical potential field methods and earlier in this paper in the development of the M M F , here the link is treated as a dipole and derivations of r o b s derive from the interaction of the dipole moment with the obstacle torque field. Eq. 8 constitutes a contraction mapping of the tensor I?. The cross product terms in Eq. 9 may be computed as outlined in Sec. 3. While the tensor form is necessarily important for higher dimensional spaces, the cross product form may be retained for classical Cartesian space development. The rationale for the above mathematical structure will be briefly outlined. The considerations governing the M M T F equations here are similar to those that went into formulating the MMF forces. Ideally, we would like to preserve link configurations in which the link lies parallel to the obstacle surface (i. e. where r o b s = sTn = 0) and reorient those in which the link lies along the surface normal. Towards that end, the sTn term is important in that this term is zero for every link configuration that lies along the surface and is only non-zero when the link axis is oriented towards the surface. Additionally, a torque expression that ensures that the work done by that torque will always be zero is desired i.e. r such that W = w.7 = 0, as will be shown to be important in the brief outline of the Lyapunov Energy analysis perform in the next paragraph. The (U x (li x s ) ) x w term in the definition of I' ensures that this requirement on the obstacle torque is met. Multiplying the dyads in Eq. 9 by the vector s causes the contraction of the tensor B, and yields the above vector, (li x s ) x w. The presence of the . x w term, this term is guaranteed to be orthogonal to U, and hence ensures that the work done by this obstacle torque is zero. To show that this choice of the obstacle torque preserves the convergence properties of this method (see [ 5 ] ) a Lyapunov candidate function of the form V = p X M T x + U ( x ) , or more verbosely, $ (XTXl + qTq) + U(x). The state velocity vector has been decomposed into the linear and angular components. The state vector x = [xl,4] where xl denotes the linear position vector, and q, the angular position quaternion. Furthermore, using the unit rotation quaternion representation, q = -($ @ q) and q = @ q + $ @ ($ @ q), where $ = [w,O] is the vector quaternion form of w and 8 represents the quaternion product, the convergence analysis is performed in this generalized position-orientation space. Further detail on the quaternion analysis may be found in [6]. The time derivative of the Lyapunov function yields 9 = M (XTxl + q'q) + VUTx, + VUTq. The rate of change of Lyapunov energy can be represented as i, = x:(-vU(xi) - k2Xl - BXl) + qT(-vU(q) - k 2 q f ( T o b s @ q - $ @ ($ 8 9))) + vU(Xl)Txi + vU(q)Tq (10) where Tabs is the quaternion form of r o b s , given by Tabs = [ r o b s , 01. Since r o b s is defined to be either zero (when s I n) or else normal to w , and may be given by the relation r o b s = (Q x w ) when not zero, the time rate of change of the Lyapunov function, upon resolution of the quaternion relations, becomes simply i, = -k2X?Xl - k2qTq 5 0 which is inherently negative semi-definite. Using the LaSalle Invariance Principle, strict negative definiteness can be shown. 5 Result of Dynamic Control on Puma560 using MMF Methods The governing robot dynamic equation is given by the relation: M ( 0 ) 8 +C(6,0)6 +k(O) = r (11) where M represents the mass matrix, C , the matrix of Coriolis and centripetal forces, k, the gravity vector and 0 the vector of joint angles, r is the applied joint force. The M M F control scheme outlined in this paper generates the set of r that will be applied to the dynamic control equation. The resulting joint positions and velocities represents the motion of the robot. In this section, an example of a robot navigating in the space of obstacles - both task space obstacles as well as Cartesian space obstacles - and required to obtain a certain goal configuration, is presented. The planner control is effected in the following fashion. The joint space obstacles (joint limits) are generated thus: upper joint limit 1 corresponds to a surface at [&,O, . . .O] and with surface normal [--I, 0 , . . .O]. Correspondingly, the surface vectors for this surface are setup as [O, 1,O.. .O], [O, 0,1, . . .O] , . . . [O, 0 . . . I] with accurate assignments for the sign of the surface vectors to ensure closed loops around the joint space boundary. This done, the joint space forces are computed using the relations Fattr = -kl(O - Od) (12) Fdamp = -m) (13) = -azo (14) Next the Cartesian space obstacle forces are computed. The Cartesian space force and torque are computed for each of the N-links of the robot. F:::t = Xzo(X:om x B:om) (15) ,xart - T T N obs - ( Xz=O(n(v (lz .)) (16) Now the generalized force vector is obtained by stacking the force and torque terms: (17) which is transformed through the generalized Jacobian matrix into joint space yielding the resultant relation: 7- = Faitr + Fdamp + FZS + JTFS,Er (18) Now by appending gravity compensation to this T , it is applied as the control to Eq. 11 Although parameter adjustment and tuning are not mandatory for convergence, the robot motion plan will be correlated with the parameters used for the control inputs. The parameters used affect the inertia in the control system. For instance, the larger the proportional gain in the attractive force, the steeper a potential well it sets up and hence the robot slides down it with correspondingly greater energy. A shallow well, on the other hand results in very straight lined paths, where the robot heads straight for the goal, but navigation around the obstacle becomes very exaggerated. The resulting task space paths are shown in the associated figures. In this problem, the objective or the desired configuration was stipulated at @, = [67.5, -45,176.4, -35.5,33,200]. The joint limits were the standard joint limits of a Puma560. and the initial configuration was given by 00 = [-75.6, -15,91.5,143, -59.7,112.3]. Task space obstacles were vertical walls located at: Wall config. Centroid Normal Vertical [0.05,0.4,0.6] [0, -1,Ol Horizontal [0.55,0.025,1.25] [O,O, -11 The robot starts with its tip very close to both, the vertical wall in X and the Joint4 joint limit. To get to the goal, without colliding with the walls or going through its limit, the robot, increases its elbow angle (dropping the forearm) but lifting the shoulder joint. To navigate the facing wall, the robot lifts its entire arm to the tool, curving up to avoid the wall, lifting the shoulder a t the same time. The presence of the short ceiling flattens the trajectory, leaving the robot having to pull out from the ceiling before it can adequately pull up to cross the second enclosing wall to the goal. The robot approaches the second vertical wall but has to approach very close to it to avoid both, its Joint3 singularity as well as the first vertical wall. Small \u201cbobbles\u201d are seen in the elbow and tip paths as the action of the M M F manifests its self strongly at this point due to the proximity of the robot to the obstacle surfaces. Removing the horizontal wall results in a much smoother and natural looking trajectory, whereby the robot tip first falls toward the floor as the forearm falls and the robot base turns toward the goal; the elbow and tip then smoothly curve up and over the second vertical wall. The corresponding joint space trajectory during this navigation are shown in Fig. 9 Joint 1 is most encumbered in this move. The robot starts off fairly close to its joint1 lower limit and has to further approach it to navigate the walls. In nearing the goal, it approaches very close to its other limit and the characteristic \u201cbobble\u201d is seen in the joint space trajectory at the highest points in the joint path arc. Vertical [0.75,0.0,0.85] [ - l , O , O ] 6 Conclusions In this paper, we reviewed the concept of the Modified Magnetic Field to robot motion planning and control in an obstacle field. The treatments in both Cartesian space and configuration space were highlighted. The fundamental idea is based on the electrodynamic principle, where a magnetic component originates from the presence of fictitious current elements wrapped around each obstacle. Extension of the planning algorithm to a linked manipulator was then presented where the objective was to navigate both joint space and Cartesian space constraints. The al- gorithm was successfully able to negotiate the constraints. Since the forces generated by the MMF can be analytically computed, the algorithm has also been implemented as a real-time feedback controller. References [I] J.C.Latombe, Robot Motion Planning. 101 Philip Drive, Assinippi Park, Norwell, MA 02061: Kluwer Academic Publishers, 1991. [2] 0. Khatib, \u201cReal-time obstacle avoidance for manipulators and mobile robots,\u201d Proc. of the IEEE Internat? Conf. on Robotics and Automation, pp. 500-505, 1985. [3] D. E. Koditschek, \u201cExact robot navigation by means of potential functions: Some topologi- cal considerations,\u2019\u2019 Proc. of the IEEE Intemat \u2019I Conf. on Robotics and Automation, pp. 1-6, 1987. [4] K. J.O. and K. P.K., \u201cReal-time obstacle avoidance using harmonic potential functions,\u2019\u2019 IEEE Ransuctions of Robotics and Automation, vol. 8, pp. 338-349, Jun. 1992. [5] L. Singh and H. Stephanou, \u201cA collision-free, realtime motion planning with guaranteed convergence using analytical circulation fields,\u201d Submitted IEEE Int? Conf. on Robotics and Automation, 1996. [6] L. Singh and H. Stephanou, \u201cTask-based servoing in vector-quaternion space,\u201d Proc. of the IEEE Internat? Conf. on Robotics and Automation, vol. 25, pp. 100-110, May 1995."
        ]
    },
    {
        "image_filename": "designv11_11_0002717_robot.2004.1308774-Figure1-1.png",
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        "caption": "Fig. 1. Modeling of sensory informarion: (a) -physical network of 2 mbots in SE(2): R, has range measuremem about R,: R, bas absolute measurements about itself and bearing measurements about R,. A body reference frame. Bi, has been atache to R j . (b) - sensing p p h representation.",
        "texts": [],
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            "P r d i n g i dthe 2004 IEEE 1nt.matlonal Conference on RobOUcs 6 Automation\nNew hleans, LA * Wl20M\nFormations for Localization of Robot Networks Fan Zhang Ben Grocholsky Vijay Kumar\nGRASP Laboratory, University of Pennsylvania, Philadelphia, PA 19104, USA {zhangfan, bpg, kumar}@grasp.cis.upenn.edu\nAbsfmcl-In this paper, we consider the problem of cooperatively localizing a formation of networked mobile mhoWvehicles in SE(2), and adapting the formation to d u c e localization errors. Firs& we propose necessary and sufficient conditions to establish when a team of robots with heterogeneous sensors can he completely localized. We present experimental measurements of range and hearing with omni-directional cameras to motivate a simple model for noisy sensory information. We propose a measure of quality of team localization, and show how this measure directly depends on a sensing graph. Finally we show how the formation and the sensing graph can he adapted to improve the measure of performance for leaqloealiition and for localization of targets through experiments and simulations.\nI. INTRODUCTION\nIn order for a team of mobile robots to navigate autonomously in some desired formations and further perform cooperative tasks, such as surveillance and target acquisition, they must be able to localize themselves in the formation as well as in a global reference frame [I], [2]. Therefore, how to estimate robots' positions and orientations (poses) in a precise and efficient way is of particular interest. Our interest in this paper is localizing a team of heterogeneous robots in 8E(2), and in localizing targets with information obtained from heterogeneous sensors. Specifically, we are interested in conditions under which all robots in the formation can be localized in the environment, and in minimizing the relative and absolute uncertainty in the estimates. Our goal in this paper is to derive necessary and sufficient conditions for localizing a formation of three or more robots in SE(2) from distributed camera measurements, quantifying the quality of the resulting estimates, and adapting the team formation to improving these estimates.\nRecent research has addressed the problem of network localization in non-deterministic domains. Examples of fusing observations from heterogeneous sensors to estimate the state of a robot team include the distributed Kalman filter [3] and maximum likelihood 14) methods. These approaches consider communication and computational cost but do not address the impact of robot formation on the quality of the solution obtained. Other studies investigate generating optimal sensing mjectories for robots engaged in target tracking tasks given the robot state is known exactly [5] , [6]. The work presented in this paper addresses the combination of these two problems. Given the fact that the quality of estimates obtained from measuremenls depends on how well sensors can be localized, we extend these ideas to find an optimal formation control scheme which will facilitate not only maximal target localization but also consider the robot configuration estimate quality.\nAlso relevant to this work is the recent literature that uses graphs to model sensor networks and cooperative control schemes [71, [SI. Results on graph rigidity theory [9], [IO], [ I l l can be directly applied to multi-robot systems in W2 [IZ], [13]. However, relatively little attention has been paid on networks with bearing observations. which is particularly important for networks of cameras.\nThis paper is organized as follows. In Section U, formations of mobile robots and sensor measurement information will be modeled topologically via graph theory notations. Without considering measurement error at first, we generate the concepts of formation constraint and constraint matrix in Section IU, and use them to find the necessary and sufficient conditions for a formation to be localizable. Measurement errors and their connection to estimate errors are introduced in Section IV, and the dependenoe of localization quality on the sensing graph and formation geometry is also investigated. A control strategy for determining optimal formations is presented. Practical application of these concepts to a small team of robots equipped with omni-directional cameras follows in Section V. The camera modelling, performance impact of the sensing graph and robot deployment to an optimal configuration are detailed. Concluding remarks are given in Section VI.\n11. MODELING\nConsider a planar world, W = Wz, occupied by a team of n-robots, 'R = { R I , Rz, . . . R,,}, and assume each robot can communicate with every other robot in the team. The physical configurations of the robots coupled with the characteristics of the hardware and the requirements of the sensing and control algorithms induce a physical network or a formation of n robots in 5E(2). We define a global reference frame F by forming a virtual robot or a beacon Ro with fixed configuration\n0-7803-82323/04/$17.00 (92004 IEEE 3369",
            "qo = 0 in the inertial frame. (See Figure I(a)). The confi U\nration of R in 7 is denoted by E W3\", where q; = E W3 is a parameterization of SE(2). with pi = ( x i , Y , ) ~ and 8i , the absolute position and orientation of the ifh robot. A body reference frame Bj at the jth robot is also defined with its x-axis aligned with the direction of heading of Rj. The configuration or the shape of the formation, R, is described in the body-fixed frame 0, by , ( q i ) T ] T , where 2 = (p j , , 6'j;)T with pji = ( ~ j i , y j i ) ~ and e,,, the relative position and orientation of R, about R,. and 4: = 0.\nIn [7], [Z]. we defined the control graph. a directed graph in which each edge represents an interconnection linking the control inputs of one robot to the state of another. Here, in order to represent the sensory information, we define another directed graph called the sensing graph, '2 = (V ,E , 2 , P ) , where V = R U {&} is a finite set of vertices. The edge set E c V x V consists of labeled edges that represent the presence of measurements (observations) between robots. We consider three types of exteroceptive sensors: range sensors, bearing sensors, and GPS sensors. The measurement set 2 consists of three type of sensory information: (i) range between two robots, p i j . (ii) bearing of one robot in relation to another, bij , and (iii) absolute position of a robot in.7, ( x j : y j ) , which can be obtained by global positioning sensors, or via triangulation with fixed, known landmarks. P i s a model of the uncertainties associated with the estimates in 2.\nIn a sensing graph 0, the jih vertex has an incoming edge from the i th vertex labeled by ( p i , , +\",) whenever robot R, can sense robot Rj. Corresponding to types of sensory information, we use (i) a shorthand relative range edge ( p i j ) to denote (p,j,null), (ii) a rehtive bearing edge ( $ i j ) for (null: $i,) and (iii) a range-bearing edge ( p i j , $ ; j ) pointed from Ri to Rj respectively. Any absolute measurements made by any robot Rj can be regarded as a range-bearing edge, b j o , 4 j O h or simply ( P j > 4 j ) .\nIn the next section we will consider a deterministic setting to determine necessary and sufficient conditions on the sensing graph for team localization. We will later, in Section IV, consider uncertainties in measurements, with P consisting of information about variances: a:ij for range measurements, a$<, for bearing measurements, and covariance matrices for range-bearing measurements.\nP - = [qy, q:, . . . , q: ]\n111. LOCALIZABILITY OF FORMATIONS\nIn order to consider whether a team of robots can be localized or not, it is necessary to fuse the information available from different sensors and verify if this information is adequate. For a team of n robots in SE(2), localization is the determination of the 3n coordinates that characterize the robot positions and orientations. Thus it is necessary to first see if 3n independent measurements are available or not. Since every measurement specifies a constraint on the 3n coordinates, we have to develop a test of functional independence for all constraints. Accordingly, we will define a constraint matrix\nwhose rank will allow us to verify if the team can be localized or not.\nFor each range and bearing measurement, the constraints on the coordinates in frame Bj are given by:\nA pair of bearing measurements, 4 ; j and 4,;. involving robots Q and R j , results in the following Type 3 constraint:\nFinally, any pair of bearing measurements, $; j and $ j k , involving three robots R,, Rj . and R k . results in the following Type 4 constraint.\nAll these constraints can be written in the form:\nL1 . P = h($) ( 5 ) where L1 is a linear combination of measurements, and h is a nonlinear function of the shape variables in some body-fixed reference frame. It is not too difficult to see that there are only four types of constraints that can be used to describe the network. All other equations that can be written are functionally dependent on the above constraint equations.\nBy differentiating the four constraint equations, we get expressions describing allowable small changes (equivalently velocities) of the robot coordinates."
        ]
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    {
        "image_filename": "designv11_11_0001005_0165-0114(94)00225-v-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001005_0165-0114(94)00225-v-Figure10-1.png",
        "caption": "Fig. 10. Definition of sat(X).",
        "texts": [
            " 9): sgn(X) = sgn(defuzz(X)), (14) where defuzz(X) is the result of the defuzzification operation on the fuzzy set X, e.g. the center of gravity (c.o.g.). R. Palm, D. Driankov / Fuzzy Sets and Systems 70 (1995) 315-335 321 Let X = {px(X(t)), x(t)} be a normal and convex fuzzy set then the division of X by a crisp number \u2022 is defined by - - ~ ~A X ~ . Then the sat-function is defined as follows: For a crisp value ~ > 0 we define X ( X ~ ~ for -q)~<defuzz(X)~<+q~, (15a) s a t \\ / ~ = sgn(X) else, (15b) where (15a) is fuzzy and (15b) is crisp (see Fig. 10). For a specific class of nonlinear systems there exists a robust control method called sliding mode control [ 17]. This method copes very well with model uncertainties, parameter fluctuation and disturbances. A little change of pure sliding mode control leads to sliding mode control with boundary layer [14]. In addition to that it has been shown that fuzzy control, as it appears in many control applications, is an extension of the principle of sliding mode with boundary layer [10, 11, 8]. In the following it will be discussed what happens if some of the signals within the control loop are fuzzy values"
        ],
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    },
    {
        "image_filename": "designv11_11_0003540_6.2005-6230-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003540_6.2005-6230-Figure1-1.png",
        "caption": "Figure 1. Aircraft and Desired Path [4]",
        "texts": [
            " Then appropriate conditions on linear combinations of state derivatives will be used to create piecewise linear contours in the state space. These contours bound the state trajectories and converge to a unique stationary point, which represents perfect following of the desired circular path. Finally, simple geometric modifications of the piecewise linear contours, will be used to demonstrate Lyapunov stability. II. Review of Previous Results The guidance law presented in Ref. [4] can be readily explained using the diagram shown in Fig. 1. It is assumed that the guidance system has perfect knowledge of the aircraft\u2019s position and velocity relative to the desired path. Using this information the guidance law determines the angle \u2020 h between the aircraft\u2019s inertial velocity vector (V) and the line 3 segment between the position of the aircraft and the reference point, which is on the desired path at a fixed look-ahead distance ( \u2020 L1), where \u2020 L1 indicates both the line segment and its length. The guidance law then creates the following side, or lateral, acceleration command \u2020 ascmd = 2V 2 L1 sinh (1) Also, as indicated by the semi-circular dotted line in Fig. 1, the circle that is tangent to the velocity vector, and which also passes through the reference point on the desired path, has radius \u2020 R1, where \u2020 L1 = 2R1 sinh (2) Upon substitution of (2) into (1) \u2020 ascmd = V 2 R1 (3) Hence the lateral acceleration command generated by the guidance law is precisely the value of centripetal acceleration necessary for the aircraft to fly in a circular path to the reference point on the desired trajectory. Whence, if the desired path is a circle and the vehicle is instantaneously at any point on that circle, with its velocity vector tangent to the circle, then the guidance law commands a centripetal acceleration to maintain the vehicle on the circle"
        ],
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    },
    {
        "image_filename": "designv11_11_0000485_a:1008111128520-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000485_a:1008111128520-Figure1-1.png",
        "caption": "Figure 1. On the top, three schematic examples of tasks specified using point geometry. On left, connecting an electrical connector is specified by making the points P, S, and T coincident with the points P\u2032, S\u2032 and T\u2032 (a conjunction of 3 \u201cpoint-coincidence tasks\u201d). In the center, a screwdriver is aligned with a screw by making P, S, P\u2032, and S\u2032 collinear (a conjunction of two \u201ccollinearity tasks\u201d). On the right, a board is moved to a point where it can be inserted into a rack by first making P, S, T, P\u2032, and S\u2032 be coplanar and then adding the constraint that P\u2032 and S\u2032 coincide with P and S. Note this does not imply that the board is parallel to the rack. Such a constraint could also be specified in terms of point geometry, by using the fact that the sides of the enclosure are parallel to the rack yielding the point T\u2032. On the bottom are physical realizations of these three tasks showing the visual information used to perform them (taken from (Hager, 1997)).",
        "texts": [
            " By a positioning task or simply a \u201ctask\u201d is meant, roughly speaking, the objective of bringing the pose of a robot to a \u201ctarget\u201d (a set of desired poses) in W . The target set is in turn specified by defining a set of desired geometric constraints on a list of simultaneously observed point-features in V . Methods of defining tasks are implicit in the work of several authors including ourselves (Castano and Hutchinson, 1994; Chaumette et al., 1997; Rizzi, 1995; Samson et al., 1992; Hager, 1997). Figure 1 depicts examples of how several robotic positioning tasks can be expressed in terms of such feature constraints. As in (Hutchinson et al., 1996; Hager, 1997; Samson et al., 1992), tasks are formally represented as equations to be satisfied. In this article, the term \u201ctask function\u201d refers, loosely speaking, to a function which maps ordered sets (i.e., lists) of n simultaneously appearing point-features { f1, f2, . . . , fn} in V into the integer3 set {0, 1}. We use an unsubscripted symbol such as f to denote each such list and we henceforth refer to f as a feature",
            " T3pt is a task function defined on F3pt 4= V \u00d7 V \u00d7 V by the rule which maps f = { f1, f2, f3} according to f 7\u2192 { 0 the fi \u2019s are all collinear in P3 1 otherwise We often refer to the task specified by T3pt as the collinearity task. Finally, Tcp is a task function defined onFcp 4= V\u00d7V\u00d7V\u00d7V by the rule which maps f = { f1, f2, f3, f4} according to f 7\u2192 { 0 the fi \u2019s are all coplanar in P3 1 otherwise We often refer to the task specified by Tcp as the coplanarity task. Note that all of the tasks depicted in Fig. 1 have been constructed by appropriate conjunctions of these task functions. Point-features are mapped into the two cameras\u2019 joint image space Y through a fixed but imprecisely known two-camera model Cactual :V \u2192 Y where, depending on the problem formulation, Y may be either R2\u2295R2 or P2\u00d7P2. Typically several point-features are observed all at once. If fi is the i th such point feature in V , then fi \u2019s observed position in Y is given by the measured output vector yi = Cactual( fi ). We model miscalibration by assuming that the actual two-camera model Cactual is a fixed but unknown element of a prescribed set of injective functions C which map V into Y "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002710_tfuzz.2005.859308-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002710_tfuzz.2005.859308-Figure3-1.png",
        "caption": "Fig. 3. Cargo ship steering.",
        "texts": [
            " To show the effectiveness of the proposed control method, it is useful to compare the performance of the closed-loop system with the MLFC and the conventional FLC. Computer simulations applied to the control of two nonlinear uncertain systems are discussed in this section. It will be found that steady-state errors are reduced tremendously and improved responses are achieved in all the systems. The controlled system considered here is the cargo ship. By applying Newton\u2019s laws of motion, the ship dynamics can be obtained. Generally, the motion of the ship is described by a coordinate system that is fixed to the ship as shown in Fig. 3 [31], [32]. For simplification, the friction and hysteresis of the rudder machine are not included in the model, and the dynamics of the system is expressed as (17) where is the heading of the ship and is the rudder angle. , , and are parameters that are a function TABLE III FUZZY RULE TABLE IN THE SELF-ORGANIZING FUZZY CONTROLLER of the ship\u2019s constant forward velocity and its length . In particular, (18) where it is assumed that the ship is traveling with a constant velocity of 5 m/s and . is a nonlinear function of , which can be approximated by (19) where and are real-valued constants with being positive"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002369_robot.1998.680727-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002369_robot.1998.680727-Figure2-1.png",
        "caption": "Figure 2: Properties of the omnidirectional vision sensor",
        "texts": [
            " These two elements are separated by a glass support and are in line. This type of perception system is also used by Yagi with the COPIS system [3]. 0-7803-4300-~-5/98 $10.00 0 1998 IEEE 2560 Finally this perception system allows to get a two dimensional sensorial model of the robot evolution world on a 360 degrees vision field. In this sensorial model the vertical objects of the environment can be characterized by a set of radial straight lines converging to the center of the cone, i.e. to the center of the image (figure 2). The extraction of the radial straight lines characterizing the vertical landmarks of the sensorial model is based on the gradient treatment. The extracting algorithm is performed in two stages [9] : 0 applying a 3x3 Sobel filter followed by a binarization, 0 applying a simplified Hough transform to group the The radial straight lines, allow to get the azimuth angles of the different vertical landmarks. The r azimuth angles (+;,..,+;) for an acquisition k are our observation set [9]. 3 Dynamic localization algorithm When starting its mission the mobile robot has only a partial knowledge of the environment map"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000902_s0302-4598(98)00066-x-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000902_s0302-4598(98)00066-x-Figure6-1.png",
        "caption": "Fig. 6. Spectral changes observed during electrooxidation of 0.05 mM of \u017d .Indole at pH 3.2. Curves 1 to 4 were recorded at an interval of 5 min \u017d .and 5\u20138 at an interval of 15 min. Curve 9 was recorded after 8 h of electrolysis Pot. 800 mV vs. SCE.",
        "texts": [
            " Witha c c a progress of electrolysis the peak current for peak I sys-a \u017d .tematically decreased curves B\u2013D , whereas peaks IIc and III merged to a single peak and increased. Thec oxidation peak I completely disappeared at the end of thea \u017d .electrolysis curve D . This cyclic voltammogram did not change even when the electrolysed solution was left for several hours at room temperature. \u017d .The UV spectra of Indole I were recorded in the entire \u017d .pH range 2.0\u201310.5 and l at 220, 270, 276 nm weremax observed along with a shoulder at around 285 nm. Curve \u017d .1 in Fig. 6 exhibits the UV spectrum of 0.05 mM solution of Indole at pH 3.2 and l at 220, 270, 276 nmmax were noticed. Upon application of potential 100 mV more positive than that of peak I the absorbance at 270, 276a \u017d .and 285 nm, first increased curve 2 and then a systematic \u017d .decrease in absorbance was noticed curves 3 to 8 . The exhaustively electrolysed solution of Indole exhibited lmax at 201 and 244 nm. Thus, the l of the product weremax \u017d .shifted to shorter wavelengths curve 9 in comparison to the starting material. The spectral changes during electrolysis were also monitored at pH 7.0 and the changes were similar to that observed at pH 3.2. The identical spectral changes indicated that products of electrooxidation of In\u017d .dole I at pH 3.2 and 7.0 are same. In a separate experiment, the applied potential was switched to 0 volt after recording curve 5 in Fig. 6 and spectral changes were monitored. It was found that the absorbance in the region 230\u2013245 nm systematically increased. Hence, it was concluded that a UV-absorbing intermediate is generated during the oxidation of Indole which absorbed in the wavelength region 230\u2013245 nm. The kinetics of decomposition of the UV-absorbing intermediate was monitored at 235 nm. For this purpose a solution of Indole was electrooxidised and when the ab\u017d .sorbance at l 270 nm reached 50% usually in 30 min ,max the potential was turned off"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001026_s0021-9673(02)00362-x-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001026_s0021-9673(02)00362-x-Figure1-1.png",
        "caption": "Fig. 1. Scheme of the optical sensor. 1, Stainless steel fiber optic probe; 2, fibers from the light source and to the DAD system; 3, reaction chamber; 4, anion-exchange membrane; 5, stainless steel membrane holder; 6, reagent outlet; 7, reagent inlet; 8, silicone ring to fix the membrane.",
        "texts": [
            " Therefore, the Cr(VI) gradient between batch transport experiments. A Metrohm AG 9100 both sides of the membrane is kept high while glass combined electrode (Metrohm, Herisau, SwitCr(VI) transport occurs and, moreover, the mem- zerland) connected to a Digilab 517 pH meter brane rejects the positively charged complex and (Crison, Barcelona, Spain) was used for pH measurethus prevents any back-diffusion of chromium. ments. 2.3.1. Sensor instrumentation reaction /detection cell and provide fresh The sensor head is shown in Fig. 1. The head chromogenic reagent for analysis; (ii) a HP 8453 includes the Fibspec fiber optic probe, to deliver and diode-array spectrophotometer coupled to a fiber collect the spectroscopic signal, with a reaction optic transmission probe to acquire spectra from the chamber (0.75 ml) inside containing the reaction chamber. 2chromogenic reagent, a planar membrane (46 mm ), which provides a mechanism to sample Cr(VI) from 2.4. Transport experiments the sample matrix and acts to seal the reagent within the sensor, and a membrane holder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001756_jsvi.2001.4016-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001756_jsvi.2001.4016-Figure6-1.png",
        "caption": "Figure 6. A bearing}rotor system geared by bevel gears.",
        "texts": [
            " In matrices M and K, there exist some entries that couple a part of components in (xK , yK , zK , G , xK , yK , zK ) and (x , y , z , , x , y , z ) respectively. These entries are related to a , b , c , d , i\"1, 2, J and (GI /l) . That is, the coupled terms are only determined by the geometric parameters of bevel gears and the rotor system. Consequently, the lateral, torsional and axial vibrations couple mutually. 4. NUMERICAL RESULTS In this section, a numerical example is given in order to examine the critical speeds, the threshold speed of stability, and the unbalance responses of the rotor}bearing system geared by bevel gears as shown in Figure 6. In this system, each rotor is discretized into four nodes (node no. 1}4 as rotor 1 and 5}8 as rotor 2), or three beam elements. In the system shown in Figure 6, each rotor is laterally supported by two journal bearings. There are two identical 3603 cylindrical bearings at nodes 1 and 3, and two 5-pad tilting-pad bearings at nodes 6 and 8 respectively. A rigid axial support is located at node 1 to constrain the axial rigid motion. The parameters of the four journal bearings were taken as follows. The diameterD was 100 mm, the ratio \u00b8/D of length to diameter 0)5, the ratio of clearance 0)002, the dynamic viscosity of oil 0)0221 N s/m . The eight coe$cients of sti",
            " The corresponding eigenvalue problem can be solved by using the generalized inverse iteration method in reference [10]. As a part of the design procedure of a geared rotor system, it is usual to compute the critical torsional speeds of the transmission train, and then the critical lateral speed of each rotor as well [1]. This is called the computation based on the uncoupled model for short. In the torsional analysis of the critical speeds or natural frequencies, the bevel gear branched system shown in Figure 6 can readily be seen as an idealized one shown in Figure 7, where J \"J r /r , J \"J r /r #J , J \"J , k \"(GI /\u00b8 ) r /r , k \"GI /\u00b8 , \u00b8 \"650 mm, \u00b8 \"850 mm. The natural frequencies are \"213)2 rad/s, \"705)7 rad/s. The critical speed of the coupled axial}lateral}torsional model is de\"ned as the speed of the rotor system when it is equal to the imaginary part of one of the eigenvalues of the system. For simplicity, only the critical speeds and corresponding modes of the rigidly supported system were computed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003307_s10704-005-8546-8-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003307_s10704-005-8546-8-Figure7-1.png",
        "caption": "Figure 7. Influence of hydraulic pressure mechanism (a) and fluid entrapment mechanism (b) on crack propagation.",
        "texts": [
            " In this case the crack propagates under mixed-mode conditions, where KI > KII and the maximum stress intensity factors KI and KII are reached when the moving loaded contact region reaches the crack mouth (Keer and Bryant, 1983; Kaneta et al., 1985; Bower, 1988; Chue and Chung, 2000; Datsyshyn and Panasyuk, 2001; Frolish et al., 2002; Ren et al., 2002; Ringsberg and Bergkvist, 2003). Kaneta and Murakami (1987) experimentally showed that this mechanism can cause steep crack propagation to the free surface, as it is shown in Figure 7a. \u2022 Fluid may be trapped inside the crack, either when the crack mouth closes, or when it is sealed by the contacting element. The trapped fluid then prevents parts of the crack from closing. In this case the mode I propagation is more pronounced during the moving contact (KI KII), when the crack experiences maximum mode I stress intensity factor (Bower, 1988; Bogdanski et al., 1996). Experimental results showed that the trapped fluid inside the crack can cause crack propagation as presented in Figure 7b (Kaneta and Murakami, 1987). \u2022 Multiple cavities could be completely or partially filled with lubricant and can join into a single cavity or get separated one from another (Kudish and Burris, 2004). The maximum stress intensity factors KI and KII are reached when the moving loaded contact region reaches the crack mouth. In this paper it is assumed that the maximum values of KI, KII and T, which occur when the moving loaded contact region reaches the crack mouth, have the strongest influence on crack propagation path (Bower, 1998; Datsyshyn and Panasyuk, 2001; Kudish and Burris, 2004)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001343_1.2832457-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001343_1.2832457-Figure2-1.png",
        "caption": "Fig. 2 Deformation and sliding at a resisting contact region",
        "texts": [
            " Contact established by a pair of asperities resisting the rela tive tangential motion is referred to as a \"resisting contact.\" Conversely, an \"assisting contact\" helps the relative tangential motion. The descriptions \"resisting\" and \"assisting\" also coin cide with the signs of the slopes of the interacting asperity pairs at contact regions. Of course, if the relative motion of Bi and B2 is reversed these roles are also reversed. Typical resisting and assisting contact regions formed by the deformation of a pair of asperities are shown in Fig. 2 and Fig. 3. The solid lines in the figure depict the shape of a deformed asperity pair, at an instant in time, compared with the dotted lines which outline the original, undeformed shapes. The dashed lines, on the other hand, indicate the position of surface ^2 prior to its motion with respect to surface S^. The contact surface between two mating asperities is not necessarily planar. The instantaneous \"measure of combined deformation,\" 6, at any point in the contact region represents the sum of the lengths of paths where material particles in each contact surface move during deformation",
            " We assume that tensile deformation is possible due to the inclusion of adhe sive forces in the theory. The normal and tangential projections of the deformation path (with respect to the mean plane) are denoted by 8\u201e and 6,. Since pressure distribution over the contact surface is not necessarily uniform or constant, 6\u201e and 6, are functions of both space and time. The kinematics of the combined motion of the asperities (and the bodies Si and B2), resulting from their deformation and sliding, is depicted in Fig. 2 where the initial position of surface S2 is indicated by a dashed line and its final position, as it moves a distance s with respect to surface ^i , is indicated by a solid line. At the initial position of the surfaces, a material point Ca on surface ^2 is in contact with a material point fli on surface Si. Following the incremental motion, the initial contact breaks up and a new contact is established between the surfaces at a material point bi on ^i , and material point Z?2 on S2. The new contact is at a tangential distance TJ from a\\, the original contact position on Si, and at a tangential distance ^ from material point 02 which has moved with surface ^2 to its new position, which is indicated as 02 in Fig. 2. By definition, the sum of the tangen tial displacements r] and <\u0302 is equal to the relative tangential displacement s of the surfaces and includes the tangential com ponents of deformation of the asperities in contact. It should be noted here that while the contact kinematics is defined by mate rial points, it is understood that the actual contact takes place over a finite area, and the \"points\" are used to describe the kinematics using the initial contact as the asperities approach each other. The kinematics of the relative motion between as sisting contact regions can be described in a similar fashion. Accordingly, referring to Fig. 2 and Fig. 3, separation h be tween the two bodies and their relative tangential displacement s are dependent on displacements arising from deformation and sliding of the surfaces. Separation h is expressed using functions representing the deformed surfaces and s is expressed as a com bination of the tangential components of the local sliding and deformation of each asperity pair: h = Zi{X\\) + Z2(X^) s = riL + ii (1) (2) where, Zi and Z2, describe the deformed surfaces. They are functions of undeformed surface functions zi and zi and the normal deformation functions 6\u201e\\ and 6\u201e2 as illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001033_a:1009832426396-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001033_a:1009832426396-Figure1-1.png",
        "caption": "Figure 1. Two adjacent flexible bodies.",
        "texts": [
            " In order to avoid such a repetitive process, this investigation proposes a concept of a virtual body and joint. The kinematics of such a concept is presented in Section 2. The equations of motion for a flexible body system is presented in Section 3. Computer implement- ation and its impact on a sparse oriented algorithm are explained in Section 4. Two flexible body systems are dynamically analyzed in Section 5 by using the proposed method to show its validity. Conclusions are drawn in Section 6. Two flexible bodies connected by a joint and their reference frames are shown in Figure 1. The Xi, Y i, Zi frame is the body reference frame of flexible body i and the X,Y,Z frame is the inertial reference frame. Suppose there exists a joint between body i and body j . Kinematic admissibility conditions among the reference frames can be divided into two categories. One is the admissibility conditions between the two joint frames and the other is the admissibility conditions among the frames within a flexible body. These two types of conditions have been mixed in formulating the kinematic joint constraints and generalized forces in previous works"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003335_0020-7403(81)90025-4-Figure21-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003335_0020-7403(81)90025-4-Figure21-1.png",
        "caption": "FIG. 21. Exit and entrance tetrahedra of two pentahedra in series. The common base (dashed), is the drawing plane in the following graphical constructions.",
        "texts": [
            " In the case of Fig. 20(b), the flow from tetrahedron AAoBoCo to AoBoCoCi, is determined by the edges AAo and CoC, which in general are not coplanar. Nevertheless. the deformation is still plane and it will be Analysis of plastic deformation according to the SERR method 143 sufficient to apply the two velocities to a common point of the edge AoCo, or, more generally, of the plane AoBoCo, in order to reduce the graphical construction to the preceding case. For simplicity only the first case is examined. In Fig. 21, two tetrahedra are given, the lower one representing the exit one from a pentahedron and the upper the entrance one into the following one. The entrance and exit velocities Vt and Vu, applied to the common face of the two figures, are along the edges Ol and OU. The vector V~ is fully known, whilst only the dirction of Vv is given; we have to define its magnitude graphically. The first step, see Fig. 9, is to determine on the base triangle (the a plane), the trace of the plane containing the edges of interest. The plane containing the triangular base common to the two tetrahedra, Fig. 21, is assumed as the plane of graphical drawing, see Fig. 22; on such a plane starting from a point 0, the orthogonal projections I ' and U' of the points I and U are constructed. Taking now as base the segment I'U', the points I\" and U\" are determined such that I 'P= I'I and U'U ~= U'U along the directions perpendicular to the base I'U'. The intersection of the segments I'U\" and I'U' obviously belongs to the trace sought, which is thus given by the line 0T. any segment AM' is drawn to intersect the direction 0T; a point B' is then constructed such that AM'= M'B', along the direction of AM'"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002319_tmag.2003.810511-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002319_tmag.2003.810511-Figure2-1.png",
        "caption": "Fig. 2. Three-dimensional finite-element mesh (except the air). (a) x\u2013y plane. (b) x\u2013z plane.",
        "texts": [
            " , , and are the number of the maximum or minimum value of the flux density of the radial direction, the rotation direction, and the -direction of the th element, respectively. , , and are the amplitude of the flux density of major and minor hysteresis loops of the radial direction, the rotation direction, and the -direction, respectively. Fig. 1 shows the analyzed model of a piece of silicon steel sheet, which has a thickness of 0.5 mm, of an IPM motor. It is 1/8 of the whole region because of the symmetry and the periodicity. The analyzed IPM motor is built up by 120 silicon steel sheets. Fig. 2 shows the 3-D finite-element mesh. Table I shows the analyzed conditions. Fig. 3 shows the distributions of flux density vectors. It is found that there are large flux density vectors in the stator teeth and in the rotation direction side of rotor core [cf. Fig. 3(a)] and those distributed in the surface of the silicon steel sheet due to the skin effects [cf. Fig. 3(b)]. Fig. 4 shows the flux density waveforms in the elements A and B as shown in Fig. 3(a) . It is found that the flux density waveforms in element A are similar to the sinusoidal waveforms, and those in element B have much more harmonic components, which are caused by the stator teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003446_1.2735339-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003446_1.2735339-Figure5-1.png",
        "caption": "Fig. 5 System of cylindroidal coordinates",
        "texts": [
            " The above expression for he speed ratio between two ruled surfaces in first-order contact is pplicable for spatial motions as well as the special case of planar nd spherical motion. f = /2\u2212 f and m= /2\u2212 m for the speial case wf =wm=0. Cylindroidal coordinates consists of pitch, transverse, and axial urfaces as defined by the coordinates u, , w where u=radial arameter; =angular parameter; and w=axial parameter. Pitch surfaces are defined by varying and w u=constant , ransverse surfaces are defined by varying u and w=constant onstant , and axial surfaces are defined by varying u and w constant . Embedded within each system of these coordinates is cylindroid or conoid. Figure 5 illustrates two systems of cylinroidal coordinates sharing a common cylindroid. A salient feaure of a system of cylindroidal coordinates is that when the shaft ngle =0, the system of cylindroidal coordinates degenerates nto a system of cylindrical coordinates and when the shaft center 68 / Vol. 129, AUGUST 2007 om: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ash distance E=0 the system of cylindroidal coordinates reduces to a system of spherical coordinates. The generalized pitch surfaces are a family of single sheet hyperboloids"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002239_3.20908-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002239_3.20908-Figure1-1.png",
        "caption": "Fig. 1 Block diagram of longitudinal flight control system at a landing approach condition.",
        "texts": [
            " In general, definition of the weighting matrices Q and R in the performance index is free for designers, and it may be used to enhance robustness of the control system. In the present approach, however, the quadratic performance index is defined as simply as possible to directly present the design objective, and robustness against uncertain dynamics is guaranteed with the multiple model approach. The control law of the multimodel approach is introduced, considering uncertain delay elements inserted into each control input, as shown in Fig. 1. The dynamics for the elevator actuation and thrust generation are not explicitly considered, but they are included in the uncertainty. Four models, which consist of two cases of delay time for the two inputs, are taken into account, i.e., ~ (11) (13) D ow nl oa de d by U N IV O F C A L IF O R N IA S A N D IE G O o n Ja nu ar y 2, 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .2 09 08 J. GUIDANCE, VOL. 15, NO. 3: ENGINEERING NOTES 787 \u2022 design points (multi-model) 5. TT (sec) 4. 3",
            " For this numerical example, Wi = diag[\u00ab0 2, 0, 0, 0, /*0 2] is given. The optimal feedback gain is obtained as follows: -0.0129 2.29 3.05 0.186 0.144 1 -0.0637 -0.278 -0.687 -0.0567 -0.0537 The performance indices for each model are obtained as /! = 2.22, /2 = 2.35, 73 = 4.16, and 74 = 4.49. For the first model, which has no delay in the loops, the performance index and control costs are broken down as U\\ = 0.967, H{ = 1.253, Ae, = 1.633, and AT[ - 10.59. The crossover frequencies and phase margins at break points e and T, which are indicated by x in Fig. 1, are uce = 3.49 rad/s, PMe = 88 deg, and coc7- = 0.50 rad/s, PMT = 89 deg. These figures are for the no-delay case. To compare the control law of the multimodel approach with the standard LQR method, the same control cost is searched in the LQR (12) under the condition of no-delay time by adjusting two weighting parameters re and rT. When re= 0.1043 and rr = 0.0830, the LQR gives the following quadratic performances as U = 0.856, H = 1.290, A<, = 1.633, and Ar = 10.59. The regulator performance is quite similar to that of the multimodel approach",
            " Taking the center of gravitational attraction as pole, the polar coordinates of the rocket will be denoted by (1/w, 9), and it will be assumed that, for both terminal orbits, 9 increases with the time /. The polar equation of an orbit will be taken in the form u = a + b cos(9 - o>) (2) where the constants ay b, and w (a > b > 0) will be termed the elements of the orbit. Denoting the semilatus rectum and the eccentricity of the orbit by \u00a3 and e, respectively, we have \u00a3= I / a , e = b/a (3) where w is called the longitude of the periapse and is measured from a convenient reference line 9 = 0. The direction of an impulsive thrust / applied to a rocket situated at a point P (1/w, 9) (Fig. 1) is determined by the angle </> it makes with the forward transverse direction (i.e., perpendicular to the radius vector OP). In the diagram, A is the periapse; </> is measured counterclockwise between 0 and 360 deg. It has been proved1 that, if the impulse transfers the rocket from an orbit (a, b, o>) into an orbit (a', b', a/), then the characteristic velocity v for the transfer is given by (4) Received June 11, 1990; revision received Dec. 20, 1990; accepted for publication Dec. 28, 1990. Copyright \u00a9 1991 by the American Institute of Aeronautics and Astronautics, Inc",
            " where yu2 is the gravitational acceleration toward the center of attraction O. Thus, if (a\\, b\\, wi) and (a2, b2, w2) are the elements of the terminal orbits, and (a, b, co) are the elements of the transfer orbit, then the characteristic velocity V for the maneuver is given by V = (tf ~ '/2 - 0f 1/2) sec</>! - a ~ 1/2) sec</>2 (5) where (1/t/i, BI) and (l/w2, 92) are the coordinates of the two junction points and (</>}, <\u00a32) specify the directions of the impulsive thrusts. If w denotes the component of rocket velocity in a direction perpendicular to the thrust (see Fig. 1), which is unaffected by the thrust, we define A by the equation A = 7~1/2w cosec</> (6) Then, if (A\\, A2) are the respective values of A for the impulsive thrusts /i, /2, it has been shown1'2 that for V to be stationary with respect to variations in the elements of the transfer orbit, it is necessary that (7) u\\ = [\u2014-A2) sin</>2 (8) I - a)( 1 + \u2014 J cos</>! + (HI - A\\aV2) A\\ tam/>i = (\u00ab 2 -a)( l+ \u2014 A2 sin</>2 tan</>2 (9) b\\ sin(9j - \u00abi) = (u\\ b sin(9i - co) = (u{ b2 sin(92 - u2) = (u2 - A2a2 2) tan</>2 b sin(92 - w) = (u2 - A2aV2) tan</>2 In the same places, it was shown that A t and A2 satisfy the equations (10) 01) (12) (13) A further four equations are derived by substitution in the equations of the three orbits, (14) (15) (16) (17) b\\ cos(9"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003256_j.jsv.2004.06.029-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003256_j.jsv.2004.06.029-Figure4-1.png",
        "caption": "Fig. 4. Jeffcott rotor model [6].",
        "texts": [
            " Fuzzy root (fuzzy inverse, fuzzy absolute value), is evaluated by taking the root (reciprocal value, absolute value) of each element of the fuzzy number, without changing the associated membership values. For trigonometry operations, for Xa \u00bc \u00bdxa 1; xa 2 ; the following equations are defined: cos\u00f0Xa\u00de \u00bc \u00bdcos\u00f0xa 2\u00de; cos\u00f0xa 1\u00de ; xa 1; x a 2 2 \u00bd0; p=2 ; sin\u00f0Xa\u00de \u00bc \u00bdsin\u00f0xa 1\u00de; sin\u00f0xa 2\u00de ; xa 1;x a 2 2 \u00bd0; p=2 ; cosh\u00f0Xa\u00de \u00bc \u00bdcosh\u00f0xa 1\u00de; cosh\u00f0xa 2\u00de ; xa 1; x a 2 2 R\u00fe; sinh\u00f0Xa\u00de \u00bc \u00bdsinh\u00f0xa 1\u00de; sinh\u00f0xa 2\u00de ; xa 1;x a 2 2 R: \u00f08\u00de Consider a Jeffcott rotor model using nonlinear ball bearings as shown in Fig. 4 [6] with a rigid disk of mass M and flexible shaft segments of identical length L on each side of the disk. The shaft segments are assumed to have negligible mass with a bending stiffness EI. The equations of motion can be written as M \u20acu \u00fe kT u \u00bc f u; M \u20acv \u00fe kT v \u00bc f v; (9) where u and v denote the components of displacement parallel to x and y axes, respectively, kT indicates the translational stiffness coefficient kT \u00bc 6EI \u00f01 \u00fe 3 \u00deL3 (10) and the factor \u00bc EI=\u00f0kGAL2\u00de is a dimensionless measure of the shear compliance of the segment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001688_s0301-679x(03)00011-2-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001688_s0301-679x(03)00011-2-Figure1-1.png",
        "caption": "Fig. 1. Physical geometry of a finite slider bearing.",
        "texts": [
            " According to the Stokes micro-continuum theory [6], the field equations of an incompressible coupled stress fluid in the absence of body forces and body couples are \u00b7V 0 (1) r DV Dt p (m h 2) 2V (2) where V is the velocity vector, r is the density, p is the pressure, m is the classical viscosity coefficient, and h is a new material constant with the dimension of momentum responsible for the couple stress fluid property. Since the ratio h /m has the dimensions of length squared, the dimension of l = (h /m)1/2 characterizes the material length of couple stress fluids. The slider-bearing geometry with sliding velocity U including the effect of squeezing action \u2202h /\u2202t is shown in Fig. 1, in which the inlet film thickness is hi(t) and the outlet film thickness is hL(t). In the beginning, the general film shape is considered to be a function of coordinates x, y and time t, i.e. h = h(x,y,t). The lubricant is taken to be an incompressible couple stress fluid. Under the usual assumption of hydrodynamic lubrication applicable to a thin film, eq. (2) reduces to the form \u2202p \u2202x m \u22022u \u2202z2 h \u22024u \u2202z4 (3) \u2202p \u2202y m \u22022w \u2202z2 h \u22024w \u2202z4 (4) \u2202p \u2202z 0 (5) The boundary conditions are the no-slip conditions u(x,y,0) U, v(x,y,0) u(x,y,h) v(x,y,h) 0 (6) and the no-couple stress conditions \u22022u \u2202z2| z=0 \u22022v \u2202z2| z=0 \u22022u \u2202z2| z=h \u22022v \u2202z2| z=h 0 (7) Integrating eq",
            " (12) reduces to the two-dimensional steadystate problem of sliding surfaces with couple stress fluids. For h = h(x) and p = p(x), eq. (12) reduces to the steady-state analysis of an one-dimensional problem using couple stress fluids [15]. For h = h(x,y), p = p(x) and l\u21920, the classical Newtonian one-dimensional steady-state case is recovered [16]. To illustrate the application of the dynamic couplestress Reynold\u2019s equation, the finite slider bearing of an inclined-plane film shape with length L and width B is depicted in Fig. 1. Let a be the difference between the inlet and minimum film thickness: hi(t) hm(t) a, hm(t) hL(t) (14) Then the film thickness is seperated into two parts: the minimum film thickness hm(t) and the slider-profile function hs(x). h(x,t) hm(t) hs(x) hm(t) a\u00b7 1 x L (15) After introducing the dimensionless quantities, the dynamic Reynold\u2019s equation can be expressed in a nondimensional form. \u2202 \u2202x\u2217 f\u2217(h\u2217,l\u2217) \u2202p\u2217 \u2202x\u2217 1 b2f \u2217(h\u2217,l\u2217) \u22022p\u2217 \u2202y\u22172 6 dh\u2217 s dx\u2217 12 dh\u2217 m dt\u2217 (16) where f\u2217(h\u2217,l\u2217) h\u22173 12l\u22172h\u2217 24l\u22173tanh h\u2217 2l\u2217 (17a) h\u2217(x\u2217,t\u2217) h\u2217 m(t\u2217) h\u2217 s (x\u2217) h\u2217 m(t\u2217) a\u00b7(1 x\u2217) (17b) In these equations a is the slider-profile parameter, b is the aspect ratio and l\u2217 represents the couple stress parameter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003335_0020-7403(81)90025-4-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003335_0020-7403(81)90025-4-Figure7-1.png",
        "caption": "FIG. 7. Quadrilateral figure. The external velocities are prescribed on two adjacent sides. The determination of the internal velocity is the same as for the trilateral figure.",
        "texts": [
            " It will be then possible to calculate the flux of the material through the two remaining sides, considering the component of the internal vector normal to each of them. In the case of the trilateral figures the two sides bearing the starting data are obviously adjacent; this does not generally happen in the case of multilateral figures. Nevertheless no new difficulty is met due to this fact, because any two sides of the figure meet in a virtual point and from this point the graphical solution is the same as that of the trilateral figure. Example 5. Quadrilateral figure When the entrance vectors are known on two adjacent sides, i.e. BC, CD in Fig. 7, the diagonal BD can be drawn and we arrive back again at 3 case. The internal vector obtained for the trilateral figure BCD is also the vector sought for the quadrilateral o n e . Example 6. Quadrilateral figure If the external vectors are given on two non-adjacent sides, e.g. AB and CD of the quadrilateral figure ABCD, see Fig. 7, these two sides are extended to their common virtual intersection P. The solution valid for the trilateral figure APD so obtained (Example 3), is the sought solution for the figure ABCD. We must nevertheless consider that, if the sides AB and CD are parallel, the information is not sufficient to solve the problem, because the normal components of the entrance velocities are now parallel. Analysis of. plastic deformation according to the SERR method 133 Example 7. Multilateral figures The case of plane figures with a higher number of sides can be immediately solved, in a manner analogous to that of Example 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002927_j.enzmictec.2004.11.016-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002927_j.enzmictec.2004.11.016-Figure2-1.png",
        "caption": "Fig. 2. Design of mini-diffusion electrochemical cell configured for packed graphite column (PGC) type electrodes.",
        "texts": [
            " Thereafter, during dc polarization tests, the electrode was housed in a larger 35 ml \u201cmini-cell\u201d that was purged with hydrogen or nitrogen via a sparging tube. Mixing (300 rpm) was provided by use of a 1\u2032\u2032 magnetic stirrer placed at the bottom of the cell. In both cases, the reference electrode (RE) was a miniature Ag/AgCl type, while the counter electrode (CE) was a 25 mm \u00d7 4.5 mm strip of platinum foil (Alfa Aesar, MA, USA). The PGC electrodes were composed of graphite carbon adsorbed onto three-dimensional metal supports (either nickel or stainless steel) confined within a glass tube (o.d. 7.2 mm, i.d. 5.6 mm, Fig. 2). For the nickel foam-based packed graphite column electrodes (Ni/PGC), a 1.5 mm thick nickel foam (Golden Champower New Materials Corp., Shenyang, C i s p l w t f e s e w w ber septum to allow submersion into a temperature (75 \u25e6C) controlled water bath (mini-gas diffusion cell, Fig. 2). Both electrodes (i.e., Ni/PGC and SS/PGC) had geometric surface areas of 0.25 cm2. The counter electrode was a platinum foil strip (25 mm \u00d7 4.5 mm) entering through the top of the cell, and the reference electrode a miniature Ag/AgCl type similarly placed. To construct the PGC electrodes it was necessary to entrap the graphite powder (Superior Graphite, IL, USA) into the nickel or stainless steel supports. The graphite powder was first pre-treated with concentrated sulfuric acid for 20 min, rinsed copiously in pH 7 phosphate buffer, and then suspended within a distilled water slurry",
            " Approximately 5 ml of this slurry was then pipetted onto the top of the metal support (i.e., nickel foam matrix or stainless steel disks) and pushed through the metal mesh under pressure applied with a 10 ml syringe. The electrode gas entry port (underneath the electrode) was left open during this period to allow slurry to completely traverse the nickel foam or stainless steel mesh and thus coat the entire surface. After drying at 130 \u25e6C for 1 h, excess carbon was removed, leaving a 150 l well space between the surface of the electrode and the upper rim of the glass tube (Fig. 2). The purpose of the electrode well was to allow a space in which, with the electrode mounted vertically and in an anaerobic environment, enzyme solution could be h 2 e hina) was cut into a 5.6 mm diameter disk and then inserted nto the glass tube, with a trailing compressed nickel foam trip left as the electrical connector. For the stainless steel acked graphite columns (SS/PGC), two adjacent 316 stainess steel mesh disks (total height or thickness of 1.5 mm) ere cut into 5.6 mm diameter disks and then inserted into he glass tube. The upper disk possessed a trailing strand or electrical connection. For both the Ni/PGC and SS/PGC lectrodes, the tapered end of a glass pipette was inverted and ealed with epoxy resin into the lower base, both to seal the lectrode end and to provide an upward gas diffusion pathay for hydrogen gas (Fig. 2). The glass tube was then placed ithin a second, larger glass tube that was sealed with a rub- eld in place during the immobilization process. .3. Enzyme immobilization Immobilization of hydrogenase enzyme onto the PCP lectrode roughly followed the procedure of [7], although it was modified for high temperature in order to allow enzyme to absorb at the optimal temperature for enzyme activity. The carbon strip was first pretreated by immersion in concentrated sulfuric acid for 30 min, washed three times by immersion in EFC buffer solution, and then left overnight in buffer",
            " Fifty microliter of enzyme solution (2 mg ml\u22121) was syringed into the 150 l electrode well space using the enzyme addition port (a 16-gauge needle sleeve) orientated to deliver solution directly into the well. The enzyme solution was left for 2 h at 75 \u25e6C, at which time it was removed using an HPLC syringe inserted through the enz fi s d 2 w f g L c t s 2 r t o i I e t l t b a w r already been immobilized to the carbon support. It should be noted that the gap between the reference and working electrode in Fig. 2 is adjustable and not to scale. 2.4.2. dc polarization Potentiostatic dc polarization was used to characterize the performance of the electrodes (with or without enzyme) in a three-electrode configuration. The enzyme and its electrode support as a working electrode (WE) were held at a constant polarization potential against the reference electrode (RE), and current flowing from the WE to platinum counter electrode (CE) was monitored. Measured current was taken after the potential step on the electrode was imposed and stabilized for 1 h",
            " For the PCP type electrode, a standard three-electrode configuration in a sealed 35-ml test cell (mini-cell) was used for electrochemical measurements (Fig. 1). The cell was continuously flushed with nitrogen or hydrogen as required and stirring was conducted via a 1\u2032\u2032 magnetic stirrer at 300 rpm. The counter electrode was made with a 5 mm \u00d7 5 mm (immersion area) platinum foil strip pretreated by immersion into 5 M HCl for 5 min. For the PGC electrode, the entire cell was filled with degassed electrolyte (3 ml), in order to allow contact with the platinum counter electrode (Fig. 2). 2 i 1 w t c i i v d a 2 a o p t t d p b t g e t b f o yme addition port. At this time, the mini-diffusion cell was lled to the 3 ml level with electrolyte, and gas purging was witched to the electrode gas addition port in order to provide iffusive gas flow directly through the electrode substrate. .4. Electrochemical measurement The equipment used for electrochemical measurements as a Solartron 1287 electrochemical interface with a 1260 requency response analyzer (Houston, TX, USA). Data loging was conducted via a custom software interface written in abVIEW (National Instruments, TX, USA)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003335_0020-7403(81)90025-4-Figure17-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003335_0020-7403(81)90025-4-Figure17-1.png",
        "caption": "FIG. 17. Internal partition adopted in the case of an extrusion from square bar to square bar.",
        "texts": [],
        "surrounding_texts": [
            "I d( + q) X2 a: ! 3( ( d 3 + p ) (d( + q) Y2 --- z2 = 0 its coordinates may be used to fix in (5) the value of the parameter K which is sought. The system of the equations (4) and (5) now determines the direction of the velocity in the internal tetrahedron, which is uniquely dependent on the geometry of the bexahedron. Analysis of plastic deformation according to the SERR method 139 The line of intersection of the two planes, the first fixed in (4) (entrance diagonal) by the value A = A(r, s), the second fixed in (5) (exit diagonal) by the value K = K(p, q), thought of as the direction of the velocity of the internal rigid block, meets simultaneously both the continuity conditions through the faces of the inside tetrahedron and the constancy of the normal compoents through the whole entrance and exit faces of the hexahedron. It must be observed that when the entrance velocity is completely specified, the velocity inside the internal tetrahedron also appears fully determined, because the displacements \u2022 and s of its entrance planes define a plane ribbon limited by the entrance diagonal and its parallel displaced image. These two parallel lines are determined respectively by the points of application and by the final points of the possible entrance vectors, that meet the entrance conditions. On this ribbon the second plane, defined in (5) by the value K = K(p, q), fully determines the vector sought. Hence we can say that by prescribing a uniform entrance velocity on the entrance face of the hexahderon, a uniform exit velocity is uniquely determined on its opposite exit face under the condition that no flux of material is present on the lateral faces. 4. SERR APPLICATIONS BASED ON THE MAIN FIGURES Some applications of the SERR figures previously analyzed will now be given as examples. They concern two different cases of extrusion, from round to round bar and from square to square bar respectively. In both cases the partition makes use of only one kind of simple solid figure, which is repeated several times as a series: more precisely, the pentahedron with trilateral bases is used in the first case, while in the second, the hexahedron with quadrilateral bases is adopted. As a general criterion, the lateral edges of the figures are taken along the flux lines of the material: as a conseauence, the lateral faces of the solid figures are flux tube surfaces, see Figs. 16 and 17. In both cases the symmetry permits calculations to be limited only to a small sector of the figure. The choice of such a sector and of the number of the elements in each series, will be justified in a following paper.- 140 F. GATTO and A. GIARDA The calculation of the parameters of interest was made by a computer. An example of the results obtained but concerning only one element, is presented in Tables I and 2, for which the entrance and exit velocity are given, together with the partial extrusion ratios,+ the volume flux through the bases, and the work of deformation in each elementary solid figure. The ratio between pressure of extrusion and yield strength, and the exit velocity of the extrusion profile have also been calculated. 5. GRAPHIC CONSTRUCTION OF SIMPLE SOLUTIONS Even if the use of graphical methods is not generally convenient in order to determine the velocities in the various solid elements of a three-dimensional partition of the volume, such a way can be followed in cases which are not too complex. An example of a graphical solution applied to a pentahedron with trilateral bases, with no flux through the lateral faces, is Oven in Fig. 18. It will be seen that this figure is particularly useful in dealing with axial deformations, especially with axisymmetric ones. Recall briefly the the partition of the volume of such a figure is made by three tetrahedra, each having a lateral edge in common with the lateral edges of the pentahedron. The flux through the lateral faces of the pentahedron, as remarked above, vanishes and, as a consequence, the directions of the velocities in the three tetrahedra coincide, in a given order, with the outer edges of the whole figure. Successive pairs of such lateral edges belong to the same lateral face and, since the deformation from one tetrahedron to the next is of a plane nature, it can be represented graphically by drawing on a single plane the lateral faces of the whole figure. The change both in the direction and in magnitude of the velocity, manife=ts itself on each lateral face, along that diagonal which is the trace of one plane of discontinuity, see Fig. 19. This consideration cannot T ab le 2 . [X T R U S X O N R A T IO [R - 4 .0 0 0 > A R T IA L E X T R U S IO N R A T IO O F T H E H E X A H E O R O H P E R 4E X A H E D R O H N . I P E R : 4 .0 0 0 ~ 0 0 R G IN A T E S O F TH E V E R T IC E S (H H ) V E R T IC E S A V E R T IC E S S S O .O .O .0 6 0 .0 6 0 .0 IO .O .0 ~ 2 .0 3 0 .0 3 0 .0 5 2 .0 E N TR A N C E V E L O C IT IE S IN T H E H E X A H E O R A (H H /5 ) ~E X A H E D R O N H . I F A C E N . I 1 .0 0 0 F A C E N . P E L O C IT Y IN T H E IN T E R N A L T E T R A H E D R O H (N H /5 ) H flE X A H E D R O N H . I 2 .1 6 0 V E R T IC E S C V E R T IC E S D \u2022 O .O 6 0 .0 .0 .0 ,O \u2022 0 3 0 .0 5 2 .0 .0 .0 1 .0 0 0 C O H P O N (N T O F T H E E X IT V E L O C IT Y P ~ R A L L E L T O T H E A X 1 S O F T H E S IL L E T (N R /G ) H E X A H E D R O N H . I F A C E N . 1 4 .0 0 0 F A C E N . 2 4 .0 0 0 ~O LU N E F LO U TH R O U G H T H E G A G E S O F T H E N E X A H E D R A (H N C /S ) |A G E H . I 3 6 0 0 .0 0 0 |A g E N . 2 3 6 0 0 ,0 0 0 U O R K O F D E F O R N A T IO N IN A N H E X A H E D R O N (H M C /G ) H E X A H E D R O N N . I F R IC T IO N U O R K 1 3 4 ~ 6 .0 3 2 1 E X T R U S IO N V E L O C IT Y (H N /G ) F A C E N . I 4 .0 0 0 E X T R U S IO N P N E R S U R E /T IE L S G T R E N O T H A T T H E T E H P E R A T U R E O F E X T R U g IO N 4 .2 4 S T O T A L U O R K 2 9 1 1 0 .3 9 1 1 3 F A C E N . 2 4 .0 0 0 .0 5 2 .0 ~ 32 13 i 1 ~% FI o. 1 5. G ra ph ic al c on st ru ct io n of t he s ol ut io n in t he c as e of a p en ta he dr on , w it h no f lu x of m at er ia l th ro ug h it s la te ra l fa ce s, m -m is a r ot at io n ax is t ha t al lo w s a pl an esk et ch . ,< 0a o 0 0 C /) 3 0 rs be applied only to that lateral face which has its edges coinciding with the velocities of the entrance and exit tetrahedra, because these tetrahedra do not follow each other in the internal partition, the diagonal of such a face must be thought of as a double-trace of discontinuity, i.e. a double line in Fig. 18. None-the-less, this fact does not imply any di~culty in the graphical construction of a solution, because it is always possible to avoid the crossing of such a double-trace. The graphical construction can be performed by expansion of the two lateral faces of interest on a common plane. When the first of the three vectors is known, the following ones can be obtained by hodographs; see Fig. 18, from which also the discontinuity vectors are obtained. The considerations up to this point concern the graphical construction of the internal velocities, which, as successive pairs, pertain to the same lateral face of the figure; they are, in consequence, capable of expansion on a common plane. The flow of the material from a pentahedron into the following one needs next to be considered. In this case the exit velocity from a tetrahedron and the entrance velocity into the following one no longer belong to a plane characterizing the adopted partition of the volume and hence a different procedure has to be followed. The graphical solution is still possible if it is considered that, also in this case, the exit velocity from a pentahedron is along one of its edges and the entrance velocity into the following one behaves in the same way. Two different situations, dependent on the special partition adopted, must be considered, see Fig. 20. In the case of Fig. 20(a), the deformation due to the flow from the tetrahedron CAoBoCo into the following AoBoCoCt, is determined by the directions of the edges CCo and CoC~; it is of a plane nature, the discontinuity vector belonging to the plane of the above quoted edges. In the case of Fig. 20(b), the flow from tetrahedron AAoBoCo to AoBoCoCi, is determined by the edges AAo and CoC, which in general are not coplanar. Nevertheless. the deformation is still plane and it will be Analysis of plastic deformation according to the SERR method 143 sufficient to apply the two velocities to a common point of the edge AoCo, or, more generally, of the plane AoBoCo, in order to reduce the graphical construction to the preceding case. For simplicity only the first case is examined. In Fig. 21, two tetrahedra are given, the lower one representing the exit one from a pentahedron and the upper the entrance one into the following one. The entrance and exit velocities Vt and Vu, applied to the common face of the two figures, are along the edges Ol and OU. The vector V~ is fully known, whilst only the dirction of Vv is given; we have to define its magnitude graphically. The first step, see Fig. 9, is to determine on the base triangle (the a plane), the trace of the plane containing the edges of interest. The plane containing the triangular base common to the two tetrahedra, Fig. 21, is assumed as the plane of graphical drawing, see Fig. 22; on such a plane starting from a point 0, the orthogonal projections I ' and U' of the points I and U are constructed. Taking now as base the segment I'U', the points I\" and U\" are determined such that I 'P= I'I and U'U ~= U'U along the directions perpendicular to the base I'U'. The intersection of the segments I'U\" and I'U' obviously belongs to the trace sought, which is thus given by the line 0T."
        ]
    },
    {
        "image_filename": "designv11_11_0003540_6.2005-6230-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003540_6.2005-6230-Figure4-1.png",
        "caption": "Figure 4. System Geometry for Following Circular Paths",
        "texts": [
            " III. Nonlinear State Space Model As stated earlier, the primary goal of this paper is to demonstrate the stability of the nonlinear guidance law for following circular paths. In particular, it is important to study transient system behavior for situations where nonlinear effects are significant, which is typically the case when the initial vehicle state is far away from any stationary point. As a first step in this development it is necessary to create an appropriate state space system model. Fig. 4 illustrates the system geometry for a desired circular path of radius R. In the following development all angles and angular velocities are defined to be positive in the clockwise direction. As shown in the figure, the vehicle velocity vector has a component \u2020 VL along the line segment from the vehicle to the reference point, and a component \u2020 V1 orthogonal to that line, where \u2020 VL = V cosh (6) and \u2020 V1 = V sinh (7) \u2020 \u2020 \u2020 \u2020 \u2020 \u2020 \u2020 \u2020 \u2020 \u2020 \u2020 \u2020 \u2020 6 Furthermore, since the reference point always lies on the desired path it must have a velocity vector \u2020 VT that is tangent to the path. Thus, from the diagram in Fig. 4 \u2020 VL = VT cosb (8) and \u2020 V2 = VT sinb (9) Combining Eqs. (8) and (6) yields an expression for \u2020 VT in terms of the states and aircraft velocity \u2020 VT = VL cosb = V cosh cos b (10) and upon substitution into Eq. (9) \u2020 V2 = V cosh tan b (11) From Fig. 4, the rates of change of the angles \u2020 h and \u2020 b can be expressed in terms of the inertial angular rotation rates \u2020 wL ,wV and wT \u2020 \u02d9 h = wL -wV \u02d9 b = wL -wT (12) Then, with reference to Fig. 4, and applying Eqs. (7), (11) and (10) \u2020 wL = V1 -V2 L1 = V L1 (sinh - cosh tanb) wT = VT R = V cosh Rcosb (13) Also, using Eq. (1) \u2020 wV = ascmd V = 2V L1 sinh (14) Substitution of equations (13) and (14) into (12) yields \u2020 \u02d9 h = - V L1 (sinh + cosh tanb ) (15) \u2020 \u02d9 b = V L1 (sinh - cosh tanb )- V cosh R cos b (16) The two angles \u2020 h and \u2020 b are system state variables and Eqs. (15) and (16) are the differential equations for the states. If the states always satisfy the conditions of Eq. (17) then the differential equations are well behaved and satisfy Lipschitz conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000343_s0736-5845(01)00005-9-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000343_s0736-5845(01)00005-9-Figure1-1.png",
        "caption": "Fig. 1. Robot arm: internal position (q ,2, q ), and external position (x, y, z, , , ).",
        "texts": [
            " Section 3 provides the mathematical background of the robot arm kinematics and dynamics. In Section 4 the mathematical formulation of the DP concept is presented and the notion of IKI is de\"ned. VFmodels are derived in Section 5. This includes the utilization of penalty functions that force a distribution of the motion in a human-like manner. Part II investigates a particular example: the problem of handwriting. A robot arm is considered as an open linkage consisting of n rigid bodies interconnected by n one-degreeof-freedom joints (Fig. 1), and so the arm has n degrees of freedom (DOFs) and the system position is fully described by means of n joint coordinates (or internal coordinates or conxguration coordinates). Each coordinate corresponds to one joint and represents the relative motion of the neighboring links. For the jth joint, the coordinate is q . It is an angle if the joint is revolute, or a longitudinal displacement if the joint is prismatic. The vector q\"[q 2 q ] is called the internal position vec- tor, or the vector of joints' positions, or the conxguration vector. From the viewpoint of the robot task, the main attention should be given to the motion of the end-ewector (which is the terminal link of the chain including the tool for a particular operation, like a spray-gun or a gripper). The spatial motion of the end-e!ector can be described by the so-called external coordinates: i.e. three Cartesian coordinates of the end-e!ector tip (x, y, z) and three orientation angles ( -jaw, -pitch, -roll), as shown in Fig. 1. The vector X\"[x y z ] is called the external position vector. Another important concept is that of the operational frame or operational space. It constitutes the subvector of the external position vector, which contains the coordinates responsible for the execution of a given task. Let this frame be of dimension m. In this case one often says that the prescribed task requires m DOFs. Let the m-vector x describe the end-e!ector position in the operational frame. We mention a few tasks as examples"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000810_s0924-0136(02)00356-4-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000810_s0924-0136(02)00356-4-Figure4-1.png",
        "caption": "Fig. 4. Mesh configuration used in tyre simulation.",
        "texts": [
            " It was therefore decided that this plane of nodes, removed as it was from the main deforming region, could also have axial direction boundary conditions imposed with minimal effect on the predicted geometry of the workpiece. In addition to this difference in the imposition of boundary conditions, the asymmetry of the tyre rolling process required both upper and lower axial rolls to be modelled. No modification to the basic model was required for this purpose. The mesh configuration of material and rollers used in the tyre simulation together with the plane of boundary condition nodes is illustrated in Fig. 4. Two 308 dense mesh regions were employed for this simulation. These are located in the two roll gap regions so as to adequately represent the deformation in those most rapidly deforming areas. The effectiveness of the dense regions in covering the areas of greatest strain rate can be seen in Fig. 5, in which the effective strain rate distribution during the process is shown. The resulting mesh was made up of 1620 nodes. The process took place over 40 revolutions at a variable feed rate, this required 4800 deformation increments and took approximately 3 weeks runtime"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003819_rspa.2005.1452-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003819_rspa.2005.1452-Figure1-1.png",
        "caption": "Figure 1. Front commercial vehicle brake disc and wheel assembly.",
        "texts": [
            " The derived linear relationship is of generic nature, enabling the calculation of the TCR for a variety of engineering bolted joints, over a wide range of interface pressures. Keywords: interface pressure; bolted joints; thermal contact resistance; thermal conductance; brake disc Rec Acc Thermal contact resistance (TCR) is of vital importance in determining heat flow through a bolted joint. The research was initiated by the need to determine accurately conductive heat dissipation from a commercial vehicle (CV) disc brake. The main area of interest was the conduction between the grey cast iron disc and the spheroidal graphite (SG) cast iron wheel carrier (see figure 1). This type of bolted joint is common to many engineering applications. Published brake thermal analyses deal with conductive heat dissipation inadequately. Since the contribution of this mode to the brake cooling is, in most service conditions, lower than convective and radiative heat dissipation, the contribution of conductive cooling is either neglected or oversimplified. This was mainly the result of lack of adequate data, since conductive cooling can be substantial. Conductive heat dissipation is speed insensitive (unlike convection), therefore, for braking applications at low speeds and high disc temperatures (such conditions are found during drag braking on long downhill descents, or in repeated brake applications), conduction becomes a very important mode of heat dissipation and can be responsible for up to 20% of the total heat dissipation (Voller 2003)",
            " Again, a practical approach in modelling a particular design and duty, but of limited scope for wider applications. There are other TCR studies of bolted assemblies and conductive heat dissipation studies from disc brakes. However, for the main area of interest, the conduction between a grey cast iron disc and a SG cast iron wheel carrier, the available data are insufficient for accurate thermal modelling. Therefore, it was considered necessary to study TCR in detail (see Voller 2003). A heavy CV wheel assembly is shown in figure 1, consisting of the brake disc, wheel carrier, wheel and tyre (22.5 in. nominal diameter). Heat is generated at the brake disc friction surfaces and conducted through the disc hat section. The assembly provides two paths for conductive heat dissipation from the disc, one through the bearing assembly, the other through the wheel carrier. Heat transfer Proc. R. Soc. A (2005) from the brake disc to the bearing must be avoided to ensure bearing temperatures are kept low. However, the wheel carrier has a substantial mass, which is approximately two-thirds of disc mass, and therefore can provide a very desirable conduction path from the brake disc",
            " Thermal contact resistance measurement (a) Experimental set-up The experimental part of the study was conducted using a specially developed spin rig (see Voller 2003). The rig has a simple, in-line arrangement of the disc/ wheel assembly, shaft with adapter, torque transducer, speed sensor and electric motor. The spin rig has been designed for measuring all modes of brake disc heat dissipation (convection, conduction and radiation) and disc airflow characteristics. Experiments have been conducted on the CV brake disc and wheel carrier assembly (see figure 1) installed on to the spin rig shaft, schematically shown in figure 6. For TCR measurements, the shaft did not rotate. The brake disc was heated using two hot air guns fitted to a heater box that shrouded the brake disc (not shown in figure 6). The heater box allowed hot air to flow over the surface of the disc providing uniform heating. The heating power could be controlled from 0 to 4 kW. The shaft adapter, disc and wheel carrier were insulated, as shown in figure 6, to prevent heat losses and ensure adequate heat flow"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002427_50009-5-Figure7.13-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002427_50009-5-Figure7.13-1.png",
        "caption": "FIGURE 7.13 2D field system with three-phase supplied magnetizer and hexagonal s}anmetry [7.52]. It is basically equivalent to the classical field source obtained by using the statoric core of a three-phase induction motor and a circular sample [7.53].",
        "texts": [
            " It is generally recognized, however, that with both these types of magnetizers it is difficult to control accurately the rotation of the magnetization in strongly anisotropic materials. This typically applies to grain-oriented Fe-Si laminations, which are very soft along RD, but quite hard along the direction making an angle of 54.7 ~ to RD (that is quite close to [001] and [111] in the individual grains, respectively). A three-phase 2D field source is expected to provide, at least in principle, better control of the flux loci, besides calling for less exciting power in each channel. An example of a 2D magnetizer with threephase supply and hexagonal test plate is shown in Fig. 7.13 [7.52]. An equivalent system is obtained in a simpler way by generating the field with the statoric core of a three-phase induction motor and placing a circular specimen in the mid-plane of the bore [7.53]. Figure 7.14 illustrates an example of the radial dependence of the magnetization in a non-oriented Fe-Si single disk of diameter 140 mm and thickness 0.50 mm, placed in a bore of diameter 200 mm and height 100 mm and subjected to a rotational field [7.54]. It is fair to say that the measured value of the tangential field 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001396_s0022-5096(01)00130-2-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001396_s0022-5096(01)00130-2-Figure6-1.png",
        "caption": "Fig. 6. Response diagram for a very long twisted rod (with = 5 7 ) under constant end-shortening. Curves (Eq. (19)) are shown for d = 0:051; 0:75; 1:05; 1:75; 145 (bold); 5:739. The curve of instability points (20) is shown dashed.",
        "texts": [
            " Yet another experiment can be devised, Fixed D experiment: keeping endshortening (xed and tuning end-rotation. It would correspond to following curves of constant end-shortening in Fig. 4. Using Eqs. (14) and (15) and eliminating t, we (nd R\u00b1 = m + 4arccos md 2 \u221a 2 \u221a 4\u00b1\u221a 16\u2212 m2d2 : (19) For this type of experiment, a distinguished diagram is obtained by plotting R against m and the destabilizing e4ect happens when following the fold in a clockwise way (Manning et al., 1998). This is illustrated in Fig. 6 where curves de(ned by Eq. (19) with di4erent values of d have been drawn together with the loci of the instability points de(ned by 9R\u00b1=9m= 0: R= m \u2212 arctan m 2 + 2 : (20) This curve (20) divides each path into a stable part (the part from (m; R) = (0; 0) up to the R-fold) and an unstable one (the part from (m; R) = (0; 2 ) up to the R-fold). The instability here is of the same nature as the one encountered before, i.e. the rod will jump to self-contact. However, we see that not all the curves have a fold in R"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003462_j.mechmat.2005.06.011-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003462_j.mechmat.2005.06.011-Figure1-1.png",
        "caption": "Fig. 1. A contact between two disks.",
        "texts": [
            " To develop a continuum description, we adopt Cauchy s notion of stress (Love, 1944). In two dimensions, the contact forces acting across a line are summed, and the resultant, divided by the length of the line, is identified as the traction. The contacts are treated as deformable. The forces developed there are expressed through the product of the stiffness at the point of interaction and the relative displacement between the disks at the point of interaction. Therefore, a detailed definition of the microkinematics underlying the system is also required. As indicated in Fig. 1, a contact is defined by its position and a unit vector, here indicated by d, aligned with the line that joins the centers. If A and B are the centers of the two disks in contact and C is their contact point, in a Cartesian counterclockwise reference frame with orthogonal unit vectors e1 and e2, d(BA) = (cosh, sinh), while the unit vector tangent to the disks at the contact is t(BA) = ( sin h, cosh). The evolution of the geometry of the contacts plays a fundamental role in the behavior of granular materials"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003070_j.mechmachtheory.2004.11.006-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003070_j.mechmachtheory.2004.11.006-Figure1-1.png",
        "caption": "Fig. 1. Dodekapod.",
        "texts": [
            " Spur et al. [1] have proposed such a manipulator for gripping application, e.g., holding a washing machine while it is painted by, say, a robot. Unlike a Stewart platform type of manipulator, which has six degree of freedom, 0094-114X/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2004.11.006 * Corresponding author. Tel.: +91 11 2659 1135; fax: +91 11 2658 2053. E-mail address: saha@mech.iitd.ernet.in (S.K. Saha). Dodekapod has six additional degree of freedom. Fig. 1 shows a schematic sketch of Dodekapod. It has six legs like Hexapod which are connected to mobile knots at the top and base platforms. The mobile knots at the base platform can be moved along three sliders that are at an angle of 120 with one another. A similar arrangement at the top platform is achieved using telescopic guides. Dodekapod can be considered as a Hexapod with variable workspace. Additional degree of freedom, as available from the movement of the mobile knots of the top and bottom platforms, can be used for varying the workspace"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003496_ias.2005.1518531-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003496_ias.2005.1518531-Figure3-1.png",
        "caption": "Figure 3. (Top) A cross section of an induction motor, (Bottom) Crossing air gap flux from a stator tooth to a rotor tooth.",
        "texts": [
            " To formulate both faults, we need to model the machine in a 3-dimensional space. Figure 2 shows a part of an unskewed rotor having some degree of misalignment fault. The rotor is divided into 4 layers. Each layer has some radial displacement with respect to the neighboring layers. Rotor bars are shown with solid black lines and the rotor core and the rotor teeth are shown with white color. The air gap length in different layers is dependent on the axial position of the layers, but in each layer it is assumed to be constant. Fig. 3(a) shows the cross sectional view of each layer of the Fig. 2. A few stator and rotor teeth around the air gap of the IAS 2005 1324 0-7803-9208-6/05/$20.00 \u00a9 2005 IEEE machine are shown. At a time, each stator (rotor) tooth can face a few rotor (stator) teeth. Fig. 3(b) shows the crossing air gap flux from a stator tooth to a rotor tooth. Since the length of air gap between each two stator and rotor teeth is much smaller than each tooth width, a trapezoidal flux tube such as shown in Fig. 4(a) and (b) can be imagined for each two stator and rotor teeth. Based on the geometric dimensions defined in Fig. 4(b), the permeance of this flux tube can be calculated as: \u222b= W xg dxxlxG 0 )( )()(\u00b5 (1) where, the g(x) dimension is parallel to flux line directions and l(x) and x are dimensions perpendicular to the flux line directions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002399_ias.2001.955985-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002399_ias.2001.955985-Figure1-1.png",
        "caption": "Fig. 1. Motor model.",
        "texts": [
            " In this paper, the method of determining the optimum voltage vector used in the estimation is also proposed to accurately implement the estimation. Using the optimum voltage vector, no mechanical break for the rotor is needed during the operation of the estimation. In the early paper, the optimum voltage vector was determined by trial and error [6]. Experimental results show that the average of the estimation error is \u00b11.83 electrical degrees, and the rotor is at standstill during the estimation. II. ESTIMATION METHOD Fig. 1 shows the model of the surface PMSM. The orthogonal two-phase \u03b1-\u03b2 frame is fixed to the stator windings. The d-axis coincides with the direction of the voltage vector provided from the inverter. Angle \u03b8v represents the angle of the voltage vector and \u03b8re is the angle of the rotor position. The angle \u03b8* represents the reference angle, and the current control used in the decision method of the optimum voltage vector is performed in the x-y frame whose angle is \u03b8*. Fig. 2 shows the measured d-axis currents for the constant amplitude voltage vectors when the rotor position is fixed at 90 electrical degrees",
            " The rotor of the motor may rotate during the estimation process if the large amplitude voltage vector is provided to the motor. Therefore, the optimum voltage vector, which can estimate the initial rotor position without the mechanical break, must be determined before the estimation process. The optimum voltage vector is defined as follows: \u00b7 The optimum voltage vector causes the effective magnetic saturation. \u00b7 The optimum voltage vector does not rotate the rotor. Fig. 8 shows the experimental system to determine the optimum voltage vector. The current control is performed in the x-y frame shown in Fig. 1. In order to set the N-pole in the direction of the x-axis, the following x-axis current reference ix*, and y-axis current reference iy* are applied to the current controller. The direct current I equals to the rated current or the current below that of the motor. * * 0 x y i I i      =       (2) To decide the amplitude of the voltage vector, the modulation factor m is introduced and it is defined as follows: m = Vm / Ed (3) where Vm is the amplitude of the voltage vector and Ed is the DC source voltage of the inverter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002266_ijmee.31.2.5-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002266_ijmee.31.2.5-Figure5-1.png",
        "caption": "Fig. 5 Point at which eqns (36 and 37) fail.",
        "texts": [
            " If the expression (eqn 34) with a positive signed square root term is substituted in eqn (10), one obtains the following for an inextensional case: (36) Eqn (36) is nothing but the curvature formula expressed in terms of arc length, in which s is replaced with x because, for an inextensional case, the coordinate of any material point in terms of s, in any configuration, is always equal to its initial coordinate x in the Lagrangian sense [18]. In fact, the curvature formula in which s is the independent variable is given by [18] as (37) The denominators of both eqn (36) and eqn (37) become zero for dv/dx = 1 and dv/ds = 1, that means q = 90\u00b0, as shown in Fig. 5, because sin q = dv/ds. Then, (d2v/ds2)ds k = - \u00ca \u00cb \u02c6 \u00af d d d d 2v s v s 2 2 1 k = \u00a2\u00a2 - \u00a2 v v1 2 \u00a2 = - \u00a2u v 1 2 2 \u00a2 = - \u00b1 - \u00a2u v1 1 2 \u00a2 + \u00a2 + \u00a2 =u u v2 22 0 at HEC Montreal on July 10, 2015ijj.sagepub.comDownloaded from International Journal of Mechanical Engineering Education 31/2 = cos q dq. For q = 90\u00b0, cos q = 0 and hence, d2v/ds2 = 0. It is seen that eqns (36 and 37) lead to an indeterminacy for dv/ds = 1 and dv/dx = 1, respectively [13]. This difficulty can be overcome by controlling the values of dv/ds and d2v/ds2 at every step of the numerical integration, and by changing the integration step so as to skip that critical point and so avoid numerical indeterminacy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001563_a:1008185917537-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001563_a:1008185917537-Figure7-1.png",
        "caption": "Figure 7. Robot model of Kawata et al. with two dual-wheel units.",
        "texts": [
            " It is assumed that the absolute coordinate system (O,X, Y ) as a movement space of the mobile robot is fixed in the plane and that the moving coordinate system (Om,Xm, Ym) is fixed at the centre of gravity (c.g.) of the robot. Here, Xm-coordinate is set so that it has the same direction as the front of the robot. Let the coordinate of each dual-wheel caster a, b be defined as (Oi,Xi, Yi), i = a, b. \u03c6 denotes the angle between X- and Xm-coordinates (i.e., an azimuth of the robot). The position vector of the c.g. of the robot with respect to the absolute coordinate system is defined as s = [x y]T. As a reference, the platform of Kawata et al. [4] is shown in Figure 7. Defining the state variable for the mobile robot as x = [x y \u03c6]T and the input variable as u = [x\u0307a y\u0307a x\u0307b y\u0307b]T, the kinematics model of the mobile robot is given by x\u0307 = Bu, (5) where the matrix B is given by B =  Lb La + Lb 0 La La + Lb 0 0 Lb La + Lb 0 La La + Lb \u2212 sin\u03c6 La + Lb cos \u03c6 La + Lb sin\u03c6 La + Lb \u2212 cos \u03c6 La + Lb  ; hereLa andLb represent the distances between the steering axis of each dual-wheel caster and the c.g. of the robot, respectively. If the following condition is satisfied: (x\u0307a \u2212 x\u0307b) cos\u03c6 + (y\u0307a \u2212 y\u0307b) sin\u03c6 = 0 (6) the slippage between the wheels and the ground will not be induced"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002144_j.jsv.2003.05.019-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002144_j.jsv.2003.05.019-Figure10-1.png",
        "caption": "Fig. 10. Experimental rig.",
        "texts": [
            " Such an increase in the weight of the machine is undesirable, because in addition to vibration disorders, workers often suffer from symptoms caused by the handling of heavy tools, such as strained muscles and joints. In order to verify the results obtained by numerical simulations, a mechanical model of handle\u2013 hand\u2013arm was built, while the electro-dynamic shaker attached to the handle reproduced the casing acceleration. Fig. 9 shows a schematic diagram of the experimental rig. The experimental rig layout is shown in Fig. 10. The electro-dynamic shaker (Ling Dynamic System, model V409) was attached to the handle by a Shock Tech1 wire isolator that represented the vibration isolator between the casing and the handle of the electro-pneumatic hammer. This wire isolator consisted of a stainless steel cable wound between light alloy bars and possesses weak non-linearity due to the friction between wires. However, such an isolator was used because the damping provided was ideal for the present experimental study. The wire isolator had freedom of motion in vertical and torsion directions. Any possible misalignment between the moving platform of the shaker and the handle, might cause handle vibration in directions other than horizontal, which are not considered in the present study. In order to eliminate such vibration, four flat springs (width\u201430mm, thickness\u20140.041mm, length\u2014200mm) were placed between the handle and the mounting table (see Fig. 10). Such springs prevented the handle from vibrating in vertical or torsion directions without affecting the behaviour of the experimental mechanical system in horizontal direction. The second smaller Shock Tech wire isolator was used as a vibration isolator between the handle and the hand\u2013arm system. The mass connected to the handle and attached to the mounting table through the two wire isolators represented the operator hand and had a stiffness and damping ratio in accordance with parameters used in numerical simulations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003746_1.2159036-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003746_1.2159036-Figure2-1.png",
        "caption": "Fig. 2 \u201ea\u2026 Bearing reference coordinate and \u201eb\u2026 inner-race groove reference center",
        "texts": [
            " The simulation results are composed of three parts: rotor drop dynamics, CB health condition, and CB thermal growths, and it is thus shown that the rotor drop simulations using the Hertzian contact bearing model with thermal growths not only provide such valuable information for the CB design as the CB life, the maximum bearing stress, and the CB thermal growths, but they also compensate for a pure rotor drop simulation. Hertzian Contact Ball Bearing Model. The bearing components, ball and races, are assumed to have contact only within the elastic region. Races are then modeled as rigid except for local contact deformation. Figure 1 shows a cross-sectioned ball bearing with reference coordinates where the points p ,q indicate the inner and outer groove centers, respectively. The inner race loaded by the force vector F has the displacement vector X as shown in Fig. 2 a . The angle is calculated based on the number of balls so that the r-Z plane passes through the center of each ball. Figure 2 b shows the cross section of an inner race at a ball loaded by the contact force vector Q at the reference point p. The vectors with respect to different reference points are related by the matrix T u = T X , Q = T f 1 where f is an equivalent force vector at the inner race reference point and the matrix T is T = cos sin 0 0 0 1 The dynamic equations of motion EOM for the inner race are mi X = F + j=1 n Tj T Q j 2 where n is the number of balls and mi is the mass of inner race. Let the vector v T= vr ,vz be the displacements of a ball center and the EOM for a ball, including the centrifugal force Fc, are then derived as APRIL 2006, Vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001724_s0022-0728(03)00063-9-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001724_s0022-0728(03)00063-9-Figure2-1.png",
        "caption": "Fig. 2. Cyclic voltammograms of a PNSA film in concentrated sulfuric acid at potential scan rates of 50 (a), 100 (b), 150 (c), 200 (d), 250 mV s 1 (e). Inset: plots of anodic or cathodic peak current density vs. potential scan rate.",
        "texts": [
            "0 V on the first cycle, however, it disappeared on successive cycles, indicating that the polymer cannot be synthesized in this medium in a large amount. BFEE containing 33% TFA was found to be the best medium for polymer growth. As shown in Fig. 1C, there are also no reversible redox waves of PNSA appearing in the successive CVs. This is mainly due to the fact that the doping and dedoping reaction rates of PNSA are much lower than that of polymerization. As a result, the doping level of the polymer is low. The electroactivity of the PNSA film was tested in a concentrated H2SO4 solution after rapid washing with water and acetone. Fig. 2 illustrates the CV of PNSA deposited electrochemically from the medium of BFEE /33% TFA, and in concentrated acid. The steady-state CV presents broad anodic and cathodic peaks. The currents are proportional to the scan rate (Fig. 2, inset), indicating a redox couple attached to the electrode [1]. Furthermore, these films can be cycled repeatedly between the conducting (oxidized) and insulating (neutral) state with no significant decomposition of the materials. As-formed PNSA film is a flat powdery film with weak strength. It cracks easily during a dry process as is shown in the scanning electron micrograph of Fig. 3. The film is in the doped state and dark blue in color. Its color changed to golden yellow quickly in the ambient atmosphere"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002668_05698190500414300-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002668_05698190500414300-Figure3-1.png",
        "caption": "Fig. 3\u2014The ball-raceway contacts under the loads being applied in the axial and radial direction and the ball\u2019s centrifugal force.",
        "texts": [
            " The coordinates for any point on the surface of the inner raceway can be written as (Liao and Lin (8))  xi = (gi + rcos\u03b8) cos \u03c8 yi = (gi + r cos \u03b8) sin \u03c8 zi = r sin \u03b8 + \u03b6i [5] where gi = di/2 + r \u03b6i = \u2212(r \u2212 D/2) sin \u03b10 In Eq. [5], \u03b10 is the nonloaded ball\u2019s contact angle, as shown in Fig. 2. Similarly, the coordinates for any point on the outer-raceway surface are given as (Liao and Lin (8))  xo = (go + r cos \u03b8) cos \u03c8 \u2212 \u03b4r yo = (go + r cos \u03b8) sin \u03c8 zo = r sin \u03b8 + \u03b6o [6] where go = do/2 \u2212 r \u03b6o = (r \u2212 D/2) sin \u03b10 + \u03b4a The two tori, which have point i and point o as the centers of two circles and r as the radius of these two circles for the inner and outer raceways, would intersect at two points, c1 and c2 (see Fig. 3). At these points, (xo, yo, zo) must be equal to (xi , yi , zi ). Then the D ow nl oa de d by [ Fl or id a St at e U ni ve rs ity ] at 0 7: 21 0 7 O ct ob er 2 01 4 equivalence of Eqs. [5] and [6] gives (Liao and Lin (8)) (gi + r cos \u03b8)2 + 2\u03b4r (gi + r cos \u03b8) cos \u03c8 + \u03b42 r = [go + \u221a r2 \u2212 (r sin \u03b8 + \u03b6i \u2212 \u03b6o)2]2 [7] The solutions of \u03b8 in Eq. [7] vary with the position angle\u03c8 of the ball bearing. The preceding nonlinear expression is obtained for the variable contact angle \u03b1, which can be solved using Newton\u2019s iterative scheme if the bearing elastic deformations in the radial and axial directions, \u03b4r and \u03b4a , are available",
            " Define the changes in contact angle formed at the inner and outer raceways as (Liao and Lin (10)) \u03b1i \u2261 \u03b1i \u2212 \u03b1 [10a] \u03b1o \u2261 \u03b1 \u2212 \u03b1o [10b] where \u03b1 is the contact angle of a bearing under a load but without taking the centrifugal forces into account; \u03b1i and \u03b1o are the real contact angles at the inner and the outer raceways, respectively, but considering the centrifugal forces. The two preceding contact angle differences are unequal if the centrifugal forces are included. Then, a triangle moi \u2032 is formed as shown in Fig. 3, where point m is the center of the ball that is tangential to both the inner raceway and the outer raceway tori and the elastic deformations at these two contact points are absent. Since r \u03b4i and r \u03b4o, the angle difference parameters, \u03b1i and \u03b1o, are approximated as \u03b1i \u223c= \u03b1o \u223c= \u03b1 [11] Let the distance between point i \u2032and point o(i \u2032o) be A, the distance between point i \u2032and point m (i \u2032m) be B, and the distance between point o and point m (om) be C. Then B and C, as Fig. 3 shows, can be expressed as (Liao and Lin (10)) B = ri + \u03b4i \u2212 D 2 = r + \u03b4i \u2212 D 2 [12a] C = ro + \u03b4o \u2212 D 2 = r + \u03b40 \u2212 D 2 [12b] where \u03b4i and \u03b4o are the elastic deformations arising at the contact points of the inner and the outer raceways, respectively. The distances B and C also satisfy C2 = A2 + B2 \u2212 2ABcos( \u03b1) [13a] B2 = A2 + C2 \u2212 2AC cos( \u03b1) [13b] Eliminating B and C from Eqs. [12a], [12b], [13a], and [13b] gives (2r \u2212 D + \u03b4i + \u03b4o) cos( \u03b1) = A [14] Because the frictional forces produced at the ball are so small, they are excluded from the force balance. The force balance equations in the y- and z- directions, as Fig. 3 shows, are written as Qi cos \u03b1i \u2212 Qo cos \u03b1o + Fc = 0 [15a] Qi sin \u03b1i \u2212 Qo sin \u03b1o = 0 [15b] where the centrifugal force Fc in Eq. [15a], which is due to a high angular velocity of the cage, can be written as Fc = dm 2 m\u03c92 c [16] where m is the mass of a ball, dm is the bearing pitch diameter, and \u03c9c is the angular velocity of the cage. By Eq. [15b], the normal contact force acting on the inner raceway is Qi = sin \u03b1o sin \u03b1i Qo [17] If the elastic deformations formed at the contact points of both the inner and the outer raceways are available, the normal contact forces can be stated as (Harris (9)) Qi = Ki\u03b4 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003081_6.2005-6284-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003081_6.2005-6284-Figure1-1.png",
        "caption": "Figure 1. Longitudinal helicopter conventions [Van Holten8]",
        "texts": [
            " Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. During the design of this adaptive flight controller, a longitudinal helicopter model is used. The dynamics of this rotorcraft are given as6\u20138 : u\u0307 = \u2212g sin \u03b8f \u2212 D m u V + T m sin(\u03b8c \u2212 a1) \u2212 qw (1) w\u0307 = g cos \u03b8f \u2212 D m w V \u2212 T m cos(\u03b8c \u2212 a1) + qu (2) q\u0307 = \u2212 T Iy h sin(\u03b8c \u2212 a1) (3) \u03b8\u0307f = q (4) The fourth expression is a kinematic equation to obtain the fuselage pitch angle. These equations apply to a rotorcraft defined by Fig. 1. The calculation of the thrust T of the rotor is done by using a combination of the blade-element method and the method of Glauert8 . The following scheme is iterated until the error between both CT is zero (i.e. F (\u03bbi) = 0). a1 = \u221216 \u03b3 q \u2126 + 8 3 \u00b5 \u03b80\u22122\u00b5(\u03bbc+\u03bbi) 1\u2212 1 2 \u00b52 CTelem = 1 4cl\u03b1\u03c3 [ 2 3\u03b80 ( 1 + 3 2\u00b52 ) \u2212 (\u03bbc + \u03bbi) ] CTGlau = 2\u03bbi \u221a ( V \u2126R cos(\u03b1c \u2212 a1) )2 + ( V \u2126R sin(\u03b1c \u2212 a1) + \u03bbi )2 F (\u03bbi) = CTelem \u2212 CTGlau This concludes the longitudinal dynamics of a rotorcraft. Given certain control inputs, the change in states can be calculated to simulate the helicopter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002781_iros.2004.1389341-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002781_iros.2004.1389341-Figure3-1.png",
        "caption": "Fig. 3. phases in thc st'cppinp-ovm",
        "texts": [
            " Each cycle consists of two kinds of phases, namely, single-support phase and double-support phase. A normal walking proceeds with these two phases taking place in turn. If there is an obstacle to step over, the robot first walks to the obstacle at a appropriate position, then cany out the following procedure, which consists of three ph&s - two single-support phases and one double-support phase: Phase 1 (single-support): Supported by one leg, the robot lifts another highly enough, swings it over the obstacle and puts it down to the ground on another side of the obstacle (see Fig. 3(a)); Phase 2 (double-support): Then the robot moves its hip forwards, transfers its center of mass (CoM) from the rear foot (see Fig. 3(b)) to the front one (see Fig. 3(c)); Phase 3 (single-support): Under the support of the front leg, the robot withdraws the rear one by lifting it highly enough, and moves it forwards. Finally, after 130 0-7803-8463-61041$20.00 @20M IEEE ::._:\" /< \\p;,\\ \"2 p ' - - - - ...... - . I \" I 4 \"I P, VI the rear leg is over the obstacle, the robot puts it down to the ground (see Fig. 3(d)). During the whole procedure, it is obvious that two requirements or constraints must be satisfied: (a) the robot maintains stability or keeps its balance, and (b) there is no any collision between the robot legs and the obstacle. In general, the walking speed of a humanoid robot is not high. And when the robot steps over an obstacle, especially if the obstacle is big, the speed should be lower than in normal walking. For simplicity of analysis, we regard the robot as a quasi-static system, and hence the stability of the robot rely on the location of its CoM with respect to the supporting area",
            " 2 shows all geomeuic parameters, where d l and dz are the horizontal distances of the toe and heel from the ankle joint, respectively; e 15 the height of ankle joint; s is step size; 1l,1z,lp and 1, are the lengths of the thigh, the shank, the hip and the chest, respectively; and qto.qtl and r ~ , ~ (i = 1,Z) are three of leg joints (their positive directions are defined in the figure) of the two legs. In the following, we examine each phase of the steppingover to setup the corresponding GO models, and then integrate them. In the first phase, we need to consider several extreme actions or cases. As stated before, the robot stands at an appropriate position with respect to the obstacle, supported by one leg, bends the knee of another one to reach the limit of q12 (see Fig. 3(a)). The robot moves its hip backward as much as possible to position p', with highest hip position and maintaining the balance (i.e., xeom 2 -d2, where xcom i s the X coordinate of the robot CoM), and then swings forwards the thigh with the shank to reach hip joint limit, swapping an arc. arc l is the trajectory of the point in the leg fastest away from the hip joint, with the radius raTC1 = moz{il + T n , maz(dp ,h , dpff; + e , dp, t ) l , where rn is the radius of the knee, dprh and dp,t are the distances from the heel and the toe to the hip when the ankle joint is at its two limits, respectively (refer to Fig",
            " -d2 5 ~ c o m 5 di where the step size s can be calculated as (see Fig. 2): s = - IlsiW(q1, + 412) - l?sin(qlz) + lisin(q21 + 4 2 2 ) + Izsin(q22). Q is the vector of all of joint angles involved, Q and are its lower and upper bounds, rrspectively. Anczp , and zp, are the hip height calculated according to the two legs, respectively: zpt = e + Ilcos(qii + q i 2 ) + lzcos(qi2), (i = 1: 2). In Phase 2 of the stepping-over, we can get the corresponding GO models in the similar way. At the beginning, the robot is still supported by the rear foot (Fig. 3(b)). The GO model is as follows: niax h Q 5 Q 5 Q I - d l 5 z 5 s - (d2 +U) where the inequalities with max( . . .) and A... are for the collision-free constraints, which can be obtained according to the lemma in Section Ill-A. At the end of Phase 2 (Fig. 3(c)), the CoM has moved forward and supported only by the front foot. Hence the constraint on stability becomes s - dz 5 xcom 4 s + dl. The constraints of the model become (3) zp, = - maz(Apn,u,Apn,v, . Av,u,,Av,v,n,) > 0 max(An,f iv .An, f lU1. AvoatnlAuov , , f , ) > 0 ' P 2 i s - dz 5 xcom 5 s + di The last phase (Fig. 3(d)) is similar to the first one. Supported by the front leg, the robot withdraws the shank of the rear leg fully, and then rotates its hip joint to lift the knee as high as possible. Keeping this configuration, the robot then moves forward by rotating about the suppating ankle. The knee swaps an arc (arcl centered at f2) whose radius can be computed according to the maximum distance from the ankle f? to the hip joint p, thigh length 11, the knee radius rn and the limit of hip joint. After the hip reaches its rhe extreme under the condition of stability, [he robot swings the thigh fonvard to joint limit, The lifted leg generates an arc (arc2 similar to arc1 in Fig. 3(a), and with the same radius). Finally, the shank is released and the foot swaps an arc (arc3 similar to that in Fig. 3(a), and with the same radius). The condition for collision avoidance is that the obstacle is within arc l , and out of arc2 and arc3. The constraints of GO model in this phase can be formulated as: (x' - s')~ + (h - e)2 5 (x' + w - xP)' + (h - zp)' 2 rivc2 (x' + U - x * > ) ~ + (h. - zn1)* 2 rz,c3 (4) { -& 5 x',,, 5 di where x' and s* are obstacle position and robot step size obtained from previous model (3). and x & is the CoM Xcoordinate with respect to the local frame of the supporting leg here",
            " To do so, we integrate (1)-(4) into one GO model by taking the maximum obstacle height as the objective, and collecting all constraints together, hut with joint angles in different phases as different variables. The solution to this integrated GO model is what we want. Note that, there may he infinite number of solutions to the integrated GO model, with unique objective value and obstacle position, but different leg joint angles in some phases. The maximum obstacle height and corresponding obstacle position may mainly be determined by one phase (say, the first stage of Phase 2 - Fig. 3(h), as shown by the example in next section). In this case, the configuration of the robot in this phase is unique, while the joint angles from the GO model are not unique for other phases, which means that various configurations satisfy the constraints in these phases. Note also that, theoretically the feasibility should be analyzed in the similar way for the whole Phase 2 when the robot moves from stage 2A to 2B. This can be done by discretizing the morion of hip along X direction and at each position of the hip (that is, with the fined x p of the hip) getting a corresponding GO model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002642_1.2165234-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002642_1.2165234-Figure3-1.png",
        "caption": "Fig. 3 Free-body diagram of a single pendulum in a spherical coordinates \u201er , , \u2026",
        "texts": [
            " 2 Likewise, the components of resultant of the tension, gravity, and drag forces acting on the ball in the Cartesian coordinates system x ,y ,z are given as Fx = \u2212 Tp sin cos \u2212 8 f l 2 \u03072 + \u03072 sin2 1/2 \u0307 cos cos \u2212 \u0307 sin sin CD Fy = \u2212 Tp sin sin \u2212 8 f l 2 \u03072 + \u03072 sin2 1/2 \u02d9 \u02d9 cos sin + sin cos CD 650 / Vol. 73, JULY 2006 rom: http://appliedmechanics.asmedigitalcollection.asme.org/ on 01/27/20 Fz = \u2212 mg \u2212 Tp cos + 8 f l 2 \u03072 + \u03072 sin2 1/2 \u0307 sin CD 3 where CD represents the coefficient of drag for a spherical particle defined as 15 CD = 24 Rep 1 + 0.1862 Rep + 0.4373 Rep 7185.4 + Rep 4 Therefore, using the classical mechanics theory the equation of motion of the single pendulum as illustrated in Fig. 3 may be written as \u0308 = sin \u2212 Dz ml + g l + cos Dx ml cos + Dy ml sin + \u03072 sin 5 \u0308 = \u2212 csc 2\u0307\u0307 cos \u2212 Dy ml cos + Dx ml sin The parameters Dx, Dy, and Dz in Eq. 5 are given as Dx = \u2212 8 f l 2 \u03072 + \u03072 sin2 1/2 \u0307 cos cos \u2212 \u0307 sin sin CD Dy = \u2212 8 f l 2 \u03072 + \u03072 sin2 1/2 \u0307 cos sin + \u0307 sin cos CD 6 Dz = 8 f l 2 \u03072 + \u03072 sin2 1/2 \u0307 sin CD Note that Eq. 5 is nonlinear and thus capable of producing chaotic behavior. When two spherical particles are brought into contact they touch initially at a single point. As the particles deform, they come into contact in the vicinity of the initial contact point over an area that is small compared with the dimensions of the particles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002591_0094-114x(85)90040-0-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002591_0094-114x(85)90040-0-Figure3-1.png",
        "caption": "Fig. 3. Geometry of involute generation.",
        "texts": [
            " 2, this cutting point will lie on the line of action of the involute mesh between the rack form and the gear. As seen in Fig. 2, the involute is 353 cut for both positive and negative rotations of the gear blank from the initial position. The normal to the rack surface, n, is directed along this line of action and can be expressed as n = - s in 611 + cos 6.1, (2) in the rack coordinate frame, where \u00a2b is the pitch circle pressure angle of the tooth. The location of the cutting point, P, on the rack surface, as shown 354 in Fig. 3, can be written as B. HEFENG et al. rl = - u cos &il - u sin dPjl, (3) where u is the distance along the rack surface from the pitch point, O~, to P. It is positive in the direction shown in Fig. 3. Since O is the instant center for the relative cutting action of the rack with respect to the gear, the value of u which causes n to pass through the pitch point, O, locates the cutting point, P. Thus u = R02 sin 6, (4) and the location of P in the fixed coordinate frame at the gear blank center is given by r2 = {R - R02 cos d~ sin d~}io2 + {R0., - R02 sin\" (b}jo.,. (5) By rotating the r., vector from the fixed coordinate frame to the rotating frame attached to the gear blank, one obtains the expression for the involute on the gear blank as a function of the gear blank rotation from the pitch point mesh: {;;}= rco~ 0~ sin 021 r: = {R cos 0: + R0: sin 02 - R02 sin (b cos(02 - O)}iz + { - R sin 02 + R0,_ cos 02 + R0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003400_j.dental.2005.12.001-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003400_j.dental.2005.12.001-Figure1-1.png",
        "caption": "Fig. 1 \u2013 Crown geometry with various gating arrangements: (a) double side sprue to cusps, (b) single side sprue, (c)",
        "texts": [
            " The etched samples were then viewed using a Neophot-21 inverted optical metallurgical microscope (Carl-Zeiss Jena) and photographed using an attached JVC 3-CCD color digital video camera. Finite-element models of the crown casting with various sprue geometries were used to simulate the cooling of the casting in the mold. Geometry for the sprue and pouring system designs were produced using standard geometry primitives and spliced to the crown geometry. Mesh of the crown and different pour system designs was produced with I-DEAS (UGS, USA) and altered with MeshCast (ESI, Group, FR) to add a surface mesh corresponding to the investment mold material. Four designs, shown in Fig. 1, were used. The crown test castings were produced using the double side sprue design (Fig. 1(b)). The heat transfer occurring during the solidification process was determined using a commercial finite-element macromodeling package Procast (ESI Group, FR) which solves the four-way sprue to cusps and (d) single sprue backside of crown. heat flow and Navier\u2013Stokes equations [25], and locates isolated liquid pockets during solidification, in order to predict shrinkage porosity. Boundary and initial conditions were selected based on the experimental conditions. The mold was assumed to be at an initial temperature of 450 \u25e6C and instantaneously filled with liquid metal of a uniform temperature of 1680 \u25e6C",
            " 6b\u2013d), these results indicate that the location of the porosity can be adjusted by altering the design. For this application, it may not be necessary to eliminate the porosity entirely, so long as the porosity is not near to or connected with the finished surface. If an interior pore is large enough, it may act as a stress riser and lead to failure through crack growth. However, this situation is only likely if the pore volume spans a substantial portion of the cross-section. Of the designs presented in Fig. 1, the y-shaped sprue design (Fig. 6(a)) was 66 d e n t a l m a t e r i a l s 2 3 ( 2 0 0 7 ) 60\u201370 begins first in the bulk material. This is due to the effect of silicon depressing the freezing point in the area, near the mold, in which it is present. With the present assumptions, this effect is, at first, greater than the temperature decrease and so and (d) back-gated single sprue simulation. (Darker areas ar viewing direction.) predicted to have a low number of pores and the smallest maximum pore size (Table 4)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003396_bf02156005-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003396_bf02156005-Figure4-1.png",
        "caption": "Figure 4. The ~ angle.",
        "texts": [
            " According to the former, due to the coupling of displacements and rotations of the wire sections, the ~2' values correspond to displacements in the direction d, while the I2\" values correspond to displacements in the direction d' , as shown in figure 3. Moreover directions d and d' result to be independent of the wave length. On the contrary, according to the theory under examination, the values I21 (o.) and I22 (v) correspond to displacement directions which vary depending on the wave number. To prove this fact, denoting by /3 the angle formed by the resulting displacement w(v) direction and the tangent t to the helix (see figure 4), in figure 5 are drawn the functions /310') and /32(o) that correspond to the solutions I21 (o) and I22(=,) calculated for different values of~x 0). The variation of /3 as o varies - shown by figure 5 - is only negligible for very low values of =, 0 ' < 0.2) for which the two values/31 == lr/2 - - 2\u00a2x and /32 ~ - 2\u00a2x correspond to the displacements w respectively in the two directions d and d' shown in figure 3. Figure 5 also shows that for values of o close to 2 cos \u00a2x the displacement directions are practically reversed compared O) For the determination of functions ~(o) see Appendix II",
            "l) d and d ' being the displacement directions shown in figure 3, and v and v' the propagation velocities of the deformation waves along the wire, given by (I.2) ,ff U r ~ Putting in the (I.l) solutions such as: d = A ei#se itot d' = B ei#S e i~t (I.3) we have: { G0 2 _- U2#2 w '2 = v'2/~2 (1.4) and taking into account the (I.2), (8) and the value of the ratio {t3y/~, ) = 1.3: . - - = - - 0 3 a (I.5) 1.14 - - Finally, taking the (9) into account, we obtain: p 7r I2\" = 1.14 - - (I.6) APPENDIX H. Angle ~ (see figure 4) is defined by: Y = arctg - - z (II.l) where the ratio y/z can be derived from one of the (4). For example, by considering the first of the (4), we have: with: (II.2) I b u -- b11(#, w) b12 _- b12(#) (II.3) It should be noted that in function bu(t t , w) the frequency w is the one which satisfies (6), or, in dimensionless form, (9) by solutions expressed by the (11). Therefore also the b l l ~ , w) can be expressed as a function of only # (or of u when in a dimensionless form). Thus assuming that: fll = bll [bt' \u00a2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002622_001-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002622_001-Figure4-1.png",
        "caption": "Figure 4. Experimental arrangement for measuring frictional force for different heights of the applied force (Shaw 1979).",
        "texts": [
            "28ms-* ~ ~ 2 % f For a disk a, = 2Fh/3rnR. 1 For a sphere a, = 5Fhf7mR. R4 in example 1, as well as for rotational and translational motions as in example 2 . D E Shaw (1979) proposes and shows a practical laboratory exercise that allows students to discover that the frictional force may be in the same direction as the velocity of the centre of mass of a rolling cylinder. The experimental arrangement used to determine the frictional force exerted on the rolling cylinder is depicted schematically in figure 4. The cylinder mass and radius are constant. Axles of various radii ( r ) are placed at each end for producing different heights of the applied force. The acceleration of the cylinder is obtained by measuring the time required to move from rest at A, to B. Subsequently, the evaluation of the frictional force is made from the measured acceleration. A simple calculus (Capell 1987) demonstrates that when striking a billiard ball (radius R) horizontally with a cue at a height above 2R/5 of the centre of mass, the initial velocity of the centre of mass ( Vco>O) and the initial angular velocity (mo > 0) are related by VC, < woR"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001922_2002-01-1003-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001922_2002-01-1003-Figure1-1.png",
        "caption": "Figure 1. Schematic drawing of the location of the modified Brugger samples machined from pinion blanks.",
        "texts": [
            " The processing histories included an asgas-carburized set as a baseline, a set shot-peened after gas carburizing, a reheated set to refine the case grain size, and a set processed by vacuum carburizing to minimize intergranular oxidation at the surface. EXPERIMENTAL PROCEDURE SAE 8620 steel, with the composition shown in Table 1, was commercially produced into pinion gear forgings. The pinion forgings were upset from 38.1 mm (1.5\u201d) diameter bar stock. Then, the forgings were machined to the final pinion dimensions. Modified Brugger samples were machined from the stems of some of the pinions. A schematic drawing of the location of the modified Brugger samples is shown in Figure 1 and the sample geometry is shown in Figure 2. The remaining pinion blanks were commercially processed into pinion gears and matched with a set of ring gears for testing on a dynamometer. In this study, only the pinions were analyzed and the ring gears were used to facilitate dynamometer testing. CARBURIZING/PROCESSING - Four processing histories, designated baseline, shot-peened, reheated, and vacuum carburized and summarized in Table 2, were used in this study. Each processing history was simultaneously applied to groups of modified Brugger samples and commercial gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000158_s002211209700760x-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000158_s002211209700760x-Figure1-1.png",
        "caption": "Figure 1. Schematic defining the coordinate system is shown in (a). The inner region DI and main region DM are sketched in (b).",
        "texts": [
            " Formally, our problem is to analyse the incompressible inviscid flow around a rigid body moving impulsively from rest at t = 0 with a constant velocity U = (U, 0, 0) into a region denoted by D, where initially the flow is at rest and the density field, \u03c10(x), has a uniform gradient, \u2207\u03c10. The solutions to the velocity and density fields u(x, t), \u03c1(x, t) satisfy the incompressibility condition D\u03c1 Dt = 0, (2.1a) the continuity equation \u2207 \u00b7 u = 0, (2.1b) and the conservation of momentum \u03c1 Du Dt = \u2212\u2207p. (2.1c) Clearly, the Boussinesq approximation, where density changes in the inertia term are negligible, is inapplicable. In order to define a suitable coordinate system, xB is taken as a reference point in the body which is initially at x0, as shown in figure 1. Then for t > 0, the position of the body is xB(t) = x0 +U t. We introduce the coordinate x\u2032 relative to the body, x = xB(t) + x\u2032, and a new velocity field v = u\u2212U relative to the body. Now the velocity and density fields are subject to the boundary conditions: far upstream of the body, as x\u2032 \u00b7U \u2192\u221e, u\u2192 0 or v \u2192 \u2212U , (2.2) and \u03c1\u2192 \u03c10(x). (2.3) On the surface SB of a rigid body (defined as the points x\u2032S which are the solutions of fS (x) = 0), the kinematic condition satisfied by the velocity field is v \u00b7 n\u0302 = 0, (2",
            "15) This equation implies that for three-dimensional bodies (where \u2202/\u2202b 6= 0), the streamwise component of vorticity persists far downstream of the body \u2013 this is described as \u2018trailing\u2019 vorticity. When the body moves perpendicularly to the density gradient, (U \u00b7 \u2207\u03c10 = 0), the density field \u03c11(x \u2032) is steady because the isopycnal surfaces are not permanently displaced forward and is weak in the sense that its gradient is O(|\u2207\u03c10|). However, in three-dimensional flows, vortex stretching generates a vorticity field which grows without limit within a thin layer located on the surface of the body SB and surrounding the attached downstream streamlines \u2013 this layer is termed region DI (see figure 1b). Despite the singularity of the vorticity distribution, the velocity field is steady everywhere in D, i.e. both in the inner region DI and in the main region DM . The perturbed velocity field is |v2| = O(|U |\u03b5) and so from (2.13) the density field \u03c12 = O(\u03c10\u03b5 2). The formal link between the flow generated by a body moving perpendicularly to the density gradient and parallel to a shear flow is explained in Appendix A. We note that both have this feature of a singularity in vorticity in region DI "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000950_20.952624-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000950_20.952624-Figure2-1.png",
        "caption": "Fig. 2. Magnetic flux and force distribution, and deformation (with a magnification of 2000) of an SRM stator.",
        "texts": [],
        "surrounding_texts": [
            "In free space ( ), all stress tensors which determine the force distributions described above, given by (10), (18), (28), (32), (37), etc., equal the well-known Maxwell stress tensor, such that the total force and torque acting on a body surrounded by free space are identical for all methods. For illustrating the different force distributions, the various force calculation methods have been implemented by using the 2-D finite element method and have been applied to a switched reluctance motor (SRM) and a transformer core. Figs. 2 and 3 show some results of static simulations where methods 1 to 5 refer to the force distributions (7), (15), (25), (29) and (38) respectively. For the SRM, the methods based on the Chu model (methods 1 and 2) and on the virtual work principle for nonlinear material (method 3) give rise to force distributions concentrated on the stator surface where the flux crosses the airgap. Although the methods based on the Amp\u00e8re model (methods 2 and 3) generate completely different force distributions, the ensuing deformations are similar for all methods. In the transformer core of Fig. 3, methods 1, 2, and 5 lead to negligible magnetic forces, as there is no flux leaving the magnetic core, and which are therefore not shown. By using the Amp\u00e8re methods 3 and 4, significantly different force distributions and deformations are obtained."
        ]
    },
    {
        "image_filename": "designv11_11_0002294_irds.2002.1043946-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002294_irds.2002.1043946-Figure3-1.png",
        "caption": "Figure 3: Sectional E m of Locomotive Mechanism",
        "texts": [
            " If the circular plate is turned by the power coming from motor, the relative motion between link connected to the circular plate and pivot in slot causes ellipsoidal motion of leg tip. The robot moves forward and backward according to the rotation direction of the circular plate. This mechanism is expected to move stably using multilegs. In addition, it will be possible to steer the robot by connecting several locomotive modules with linear actuators as shown in Figure 2. We verified the usefulness of this new mechanism by constructing and testing on an artificial colon and in real dead pig's colon. 2.2 Structure of link Mechanism Figure 3 shows the prototype of the proposed locomotive device. The prototype is built with the length of 125mm, the diameter of 3Omm-40 mm depending on the position of leg end and a mass of 90g. A DC motor of Maxon CO that serves as an actuator for locomotion is employed and the specifications are shown in Table 1. Silicone' The prototype of robot is consisted of locomotion unit, body unit and leg unit. The leg unit for locomotion comprises a crankshaft, a link, a pivot and a foot as shown in Figure 4. The link mechanism for locomotion works as followings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000765_s0043-1648(02)00108-4-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000765_s0043-1648(02)00108-4-Figure2-1.png",
        "caption": "Fig. 2. Turnover deformation of rail.",
        "texts": [
            " 1 and 2. The bending deformation of wheelset shown in Fig. 1a is mainly caused by vertical dynamic loads \u2217 Corresponding author. Tel.: +86-28-7600882; fax: +86-28-7600868. E-mail address: xuesongjin@263.net (X. Jin). of vehicle and wheelset/rail. The torsional deformation of wheelset described in Fig. 1b is produced due to the action of longitudinal creep forces between wheels and rails. The oblique bending deformation of wheelset shown in Fig. 1c and the turnover deformation of rail shown in Fig. 2 are mainly caused by lateral dynamic loads of vehicle and wheelset/rail. The torsional deformations with the same direction of rotation around the axle of wheelset (see Fig. 1d), available for locomotive, are mainly caused by traction on the contact patch of wheel/rail and driving torque of motor. Up to now very few published papers have discussions on the effects of the SED on creepages and creep forces between wheelset and track in rolling contact. In fact, the SED of wheelset/rail mentioned above runs low the normal and tangential contact stiffness of wheel/rail",
            " 4b it is known that the tangent traction F1 reaches its maximum F1max at w1 = w\u2032 1 without considering the effect of u0 and F1 reaches its maximum F1max at w1 = w\u2032 1 with considering the effect of u0, and w\u2032 1 < w\u2032\u2032 1 . u0 depends mainly on the SED of the bodies and the traction on the contact area. The large SED causes large u0 and the small contact stiffness between the two bodies in rolling contact. That is why the reduced contact stiffness increases the ratio of stick/slip area of a contact area and decreases the total tangent traction under the condition of the contact area without full-slip. In order to calculate the SED described in Fig. 1b\u2013d, and Fig. 2, discretization of the wheelset and the rail is made. Their schemes of FEM mesh are shown in Figs. 5, 7 and 9. It is assumed that the materials of the wheelset and rail have the same physical properties. Shear modulus: G = 82,000 N/mm2, Poisson ratio: \u00b5 = 0.28. Fig. 5 is used to determine the torsional deformation of the wheelset. Since, it is symmetrical about the center of wheelset (see Fig. 1b), a half of the wheelset is selected for analysis. The cutting cross section of the wheelset is fixed, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002274_0379-6779(90)90102-q-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002274_0379-6779(90)90102-q-Figure3-1.png",
        "caption": "Fig. 3. Cyclic vol tammograms of sample L in the ranges 2 - 3 V (n-type doping-undoping) and 3--4 V (p-type doping-undoping) . The scanning rate was 5 mV/s.",
        "texts": [
            " This finding is consistent with the fact that the porous PAS of lower [H]/[C] molar ratio has a similar diameter of micropore as that expected for active carbons, as has been studied in ref. 6. The initial potential of the fresh porous PAS was in the range 2 .9-3 .0 V versus Li/Li + reference electrode independent of the kind of sample. In order to further investigate potential scanning was made in the ranges 3 - 4 V and 2 -3 V for sample L considering the result in Section 3.1. After a few cycles, the shape of the CV curve approached a stationary state shown in Fig. 3. Sample L shows redox reactions in both ranges 2 -3 V and 3 -4 V. The reaction occurring at the higher voltage is the p-type doping, in which the C104- ion is reversibly doped into and undoped from the electrode. In the range 2 -3 V, the n-type doping in which the Li + ion is doped and undoped occurs. In short, the porous PAS is available in both the p-type and n-type doping regions. Although quite a few conductive polymers are known, there are only a few that can be doped with both an acceptor and donor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003842_cdc.2006.376730-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003842_cdc.2006.376730-Figure3-1.png",
        "caption": "Fig. 3. Leader-follower setup in [3].",
        "texts": [
            " Then by definition of vF , \u03c9F and \u03b7, the follower bounds are satisfied, being \u2200 t \u2265 t0 (by (18), (19)): |\u03c9F | \u2264 \u03b7 \u3008E, \u03bd(\u03b8F )\u3009+ vL sin \u03b1\u03c7 d cos\u03c6 \u2264 \u2126 \u2212 KvL + KvL \u2264 \u2126, 0 \u2264 \u2212\u03b7 |\u3008E, \u03c4(\u03b8F + \u03c6)\u3009| + vL cos(\u03b2 \u2212 \u03c6) cos\u03c6 \u2264 VF \u2264 vF \u2264 \u03b7 |\u3008E, \u03c4(\u03b8F + \u03c6)\u3009| + vL cos(\u03b2 \u2212 \u03c6) cos\u03c6 \u2264 VF . Furthermore for every t \u2265 t0, the error dynamic is E\u0307(t) = \u2212\u03b7(t)E(t). Finally, from (19) it follows that \u03b7 \u2265 min { \u2126 \u2212 KVL \u2016E\u2016 , (K \u2212 \u03c71)V0L \u2016E\u2016 , (VF \u2212 cos (0 \u2228 arcsin(K d cos\u03c6)) (cos \u03c6)\u22121) cos\u03c6 \u2016E\u2016 , V0L cos(\u03c6 + \u03b1\u03c7) \u2016E\u2016 , M } = c \u2016E\u2016 \u2227 M . Therefore \u2200 t \u2265 t0, \u02d9\u2016E(t)\u2016 2 \u2264 \u2212 ( c \u2016E(t)\u2016\u22121 \u2227 M ) \u2016E(t)\u20162 which implies that lim t\u2192\u221e \u2016E(t)\u2016 = 0. A different approach to leader-follower formation control is that proposed in [3]. The authors consider the setup in Fig. 3 (for the sake of simplicity a single follower is shown). Two are the main differences from this setup and that proposed in our paper (Sect. II): \u2022 the desired distance \u03c1d between the leader and the follower is calculated with respect to a point P placed at distance \u03b4 < \u03c1d along the follower translational axis. \u2022 the desired relative orientation of the follower with respect to the leader \u03c8d, is expressed in the leader reference frame. Note that \u03c1d and \u03c8d play the same role of d and \u03c6. Hereafter we will use the terms \u201ccentralized\u201d and \u201cdecentralized\u201d to refer respectively to the approach presented in [3] and our approach. These terms do not refer here to the control of the formation, as usual in the literature, but to the sensing system. In fact in our approach the relative angles between the leader and followers are referred to the follower frame (angle \u03c6 in Fig. 1), and can be measured, for instance, by on-board cameras mounted on each follower. On the other hand in [3] the angle variables used to control the formation are referred to the leader (angle \u03c8d in Fig. 3) and in general require a centralized sensing system to be measured. Centralized systems are usually cheaper but less reliable than decentralized ones. The formation control problem in [3] can be formalized in our geometric setting analogously to Problem 1, where, instead of (3) and (4), it is now required that \u03c1(t) = \u03c1d (21) \u03c8(t) = \u03c8d (22) hold for all t \u2264 0. Proposition 1 gives a solution to this problem. Proposition 1: Let \u03c1d > 0 and \u03c8d be given. There exist initial conditions xF (0), yF (0), \u03b8F (0) and controls vF (t), \u03c9F (t) defined in (27), that guarantee (21), (22) for all t and for any trajectory of RL, if and only if the following conditions hold K \u03b4\u221a 1 + (\u03c1d)2K2 \u2212 2K | sin\u03c8d|\u03c1d \u2264 1 (23) VL K \u2264 \u2126 (24) VL \u221a 1 + (\u03c1d)2K2 \u2212 2K | sin \u03c8d|\u03c1d \u2264 VF "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003346_j.jsg.2004.07.005-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003346_j.jsg.2004.07.005-Figure5-1.png",
        "caption": "Fig. 5. Comparison between kink-style (a) and curvilinear (b) fault-bend folding. Fault-bend anticlines developed from identical undeformed multilayers, above identical fault shapes and by the same amount of fault displacement.",
        "texts": [
            " Linear parameters include the amount of slip along the lower (S1), central (S2) and upper ramp (S3), and the length of the central ramp (R). The adoption of circular hinge sectors (e.g. Julivert and Arboleya, 1984; Rafini and Mercier, 2002) to geometrically model fault-bend anticlines (Rich, 1934), produces an overall fold shape resembling that of the kink-style folding. Circular sectors pinned at the fault surface replace straight axial surfaces characterising the backlimb\u2013crest and crest\u2013 forelimb transition in the kink-style model (Fig. 5). Pinning the circular sectors at the fault surface (e.g. Julivert and Arboleya, 1984) is the easiest geometrical and analytical solution and provides a reasonable approximation of natural structures (Fig. 6). In our model, line-length and bed thickness are preserved and flexural slip folding is assumed (Suppe, 1983). This means that the fault shape and the amount of shortening impose the fold shape. In the early stages of contraction (Step I), the BP and FP panels and the circular hinge sectors BP 0 and FP 0 are still incomplete (Fig",
            " (1) The fold shape widens upward, both in the forelimb and in the backlimb (Fig. 3). It follows that the geometry of folded layers depends on their distance from the fault. In contrast, kink-band fault-bend folding generates constantly-dipping panels. (2) Analysing the position of circular sector curvature centres allows discrimination between Step I and Step II configurations and the unequivocal reconstruction of some aspects of the fault shape. In contrast, in kink style fault-bend folding (Fig. 5a), fold geometry does not distinguish between large and small slip faults. (3) Curvilinear fault-bend folding predicts faultfold angular relationships that are comparable with those obtained with the kink-band model in the most frequent range of fault ramp cutoff angles (!308, e.g. Suppe, 1985). Ramp cutoff angles approaching 308 predict different forelimb dip values in the two models. In particular a steeper forelimb can be simulated by circular fault-bend folding due to steeper admissible ramp cutoff angles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000959_ijcnn.2000.860795-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000959_ijcnn.2000.860795-Figure3-1.png",
        "caption": "Fig. 3 Double inverted pe,ndulum control system",
        "texts": [
            ") are not available if the plant parameters are unknown. To cope with this situation we introduce an emulator which mimics the inputloutput map of the plant. By using the emulator added in parallel to the actual plant, we can apply the BP method to adjust the connection weights. We have obtained satisfactory results of PID gain tuning in many cases. 3 Control of double inverted pendulum We consider the application of the self-tuning PID controller to stabilization of a double inverted pendulum shown in Fig. 3. Our aim is to move the cart of the pendulum to the center of the bar (x = 0) and let the pendulum stand at the upright position (01 = 0 2 = 0). The PID gains are adjusted by the neural network, in which the minimum cost function for tuning is the squared error between the actual output and the desired values. As we need the system Jacobian of the inverted pendulum, we use the value derived by using the emulator shown in Fig. 4. The input layer of the emulator consists of seven units, which are connected to nine units of the hidden layer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003346_j.jsg.2004.07.005-Figure22-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003346_j.jsg.2004.07.005-Figure22-1.png",
        "caption": "Fig. 22. Geometrical construction for Eqs. (86), (87), (53), (54), (56), (58), (59), (63), (66), (68), (81) and (83).",
        "texts": [
            " (51), we obtain: S3 Z S1\u2020\u00bdsin\u00f0a1\u00de=sin\u00f0 b1\u00de \u2020\u00bdsin\u00f0b2\u00de=sin\u00f0 b3\u00de (52a) which relates the amount of shortening along the lower and upper ramp in the step I configuration. During step II, the hanging wall cut-off angles along the central and upper ramp become b1 and b 0 1, respectively. As a consequence, Eq. (52a) becomes: S0 3 Z S0 1\u2020\u00bdsin\u00f0a1\u00de=sin\u00f0 b1\u00de \u2020\u00bdsin\u00f0b1\u00de=sin\u00f0 b 0 1\u00de (52b) with S0 3 and S0 1 being the amount of slip after the transition from step I to step II. A.10. Equations 53, 54 and 56 (see Fig. 22a) These describe the incremental position of C2 during the fold evolution, calculated with respect to C1 (0,0): YC2 ZDC2\u2020cos\u00f0a2 Kb1\u00de (53) XC2 ZKDC2\u2020sin\u00f0a2 Kb1\u00de (54) with XC2 and YC2 being the incremental coordinates of C2 at shortening S1: S2=sin\u00f0f1\u00deZDC2=sin\u00f090Ka2 Cf1\u00de (55) Substituting Eq. (48) into Eq. (55) and rearranging: DC2 Z S1\u2020\u00bdsin\u00f0a1\u00de=sin\u00f0b1\u00de \u2020\u00bdcos\u00f0a2 Kf1\u00de=sin\u00f0f1\u00de (56) A.11. Equations 58, 59 and 63 (see Fig. 22b) These describe the incremental position of C4, respect to the upper inflection point of the central ramp I2 (0,0): DC4 ZL1CL2 (57) YC4 ZDC4\u2020cos\u00f0d2\u00de (58) XC4 ZDC4\u2020sin\u00f0d2\u00de (59) with XC4 and YC4 being the incremental coordinates of C4 at shortening S1: L1Z S3\u2020sin\u00f0b3\u00de (60) L2Z S3\u2020cos\u00f0b3\u00de=tan\u00f0f2\u00de (61) Substituting Eqs. (62) and (63) into Eq. (57): DC4 Z S3\u2020\u00bdsin\u00f0b3\u00deCcos\u00f0b3\u00de=tan\u00f0f2\u00de (62) Substituting Eq. (52a) into Eq. (62) and simplifying: DC4 Z S1\u2020\u00bdsin\u00f0a1\u00de=sin\u00f0b1\u00de \u2020\u00bdsin\u00f0b2\u00de \u2020\u00bd1 Ccot\u00f0b3\u00de\u2020cot\u00f0f2\u00de (63) These describe the parabolic shape of g7, which is the locus of the points whose distance from C1 and from the line r is constant, with C1 being the origin of the reference Cartesian system: r : y ZKS2\u2020sin\u00f0a2\u00deCS1\u2020sin\u00f0a1\u00de (64) Substituting Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003038_physreve.72.011706-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003038_physreve.72.011706-Figure4-1.png",
        "caption": "FIG. 4. a Schematic of the components of the interfacial stress tensor Ts, on a surface patch defined by a local coordinate system u1 ,u2 and the unit normal k. Surface stresses have tangential T11,T22,T21,T12 and bending T13,T23 components. b Schematic of the torques acting on the surface director on a surface patch defined by a surface coordinate system u1 ,u2 and the outward unit normal k. Here is the polar angle, and the azimuthal angle.",
        "texts": [
            " In addition we have to take into account the nematic bulk couple stress tensor Cb N energy/area 22,26,27 . In this paper we assume that the interface energy is independent of orientation gradients and hence no interface couples Cs=0 are taken into account; if warranted by experimental observation, interface couple effects can be incorporated in future work. Due to their 2 3 dimensionality the interface stress tensor Ts obey 23 Ts = Is \u00b7 Ts, 4 where Is=Is T=I\u2212k \u00b7k is the interface idem factor and k is the unit normal. Figure 4 a shows a schematic of the components of the surface stresses Ts, on a surface patch defined by a local coordinate system u1 ,u2 and the unit normal k. Surface stresses have tangential T11,T22,T21,T12 and bending T13,T23 components and arise through the interactions between the soft solid and the nematic liquid crystal. Jumps in the bulk stresses k \u00b7Tb and couple stresses across interfaces are defined by 24 k \u00b7 Tb = k \u00b7 Tb SS \u2212 Tb N , 5a k \u00b7 Cb = k \u00b7 Cb SS \u2212 Cb N = k \u00b7 Cb N, 5b where Cb SS=0 was used. The bulk b and interface s torques acting on the director are given in terms of the stress duals and couples as follows 23 : b = Tbx + \u00b7 Cb 6a s = Tsx + s \u00b7 Cs = Tsx, 6b where Cs=0 was used. The original Leslie-Ericksen model uses torques b , s , while the polar nematic version of the model uses stress duals Tbx,Tsx and couples Cb ,Cs . In the absence of interface couples Cs=0 , the interface 011706-3 torques s acting on the director arise from asymmetric stress Tsx . Figure 4 b shows a schematic of the torques acting on the surface director on a surface patch defined by a surface coordinate system u1 ,u2 and the outward unit normal k. Under the action of 1 , 2 the director tilts away or toward the unit normal k; here is the polar angle. On the other hand, 3 causes a precession around k, described by change in the the azimuthal angle . In the present model 3=0 and the surface imparts no preference on the selection of the azimuthal angle. When all the interfacial energy is independent of the azimuthal angles, the state is known as conical degeneracy p"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001551_robot.1996.503859-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001551_robot.1996.503859-Figure11-1.png",
        "caption": "Figure 11: Movements of the space robot (Au, = O.5[m], single-turn spiral motion)",
        "texts": [
            " X 0 :joints Figure 5: Structure of a space robot Figure 7 shows the satellite orientation variation in response to the end-effector desired trajectory without spiral motion. The solid, broken and chained line denotes the 3 vector elements of the Euler parameters in the order. Figure 8 shows the same motion every 0.2[s]. The results of the single-turn spiral motion are shown in Figs.9 through 11. In Fig.9, the solid line denotes xcoordinates variation of the end-effector. the broken and the chain line denotes y's and z's, respectively. The dotted lines denote the desired trajectories. Fig- ure 10 shows the satellite orientation variation. Figure 11 illustrates the motion every 0.2[s]. The Figs.12 through 14 correspond to the multiturn spiral motion when the spiral radius limit g d sets O.l[m]. Figures 12 and 13, similarly to Figs.9 and 10, show the end-effector coordinate variation and the satellite orientation variation. Figure 14 illustrates the motion, where we plotted only the trajectory of the end-effector position. The satellite with solid line denotes the final state and that with broken line denotes the initial state. Note that the satellite makes small fluctuation while making the multi-turn spiral motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003184_2005-01-1651-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003184_2005-01-1651-Figure11-1.png",
        "caption": "Figure 11. Diagram of contact",
        "texts": [
            " For this purpose, the combined parameters of the resulting rough surface, which could be called composite parameters, will be obtained using the following rules: the mean values are simply added up, and the root mean square values are added up by root mean square. For example, for surface condition parameters, the following expression can be written [14]. The parameters identified by the index i with a value of 1 or 2, refer to surfaces 1 and 2, while index c denotes a composite parameter. 21c 21c RRR (8) with Ri = roughness R of the surface i i = standard deviation of i Having obtained these different simplifications, the representation of the contact between a pin and its bore takes the schematic form shown in Figure 11. In this figure, the variables with i indices are used to calculate the parameters of each surface - i.e. R, AR, SAR, W of the ISO 12085 standard. The coordinate system of reference is the bore, and any point M will be described by its polar coordinates. To complete this description of the surface asperities, the assumptions for asperity height distribution and their adopted curvature radii amongst others, are those of Robbe-Valloire [14] to which the index RV, is added i.e.: 2 SM SMrr 2 1 SM RV e 2 1,rf 2 22 2 cln c2 1 1 RV e 2c 1F (9) with the variable r( ) represents the distance from an asperity summit with angle at the system centre, zrms corresponds to the standard deviation of the heights of the asperity summits around the mean line of asperity summits which is denoted by SM, SM is the position of the mean line of asperity summits, is the standard deviation of the radius distribution and 1c and 2c are constants defined in the appendix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002597_j.chaos.2004.06.052-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002597_j.chaos.2004.06.052-Figure3-1.png",
        "caption": "Fig. 3. Element of beam.",
        "texts": [
            " To gain a flavour of the quantitative advantages of moving away from a linear approximation, not to mention the qualitative advantages, we can look at the difference in percentage error incurred for the linear case and the third order approximation from the Taylor expansion for the sine function, which is used essentially to describe the deflection of a typical element of the cantilever beam from horizontal, see Fig. 2. Even the analysis which considers the third order Taylor expansion enhances the accuracy of the angle calculation (see Fig. 2), hence more precise approximations of the beam deflection and consequently the overall stiffness are needed, and one of such approaches is given below. Consider an infinitesimal section of one of the beams with forces R and R + dR, and moments as shown in Fig. 3, where u, v, and s are the horizontal, vertical, and natural co-ordinates of the beam section, / is the inclination angle of the beam section. R has only a vertical component as the length of the beams must be conserved and rotation at the end of the beams is prevented. Therefore taking moments about the left-hand side of the element, we have \u00f0M \u00fe dM\u00de M \u00fe Rdu \u00bc 0; \u00f01\u00de after some manipulation we obtain X M L F0(t) = cos\u03c9t EI Fig. 1. A simple beam system. /00 \u00fe R EI cos / \u00bc 0; \u00f02\u00de where ( 0) represents differentiation with respect to s, and assuming d/ ds \u00bc M EI, where E is Young s modulus and I is second moment of inertia",
            "12), leads to / \u00bc sx0 qs2 2 \u00fe e qx4 0 10x2 0f 4 6x0f 5 \u00fe f6 : \u00f0A:13\u00de For s = L and / = 0, the quantity x0 is approximately equal to x0 \u00bc qL 2 : \u00f0A:14\u00de Using this approximation in the terms of (A.13) which are multiplied by small parameter e, substituting (A.12) and neglecting terms smaller than e and evaluating at s = L we have the more accurate solution that x0 \u00bc qL 2 \u00f01 16e\u00de: \u00f0A:15\u00de Substituting (A.15) into the term in (A.13) which is not multiplied by e, substituting (A.14) in the terms multiplied by e and using (A.12) to substitute for f and neglecting terms smaller than e gives us / \u00bc qls 2 qs2 2 \u00fe e 40qs4 L2 48qs5 L3 \u00fe 16qs6 L4 8qls : \u00f0A:16\u00de It can be seen from Fig. 3 and (A.2) that dv ds \u00bc sin / / /3 6 ; \u00f0A:17\u00de therefore using (A.16) and (A.17) and neglecting terms smaller than e we have dv ds \u00bc qls 2 qs2 2 1 48 q3L3s3 \u00fe 1 16 q3L2s4 1 16 q3Ls5 \u00fe 1 48 q3s6 \u00fe e 40qs4 L2 48qs5 L3 \u00fe 16qs6 L4 8qls : \u00f0A:18\u00de Using (A.14) and (A.10) to substitute for e provides dv ds \u00bc qls 2 qs2 2 1 480 q3L5s 1 48 q3L3s3 \u00fe 7 96 q3L2s4 3 40 q3Ls5 \u00fe 1 40 q3s6 \u00f0A:19\u00de and integrating gives v \u00bc qls2 4 qs3 6 1 960 q3L5s2 1 192 q3L3s4 \u00fe 7 480 q3L2s5 3 80 q3Ls6 \u00fe 1 280 q3s7 \u00fe C1: \u00f0A:20\u00de For s = 0, v = 0, thus it can be seen that the constant of integration is zero, and so evaluating at L and taking the first two terms of the equation for x = vjs=L yields x \u00bc qL3 12 1 1680 q3L7: \u00f0A:21\u00de Using the first term to approximate the smaller term we have q \u00bc 12 x L3 1 36x2 35L2 : \u00f0A:22\u00de Which is, approximating with a binomial expansion and remembering q \u00bc R EI R \u00bc 12 EI L3 x\u00fe 432 35 EI L5 x3: \u00f0A:23\u00de The stiffness of the beam, k, is defined as dR/dv which leads to k\u00f0x\u00de \u00bc 12 EI L3 \u00fe 1296 35 EI L5 x2: \u00f0A:24\u00de [1] Lurie AI"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003184_2005-01-1651-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003184_2005-01-1651-Figure1-1.png",
        "caption": "Figure 1. Diagram of a piston / conrod system",
        "texts": [
            " Assuming it was true, the heating of the piston bosses and the small end bearings would be very high indeed, and would lead to systematic seizure of the pins. In this respect, it is critical to keep in mind that the total product PV of a small end bush is in the order of 25 to 35 MPa.m/s around the maximum power rate for gasoline and Diesel engines. The definition of the total PV is: 4 0 sp r dP 4 R PV (1) with: Psp = specific or diametral pressure 2005-01-1651 Piston Pin: Wear and Rotating Motion Jean-Louis Ligier and Patrick Ragot Powertrain Division - Renault S.A. Copyright \u00a9 2005 SAE International = angular velocity of the conrod (see Figure 1) Rr = piston pin radius = crankshaft angle With a fixed friction coefficient of 1/100, according to mixed lubrication, a pin rotating only in the conrod small end with a bearing 30 mm in diameter and 21 mm wide will consume around 180 W due to friction (fixed in relation to the piston). In addition, if we assume the heat exchange coefficient between the small end and the oil mist under the piston is in the order of 2500 W/m2\u00b0K, the mean thermal equilibrium temperature of a small end bush in mixed lubrication will be in the order of 400\u00b0C",
            " This program will be used to precisely define the piston pin bearings at the end of the engine development. To summarize the purpose of this paper is to point out some of the operating characteristics of piston pin bearings, to show it is possible to simulate piston pin lubrication with simple tools, and to demonstrate the contribution of contact modelling for mixed lubrication which could occurs in the piston pin bearings. In order to investigate the behaviour of piston pin, it is useful to carry out the following analysis of the piston / conrod system represented in Figure 1. Point A on Figure 1 represents the piston pin axes, point M corresponds to the center of the crankpin. Point B is located on the piston pin and point O is the centre of the main journal. The angles , and are counted positively in the trigonometric orientation. Therefore, the angular acceleration of the conrod can be expressed as : ____ r 22 2 2 3 22 2 AMdistanceLand R Lwith sin cos sin 1sin (2) We assume that the friction torque of the small end with modulus Cfpdb applying to the piston pin drives it in rotation without slippage (between piston pin and conrod)",
            " With the previous relationships, the squeeze of lubricant films in the piston and small end bearings is simulated numerically and shown in Figure 6. The mean film temperatures were assumed to be 160\u00b0C for the small end and 220\u00b0C for the piston bosses, which corresponds to the temperatures of gasoline engine at maximum power. Figure 6 shows that the minimum thicknesses are lower on the small end. To analyse the piston pin rotation, we consider in this part that there is no contact. The angular position of the piston pin is identified by the angle in the coordinate system of figure 1,. It follows that the dynamic equilibrium of the pin is written: bdppdbayz cfcfI (7) with cfxxx( )= instantaneous friction torques estimated from hydrodynamic shear stress. Once the calculations have been carried out, we obtain the instantaneous angular speed of the pin, as shown in the example in Figure 7. Figure 7 indicates can see that the pin rotates mainly in one direction, and that the mean rotation speed remains very low. It means that the pin inertia effect is predominant. To illustrate this characteristic, it is interesting to plot the torques cfpdp, cfbdp as function of the crankshaft angle (Figure 8): Figure 8 shows that the torque in the piston bosses is negligible and that the torque in the small end oscillates with big amplitude"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001444_s0301-679x(03)00006-9-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001444_s0301-679x(03)00006-9-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of the general multi-recess hydrostatic journal bearing with N recesses.",
        "texts": [],
        "surrounding_texts": [
            "The geometry of multilobe and multirecess hydrostatic journal bearing having N recesses are shown in Fig. 1 and 2, respectively. The film thickness in the clearance space of the nth lobe and the journal surface can be expressed in the dimensionless form in cartesian coordinates as: Hn 1 d (xj xn 1)cosq (yj yn 1)sinq (1) where dimensionless equilibrium coordinates of the journal centre (xj, yj) can be written as (xj,yj) e C1 cosa, e C1 sina (2) While the dimensionless coordinates of the nth lobe centre (xn 1,yn 1) of an N lobe bearing can be expressed as (xn 1,yn 1) 1 d d cos p N (N 1 2n), 1 d d sin p N (N 1 (3) 2n) Unsteady State recess flow continuity equation for nth recess. The X, Y coordinates are chosen such that X-axis is in line with the static load vector in the absence of any dynamic disturbance. Attitude angle a becomes zero in this case. Using the assumptions of Davies [6], the net rate of accumulation of fluid in the nth recess for an orifice compensated bearing is written in the dimensionless form as: Q\u0304 l 1 p\u0304n Sn (p\u0304n 1 p\u0304n)Cn 1 Anp\u0304n (p\u0304n (4) p\u0304n+1)Cn when p\u0304n 1 p\u0304n p\u0304n+1 and An, Cn, Cn 1 and Sn are flow coefficients defined for the steady state position of the journal centre given by its eccentricity ratio, and attitude angle a as: An 2pn N 2p N (n 1) 1 d (xj xn 1)cosq (yj yn 1)sinq 3 dq Cn m 1 d (xj xn 1)cos 2pn N (yj yn 1)sin 2pn N 3 Sn (xj xn 1) cos 2p N (n 1) cos 2pn N (yj yn 1) sin 2p N (n 1) sin 2pn N Under dynamic conditions when the journal centre undergoes vibrations with amplitude d and da, respectively and thereby induces dynamic pressures in the recess dp\u0304n 1, dp\u0304n and dp\u0304n + 1, respectively. Perturbed flow dQ\u0304 can be written as: dQ\u0304 \u2202Q\u0304 \u2202p\u0304n 1 dp\u0304n 1 \u2202Q\u0304 \u2202p\u0304n dp\u0304n 1 \u2202Q\u0304 \u2202p\u0304n+1 dp\u0304n+1 (5) \u2202Q\u0304 \u2202e de \u2202Q\u0304 \u2202ada This rate of accumulation must be equal to the rate at which the volume of nth recess clearance space changes due to movement of the shaft expressed as \u2202V \u2202t \u2202V \u2202e \u00b7 \u2202e \u2202t \u2202V \u2202a\u00b7 \u2202a \u2202t (6) where V 1tdC1 2 2p N n 2p N (n 1) 1 d (xj xn 1)cosq (yj yn 1)sinq dq Simplification of the above expression gives the following: \u2202V\u0304 \u2202t 4w dx\u0307cos 2p N (n 1) 2 (7) dy\u0307sin 2p N (n 1) 2 \u00b7sin p N Eqs. (4), (5) and (7) yield unsteady state recess flow continuity equation using the following relationship, de dxcosa dysina da dx e sina dy e cosa as: Cn 1dp\u0304n 1 l 2 1 p\u0304n An Cn 1 Cn dp\u0304n p\u0304n dAn de \u2202Sn \u2202e (p\u0304n 1 p\u0304n) \u2202Cn 1 \u2202e (p\u0304n p\u0304n+1) \u2202Cn \u2202e \u00b7(dxcosa dysina) p\u0304n \u2202An \u2202a \u2202Sn \u2202a (p\u0304n 1 p\u0304n ) \u2202Cn 1 \u2202a (p\u0304n p\u0304n+1) \u2202Cn \u2202a \u00b7 dxsina dycosa e 4w dx\u0307sin 2p N n 1 2 dy\u0307cos 2p N n 1 2 \u00b7sin p N (8)"
        ]
    },
    {
        "image_filename": "designv11_11_0000519_a:1007949601160-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000519_a:1007949601160-Figure5-1.png",
        "caption": "Figure 5. End-effector trajectory and workspace obstacle used in the example.",
        "texts": [
            " Using an example, we will show the need for normalizing the performance criteria and the effectiveness of the weighting schemes presented in this paper. In this example, the manipulator is required to track a specified trajectory without exceeding a joint limit or colliding with an obstacle. Since optimizing either the joint limit criterion or the collision avoidance criterion forces the manipulator to exceed the other monitored physical limitation, an acceptable solution can only be generated by balancing the requirements of both. The workspace obstacle and end-effector trajectory for this example is shown in Figure 5. Figures 6 and 7 present the collision avoidance criterion and the joint limit avoidance criterion for the case when only a single performance criterion is optimized. For the plots, it can be concluded that optimization of a single performance criterion results in the manipulator\u2019s reaching either a joint limit or colliding with an obstacle. Figures 8 and 9 present the collision avoidance criterion and the joint limit criterion, respectively, obtained during multiple criteria optimization using the different weighting methods"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001525_5.301683-Figure31-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001525_5.301683-Figure31-1.png",
        "caption": "Fig. 31. used to integrate the converter. Schematic representation of hybrid planar technology",
        "texts": [
            " 2) Integration of a Complete Converter: The technology demonstrated in the above applications can concievably also be used to build a planar integrated multikilowatt converter. This was recently demonstrated in a pilot project on a 300-V dc/dc converter [216], [217]. In this case the converter was integrated in two packages. On the source side it was integrated into the transformer structure of the main transformer, while on the load side the other part was integrated into the window of the filter inddctorsee Fig 30. In Fig. 31, a schematic representation is given how this was achieved. The semiconductor devices were mounted on a heat pipe inside the transformer window, while all capacitive and inductive effects where obtained by using planar magnetic and dielectric materials, stacked as necessary, with the appropriate metallization. In order to check for unforeseen effects within the integrated structure the converter efficiency was compared to that of an electrically equivalent converter constructed in conventional technology, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000131_s0022-0248(97)00273-x-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000131_s0022-0248(97)00273-x-Figure2-1.png",
        "caption": "Fig. 2b]",
        "texts": [
            " During the laser treatment, a continuous flow of 5 1/min of helium was blown to the melted zone through a 6 mm diameter pipe to prevent heavy oxidation. Laser beam scanning velocity (Vb) between 0.001 and 1 m/s were used in this study. At low scanning velocity, the laser power output was decreased to avoid the formation of plasma. Table 1 gives the laser processing conditions. In order to measure the primary spacing and its distribution as well as to correlate them with the corresponding growth rate, the approach described below was used. Fig. 2 schematically shows the measurement process. Firstly, we serially made the metallographic preparations along XX1 ...XXn sections of the laser traces [see Fig. 2a] to ensure the selected section to be as perpendicular as possible to the directional growth dendrites/cells within the center part of the section. PIXAR image processing system (VICOM SYSTEMS INC.) was then used to measure the average spacing and its distribution range according to the Neighbour Criterion [19], i.e. looking the structure as a whole, the nearest neighbours of each of the cells are determined. The primary spacing is defined as the average distance between the centre of gravity of neighbouring cells"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000737_s0890-6955(01)00101-8-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000737_s0890-6955(01)00101-8-Figure4-1.png",
        "caption": "Fig. 4. The co-ordinate system for the gear train.",
        "texts": [
            " A numerical computation was performed to the following design specification: tooth module, m=2 mm and number of teeth, z=30. Tool axis inclination w=25\u00b0 and the radius of the generating circle R was 20 mm. Fig. 3 shows the gear tooth profile in some views perpendicular to the gear axis Z=hi. This shows that the generated tooth profile are of involute form except at the extreme ends of the face. Gears manufactured to prove the numerical simulation and generation were made to this specification. Consider a gear train designated by Rr1 and Rr2 (Fig. 4) which transforms rotational motion between parallel axes with the given function j2 Rr1 Rr2 j1 (the rolling motion) (8) We assume here that the shape of the gear tooth 1 is the curve x which is given in parametric form as follows: X=X(v,j) Y=Y(v,j) Z=Z(v,j) (9) Eq. (9) are the gear convex flank equations given by Eq. (7), relative to the pinion coordinate system. The problem to be solved is to determine the shape of the pinion teeth which will provide conjugate action when in mesh with gear teeth. To do this the following coordinate systems are set up as shown in Fig. 4: x0y0z0, xyz the fixed coordinate systems, rigidly connected to the pinion rotating about O2 and gear rotating about O1 respectively; XYZ a movable coordinate system, rigidly connected to the gear 1; xhz a movable coordinate system, rigidly connected to the pinion 2. The coordinate transformations from the movable sys- tems to the fixed systems, for both gears, are represented by the matrix equations: x= T 3(j1)\u00b7X x0= T 3(\u2212j2)\u00b7x (10) where j1 and j2 are the angles of gear and pinion rotations, respectively",
            " (13)\u2013(15) the equation of meshing can be expressed as: (1 i)R\u00b7Rb(1 cosv)cosw i\u00b7R\u00b7A12(1 cosv)cos(w j j1) (1 i)R2 b\u00b7j (16) iA12\u00b7Rb\u00b7j\u00b7cos(j j1) 0 Taking into account Eq. (12b), the pinion tooth concave flank can be represented as a surface in a threeparametric form, with parameters j and j1 related by the equation of meshing Eq. (16). After elimination of the variable j1, we represent C in a two-parametric form, in terms of parameters v and j. The line of action, defined as the set of contact points between the contacting gear and pinion tooth profiles, in the fixed coordinate system xyz (Fig. 4) is given by Eqs. (16) and (17): x T 3(j1)\u00b7X (17) The parametric equations of the line of action are represented as: x=\u2212R(1\u2212cosv)sin(w\u2212j+j1)\u2212Rbcos(j\u2212j1)\u2212Rbjsin(j\u2212j1) y=R(1\u2212cosv)cos(w\u2212j+j1)+Rbsin(j\u2212j1)\u2212Rbjcos(j\u2212j) z=Rsinv (18) where the angular parameters j and j1 are related by the meshing equation. Fig. 5 shows the line of action in some views perpendicular to the gear axes, z=hi. The lines shown are for curved face width gears to the specification given in Section 2.3. The x and y axes represent the co-ordinates of the start and end of the lines of action"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001374_1.2801491-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001374_1.2801491-Figure1-1.png",
        "caption": "Fig. 1 Two rigid bodies mutually supported by an elastic beam with constant cross section, shown in (a) undeformed, relaxed configuration and (b) deformed, strained configuration",
        "texts": [
            " Patterson and Lipkin (1993b, 1993a) went on to classify compliance in terms of screw eigenvalues and eigenvectors. Zefran and Kumar (1997) and Howard et al. (1995) have also looked at the geometry of compliance, explaining for example differences in the structure of the stiffness matrix when defined using different implicitly defined affine connections. Huang and Schimmels (1997) look at the realizability of spatial stiffnesses using parallel connec tions of \"simple springs.\" 2 Problem Statement Shown in Fig. 1 is a pair of rigid bodies connected by an elastic body. The elastic body need not be an axisymmetric beam. Panel (A) depicts the undeformed system in static equilib rium. Panel (b) depicts the deformed system. The configuration of a rigid body can be represented by a frame,-which in turn can be identified with a homogeneous matrix H R p 0' 1 (1) where R = [e, e^ 63] is an orthonormal matrix and p is a linear displacement vector. Six such frames are shown in Fig. 1. Frames \"A , \" \"a ,\" and \" a \" ' are attached to one of the rigid bodies, so that they do not move with respect to each other. Frames \" B , \" \" b \" and \" b \" ' are attached to the other rigid body. Frames A and B are distinguished frames on the rigid bodies, located at any point of interest. Frames a and b are located at the to-be-defined centers of stiffness of the two bodies. It shall be shown that given certain assumptions these centers must coincide in equi- Contributed by the Dynamic Systems and Control Division for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL",
            " Subscripts will be used to identify particular wrenches. For example, w-a = w1 will denote the wrench exerted by body B on the elastic element with respect to the distin guished inertial frame. Given a homogeneous matrix Hi, the associated adjoint ma trix is Ad\u201ef = 0 The adjoint matrix relates twists and wrenches in different base frames. 4.1 Canonical Stiffness Parameters. We use the stiff ness parameterization of Loncaric (1987), which concerns the compliant behavior near equilibrium. As shown in Fig. 1, attached to body A is a frame A at some point of interest. Attached to body B is a frame B at some point of interest. Temporarily, assume that 'b' is any frame attached to body B. Assume that 'a' is the frame attached to body A that coincides with frame b in equilibrium. Let 6TI be an infinitesimal dis placement of frame 'b' from the equilibrium frame 'a'. Let wS be the wrench exerted by rigid body B on the elastic body, so that positive work is done on the elastic body when corre sponding elements of 6TI and wl are positive",
            " Columns of orthonormal matrix Rf = [e* ef^ e'f\u201e] are the principal coupling axes of stiffness. Matrix T^ = diag (71,., 72^, 73c) is a matrix of principal coupling stiffnesses. A displacement along any one of the principal axes results in a torque about the same axis. A displacement about any one of the principal axes results in a translational force along the same axis. 4.2 Elastic Beam Example. A simple example of consid erable practical relevance is a pair of rigid bodies mutually supported by an elastic beam of length L with constant cross section, as depicted in Fig. 1. Let A be the cross-sectional area of the beam. The beam material is assumed to be an ideal ' The stiffness matrix can be asymmetfic away from equilibrium when it is defined in terms of twist-displacements and wrenches as here, and not in terms of generalized displacements and generalized forces (Zefran and Kumar, 1997). Journal of Dynamic Systems, Measurement, and Control DECEMBER 1998, Vol. 120 / 497 Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www",
            " Consider, for example, the special case of a circular beam with diameter D. Then A = 7rDV4, h = h = TTDVGA, and h = 7rZ)''/32. 4.3 Transformation of Stiffness in Equilibrium. This section shows how the stiffness at the centers of stiffness can be computed given the stiffness at other points. Let frames 'a' and 'a ' ' be frames attached to body A. Let frames 'b' and ' b ' ' be frames attached to body B. Frame 'a' coincides with frame 'b' in equilibrium. Frame 'a ' ' coincides with frame ' b ' ' in equilibrium. Such a system in equilibrium is shown in Fig. 1. Let Wb' be the wrench exerted by body B on the compliant element. Suppose that we know the stiffness K' at ' a \" , so that wg'. = K'STt. It is well known that 6Tt = Ad\u201e\u00ab'SrS, where Ad^;' is computed according to (3). Given wrench wj ' , equiva lent wrench wl' is given by vy^ = KA'H^WW- We can then conclude that w^ = Ad'^'^ K'MH^STI. This proves that K = Ad'H-^'K'AdH'' = Ad'HlK'Ad,^^' (8) It may be that the location of the centers of stiffness, and thus HI , is known from material symmetries. If not, p\" can be determined from (8) by requiring that the coupling stiffness matrix be symmetric"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001209_107754639800400503-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001209_107754639800400503-Figure3-1.png",
        "caption": "Figure 3. Rotor deflected element.",
        "texts": [
            " These supporting bearings, however, are mounted into their rigid housings. The details of the bearing are shown in Figure 2. In Figure 1, the triad XYZ is a global coordinates system with its origin at the geometrical center of the shaft\u2019s left bearing, where the X-axis coincides with the shaft bearings centerline in the nonworking (zero-speed) position of the system. at EASTERN KENTUCKY UNIV on April 22, 2015jvc.sagepub.comDownloaded from 543 Figure 1. Elastic shaft-bearings configuration. The orientation of the deflected rotor element in space (see Figure 3) is monitored using Euler angles (see Figure 4). The elastic rotating shaft is discritized using a Co four-node isoparametric Timoshenko beam element (see Figure 5) with four degrees of freedom assigned to each node-namely, two translational motions plus two total rotations. 3. ROTATING SHAFT FINITE ELEMENT MODEL Currently, two main numerical procedures are employed in the area of rotating machinery analysis-namely, the transfer matrix (Lund and Orcutt, 1967) and the finite element method (Ruhl and Booker, 1972)",
            "sagepub.comDownloaded from 546 at EASTERN KENTUCKY UNIV on April 22, 2015jvc.sagepub.comDownloaded from 547 3.1. Euler Angles To describe the orientation of the deflected rotating shaft element, Euler angles may be used as follows. In Figure 4, X Y Z is an inertial coordinates system, and abc is a body fixed-coordinates system that rotates with the shaft differential element and represents its principal directions where ia, ib, and ic are unit vectors along the axes a, b, and c, respectively (see Figure 3). xyz is an auxiliary (moving) frame system, initially coinciding with the inertial frame. Euler angles are not unique and are defined as three successive rotations that we adopt as the following: 1. Rotation * about the X-axis results in Y and coincides with y. 2. Rotation 8 about y results in the moving frame that coincides with ayz. 3. Spin 0 about the a-axis results in the moving frame, which coincides with the body frame abc. These rotations are characterized by three orthogonal rotation matrices-namely, 8",
            " Again, the reaction forces are due to repeated random impacts, as it is discussed for the left bearing. The FFT spectra of these two plots are shown in Figures 36 and 37, respectively. Here, in Figures 36b and 37b, fs has the maximum amplitude. Also, other peaks share the same frequency-for example, numbers 3, 4, 5, 6, 7, 8,13, and 14 in each of the two plots have the following frequencies, respectively: 114.441,123.98,143.051,147.819,190.735, 209.808, 305.176, and 324.249 Hz. Vibration number 2 is due to 2 fs and (3 fs-2 f~) along the Y and Z directions, respectively. However, in Figure 3 6b, the vibration numbers 10, 11, 12, and 16 have the frequencies 262.260, 281.334, 286.102, and 348.091 Hz, respectively. In view of Tables 1, 2, and 4, the interpretation of the various spectral peaks of both plots is quite possible. at EASTERN KENTUCKY UNIV on April 22, 2015jvc.sagepub.comDownloaded from 594 71 Figure 33a. FFT of the right bearing yb motion (Ab I = Ab r = 10 AM). at EASTERN KENTUCKY UNIV on April 22, 2015jvc.sagepub.comDownloaded from 595 at EASTERN KENTUCKY UNIV on April 22, 2015jvc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000817_jsvi.1997.1051-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000817_jsvi.1997.1051-Figure1-1.png",
        "caption": "Figure 1. (a) Undeformed rotating beam, (b) deformed rotating beam.",
        "texts": [
            " A third model that leads to a stable solution for the rotating beam has also been developed in this study. In this model, the effect of longitudinal displacement caused by bending is neglected in formulating the elastic forces and this effect is considered in formulating the inertia forces. The effect of longitudinal displacement due to bending on the stability of the rigid body modes of a translating and rotating beam model is also examined in this investigation. In this section, the two-dimensional rotating flexible beam model shown in Figure 1(a) is first considered. The beam is assumed to rotate about the Z-axis with an angular    467 velocity u . The origin of the beam co-ordinate system is assumed to be fixed, and therefore, the beam does not undergo a translational motion. The global position vector of an arbitrary point on the beam can be written as r=Au\u0304, (1) where A is the planar rotation matrix defined as A=$cos u sin u \u2212sin u cos u %, (2) and u\u0304 is the local position vector of the arbitrary point on the beam, which is defined as u\u0304= u\u0304o + u\u0304f ",
            " (3) In this equation, u\u0304o =[x 0]T is the position vector of an arbitrary point on the beam in the undeformed configuration, u\u0304f =[ut v]T is the deformation vector, v is the transverse displacement, and ut is the total longitudinal displacement which is defined as [5] ut = u+ ur + ug . (4) The displacement u is the longitudinal deformation due to the axial elastic motion of the points on the center line of the beam, ug is the longitudinal displacement caused by the transverse deflection of the beam, and ur =\u2212y 1v/1x is the result of the rotation of the cross-section. In the case of a slender beam, the effect of the displacement ur can be neglected. In order to evaluate the displacement ug , one observes from Figure 1(b) that ds\u2212 dx=z(dx)2 + (dv)2 \u2212 dx=z1+ (1v/1x)2dx\u2212 dx= 1 2 (1v/1x)2dx, where ds is an infinitesimal arc length. It follows from the preceding equation that ug =\u2212g x 0 (ds\u2212 dx)=\u2212 1 2 g x 0 01v 1x1 2 dx. (5) The axial and bending displacements can be expressed in terms of space dependent shape functions and time dependent co-ordinates as $uv%=Sqf =$S1 0 0 S2%$qf1 qf2%, (6) where S1 and S2 are the rows of the shape function matrix S associated with the axial and in-plane directions respectively, and qf1 and qf2 are the axial and in-plane transverse components of the time dependent elastic co-ordinate vector qf "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002591_0094-114x(85)90040-0-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002591_0094-114x(85)90040-0-Figure6-1.png",
        "caption": "Fig. 6. Tip radius cutting.",
        "texts": [
            " 4(a) and 4(c) are limits of the cutter tip with both a bottom land and a tip radius, generation of gear tooth fillets by these two cutters is not treated separately from the generation of a gear tooth fillet by the rack form tip of Fig. 4(b). For a cutter of this form the tip has two distinct surface normals: one for the bottom land. and one for the tip radius. For the bottom land the surface normal is and the tooth root base has the values r_, = (R - d) cos0.,i_~ - (R - d) sin0,,j.~ (15) for the start of the right side root. The second tip surface normal is for the section of tip produced by the radius, r,. This normal passes through the arc center, C, as shown in Fig. 6. As the gear blank rotation angle. 0,,, decreases past R-I(Pc/4 - ~/2), the angle that this normal vector makes with the Y, direction. 13, decreases from ~/2 to the pitch line pressure angle. ,b. For no cutting interference the fillet cutting point, Q, will meet the involute cutting point, P, when 13 equals ~ and the gear blank rotation angle becomes 02 = aJ(R cos ,b sin ,b). (16) n = - i ) and is only normal to the coincident point relative velocity between the rack form and the gear blank on the line of centers between points O and O:",
            " Thus, an arc of radius r : = R - d (12) If there is involute interference, the trochoid traced out by Q will cross the involute of P before the surface normal direction, angle 13, drops to the value of the pitch line pressure angle, 4. The determination of the fillet trochoid for values of 0: between pc/4R and that given by eqn (16) will complete the information required to describe the tooth (13) fillet. For this trochoid the surface normal is is cut at the center of the tooth root by the rack tip n = - s i n 13il + cos 13jj. (17) land, as shown in Fig. 5. For plotting purposes the tooth is constructed from the center of its right side As shown in Fig. 6, the angle 13, which causes n to root to the center of its left side root. Thus, the gear pa_._~ss through the pitch point, is defined by line blank rotation angle, 02, has the limits OC. The equation for the slope of this line is pfl4 - hi2 < 02 < p--~ (14) tan 13 = ac - rc s in ~ (18) R 4R ' R02 - ac tan ~ - r, cos \u00a2b 356 B. HEFENG el al, as a direct function of the gear blank rotation angle 0:. The position vector from O_, to the cutting point. Q, expressed in the fixed coordinate frame at the gear blank center is given by r: = {R - a~ + rc sin 6 - r, sin 13}1o2 + {R0: - ac tan 6 - r, cos 6 + r, cos 13}jo:"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003047_iros.2003.1249198-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003047_iros.2003.1249198-Figure1-1.png",
        "caption": "Figure 1: Fixed base single am,",
        "texts": [
            " Then, in section four, the previously obtained results will be extended to the more general case of, still 3D and non-holonomic, multiarm mobile manipulators when performing grasping operations. Finally, section 5 will deal the case of object manipulation and transportation performed by multiarm mobile systems. Some conclusions and indications concerning the future research activities will finally conclude the present work. 2 Control of a Fixed Base Single Arm with Singularity Avoidance Let us consider a redundant (i.e. Mof > 6) fixed base single arm having a kinematics structure similar to the commonly used one reported in Fig. 1, where the set of joints 1,2,3 (shoulder) and 5,6,7 (wrist) constitute, each one, a 3-dof rotational joint (typically of Euler and/or Roll-Pitch-Yaw type). In such figure, frame <g> represents the \u201cgoal frame\u201d, which bas to be reached (in position and orientation) by the \u201cend-effector frame\u201d <e> of the manipulator. Then, by letting be the collection of the (projected on world frame <O>) misalignment error vector and distance error vector d, of frame <e> with respect to <g>; and moreover by also letting XT [UT, J] (7",
            "j-k$) (13) Finally note that, in order to be comprehensive of the overall cases fi 5 f i ~ , while avoiding any possibility of chattering in the vicinity of the threshold value po, it is practically convenient to adopt the following expression for i, automatically guaranteeing a smooth transition between the two different cases: where a ( p ) is a continuous scalar function of p, which is unitary for p I po and hell-shaped, tending to zero within a finite support, for p > f i ~ . 3 Control of a Single Arm Non-Holonomic Mobile Manipulator The case of an arm of the same type of Fig. 1, now mounted on a 3D moving base as in Fig. 2, is now considered. The vehicle is assumed to be a non-holonomic one, in the sense that it allows a linear velocity vector only directed along its principal axis, and an angular velocity vector Q only lying on a plane passing through a known point of such principal axis, and orthogonal to it. The arm and the ve- hicle are regarded as two separate \u201cbasic robotic units\u201d, whose motions however needs to be suitably coordinated to obtain the accomplishment of the assigned common task in a cooperative way"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.36-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.36-1.png",
        "caption": "Figure 3.36 Shape of a wire in a centrifugal field. Geometrical definitions",
        "texts": [
            " The basic assumptions are that the bending stiffness of the wires or fibre is negligible and that the winding can be considered to be composed of a certain number of layers in which the various wires behave exactly in the same way. The shape taken by the various layers is computed and then the interaction between the layers and between the first layer and the hub is taken into account via an iterative procedure. The starting point is the evaluation of the shape taken by a wire in a centrifugal field, i.e. the polar catenary.* With reference to Figure 3.36, the potential energy of the wire in the centrifugal field can be expressed as: r-^^-^r^fc+ffi] d0 (3.145) The problem of finding the equilibrium configuration reduces to the one of finding the function r(9) which causes the potential energy to be minimum.t As * A similar problem was first studied, with reference to the statics of arches, by L. Mascheroni in 1785 in his Nuove richerche suW equilibrio delle volte. t For a complete study of similar problems, see, among other texts, Meirovitch, L., Methods of Analytical Dynamics, McGraw-Hill, New York (1970)",
            " The series of equation (3.151) cannot be used as its radius of convergence reduces when K\u2014*1. If K = 0 the arc of circumference is found. All values of K between 0 and 1 lead to sub-circular shapes and equation (3.151) holds for all cases of practical interest. If K is negative 'supercircular' shapes are found, and equation (3.151) again can be used. Supercircular solutions lead, however, to outward radial forces on the spokes and are of little practical interest. The stress crw in the wire at midspan (C, Figure 3.36) or on the spoke (point A), the radial force / exerted by the wire on its supporting points, the length L of the wire and its stretching AL are easily computed using the following formulae: f=niip\u201eco2R* cos ( 0 o - 0 i ) 6 (3.152) (<TJA = P\u201eCD2R2P (3.153) ((TJC = P\u201e(D2R2 0S (3.154) L = RQN (3.155) AL = pv/a)2R*M/Ey, (3.156) where rw is the radius of the wire, the subscript w indicates the wire and the five functions of K designated by M, N, P, Q and S are: P=W+K)/(l-K)-\u00a3]/2ti Q = 2P sin cpA S = [(3+K)/(l-K)-l-\\/2Xl N 2 r x =\u2014 -^d8 XAJO C\u00b0S<P 1 f \" - [ (3 -X) - ( l -X) Z 2 ] Z xid-x) Jo d6 cos q> (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002366_b401831a-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002366_b401831a-Figure1-1.png",
        "caption": "Fig. 1 The mSI-LOV system consists of a 1000 mL high precision syringe pump, two-way valve, holding coil, and a lab-on-valve manifold mounted atop a six-port multi-position valve. The ends of the fiber optic cables were spaced 3.5 mm apart, resulting in a flow cell volume of 6.8 mL.",
        "texts": [
            " A drawback of conventional SI is that it has to use syringe pump to flush a long sampling line between samples to eliminate carryover. This operation slows down sampling frequency, making it considerably lower than that of a comparable FI system, where a multi-channel peristaltic pump serves sample and reagent lines simultaneously. Miniaturization of a conventional SI system has been achieved by integrating the sampling conduit and flow cell into a microfabricated compact structure called the lab-on-valve (LOV) mounted atop a multi-position valve (Fig. 1).4,5 Operating in the microlitre range, this SI system in the LOV format (mSI-LOV) reduces sample and reagent consumption and waste generation. Since the sampling line inherent in the conventional SI system has been eliminated through integration and miniaturization, carryover is reduced, and the sampling frequency of mSI-LOV is higher than that of conventional SI systems. For example, glucose, ammonia, and glycerol stopped-flow assays using the LOV format take about 60 to 100 s to complete one run,6 while conventional SI requires typically 200 s to complete the similar assay",
            " The model chemistries, enzymatic assays of glucose and ethanol, were chosen since their assay protocols can be easily modified to accommodate many other reagent-based assays that use spectrophotometric detection.3 The sequential injection system (FIAlab-3000, FIAlab Instruments, Inc., Medina, WA, USA, http://www.flowinjection.com/) consists of a high-precision bi-directional syringe pump (1000 mL volume) driven by a stepper motor, a two-way valve, holding coil, six-port selector valve, and lab-on-valve central sample-processing unit (FIAlab Instruments, Inc.) (Fig. 1). The entire system was placed inside an incubator (Model 6M, Precision Scientific, Winchester, VA, USA, http://www.precisionsci.com/) to provide temperature control. For the glucose assay, a homemade tungsten lamp was used as the visible light source for a UV-VIS spectrophotometer (USB2000, Ocean Optics, Inc., El Dorado Hills, CA, USA, http:// www.oceanoptics.com/). Two fiber optic cables, furnished with a stainless steel tip (0.159 cm od) were used to connect the flow cell to the light source and the spectrophotometer, with fiber diameters T h i s j o u r n a l i s \u00a9 T h e R o y a l S o c i e t y o f C h e m i s t r y 2 0 0 4 D O I: 10 .1 03 9/ b 40 18 31 a 5 9 7A n a l y s t , 2 0 0 4 , 1 2 9 , 5 9 7 \u2013 6 0 1 Pu bl is he d on 1 1 Ju ne 2 00 4. D ow nl oa de d by G eo rg ia I ns tit ut e of T ec hn ol og y on 3 0/ 10 /2 01 4 12 :3 3: 58 . View Article Online / Journal Homepage / Table of Contents for this issue of 400 mm and 600 mm, respectively. The fiber optic cables were spaced 3.5 mm apart, resulting in a flow cell volume of 6.8 mL (Fig. 1). The entire system was controlled by a personal computer running FIAlab software, version 5.9.137. For the ethanol assay, a deuterium lamp (Model D 1000, Analytical Instrument Systems, Inc., Flemington, NJ, USA, http:// www.aishome.com/) was used as the ultraviolet light source. A 400 mm fiber optic cable was connected to the light source, and a 200 mm fiber optic cable was connected to the spectrophotometer (S2000, Ocean Optics, Inc.). The flow cell volume and configuration remained the same as for the glucose assay",
            " Following a flow stop, a short period (about 5 s) of residual mixing takes place during which the reaction mixture settles within the flow cell and the monitored signal is noisy. After the solution settles, a linear portion of the reaction rate curve (AB in Fig. 2) is recorded while data is collected. In order to accelerate the assay, the stopped-flow period needs to be utilized for preparation of the next run and the mixing of sample/ regent zones has to be accelerated. Since the flow cell can be isolated from the rest of the system by turning the groove of the multi-position valve away from the flow cell port (Fig. 1), the sample, reagent, and spacer of run #2 can be stacked into the holding coil, while the reacting mixture from run #1 is being monitored in the flow cell (Fig. 3). By choosing a large volume of Fig. 2 Stopped-flow reaction based assay of glucose. The response curve was recorded as the stacked zones entered the flow cell, followed by stopped-flow and washout. When the flow was resumed, the signal returned to baseline as the flow cell was washed out. (400 ppm glucose, sample 30 mL, reagent 80 mL, spacer 100 mL, dispensed volume 210 mL, flow rate 200 mL s21, stopped-flow 20"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000363_s0168-874x(99)00042-6-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000363_s0168-874x(99)00042-6-Figure3-1.png",
        "caption": "Fig. 3. Finite element model of the modi\"ed bearing outer ring.",
        "texts": [
            " It is further assumed that the bearing carries a pure radial load. If gravity is neglected, then the outer ring is loaded only on its inner surface (raceway) and outer surface. The load on the outer surface is the reaction force between the ring and the housing. The load on the inner surface (i.e. the groove) is caused by contact with the rolling elements. The boundary conditions for the outer ring were therefore established as completely \"xed on the outside surface, and contact loads were applied to the inside surface. In Fig. 3, a \"nite element model for a outer ring-modi\"ed bearing is shown, which was created using eight noded structural brick elements with three translational degrees-of-freedom at each node. The response of the bearing was estimated using cubic shape functions, and eight integration points (2]2]2) were located within the domain of each element. Since rolling elements under loading form ellipsoidal contact areas with the raceway [3], the loads were approximated by a surface pressure over a small area as shown in Fig. 3. The applied surface pressures varied bilinearly across the face of each element. A rolling element was assumed to be located directly over the center of the modi\"ed section of the ring, and twelve element faces were covered by the contact area. In order to reduce computational complexity, an analysis was \"rst conducted only on the modi\"ed portion of the outer ring, as shown in Fig. 4. The analysis showed that the loads produced highly localized stresses and de#ections. To ensure that the simpli\"ed outer ring model would produce results as accurate as the computationally expensive model of the entire ring, proper boundary conditions had to be applied on the surfaces that were created by cutting the segment away from the complete ring structure",
            ", the diameter of the rolling elements does not exceed the space between the inner and outer rings), then 0(e(0.5 and 0( t - (903, where t - is given by t - \"cos~1(1!2e). (8) For a given radial load F 3 , the output of the piezoelectric load sensor (in picocoulomb), as shown in Fig. 9, is due to the portion of q .!9 that is not supported by the bearing structure. The relationship between the sensor output and the value of q .!9 is determined from a \"nite element model with an integrated sensor module, shown in Fig. 3. The piezoelectric load sensor was modeled as a piezoceramic chip interposed between two steel \"xtures. The piezoceramic chip was modeled using eight noded coupled-\"eld brick elements. Each node had three translational degrees-offreedom and one voltage degree-of-freedom. In addition to the elastic constants, the dielectric and piezoelectric voltage constants were also needed. The material properties for type PXE-5 piezoceramic (Philips Components) were given as follows: relative permittivities of the material eT 33 /e o \" 2000 and eT 11 /e o \" 1800, compliances sE 11 \"15 lm2 / N and sE 33 \"18 lm2/N, piezoelectric voltage constants g 33 \"22.0 V mm/N and g 31 \"!10.9 V mm/N, material density o\"7700 kg/m3, and Poisson's ratio t\"0.3. For the various module dimensions analyzed, the size of the piezoceramic chip was held constant at 1.7 mm long, 2.6 mm wide, and 0.58 mm high. The outer ring, \"xtures, and module housing were modeled with the same type of solid elements as used in Fig. 4. By applying a nominal contact pressure of 100 kPa as shown in Fig. 3 and varying the size of the module, the \"nite element model produced the load sensor outputs shown in Fig. 9. (Note that the location of the sensor module corresponded to t\"0 in Fig. 8.) The charge produced by the piezoelectric force sensor is given by Q\"!d 33 F, (9) where d 33 is the piezoelectric charge constant for the sensor material and F is the force applied to the sensor. Note that the charge Q is independent of the sensor dimensions, because of the longitudinal e!ect. However, the support provided by the bearing structure varies with the module size, and the sensor output will vary with the load on the module"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002591_0094-114x(85)90040-0-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002591_0094-114x(85)90040-0-Figure1-1.png",
        "caption": "Fig. 1. Gear cutting coordinate frames.",
        "texts": [
            " V u = 0 , (1) where n is the unit normal vector of the rack surface at a given point, and Vu is the relative velocity between that point on the rack and the coincident point on the gear blank. Equation (1) is used with three separate coordinate systems to obtain the equations of the gear tooth and fillet relative to the gear blank from the equation of the rack form relative to itself. One of these coordinate frames is fixed in space. The fixed frame (Xo:, Yo:) is fixed in space at the gear blank center, Oz. As shown in Fig. 1, Xo= is directed'from 02 to the instant center or pitch point, O, in the radial gear blank direction, and Yo~. is directed in the tangential direction parallel to the rack centrode. The moving coordinate attached to the rack form (X~, Y1) is attached to the rack at the intersection of the rack face with the rack centrode or pitch line. O1. This is the point on the rack which is initially coincident with O. The directions of X and Y are parallel to those of X02 and Y02. The third coordinate frame (,1\"2, Y2) is attached to the gear blank at 02 and rotates with the gear blank. In the initial position this coordinate frame is coincident with (Xm, Y02). Due to the rolling motion of the centrodes, as (,1\"2, }'2) rotates through the angle 0=, (X~, }'1) translates through the distance R02 as shown in Fig. 1. Here, R is the pitch radius of the gear. Since the coordinate frame (.t\"2, }2) on the gear blank has a radial direction X2 which crosses the involute surface at the pitch circle, a fourth coordinate frame will be utilized for the final tooth and fdlet description. This coordinate frame (X3, Y3), which is not shown in Fig. 1, has its radial direction, ,t\"3, aligned through the tooth centerline. The unit common normal vector, n, has the same description in the fixed coordinate frame as it does in the rack coordinate frame (Xj, Y]) in which it is initially defined, because it is a free vector. Since the relative velocity vector for two coincident points is normal to the line from the instant center of the two bodies, O. to the coincident point. P, eqn (1) is satisified by those points on the rack surface for which the surface normal passes through the mesh pitch point, O"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000931_s0890-6955(97)00090-4-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000931_s0890-6955(97)00090-4-Figure2-1.png",
        "caption": "Figure 2. Principle of BUT-test.",
        "texts": [
            " Material EBT-G EBT-S Sheet Rpo.2 HV thickness (MPa) (m=15g) (mm) 0,79 145 73 0,79 166 135 EDT-R 0,80 163 123 EDT-S 0,79 176 151 One of the EBT materials was hot-dip galvanised but similar to the other EBT sheet in surface topography. The difference between the two EDT materials was that one of them was significantly rougher. Table 1 displays the mechanical properties of the sheets used in this study. 2.2 Friction tests The friction tests were performed in a BUT-test (Bending Under Tension), illustrated in figure 2. The back tension force can be predetermined from the control system and is held constant during the draw. The tool material was a quenched and tempered tool steel ground with a The test material was cut into 550x50 mm strips, deburred and degreased in an ultrasonic bath with an alkaline solution at 60\u00b0C for five minutes. Each strip was then flushed with water for approximately 30 s followed by flushing it with excess of alcohol and left to dry followed by application of lubricant. In the BUT-test several parameters can be set"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001686_1.1567749-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001686_1.1567749-Figure1-1.png",
        "caption": "FIG. 1. Local geometrical equilibrium at the cutting front.",
        "texts": [
            " The starting point of this work needs to describe the local physical equilibrium of each cell of the cutting front. This is the case for constant cutting velocity and also after the nonstationary phase of cutting kerf generation. So, we consider that the cutting front is in a quasisteady state and we will neglect local fluctuations or perturbations of laser or gas parameters. In the laser beam frame ~that also corresponds to the laboratory frame! and as the result of laser interaction, an elementary surface of the cutting front is displaced with a \u2018\u2018drilling\u2019\u2019 velocity vd that is normal to this surface ~Fig. 1!. This elementary surface is also displaced in the laboratory frame with the cutting velocity vc . Therefore, the final velocity of this surface is the vector sum of these two velocities. It is easy to understand that the surface will be stationary in the laboratory frame if this resulting velocity is parallel to this surface.7 Therefore, if the local inclination of the surface is aeq ~Fig. 1!, this condition will be satisfied only if7 vd~aeq!5vc cos aeq . ~1! Equation ~1! defined on very simple geometrical considerations, can also be also demonstrated by writing the cinematic compatibility of the surface.8,9 This relation is an important one, because it defines the condition of stationarity in the laboratory frame of any surface, irradiated by a laser \u00a9 2003 Laser Institute of America IA license or copyright; see http://jla.aip.org/about/about_the_journal beam, subjected to displacements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003606_detc2005-85337-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003606_detc2005-85337-Figure2-1.png",
        "caption": "Fig. 2 k-legged PKC of an m-legged PKC: (a) The original one and (b) The one with the equivalent kinematic chain added.",
        "texts": [
            "org/ on 02/07/2016 Te W and Wi denote, respectively, the wrench system of the moving platform and the wrench system of leg i. We have W = m\u2211 i=1 Wi (1) Equation (1) states that the wrench system W of a PKC is the linear combination of the wrench systems Wi of all its legs. Since the twist system, T , of the moving platform is the reciprocal screw system of its wrench system, we obtain T = WT (2) where WT denotes the reciprocal screw system of the wrench system of the moving platform. For a k-legged PKC [Fig. 2(a)], which is composed of k legs of an m-legged PKC (Fig. 1), letW[k] denote the wrench system of the k-legged PKC. An equivalent serial kinematic chain of the klegged PKC is defined as a serial kinematic chain which has the same twist system and the wrench system as the k-legged PKC. For a specified twist system of the moving platform, there is no difficulty in determining a serial kinematic chain with the same twist system. For example, if a twist system of a PKC is a 3-\u03be\u221e-system, a serial kinematic chain with the same twist system can be any one PPP serial chain in which the direction of the P (prismatic) joints are not all parallel to one plane",
            " If a twist system of a PKC is a 3-\u03be\u221e-1-\u03be0-system, a serial kinematic chain with the same twist system can be any one PPPR serial chain in which the axis of the R (revolute) joint is parallel to the axis of the \u03be0 and the direction of the P joints are not all parallel to one plane. If for a k-legged PKC, there exists a leg i which satisfies Copyright  2005 by ASME rms of Use: http://www.asme.org/about-asme/terms-of-use D Wi = W[k], leg i can be directly selected as the equivalent serial kinematic chain. If the equivalent serial kinematic chain is not a leg of the klegged PKC, we can connect the moving platform and the base of the k-legged PKC using the equivalent serial kinematic chain [Fig. 2(b)] without affecting the instantaneous mobility of the klegged PKC. The instantaneous mobility of the (k + 1)-legged PKC obtained above will be (F[k] + Re), where (F[k] is the mobility of the k-legged PKC, and Re denotes the number of independent parameters to determine the configuration of the equivalent serial kinematic chain with the moving platform fixed. Just as in the above examples, the equivalent serial kinematic chain is generally selected in such a way that Re = 0. It is evident that a sufficient condition for the twist systems of the equivalent serial kinematic chain and the k-legged parallel kinematic chain are still equal to each other with the change of configurations of the equivalent serial kinematic chain and the k-legged PKC is that the equivalent serial kinematic chain and each leg of the k-legged PKC comprise a (C[k] + Re + Ri)DOF (degree-of-freedom) single-loop kinematic chain of fullcycle mobility"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000765_s0043-1648(02)00108-4-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000765_s0043-1648(02)00108-4-Figure4-1.png",
        "caption": "Fig. 4. (a) Change of stick/slip area under two kinds of the conditions and (b) change of the total tangent traction.",
        "texts": [
            " If |S1| = |S\u2217 1 | > 0, |w1| in (2) has to be larger than that in (1). Namely the pairs of contact particles without the effect of u0 get into the slip situation faster than that with the effect of u0. Correspondingly the whole contact area without the effect of u0 gets into the slip situation fast than that with the effect of u0. Therefore, the ratios of stick/slip areas and the total traction on contact areas for two kinds of the conditions discussed above are different, they are simply described with Fig. 4a and b. Fig. 4a shows the situation of stick/slip areas. Sign in Fig. 4a indicates the case without considering the effect of u0 and indicates that with the effect of u0. Fig. 4b expresses a relationship law between the total tangent traction F1 of a contact area and the creepage w1 of the bodies. Signs and in Fig. 4b have the same meaning as those in Fig. 4a. From Fig. 4b it is known that the tangent traction F1 reaches its maximum F1max at w1 = w\u2032 1 without considering the effect of u0 and F1 reaches its maximum F1max at w1 = w\u2032 1 with considering the effect of u0, and w\u2032 1 < w\u2032\u2032 1 . u0 depends mainly on the SED of the bodies and the traction on the contact area. The large SED causes large u0 and the small contact stiffness between the two bodies in rolling contact. That is why the reduced contact stiffness increases the ratio of stick/slip area of a contact area and decreases the total tangent traction under the condition of the contact area without full-slip"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003803_j.ijmecsci.2006.07.009-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003803_j.ijmecsci.2006.07.009-Figure4-1.png",
        "caption": "Fig. 4. Schematic diagram of the symmetrical three-lobe bearing.",
        "texts": [
            " The main objective here is the use of method of feasible directions and the genetic algorithm in the optimum design of a typical high-speed overhung centrifugal compressor, shown in Fig. 3, partially adapted from Roso [17], and developing the bearing configurations that optimize stability along the other criteria such as minimum film thickness, power loss, maximum film temperature, and maximum film pressure. The system consists of a large disc ARTICLE IN PRESS H. Saruhan / International Journal of Mechanical Sciences 48 (2006) 1341\u201313511344 (impeller) at the left-end side of the shaft, with the shaft is supported in hydrodynamic fixed three-lobe bearings, see Fig. 4, at the station number I and II. The bearing optimized in this study is the one located at the station number I. A number of design requirements are specified based on stability and other design criteria are formulated as constraints which must be satisfied in order to for acceptable choice of parameters to be found. The formulation for the rotor-bearing system calculation is based on a finite element method using matrix reduction method. The reliable model for the design of the rotor system is very important"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000499_3516.891047-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000499_3516.891047-Figure1-1.png",
        "caption": "Fig. 1. Harmonic drive. (a) Configuration. (b) Operation.",
        "texts": [
            "00 \u00a9 2000 IEEE In Section II, we give an overview of the research on Harmonic Drive built-in torque sensing and summarize the achieved results. In Section III, we analyze the signal fluctuation caused by the gear operation, and provide a solution to the signal fluctuation compensation problem by adjusting sensitivities of the strain gauges. We also define the minimum number of strain gauges needed to compensate the signal fluctuation. In Section IV, we show a recently obtained experimental result. A Harmonic Drive is composed of three main parts: wave generator, flexpline, and circular spline, as shown in Fig. 1(a). A wave generator is of an elliptic shape with a thin ring ball bearing assembled on it and an Oldham coupling in the center of it. The wave generator is inserted into the flexpline just under the teeth, so that the teeth are deformed into an elliptic shape. The elliptically shaped flexpline is then inserted into the circular spline so that the teeth of the flexpline and the circular spline engage only on the major axis of the ellipse. The total number of teeth on the flexpline is smaller for two compared to the total number of teeth on the circular spline. In this way, a high reduction ratio is realized in one stage. When the gear is used as a reducer, the wave generator is coupled to the input shaft, while either of the flexpline or the circular spline is coupled to the output shaft, and the other of both is fixed to the gear\u2019s housing. Operation of the Harmonic Drive with a circular spline fixed is shown in Fig. 1(b). The gear\u2019s nominal reduction ratio is a ratio between the number of teeth on the flexpline divided by the difference of the number of teeth on the circular spline and flexpline (1) For the designs with circular spline fixed the gear reduction ratio , and for the designs with flexpline fixed the gear reduction ratio are (2) Here, the negative sign of denotes that the output shaft of the gear rotates in the opposite direction of the input shaft. A. Initially Proposed Built-In Torque Sensing In 1989, Hashimoto first proposed a principle of torque detection from strain in the flexpline [3]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002418_s0967-0661(02)00319-2-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002418_s0967-0661(02)00319-2-Figure8-1.png",
        "caption": "Fig. 8. Planar view of the UVMS. At point A, joint 2 is reaching its mechanical limit. This is avoided making the vehicle participate to the end-effector motion (up to point B).",
        "texts": [
            " It can be recognized that the vehicle is asked to move only when the manipulator itself is in critical situations. In detail, at point A, the vehicle starts moving after the joint 2 approaches the joint limit \u00f0120 \u00de: At point B, when the second joint comes back to a safe working configuration, the vehicle is not asked anymore to move. Finally, at point C, the vehicle moves to avoid a singular configuration that would occur if the manipulator is outstretched. A planar framed view of the UVMS\u2019s movement is reported in Fig. 8. Point A is shown where the vehicle has to contribute to the end-effector motion to avoid that the second joint reaches the joint limit. Then, the end-effector trajectory is fulfilled up to point B; where the movement of the vehicle keeps the manipulator again in a safe configuration. A similar situation could be drawn for the kinematic singularity case (point C). In Figs. 9 and 10 the outputs ai\u2019s and a of the fuzzy inference system are shown. It can be recognized that a smooth transition between the movement of the vehicle and the movement of the manipulator and between the different secondary tasks is realized"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001532_s0022-460x(03)00283-9-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001532_s0022-460x(03)00283-9-Figure6-1.png",
        "caption": "Fig. 6. Predicted lengths of the actuators.",
        "texts": [
            " The position of the base platform %ra\u00f0k \u00fe 1\u00de can be predicted in the next T with %ra\u00f0k \u00fe 1\u00de \u00bc #ra\u00f0k\u00de \u00fe #va\u00f0k\u00deT \u00fe 0:5#aa\u00f0k\u00deT2 \u00f016\u00de Here, #ra\u00f0k\u00de; #va\u00f0k\u00de and #aa\u00f0k\u00de are, respectively, the current observed position vector, the velocity vector and acceleration vector of the base platform. So the predicted position %rP ai\u00f0k \u00fe 1\u00de of the upper mounting point of the ith actuator Pai (see Fig. 4) is %rP ai\u00f0k \u00fe 1\u00de \u00bc %ra\u00f0k \u00fe 1\u00de \u00fe Aa\u00f0k \u00fe 1\u00des0ai: \u00f017\u00de Take the predicted position of the base platform as reference signals, a control for the next T is: adjust the lengths of the legs making the stabilized platform at the ideal position while the base platform at the predicted position. It is illustrated in Fig. 6, where %li\u00f0k \u00fe 1\u00de and li\u00f0k\u00de are, respectively, the predicted and current length of the ith actuator strut. As shown in Fig. 4, denote %rP bi \u00bc %rb \u00fe Abs 0 bi the ideal position vectors of point Pai of the stabilized platform in the global reference frame. The predicted lengths of the legs can be expressed as %li\u00f0k \u00fe 1\u00de \u00bc jj%rP ai\u00f0k \u00fe 1\u00de %rP bi\u00f0k \u00fe 1\u00dejj \u00f0i \u00bc 1;y; 6\u00de: \u00f018\u00de By the same method of obtaining Eq. (11), the sliding velocities of the ith leg are %\u2019li\u00f0k \u00fe 1\u00de \u00bc \u00f0%rP ai\u00f0k \u00fe 1\u00de %rP bi\u00f0k \u00fe 1\u00de\u00deT %li\u00f0k \u00fe 1\u00de \u00f0#va\u00f0k\u00de \u00fe \u2019Aas 0 ai %vb\u00f0k\u00de \u2019Abs0bi\u00de; \u00f019\u00de where %vb is the ideal velocity of the stabilized platform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000245_1.2889764-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000245_1.2889764-Figure4-1.png",
        "caption": "Fig. 4 (a) Slider-crank mechanism (b) starting position",
        "texts": [
            " It is therefore very easy to implement in a existing code as it only entails adding new terms. 6 Numerical Results Two different applications will be analysed. One is a slidercrank mechanism (Bakr and Shabana, 1986; Koppens, 1989; Mayo, 1993), which is used to validate the proposed formula tion. The second is a classical example for geometrically elastic nonUnear formulations (Kane et al , 1987; Wu and Haug, 1988; Ider and Amirouche, 1989; Banerjee and Dickens, 1990; Ryu, 1991), viz. a spinning cantilever beam. 6.1 The Slider-Crank Meclianism. In this mechanism, illustrated in Fig. 4 (a ) , the crank is assumed to be rigid, and so is the slider, of mass tUsh \u2022 The connecting rod is assumed to be elastic and have a circular cross-section A of diameter d = 0.006 m; it is made of steel with a modulus of elasticity E = 0.2 X 10'^ Pa and density p = 7878 kg/m^ The gravity effect is excluded from the numerical simulation. The rod response will be analysed. It is represented by the dimensionless deflec tion v/b at its centre during the first four turns of the crank at a constant angular speed a; = 180 rad/s and two different m,,i, values. The starting position is shown in Fig. 4(b) and the following conditions hold at the start: Pf = 0 Pf = 0 (33) (34) The results are compared with those obtained by Bakr and Shabana (1986). The flexible rod is discretized into four beam elements, with two nodes and three degrees of freedom per node, the shape functions for which are Hermitian polynomials. The reference conditions used are those for a simply-supported beam (Agrawal and Shabana, 1985). In the first example, the slider mass is one-half that of the rod, i.e. the slider-to-rod mass ratio is rm = 1/2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002427_50009-5-Figure7.46-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002427_50009-5-Figure7.46-1.png",
        "caption": "FIGURE 7.46 Schematic description of the setup for the characterization of soft magnets at medium and high frequencies. Primary and secondary windings are laid down as a single bifilar layer, with well-separated turns. A digital voltmeter or a digital oscilloscope can be employed for synchronous two-channel signal acquisition. The calibrated resistor R H is physically located close to the leads of the magnetizing winding and the shielded cables, which connect RH and the secondary winding with the acquisition device, are as short as possible. Notice that the lowpotential lead of the primary winding is separated from the ground by R H.",
        "texts": [
            "45 provides an idea of the effect on the hysteresis loop, observed at 1 MHz in an M n - Z n ferrite ring, of a capacitance of 50 pF, equivalent to about a I m long connecting cable, inserted in parallel with the magnetizing winding (N1 = 5, N2 = 5, average ring diameter 30 mm). One can notice the tilting of the loop towards the second quadrant due to the fact that the measured primary current is the sum of the current leaking through the stray capacitance and the active magnetizing current and is consequently associated with an abnormal phase relationship with the magnetic induction. Figure 7.46a provides a qualitative description of the arrangement of connections and windings in a setup for the characterization of soft magnetic cores at medium and high frequencies. Bifilar single-layer windings are used and the connections are made by means of shielded cables. These cables should be short, as a rule, that is, of the order of a few centimeters at most in the MHz range to minimize the associated capacitances. In addition, the resistor R H should be connected to the magnetizing winding by a very short lead. Since the sample is flux-closed, there are no stray fields generated by it and the value of a H is not perturbed. Because N1 and N2 can be very low at high frequencies, the effect of coupling between the fictitious primary and secondary single turns located along the median circumference of the ring specimen could be appreciated. This effect should therefore be checked and possibly compensated. The setup in Fig. 7.46a is given a complete description in terms of lumped and stray parameters by the equivalent circuit shown in Fig. 7.47. Here, in particular, we have considered the self-capacitances (C1, C2) , the leakage inductances (Lwl, Lw2)~ and the resistances (Rwl ~ Rw2 ) (primary and secondary windings), the interwinding capacitance Co, and the capacitances CH and Cj, which include the contribution of the cables and the input channels of the acquisition device. The value of RH~ typically ranging between I and 10 f~, is actually so small with respect to XcH = 1/~CH that we can safely disregard the role of CH and assume that the related voltage drop is always uH(t ) -- RHiH(t )"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003907_bf01517467-Figure7.4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003907_bf01517467-Figure7.4-1.png",
        "caption": "Fig. 7.4a. The radial component of velocity in the pipe (( = 0)",
        "texts": [
            " Here, as in Part I, the basic dynamics o f the jet are reflected in the velocity adjustments shown in figures 7.3 and 7.4. Figure 7.5 shows the variation of the final velocity, Uf, with the surface tension parameter, ( . As expected Uf --, 2, the value of Part I, as ( ~ c~. The remaining figures are plots of the stresses and the pressure for various axial coordinates, x. Again as in Part I, the singular nature of the stresses (except S<oo>) and the pressure is apparent at the exit lip, x = 0 , r = l . Fig. 7.3b. The axial component of velocity in the jet Fig. 7.4b. The radial component of velocity in the jet (( = 0) (( = 0) 2.0 1.9 1.8 1.7 1.636 I.( \u00f901 o.__.._.o --~ ~~-ASYMPTOTE FOR ~= 0 I I I 0.1 1.0 I0 I00 10 Rheologica Acta, Vol. 20, No. 1 (1981) Fig. 7.5. Final jet velocity as a function of the dimensionless surface tension parameter. The final diameter decreases for increasing ( so the final velocity must increase [. o . 8 0.6 ~ x = O ~ x = - 0 . 2 0.4 ~ x = - 0 . 4 r x = - 0 . 8 0.2 -- x--,- oO i O\u00f6 1.0 2.0 S < 0 0 > 1.0 0.8 =0 0.6 0.4 ~ . -x=0 .9 ~(-\u00d7= 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001549_1.1576428-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001549_1.1576428-Figure12-1.png",
        "caption": "Fig. 12 \u201ea\u2026 Schematic of a basic oil lift system \u201e1. Thrust pad, 2. Pad check valve, 3. Pad orifice, 4. Flexible line, 5. Manifold, 6. Oil bath, 7. Suction line isolation valve, 8. Pressure line isolation valve, 9. Suction line, 10. Pressure line, 11. Pressure line check valve, 12. High-pressure filter, 13. Pressure gauge, 14. Pressure relief valve, 15. Pressure relief line, 16. Hydraulic pump with A.C. motor, 17. Electrical control panel, 18. Electrical connection\u2026; and \u201eb\u2026 Schematic of an advanced oil lift system \u201eAdditional items: 19. Pressure gauge, 20. Orifice or flow meter, 21. Pressure switch alarm for low system pressure, 22. Pressure switch to indicate normal system pressure, 23. Pressure difference switch, to indicate that flow is obtained, 24. High pressure switch alarm-indicator that relief valve setting has been reached, 25. Suction line filter, 26. Vacuum gauge on suction line\u2026.",
        "texts": [
            " Bendarek @16# has studied the effect of recess size on the \u2018\u2018dwell\u2019\u2019 time before lift-off. In general the dwell time increases as the size of the recess is reduced. In its simplest form, an oil lift system requires only an on-off switch. More advanced systems have remote control capability, with operational feed back. A simple form of circuit will give an OCTOBER 2003, Vol. 125 \u00d5 829 s of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F indication of the current pressure in the main manifold. This requirement is given by the \u2018\u2018basic\u2019\u2019 circuit in Fig. 12~a!. Each pad has a check valve ~2! to ensure that no back-flow can occur into the manifold ~5!. The orifice ~3! aids the balance of flow between pads. If the flow to one pad is higher than the average ~due, say, to a warped pad surface! the increased pressure drop across that orifice will tend to partly reduce the flow. Part of the pipework between the manifold ~5! and the pad should be flexible ~4!. The pressure drop DP across the orifice is proportional to the square of the velocity V through the orifice, DP51/2",
            ", which should be accessible for cleaning and sized to remove all particles above ten micron. The pressure gauge is upstream of the pressure relief valve, which discharges to the suction line. An optional alarm in the relief valve can indicate if the valve is open. This may be due to a blockage or to too low a setting of the valve. There is an increasing trend towards remote operation of systems or of entire power stations. Typically there are few, if any, personnel available to manually start a hydro-generator and observe all the systems. A more complex system as in Fig. 12b can allow remote operation. The relief valve line is led directly to the oil bath, so that there are no devices that could provide an obstruction to flow in this line. The pressure gauge supplies a visual indication ~if necessary! of the pressure supplied to the manifold. The orifice ~20! is sized to provide a suitable pressure drop that can be used to monitor the oil flow throughout the operating range of temperature. Item ~21! is a low-pressure alarm. The contacts will close in the event of a line break and can provide a remote alarm",
            " A pressure relief valve The setting of the relief valve should be sufficient to accommodate the pressure peak before lift-off and any increase in the recess pressure that may occur during a stop if the pads are thermally crowned. The necessary setting may have to accommodate a recess pressure that is 2\u20133 times the value corresponding to a \u2018\u2018cold\u2019\u2019 pad with no thermal gradient. Safeguards can be included in the jacking circuit to give an \u2018\u2018Oil Film Established\u2019\u2019 signal to the operator before starting the turbine. This signal is given by the closure of both the pressure switch ~item 22 in Fig. 12~b!! and closure of the flow switch ~item 23!. The same safety system could be applied during stopping. The photograph in Fig. 1~b! was supplied by Mr George Staniewski of Ontario Power Generation. The authors are grateful for his contribution to this work. The authors wish to thank the Society of Tribologists and Lubrication Engineers for permission to use material in Figs. 1~a!, 3, and 4~b! of this paper. This material is taken from the Transactions of the Society, from references @1#, @7#, and @10#"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003750_05698190500225334-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003750_05698190500225334-Figure10-1.png",
        "caption": "Fig. 10\u2014Profile measurements using the Mahr profilometer.",
        "texts": [
            " For various normal load values ranging from 1 to 40 N, the normal and tangential loads are recorded from which the tangential-to-normal force ratios are computed. The average of four tests is used at each load. As depicted in Fig. 8, the tests are performed for each steel-on-steel and aluminum-onaluminum contact. Since the theoretical estimates of tangential and normal loads require characterization of the surface, the Mahr profilometer is used to obtain the profile of each aluminum and steel disk. In each case, nine profiles are measured along the circumference, as illustrated in Fig. 10. Each profile measurement consists of 128 traces with each trace taken over a 10-mm-long distance. The 128 traces are separated so as to occupy a width of 0.57 mm, providing a reasonable aspect ratio for the sampled area. In each case, the nine profiles are used to establish the three surface parameters that include average areal asperity density, Fig. 19\u2014Theoretical prediction using uncertainty with 95% confidence and experimental results for stainless steel: elastic formulations. D ow nl oa de d by [ U N A M C iu da d U ni ve rs ita ri a] a t 0 1: 10 2 9 D ec em be r 20 14 Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002319_tmag.2003.810511-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002319_tmag.2003.810511-Figure8-1.png",
        "caption": "Fig. 8. Contours of hysteresis loss (z-direction average). (a) Phase difference 20 . (b) Phase difference 30 . (c) Phase difference 40 . (d) Phase difference 50 .",
        "texts": [
            " It is found that there is much more eddy current loss in the stator teeth and in the rotation direction side of rotor core. It is found that the eddy current loss in the stator yoke decreases, and that in the stator teeth increases, when the phase difference varies from 20 to 50 . It is also found that the eddy current loss in bridge of the rotor core increases as the phase difference increases. Fig. 7 shows the eddy current loss. It is found that the eddy current loss in the stator core has a minimum value when the phase difference is 35 and that in the rotor core decreases as the phase difference increases. Fig. 8 shows the distributions of hysteresis loss. It is found that the hysteresis loss is similar to the eddy current loss. Fig. 9 shows the hysteresis loss. It is found that the hysteresis loss in the stator core decreases as the phase difference increases, and that in the rotor core has a minimum value when the phase difference is 35 Fig. 10 shows the loss in stator and rotor core, and the total loss as a whole IPM motor. It is found that the loss in the stator core is larger than that in the rotor core"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002720_acc.2005.1470274-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002720_acc.2005.1470274-Figure10-1.png",
        "caption": "Fig. 10. Phase Portrait when Reference Modification and Instability Protection are Switched On",
        "texts": [
            " The adaptive parameters oscillate haphazardly between the bounds as seen from Fig.8. However, the transition of the control uc between ut and us is smooth and no control chattering is seen. C. Case 3: Instability Protection & Reference Modification Switched On In this simulation both the instability protection and the reference modification are turned on. The tracking error is bounded and asymptotically approaches zero as the original desired reference lies in the trackable region and within the points of no return, as shown in Fig.9. From Fig.10 we see that the controller does a better job of tracking than in Fig.7. Fig.11 shows that the estimated parameters converge to the true parameters. This is because the reference is persistently exciting and may not be true otherwise. VII. CONCLUSIONS AND FUTURE RESEARCH This paper presented a methodology for stable adaptation in the presence of control position limits for scalar linear time invariant systems with uncertain parameters. For unstable systems, the paper identifies the points of no return and proposes a switching control strategy to restrict the state within the points of no return"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000969_iros.2001.976369-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000969_iros.2001.976369-Figure3-1.png",
        "caption": "Figure 3: Wheelchair's actions.",
        "texts": [
            " Second, we performed an experiment to examine what action by wheelchairs is most comfortable for pedestrians. Possible actions for a wheelchair when it comes close to a pedestrian are: 3 Preliminary Researches To devise a collision avoidance strategy and a method of choosing the wheelchair\u2019s action for smooth passing, we performed two preliminary researches. 1. Go straight keeping its speed and direction, 2. Try to avoid the pedestrian by turning, 3. Slow down its speed while keeping its direction. Fig. 3 shows these wheelchair\u2019s avoidance actions. In this experiment, we used six subjects, asking them to walk toward the wheelchair one by one. First, the wheelchair took action (1) during passing. In this case, we asked the subjects to avoid the wheelchair before collision. This result was used as the evaluation basis for comfortableness. Then, it did actions (2) and (3) at three different distances (2m,3m,4m) from the subjects. They were asked to give their subjective evaluation score for each passing case from the viewpoint of comfortableness: 1 for uncomfortable, 2 for a little uncomfortable, 3 for moderate ( action (1) ), 4 for a little comfortable, 5 for comfortable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003026_0191-8141(83)90020-2-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003026_0191-8141(83)90020-2-Figure8-1.png",
        "caption": "Fig. 8. (a) Strain field resulting from the superposition of a doublet and a pure shear (equation 3). (b) Strain field associated with buckle folds, after an experimental model by Roberts & Str6mg~rd (1973). (IP, isotropic point; IL, isotropic line; broken lines, At trajectories.)",
        "texts": [
            " As buckling progresses the flow cells take on an elongate shape (Fig. 7). Elongate flow cells may be readily obtained if a doublet s t ream function is superimposed on a 'regional flow' such as pure shear or simple shear. Taking the example of a pure-shear doublet superposition, the corresponding stream function is: q~ _ X Y + Vxy (3) 2~ x 2 + y2 where the second term is the stream function of the pure shear, V being a velocity constant. A strain field for particular values of X and V is given by Fig. 8(a). Only the upper half of the doublet is shown representing an anticline; the neighbouring syncline has a rotational symmetry. We note the existence of one isotropic line and one isotropic point above it. This strain pattern is well known in numerical models (Dieterich 1969), and in experiments (Roberts & StrOmg~rd 1973, Cobbold 1975, Soula 1981) (Fig. 8b), and the corresponding cleavage pattern has been observed in the field (Ramsay 1967, Roberts 1971). These experimental models show that isotropic points and lines migrate during deformation (see for example fig. 15 in Roberts & StrOmg~rd 1973). The same effect can be produced in the stream-function model (equation 3) if we give different lifetimes to the doublet and the pure shear. During the doublet life, the isotropic features migrate slowly outwards from the centre of the doublet. At the death of the doublet, if the pure shear goes further, the isotropic point migrates inwards to meet the isotropic line"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.18-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.18-1.png",
        "caption": "Figure 3.18 (a) Cross section of the flywheel used on the Oerlikon bus. [55-1] (b) Cross section of two of the six discs from the rotor designed by General Electric for a hybrid bus:. (Rinehart [80-64])",
        "texts": [
            "2 5, a= l; (a ) M es h fo r fin ite e le m en t ca lc ul at io ns f or th e ca se i n (c ) 13 2 is op ar am et ri c ax is ym m et ric al e le m en ts ; (b ) N o fil le t at t he d is crim c on ne ct io n; (c ) F ill et a s in F ig ur e 3. 16 ; Tr an sv er sa lly i so tr op ic m at er ia l Isotropic flywheels 89 At the connection between the disc and the rim there is a fillet, whose slope and radius are controlled by the coefficient a: a = hc 1 -\"' [GL + 2B/ihce-Bfi2 (3.90) If a\u2014\u25ba() the profile tends to the one with sharp edges while more blended shapes can be described by increasing the value of a. A good example of constant stress disc with an outer rim is the flywheel used for the Oerlikon Electrogyro (Figure 3.18a). Apart from the fillet at the rim, particular attention was given to the design of the flanges connecting the flywheel to the shaft, the design of which must only marginally affect the stress distribution of the disc, while achieving the required strength and stiffness at the shaft-disc connection. A more modern example is shown in Figure 3.18b which shows two discs from the six-disc assembly designed by General Electric for a hybrid city bus. The discs are connected to each other and to the shaft by friction welding. The constant-stress profile can easily be approximated by two or three straight lines and correspondingly a constant-stress disc can be obtained using conical surfaces. Simple tapered conical discs can be used, as usually the stress distribution is more favourable than in constant thickness ones. This is also true in the case of discs with a central hole but any increase of the shape factor K is connected with an increase of the velocity factor \u00a3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001157_jsvi.1998.1528-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001157_jsvi.1998.1528-Figure2-1.png",
        "caption": "Figure 2. Schemes of: (a) Beck\u2019s column: ba =W '(l, t)=/ W(l. t)/lc , W 0(l. t)=W1(l, t)=0; (b) column loaded by a force passing through a fixed point: bb =W(l, t)/lc =/ W '(l, t), EJW1(l, t)+P[W '(l, t)\u2212W(, t)/ lc ]=0, W 0(l, t)=0; and (c) column of present investigation: bc =W '(l, t)=W(l, t)/lc . .",
        "texts": [
            " An experimental verification of theoretical results obtained for a divergence\u2013pseudo-flutter column has been presented in references [13, 16] and for an identically loaded planar frame. It should be noticed that in references [18, 19] experimental variation of the natural frequency curves of a type as in Figure 1(c), have been demonstrated for columns of an unknown loading scheme. An idea of the elastic system presented in this work was inspired by two different columns described in references [20, 21]. For the first one\u2014Beck\u2019s column [20] which is presented in Figure 2(a), its compressive force is tangent to the deflected end of the column (the angle of force P inclination to the vertical is ba =W'(l, t), where ' denotes differentiation with respect to x). Boundary conditions for this column are presented in the figure caption. Such a load appears, for example, for structures exposed to streaming media [22], as well as for a clamped-free [23, 24] or a free-free column [25] loaded by a rocket trust. Experimental investigations of such problems were published in references [23, 24] where it was stated that a cantilever column can lose its stability by flutter, i",
            " oscillations with increasing amplitudes. An influence of a variety of parameters such as elastic spring supports, concentrated masses, transverse shear deformation as well as rotary inertia on the stability of a cantilever column subjected to a tangential load has been discussed by Kounadis [26]. The second system which was described in reference [21] and caused the present investigation is a column which is compressed by a force passing through a fixed point independently from the deflection of the column [Figure 2(b)]. The distance of that point from the free end of the column is taken to be q0 for the case as in Figure 2(b) or Q0 when the fixed point is placed above the point of force application [27]. The angle of the compressive force is bb =W(l, t)/lc . A variation of the natural vibration curves for the system depends on the value of lc and can be as in Figure 1(b) [28] or as in Figure 1(c) [28, 29]. Constructional variants of a column loaded by a force passing through a fixed point were given in references [30, 31] where experimental models were developed to simulate Beck\u2019s column. The theoretical analysis given in reference [29] led to a conclusion that a conservative system associated with Beck\u2019s column may be found to study its dynamic behaviour. Taking into account the above considerations a question was asked concerning the possibility of constructing such a real system which has features characteristic of columns from Figures 2(a) and (b). This system is presented in Figure 2(c) together with the boundary condition for angle bc . Two different variants of the system are schematically drawn in Figures 3(a) and (b). Experiments presented in this study concern the column from Figure 2(b); the second boundary condition for x= l is given in the third part of the work [equation (7)]. In this work the stability and natural vibration of a cantilever column subjected to a follower force passing through a fixed point has been considered. This load can be realised in two constructional variants shown in Figures 3(a, b). Column I [Figure 3(a)] is loaded by a force P tangent to the deflection at the point of the force application (x= l), and passing through a fixed point O. A stiff element 1 of the length lc of column II\u2014Figure 3(b), is carrying a vertical force P"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001147_s0924-4247(00)00355-1-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001147_s0924-4247(00)00355-1-Figure8-1.png",
        "caption": "Fig. 8. Schematic view of the convex and the concave unit.",
        "texts": [
            "its direction is tangential, the so-called forced vortex , the relative velocity between the bottom of the vessel and the fluid becomes zero. The only force working between the unit and the wafer is the centrifugal force, F, given by Fs r X yr Vrv 2 , 6\u017d . \u017d . where, r X and r are the densities of the units and of water respectively, V is the volume of the unit, r is the distance from the center, and v is the angular velocity. The adhesion is calculated to be about 20 nN at the speed of 250 rpm when the ratio of adhering units becomes 0.5. To demonstrate 3D self-assembly, convex and concave units are fabricated as shown in Fig. 8. They are bonded to each other by bridging flocculation as shown in Fig. 9. If the polymer adsorption satisfies Langmuir\u2019s law, the surface coverage u is expressed as ac us , 7\u017d . 1qac where a is a constant determined by the experiment and c is the concentration of the polymer. \u017d .The collision and bonding process of a concave unit C \u017d .with a convex unit V is similar to a chemical formula. CqVlCV 8\u017d . After sufficient time for the balanced reaction, the rate equation of the reaction can be related only to the rate constant of forward reaction k, and the reverse reaction kX, w x w x X w xk C V sk CV , 9\u017d "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000644_005-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000644_005-Figure1-1.png",
        "caption": "Fig. 1. (Color online) Schematic illustration of the liquid-environment AFM heads. (a) Open fluid cell. (b) Closed fluid cell with liquid-sealing mechanism.",
        "texts": [
            "24\u201326) For example, submicrometer-scale wiring patterns in an integrated circuit are fabricated through a number of wet processes, such as electroplating, etching, and chemical mechanical polishing (CMP).27,28) To understand the nanoscale mechanisms of these processes, the direct imaging of atomic-scale structures by liquid-environment AFM may play a critical role. However, the application of the atomic-resolution liquidenvironment AFM has been limited owing to the difficulties in maintaining a constant imaging condition. One of the main problems is the long-term stability of the imaging solution. Figure 1(a) shows a typical liquid-environment AFM setup. The system consists of the upper part supporting a cantilever and the lower part supporting a scanner. The imaging solution is sandwiched between the sample and the upper part to form a ring-shaped meniscus at the liquid/air interface. In this setup, the solution is placed in an open space (open fluid cell). Thus, the solution keeps evaporating Japanese Journal of Applied Physics 52 (2013) 110109 110109-1 # 2013 The Japan Society of Applied Physics SELECTED TOPICS IN APPLIED PHYSICS Nano Electronics and Deviceshttp://dx.doi.org/10.7567/JJAP.52.110109 from the liquid/air interface during the imaging. The evaporation can cause drift in the tip position and the deflection signal and hence deteriorates the long-term stability and accuracy of AFM measurements. To prevent the evaporation of the imaging solution, a ringshaped elastomer, such as an O-ring, is typically sandwiched between the upper and lower parts [dashed lines in Fig. 1(a)] to confine the solution in a closed space (closed fluid cell). In this design, the evaporation eventually stops at the saturation of the vapor pressure. However, owing to the mechanical coupling between the upper and lower parts through the elastomer, the vibration induced by the scanner propagates to the AFM probe and causes instabilities in the tip-sample distance regulation. In addition, the XY range of the coarse tip positioning is limited by that of the lateral deformation of the compressed elastomer, which is typically less than 1mm",
            " We used the photothermal excitation technique for the cantilever excitation.30) A phaselocked loop circuit (SPECS Nanonis OC4) was used for detecting the frequency shift ( f ) of the cantilever oscillation and oscillating the cantilever at its resonance frequency with a constant amplitude (A). The AFM imaging of a Cu wiring pattern was performed by amplitude-modulation AFM (AM-AFM)31) in pure water. For this experiment, we used the acoustic excitation technique for exciting the cantilever vibration. Figure 1(b) shows a schematic illustration of the developed 110109-2 # 2013 The Japan Society of Applied Physics closed fluid cell integrated in our custom-built AFM. We placed two hydrophobic rings (silicone rubber) with different diameters on each of the upper and lower parts (stainless steel: SS316). If we feed an aqueous solution into the circular channel surrounded by the four hydrophobic rings, the hydrophobicity of the rings prevents the solution from spreading beyond the rings. Thus, the solution is confined in the channel to form a ring-shaped meniscus that encloses the internal space [sealing liquid in Fig. 1(b)]. In this design, the evaporation of the imaging solution eventually stops at the saturation of the vapor pressure. In addition to the aqueous solution, we can use other liquids, such as a solution of organic solvent. In general, we should use the solvent of the imaging solution as the sealing liquid. Otherwise, molecules evaporated from the sealing solution may contaminate the imaging solution. One exception is the use of ionic liquids. As they do not evaporate at room temperature, they should not contaminate the imaging solution",
            " The results show that we should be able to keep the concentration of the imaging solution constant during AFM measurements using the developed closed fluid cell. In this experiment, we used pure water as the sealing liquid and confirmed that its meniscus can be maintained for more than several hours. However, if we perform the experiment for a longer time or use a more volatile sealing liquid, the meniscus will eventually break down owing to the evaporation of the sealing liquid. To solve this problem, we prepared an inlet of the sealing liquid in the upper part, as shown in Fig. 1(b). We can add the sealing liquid through this inlet to prevent the breaking of the meniscus. In fact, we experimentally confirmed that the volume of the imaging solution is perfectly sustained for more than 40 h using this setup. Another solution would be the use of a nonvolatile ionic liquid as the sealing liquid. In this case, however, we may encounter difficulties in cleaning up the liquid compared with the case of water. Figure 2(b) shows that even if we use the open fluid cell, the volume of the imaging solution decreases only by 10% in the first hour"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000710_mech-34246-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000710_mech-34246-Figure4-1.png",
        "caption": "Figure 4b. The Instant Centers 13I and 17I .",
        "texts": [
            " Draw a line through the instant center ++95I parallel to the line ++ BI 5 13 , see Figure 3a. This line represents the locus of ++95I for all possible directions of the path tangent of link +9 (an analytical proof is presented in the appendix). Similarly, draw a line through the instant center **95I parallel to the line *5 17 * BI , see Figure 3b. This line represents the locus of **95I for all possible directions of the path tangent of link *9 . Therefore, the point of intersection of these two lines is the instant center 59I , henceforth denoted as point Q, as shown in Figure 4a. Since the ground pivot 5O is the instant center 15I then the path tangent of point Q is perpendicular to the line QO5 as shown in Figure 4b. Note that the velocity of the coupler point B of the double butterfly linkage is equal to the velocity of point Q. Therefore, the line through point B parallel to the line QO5 is the path normal of point B. The intersection of the path normal with link 2, or link 2 extended; i.e., the line containing instant centers 12I and 23I , is the absolute instant center 13I . Similarly, the intersection of the path normal with link 8, or link 8 extended; i.e., the line containing instant centers 18I and 78I , is the absolute instant center 17I ",
            " Find the point of intersection of link 4 (or link 4 extended) with the line through 5O that is parallel to link 2. Through this point, draw a line parallel to the line between point B and the point of intersection of links 2 and 4. (See Figure 3a). 2. Find the point of intersection of link 6 (or link 6 extended) with the line through 5O that is parallel to link 8. Through this point, draw a line parallel to the line between point B and the point of intersection of links 6 and 8. (See Figure 3b). 3. The point of intersection of the two lines, in steps 1 and 2, is the instant center 59I . (See Figure 4a). 4. Draw a line through coupler point B parallel to the line 559OI . The intersection of this line with link 2 (or link 2 extended) is the instant center 13I , and the intersection of this line with link 8 (or link 8 extended) is the instant center 17I . (See Figure 4b). Copyright \u00a9 2002 by ASME s of Use: http://www.asme.org/about-asme/terms-of-use Down Consider the double butterfly linkage shown in Figure 5 with the link dimensions as tabulated in Table 1 (the link lengths are specified to the nearest 0.01 cm). For the chosen position of the input link 2 (i.e., 1352 =\u03b8 counterclockwise from the horizontal axis), the position solution of the linkage is obtained from a vector loop analysis and a MATLAB computer program (Waldron and Sreenivasan, 1996; and Hasan, 1999)",
            " For the specified input position, assume that the angular velocity of the input link is 1 rad/s clockwise. The angular velocity of link j (= 3, 4, 5, 6, 7, and 8) can be expressed in terms of the angular velocity of the input link 2 and the instant centers as 2 21 212 \u03c9\u03c9 jj j j II II = (1) Therefore, the angular velocity of the coupler links 3 and 7 can be written as 2 2313 2312 3 \u03c9\u03c9 II II = and 2 2717 2712 7 \u03c9\u03c9 II II = (2) The locations of the secondary instant centers 13I and 17I are shown in Figure 4b and the distances between the instant centers are measured on the AutoCAD drawing of the linkage. The other instant centers are not shown on the figure, however, the complete set of results is presented in Table 2. 5 loaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/02/2016 Te Substituting the appropriate values into Eq. (2), the angular velocity of coupler link 3 is 1 1114.8 00.6 3 \u00d7=\u03c9 = 0.7397 rad/s clockwise (3a) and the angular velocity of coupler link 7 is 1 9221.12 0529",
            " Substituting these values and Eq. (4b) into Eq. (5a), the angular velocity of link 7 is 8174.0 9714.17 0.12 7 \u00d7=\u03c9 = 0.5458 rad/s clockwise (5b) which agrees with Eq. (3b). The magnitude of the velocity of the coupler point B can be written as ( ) 313 \u03c9BIVB = (6a) where the distance cm 1817.1113 =BI . Substituting this measurement and Eq. (3a) into Eq. (6a), the magnitude of the velocity of point B is cm/s 2711.8=BV (6b) The direction of the velocity of point B is inclined at 12.20\u00b0 above the horizontal axis, as shown in Figure 4b. The magnitude of the velocity of point B can also be written as ( ) 717 \u03c9BIVB = (7a) where the distance cm 1541.1517 =BI . Substituting this measurement and Eq. (3b) into Eq. (7a), the velocity of point B is cm/s 2711.8=BV (7b) which agrees with Eq. (6b). The magnitude of the velocity of point B can also be written as ( ) 515 \u03c9QIVV QB == (8) Therefore, the angular velocity of link 5 can be written as 6 loaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/02/2016 Ter QI VB 15 5 =\u03c9 (9a) where, from the AutoCAD drawing, the distance cm 0872"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003307_s10704-005-8546-8-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003307_s10704-005-8546-8-Figure2-1.png",
        "caption": "Figure 2. Crack surfaces loaded with pressure.",
        "texts": [
            " T is referred to as T-stress and is a non-singular stress. It acts parallel to the crack plane, is independent of r and proportional to the applied stresses. Stress intensity factors and T are for \u03b8 =0\u25e6 defined as: KI = lim r\u21920 \u03c3yy \u221a 2\u03c0r, KII = lim r\u21920 \u03c3xy \u221a 2\u03c0r, (2) T = lim r\u21920 ( \u03c3xx \u2212\u03c3yy ) . The Equations (1) and (2) are valid for traction free boundary conditions along the crack surfaces. When the crack surfaces are not traction free (e.g. crack surfaces loaded with pressure p\u03b1(\u03b1=x, y) as it is shown in Figure 2) the influence of constant term in equation (1) is even more pronounced (Parteymu\u0308ller, 1999). For pressurised crack surfaces the stress field around the crack tip can then be expressed as (Parteymu\u0308ller, 1999):   \u03c3xx \u03c3yy \u03c3xy  = KI cos \u03b8 2\u221a 2\u03c0r   1\u2212 sin \u03b8 2 sin 3\u03b8 2 1+ sin \u03b8 2 sin 3\u03b8 2 sin \u03b8 2 cos 3\u03b8 2  + KII sin \u03b8 2\u221a 2\u03c0r   \u2212 ( 2+ cos \u03b8 2 cos 3\u03b8 2 ) cos \u03b8 2 cos 3\u03b8 2 cot \u03b8 2 \u2212 cos \u03b8 2 sin 3\u03b8 2  +   T \u03c3 c yy \u03c3 c xy  , (3) where the tractions \u03c3 c xy and \u03c3 c yy are defined at the crack tip and their distribution is smooth enough along the crack surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001516_iros.1997.649040-Figure15-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001516_iros.1997.649040-Figure15-1.png",
        "caption": "Figure 15: Selection of throwing point",
        "texts": [
            " If we define this time and the length of the major axis of the elliptic orbit as t,[sec] and 81,. respectively, then the relationship between t , and 8 1 ~ is as shown in Figure 14. 5 Conclusions Considering the error of throwing timing, a larger t,,, is more effective for the time delay of throwing the gripper. Since t,,, becomes maximum when Blm =0.37rad in Figure 14, we can select the elliptic orbit whose major axis length is 0.37rad in Figure 13. We can choose the throwing point on the elliptic orbit as point A in Figure 15 in consideration of the time delay of the throwing command data. In this paper, a casting manipulator consisting of an unformed flexible link of variable length was proposed for enlarging the work space of a robot. For this manipulator, we first proposed a method of generating the desired swing motion for throwing the gripper by choosing a timepefiodx input for the second joint based on the error between the current amplitude and the desired amplitude. The method was evaluated by numerical experiments and shown to be effective"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000499_3516.891047-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000499_3516.891047-Figure5-1.png",
        "caption": "Fig. 5. Strain gauges for improved accuracy.",
        "texts": [
            " Equations (4) show that the higher frequency component is not reduced by sum of two signals from strain gauges placed at 90 positions. This fact was not originally recognized. However, by analogy to the basic frequency signal fluctuation compensation, a compensation signal of opposite phase to the remaining signal fluctuation should be generated to compensate the higher frequency signal fluctuation component. This leads to another pair of strain gauges positioned at 45 relatively to the original pair of the strain gauges, as shown in Fig. 5. The signal fluctuations from the strain gauges R1, R2, R3, and R4 are now (5) The basic frequency component of the signal fluctuation is compensated within each pair of the strain gauges, while both pairs mutually compensate the higher frequency component. A sum of (5) should become zero, but again the experimental result in Fig. 6 shows that some signal fluctuation remains uncompensated. Amplitude of the signal fluctuation is reduced to approximately 1% of the gear torque capacity, while the frequency of the signal fluctuation is dominated by the basic one"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002706_tmag.2004.832263-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002706_tmag.2004.832263-Figure8-1.png",
        "caption": "Fig. 8. The principle of operation of the conveyor system. Both rotation and revolution of the levitator have occurred simultaneously due to the slight friction.",
        "texts": [
            " All the levitators oscillate and rotate synchronously by connecting the coils in each direction in series. When the voltage of each phase is switched, the direction of rotation will change. For the same applied voltage and same coil connection, each shaft oscillates simultaneously as shown in Fig. 6. The shaft will rotate in the clockwise direction due to the existence of slight friction on one end of the levitator. Consequently, the conveyance movement will be along the direction as shown in Fig. 8. An experimental result of the conveyance test by oscillation and rotation is shown in Fig. 9. A thin sponge sheet, of dimensions mm mm mm, was used for the object on the shafts. The pitch between the levitators is 75 mm. When a thin sponge sheet is placed on the shafts, it moves by the maximum speed of 0.1 m/s. Since the number of levitators in contact with the sheet decreases, conveyance speed slows down. On phase reversal, the direction of rotation will be reversed. This paper has presented the fundamental structure and the operating characteristics of the proposed new conveyor system using repulsive-type magnetic bearings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000925_20.917621-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000925_20.917621-Figure10-1.png",
        "caption": "Fig. 10. Groove pattern and pressure.",
        "texts": [
            " 4) The liquid boundary interface shows stability in all cases when the groove angle is 15 degrees and is accompanied by a narrow clearance. Air bubbles, under these condition, do not appear. It was conjectured that a radial herringbone groove pattern, with at least one side of the two sets of herringbone grooves designed to follow an asymmetrical pattern, (asymmetrical part length: 0.1\u20130.3 mm), which generated an external pump-in force that pushed the oil from the oil enriched part to the oil-depleted part of the groove pattern would lead to sufficient oil film formation even during shuttle movement (Fig. 10). This effect of an asymmetric herringbone groove pattern was confirmed by experiment. A prototype high-speed hydrodynamic bearing was made (Fig. 11) and evaluated. Here the experiment result and the calculation result are utilized. 1) The bearing\u2019s shaft has a shaft both-end tied structure to enhance mechanical strength at high speed rotation. 2) Furthermore, the diameters of the two portions near both ends of the tied shaft are smaller by 0.2 mm than that of the bearing portion. Centrifugal force applied to the oil serves to prevent any oil leakage from the bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001659_s0094-114x(02)00003-4-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001659_s0094-114x(02)00003-4-Figure1-1.png",
        "caption": "Fig. 1. Coordinate systems applied for the worm-gear set.",
        "texts": [
            " School of Engineering, The Nottingham Trent University, Burton Street, Nottingham NG1 4BU, UK. E-mail address: donganzhan@hotmail.com (D. Zhan). 0094-114X/02/$ - see front matter 2002 Published by Elsevier Science Ltd. PII: S0094-114X(02)00003-4 and so on. The theoretical researches reported in this paper lay a foundation for finish-grinding the TI worm tooth surface and the application of the worm-gear set. The worm-gear drive is discussed only in the case of an orthogonal drive with the crossing angle of 90 as shown in Fig. 1. The moveable coordinate systems S1\u00f0O1 X1Y1Z1\u00de and S2\u00f0O2 X2Y2Z2\u00de are rigidly connected to the gear and the TI worm, while the fixed coordinate systems S\u00f0O XYZ\u00de and Sp\u00f0Op XpYpZp\u00de are attached to the machine housing and are the original position of S1 and S2, respectively. The gear and the TI worm rotate about axes Z1 and Z2 with the angular velocities x1 and x2, respectively. The rotating angles are u1 and u2 at some instant. Between axes of Z1 and Z2, the shortest distance is a. The directions of rotation correspond to the right-hand worm-gear drive are shown in Fig. 1. For the gear and the TI worm (Fig. 2), the helical angles are b1 and b2, the rotating velocities are v1 and v2, respectively. The drive ratio i21 may be determined by considering that the velocity v1 equals to v2 on the direction perpendicular to the helical line. Then, we obtain i21 \u00bc x2 x1 \u00bc r1 \u00f0a r1\u00de tan b1 ; \u00f01\u00de a \u00bc mnz2 2 cos b2 \u00fe mnz1 2 cos b1 ; \u00f02\u00de where mn is the normal module, z1 and z2 are the tooth numbers of the gear and the TI worm, respectively, and r1 is the gear pitch radius. To perform TCA on the worm-gear set, the following analyses are based on the hypothesis: the gear tooth surface RI is known, while the TI worm tooth surface RII is to be derived"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002299_027836402761393487-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002299_027836402761393487-Figure3-1.png",
        "caption": "Fig. 3. Overview of the example.",
        "texts": [
            " Here, we introduce an idea of the Neighborhood Equilibrium with the following definition: DEFINITION 2. (Neighborhood Equilibrium) Let \u03bbo be the initial value of \u03bb. If the system can reach the state+U = 0 in the open neighborhood satisfying ||\u03bb \u2212 \u03bbo|| < l\u03b5 , the objects are defined as being in Neighborhood Equilibrium (NE). l\u03b5 denotes a real value; some comments on l\u03b5 are described in Section 9. at UNIV OF WISCONSIN MADISON on July 19, 2012ijr.sagepub.comDownloaded from We performed a numerical example for the system shown in Figure 3, where (a) and (b) show the 2D manipulation of an ellipsoidal and a circular object, respectively. We set \u03bb = xOx , where xOx denotes the displacement of the object in the horizontal direction. The results of the calculations are shown in Figure 4, where (a), (b), and (c) show the change of potential energy for the ellipsoid when \u03b8 = \u22120.649 rad, that for the ellipsoid when \u03b8 = \u22120.62 rad, and that for the circle when \u03b8 = \u22120.649 rad. The case shown in Figure 4(b) satisfies NE while the others do not"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003259_095440604322900435-Figure13-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003259_095440604322900435-Figure13-1.png",
        "caption": "Fig. 13 Finite element mesh for the hydrostatic table and rails",
        "texts": [
            " Speci cations of the hydrostatic table and rail assembly are listed in Table 3. Geometrical imperfections of the rails are expected to induce linear motion errors of the table. Park et al. {6}have reported linear motion errors for known pro les of the rails shown in F ig. 12. Vertical pro les of the top rails averaged in the width direction have been plotted along the length. In this work, only the vertical deviations of the table motion will be discussed. Meshes of eight-node solid elements and null elements for the hydrostatic table, rails and uid lm are shown in Fig. 13. Predictions on the vertical deviation of the table during horizontal drive are compared against the experiments in F ig. 14. Predicted table motion trajectories based on the uid lm model are in good agreement with the experiments for the three top rails. A new method for analysing the behaviour of linear hydrostatic bearings has been developed based on the commercial nite element analysis code ABAQUS. A large user-de ned superelement is formulated which includes a mesh of eight-node null elements covering the uid lm between the bearing pad and rail"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003653_hxh083-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003653_hxh083-Figure1-1.png",
        "caption": "FIG. 1. TSS, consisting of two satellites connected by a massive tether, in orbit around a planet. The orbital coordinate system (x, y) is also shown.",
        "texts": [
            " Instead, a strong deviation from the local vertical direction occurs, which after the deployment process is finished results in weakly damped large-amplitude oscillations, which in some cases are even transient chaotic. This chaotic dynamics will be used to steer the satellite with small control actions into the final radial relative equilibrium position far away from the spaceship. Both deployment time and energy input are computed and compared to other deployment strategies. Keywords: deployment; optimal control; space flight dynamics; tethered satellite; transient chaos. The concept of tethered satellite systems (TSS) (Fig. 1), i.e. two or more satellites in orbit connected by thin and long cables\u2014a length of 100 km is not unusual\u2014has now been well established in astrodynamics. The great potential of this concept for future space applications is indicated, e.g. in Beardsley (1999), Beletsky & Levin (1993), Krupa et al. (2000) and Proceedings (1995). Several successful (Small Expendable Deployer System (SEDS) project) and not completely successful (TSS-1 project) flights in orbit around the Earth were performed during the last decade of the 20th century",
            " During uncontrolled (free) deployment, due to the Coriolis acceleration, the motion of the subsatellite strongly deviates from the radial vertical and, hence, after the full tether length has been deployed a long-lasting oscillatory process starts, since the only source of energy dissipation, which has a noticable short-term effect, is the viscoelasticity of the tether. Other external forces (air drag, solar pressure) are weak and will not give an essential contribution. The effect of the Coriolis acceleration, aC = 2\u03c9c \u00d7 vr , (1) can be best understood from Fig. 1. The orbital frame is not an inertial frame since it rotates with \u03c9c = \u03c9cez . If the subsatellite deploys in the negative x-direction with vr = \u2212vex , from (1) it follows that the Coriolis acceleration aC = \u22122v\u03c9cey , which acts in the orbital plane transversal to the local vertical, hence resulting in a deviation of the satellite\u2019s motion from the local vertical. In the considered case, the subsatellite moves in front of the satellite from which it is deployed similarly as it is depicted in Fig. 1. Consequently, for a practically meaningful deployment process one must use some form of control, e.g. an optimal control strategy (Steindl & Troger, 2003), which results in a fast deployment into the radial relative equilibrium far away from the spaceship. However, the transient chaotic character of the first phase of the free deployment process (Steiner, 1998) suggests to use targeting and finally, if necessary, linear control to achieve a fast deployment process. To explain such a targeting strategy is the aim of this paper",
            " (8) Hence, the linearization of (5) reads x\u0308 = gM 2x rM \u2212 N m x q + 2\u03c9c y\u0307 + \u03c9\u0307c y + \u03c92 c x, y\u0308 = \u2212 gM y rM \u2212 N m y q \u2212 2\u03c9c x\u0307 \u2212 \u03c9\u0307cx + \u03c92 c y. (9) If the main satellite is in a circular orbit, \u03c9\u0307c = 0 and \u03c9c = \u221a gM/rM , and (9) becomes x\u0308 = \u2212 N m x q + 2\u03c9c y\u0307 + 3\u03c92 c x, y\u0308 = \u2212 N m y q \u2212 2\u03c9c x\u0307 . (10) For the free motion, (10) reduces to (Steiner, 1998) x\u0308(t) \u2212 2\u03c9c y\u0307(t) \u2212 3\u03c92 c x(t) = 0, y\u0308(t) + 2\u03c9c x\u0307(t) = 0. (11) As soon as the distance between the two satellites q = \u2016rM \u2212 rS\u2016 (12) reaches the tether length (Fig. 1), we do not use the impact models used in Beletsky & Levin (1993) and Steiner (1998), but calculate the tension force N = E A(\u03b5 + \u03b1\u03b5\u0307) = E A ( q \u2212 + \u03b1 q\u0307 ) = E A [ q \u2212 + \u03b1 (x x\u0307 + y y\u0307) ] (13) due to the stretching process of the viscoelastic tether, according to Kelvin\u2013Voigt\u2019s law of viscoelasticity. We denote by q the strained and by the unstrained tether length. In (13), E is Young\u2019s modulus, A the tether\u2019s cross section, \u03b5 = (q \u2212 )/ the tether strain and \u03b1 the damping parameter of the tether material",
            " But the energy decreases every time the tether is stretched, H\u0304i \u2212 H\u0304i\u22121 < 0, due to the dissipative viscoelastic processes in the tether. Here H\u0304i denotes the energy level after stretching number i . How much energy is dissipated at each stretching depends strongly on the detailed situation. Consequently, the energy variation is rather complicated, as illustrated in Figs 5 and 11. Another important aspect has been shown in Beletsky & Levin (1993) and Steiner (1998), namely, that if the energy given by (24) is positive, then the deployed satellite can pass the line x = 0 (Fig. 1). Hence, if the initial conditions are such that H\u0304 < 0 or as soon as H\u0304 becomes less than 0, the satellites in their further motion will stay on their respective side of the orbit forever and the resulting relative equilibrium state is specified by H\u0304 = \u2212 3 2 m\u03c92 c 2. When the tension force is applied during a stretched tether phase, pulling the tether increases the system\u2019s energy level and reduces the tether length, whereas releasing the tether relaxes the tether tension, hence extinguishes the stored strain energy in the stretched tether and consequently decreases the system\u2019s energy and increases the free tether length"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003901_2006-01-0888-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003901_2006-01-0888-Figure3-1.png",
        "caption": "Figure 3: Journal Bearing Configuration",
        "texts": [],
        "surrounding_texts": [
            "Friction losses from the engine bearings are also included in the proposed friction model. It is assumed that each cylinder unit consists of two main crankshaft bearings, a big-end connecting rod bearing and a piston gudgeon pin. Each bearing carries loads that vary in magnitude and direction. The angular velocity of load and sleeve may also vary in direction and magnitude. The big end connecting rod bearing is the most dynamically loaded bearing and is often considered in the literature. Several approaches have been adopted for the dynamic investigation of bearings. There are in literature analytical models for short, long and finite loaded bearings [21], [22], numerical models that apply the Finite Element method to solve the Reynolds equation either in the simple case of isothermal conditions [23] or in the more complicated case of Thermo-ElastoHydrodynamic lubrication [24]. Since the developed engine friction model was required to have a reduced computational time, and therefore be easily used in conjunction with a thermodynamic simulation code, it was decided to use the analytical solution of Hirani et al [22] in the case of engine bearings. Bearing Lubrication Model The Reynolds equation in the case of a dynamically loaded journal bearing can be written as [25]: 3 32 bearing 2 bearing P P 1 cos R 1 cos z z R 12 cos sin C This equation can be solved analytically in the case of the short bearing and long bearing approximations. Hirani et al. [22] proposed an analytical algebraic expression, for the pressure distribution in dynamically loaded journal bearings, which it was in good agreement with results obtained by the Finite Element Method [23]. This analytical expression has been used by the proposed friction model for the case of the journal bearings (main bearings, big end connecting rod bearing and piston pin). After determining the pressure field developed around each engine bearing, the power losses are easily calculated using the method presented in the case of piston rings. VALVE TRAIN MODEL Since the valve train friction contribution in total engine friction is expected to be quite small, a simple model was used [6]. According to this model the valve train friction torque is expressed as follows: 4 i V f l v3 o t d G T V N (1 c )r G( ) 8d N , where 1 G sin cos , =crank angle This model assumes that the predominant regime of lubrication in the valve train at the low speed regime is boundary lubrication, and at high speed regime is mixed lubrication. Therefore, friction decreases with decreasing speed."
        ]
    },
    {
        "image_filename": "designv11_11_0001147_s0924-4247(00)00355-1-Figure13-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001147_s0924-4247(00)00355-1-Figure13-1.png",
        "caption": "Fig. 13. The names of the connecting areas of the convex and the concave units.",
        "texts": [
            " The fabrication of the convex and the concave units is similar to that of the cube units except for the anisotropic etching by KOH for inlaid structures. Al patterning process is added in the case of the concave units. Fig. 11 shows the fabrication processes of the concave units. The fabricated convex and concave units are shown in Fig. 12. We provide two kinds of concave units, type-A and type-B, which have different tolerances. The exact sizes of the connecting areas, the areas where the convex and the \u017d .concave units are bonded together see Fig. 13 , are shown in Table 2. Three hundred convex and 300 concave units are stirred with 5.0 ppm PAAM in the apparatus which is shown in Fig. 5. This apparatus is usually used in order to shake beakers. After 5 min stirring at 150 rpm, the units are counted in order to evaluate the yield. The relationship between the initial concentration of the flocculant and the yield was examined. Fig. 14 shows the units released and dispersed. After stirring, the bonded units are shown in Fig. 15. In the case of the type A concave units, e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000516_20.952635-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000516_20.952635-Figure4-1.png",
        "caption": "Fig. 4. Centrifugal force due to mechanical unbalance mass.",
        "texts": [],
        "surrounding_texts": [
            "Index Terms\u2014Dynamic response, electric machines, finite element method, magnetic forces, vibration.\nI. INTRODUCTION\nTHE NOISE and vibration in electric motors is generated by the interaction of electromagnetic force and mechanical structure [1], [2]. All of the mechanical components contribute to the acoustic noise and vibration. Especially, in rotating electrical machines the subject of investigation for the vibration and acoustic noise can be classified into the stator and the rotor, because these parts are the principal source of vibration related to the electromagnetic force. Many researchers have studied the characteristics of magnetic force due to eccentricity and unbalanced magnetic pull [3]\u2013[5].\nThis paper also deals with the mechanical motion of the rotor due to the unbalanced magnetic pull. The rotor vibration takes into account the coupling effect between magnetic and mechanical field so it is possible to explain the interaction between the rotor vibration behavior and its resulting change of magnetic field.\nThe unbalanced forces acting on the rotor can be divided into two types, which are the centrifugal force due to mechanical unbalance mass and the magnetic unbalance force due to the eccentricity [3]\u2013[5].\nThe former is due to nonuniform characteristics of materials, such as manufacturing error, lamination punching and tolerances that produce mechanically the centrifugal force and a nonuniform distribution of magnetic flux, which cause both the magnetic and mechanical forces on the rotor.\nManuscript received July 5, 2000. This work was supported in part by the Korea Science and Engineering Foundation (KOSEF) through the Machine Tool Research Center at Changwon National University. This work was also supported by the Brain Korea 21 Project Corps at Changwon National University.\nThe authors are with the Department of Electrical Engineering, Changwon National University, Changwon, Kyungnam, 641-773, Korea (e-mail: haroom@netian.com; jphong@sarim.changwon.ac.kr).\nPublisher Item Identifier S 0018-9464(01)07843-8.\nThe latter is that the rotor does not have a concentric rotation with respect to its geometric center or a shaft, called as the eccentricity. The eccentricity causes the unbalanced radial force with the rotor position that increases the separation of the rotor from the stator bore center.\nAccordingly, when any displacement of the rotor in the radial direction occurs as a consequence of the unbalance magnetic force and mechanical unbalanced mass, it changes the uniform air gap between stator and rotor. It results in the change of magnetic field, magnetic force and torque. They also affect the motion of rotor and vice versa.\nThe vibrations associated with the unbalance force develop excessive stress in bearings on the rotor, deteriorate the performance of motor and reduce the lifetime. With a smaller air gap, this phenomenon especially becomes severe. Therefore, it is necessary to predict the dynamic response caused by the electromagnetic unbalance force and mechanical unbalance mass to reduce the vibrations.\nThis paper investigates the various dynamic response of the rotor caused by the mechanical and magnetic coupled origins according to the variation of the unbalance mass and bearing stiffness. The rotor behavior is analyzed by the coupled electromagnetic and structural time stepping FEM. The rotor in a SRM is used in this study.\nFig. 1 shows the cutaway view of a SRM with four rotor poles and six stator poles with three phases winding in the stator, which is used for two-dimensional electromagnetic field analysis.\nFig. 2 shows the rotor configuration supported on both bearings and its mesh for rotor dynamics analysis. For the structural FEM, the analysis model is divided into 23 beam elements. The\n0018\u20139464/01$10.00 \u00a9 2001 IEEE",
            "beam elements are defined by two nodes having four degrees of freedom at each node. Two independent element meshes are created to analyze the coupled problem.\nFig. 3 describes the computational procedure with aid of the structural and electromagnetic 2-D FEM by time stepping.\nTo obtain the displacement of rotor as a function of time due to the unbalance forces, the Houbolt algorithm coupled with structural FEM is used [6]. The transient analysis of the differential equation of a rotor vibrating systems is solved by a step-by-step procedure with respect to time when the unbalance force acting on the rotor pole.\nThe electromagnetic field is performed using the FEM coupled with exciting voltage. The exciting magnetic force is determined from Maxwell stress tensor. To compute the radial force acting on the rotor pole with a rotor position, the rotation is taken into account by means of the moving line technique [7]. This process as shown in Fig. 3 is iterated until the steady state.\nThe governing equation for the analysis model is expressed as (1)\n(1)\nwhere is -component of magnetic vector potential. and are reluctivity of the material and current density supplied by power, respectively. As the inductance is varying with the\nrotor position, the current injected into a phase is calculated in terms of voltage source and circuit parameter. The matrix form of circuit equation can be expressed as (2)\n(2)\nwhere is resistance of stator winding per phase. is inductance of end-winding.\nBy applying the backward time difference method, the whole system matrix can be expressed as (3).\n(3)\nThe Maxwell stress tensor from the magnetic field analysis is used in order to obtain the exciting force acting on the rotor. The force density between stator core and air is represented as follows [2]:\n(4)\nwhere is the direction of the normal unit vector on the pole face, is flux density solved by electromagnetic FEA.\nThe geometric center of rotor is and its center of gravity is at a distance called eccentricity. In the fixed OXY axis system, the geometry of unbalance whirl at the rotor is shown in Fig. 3. The mass unbalance is defined as product of the residual unbalance mass and eccentricity , and the centrifugal force\nin \u2013 plan when the rotational speed is then expressed as (5) [8].\n(5)\nThe matrix equations of motion for a beam element can be written as [9]\n(6)",
            "where and are element mass, gyroscopic and stiffness matrices (8 by 8), respectively. is vector of node displacement. The exciting force term includes the unbalance radial force and centrifugal force due to mass unbalance.\nThe second-order differential equation (6) combined with Houbolt algorithm result in an equation, which needs to be solved to find the displacement. The step-by-step procedure is given below [10].\n1) From the known initial conditions and , find using (7).\n(7)\n2) Select a suitable time step 3) Determine using (8).\n(8)\n4) Find and using the central difference equation (9).\n(9)\n5) Compute , starting with the and using (10).\n(10)\nThe initial value of node displacement is zero. The rotor has a residual unbalance mass of 10 (g mm) and the rotation speed is 2000 (rpm).\nFig. 5 shows the equipotential lines of the analysis model just before the phase is turned off. In order to simply the magnetic field analysis, a half model with about 4532 triangle elements is used.\nFig. 6 shows the instantaneous global radial magnetic for one phase excitation when the air gap is uniform without the\neccentricity. This radial force as a faction of time is obtained by the electromagnetic FEM using time stepping. This rapidly change of the radial force can excite the rotor and stator so that the vibration become severe.\nThe basic assumption to simplify analysis is that the bearings and stator core is isotropic and homogeneous and the mechanical damping is neglected. For the dynamic response of the rotor, the displacement is observed at a selected point A as shown in Fig. 2. The displacement of the rotor with a change of time, which means a locus of the geometry center of rotor, is displayed on the \u2013 plane. The starting point is the stator bore center.\nFig. 7 shows the eccentricity caused by only the mechanical unbalance mass 10(g mm) when the current is not excited. This displacement of the rotor turn around the stator bore center as the circle radius about 7 ( m).\nThe results of transient response are presented in Fig. 8 and Fig. 9 during the integration time \u20131 (sec). Fig. 8 shows the rotor dynamic response caused by the unbalance mass without coupling with the magnetic origin in the transient state. The unbalance mass is equal to that used in Fig. 7. This whirling motion as times passes on shows the tendency to remain stable. After finishing the transient state, the locus has the rotation radius of 7 ( m), which is similar to that obtained in Fig. 7.\nFig. 9 presents the dynamic displacement of the rotor due to the unbalance magnetic coupled with the unbalance mass.\nIn the comparison of Figs. 8 and 9, the whirl magnitude with the coupled with origins is larger than that with mechanical"
        ]
    },
    {
        "image_filename": "designv11_11_0000737_s0890-6955(01)00101-8-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000737_s0890-6955(01)00101-8-Figure6-1.png",
        "caption": "Fig. 6. Showing the cutting tool and gear blank and motions to generate curved face width forms.",
        "texts": [
            " (16) and (17): x T 3(j1)\u00b7X (17) The parametric equations of the line of action are represented as: x=\u2212R(1\u2212cosv)sin(w\u2212j+j1)\u2212Rbcos(j\u2212j1)\u2212Rbjsin(j\u2212j1) y=R(1\u2212cosv)cos(w\u2212j+j1)+Rbsin(j\u2212j1)\u2212Rbjcos(j\u2212j) z=Rsinv (18) where the angular parameters j and j1 are related by the meshing equation. Fig. 5 shows the line of action in some views perpendicular to the gear axes, z=hi. The lines shown are for curved face width gears to the specification given in Section 2.3. The x and y axes represent the co-ordinates of the start and end of the lines of action. The lines shown are linear and indicate conjugate motion, and also show how the line of action decreases in length at all sections from the center of the face width. Fig. 6 shows the kinematics of the tooth generating system. The cutting tool rotates at a constant speed and is radially advanced into the gear blank. The blank rotates and is translated to obtain the rolling motion required to generate the involute profiles. The concave tooth flanks are generated first and the cutting tool is replaced by another to form the convex tooth flanks. A manufactured gear is shown in Fig. 7. This gear was made to the specification given in Section 2.3. A face width of 24 mm was chosen as this allowed an adequate radius of curvature for the curved face width"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001964_robot.1997.614291-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001964_robot.1997.614291-Figure5-1.png",
        "caption": "Figure 5: Upper arm rises, while lower arm drops to navigate wall",
        "texts": [],
        "surrounding_texts": [
            "In this section, the MMF method is bricfly summarizcd. While conventional potential field methods are derived from principles of electrostatics, the Modified Magnetic Field method is derived from electrodynamical considerations. The obstacle forces are obtained from a current based formalism. This distinction and the methods of their computation are briefly summarized in this section and shown in greater detail in [ 5 ] . The conventional attractive potential field form is used to represent the field setup by the attractor: where -kattr is some positive constant used to represent the intensity of the force field and x is the location of the operating point with respect to the goal location Xd. A damping force is used to damp out oscillations that accrue from the specification of the above attractive field and is given in the following form. where x represents the velocity of the robot. The damping field force is a non-conservative force that tends to oppose the motion of the system. The definition of the obstacle field and force is the key innovation of the MMF method. The basis of the MMF is a set of virtual closed current loops enclosing the obstacle. These virtual current loops generate virtual forces that are termed the Modified Magnetic Field . The obstacle force and field are defined by the following relations: Fobs = X x B (3) (4) where B represents the obstacle field, the MMF , and Fobs represents the obstacle force due to this field. Again, x represents the robot velocity, x the unit velocity vector, l represents the direction of the current loop enclosing the obstacle face and p represents the magnitude of the perpendicular distance of the robot from the given obstacle face. The obstacle field definition is similar in structure to the conventional electro-magnetic Magnetic field, however, the structure of the M M F is somewhat different from that of the classical Magnetic field. Using the redefined Eq. 4 B improves the behavior of the control law, resulting in less convoluted paths, than the classical form. This is shown in Fig. 2. Rather than spiral endlessly, the M M F field has some preferred directions such that motions in those directions remain unaffected while others are turned into those directions. 3 Domain Extension of the MMP The form introduced for the obstacle force has been delineated in terms of the vector cross product operation. To address planning in higher dimensional spaces such as configuration or task spaces, the definition needs to be extended to consistently and exactly address force generation. Towards this end, we use the tensor notation to compute the B = B x . = C,(l,x)X) x . (5) term so that the computation of the corresponding obstacle force Fobs becomes a tensor reduction operation with the robot velocity, as Fobs = -BX. In this section, we briefly recount the computation of B for any given obstacle surface and robot velocity given that the form selected for the MMF was given by B = We also discuss the computation of the obstacle forces and torques applied to a robotic link. Previously, we presented control forces that applied to a point robot - whether operating in Cartesian or in joint space. Here we extend the definition of the obstacle force to apply to linked manipulators. The method of computing the B tensor is briefly summarized for its relevance to the next section. Let the n-dimensional obstacle surface be characterized by a minimal set of n orthonormal vectors: 1 surface normal and (n-1) surface vectors. The B tensor matrix is then computed from these vectors. Given that Fobs = x x B or Fobs = -Bx using new notation, it follows that x.(Bx) = 0 from the scalar triple product result. Now this must be true for all x, including those velocity directions that are parallel to the eigenvectors of B. $ in Eq. 4. P For x = [,[ E [EV set ofB] . 1 1 [ 1 1 2 = o (6) To satisfy this requirement, either X g = 0 or llE112 = 0. Skew-symmetric matrices meet these criteria since the roots of skew-symmetric matrices are either zero or strictly imaginary. Now, if X g = 0, then Fobs = AB . = 0 which is exactly the desired behavior if the robot velocity runs parallel to the surface. However, if the robot velocity runs along the surface normal the 1 1 [ 1 1 2 = 0 solution is used, which corresponds to an imaginary root. To choose a real 13 with 2 complex conjugate pairs (to ensure realness of a), select any (n - 2) of the surface vectors as the B eigenvectors with eigenvalues of 0, and choose f~ as the two remaining eigenvalues. Eigenvectors for these last two values are constrained to lie in the plane of the surface normal direction and the last (n-1)th surface vector. Now select any 2-d skew-symmetric matrix with eigenvalues f i , find its eigenvectors and the last two eigenvectors of our MMF matrix is now known in terms of the 2 known basis vectors scaled by the components of the 2-d eigenvectors just found for the known 2-d matrix. Now, the eigenvalues and the eigenvectors are known and the computation of B may be computed. 4 Computing the Obstacle Fields and Forces for a Linked Manipulator An outline of the computation of the obstacle forces for a linked manipulator navigating in a Cartesian or task space are presented herein. Consider the situation shown in Fig. 3. The joint space obstacle forces are generated in joint space and joint limit avoidance is performed by treating each limit or singularity as an obstacle and computing the resulting set of forces as described earlier. Subsequently, task space motion planning is performed whereby the obstacle forces and torques are computed for the task space obstacles. These task space forces and torques are then transformed back to joint space through the manipulator Jacobian, where they are integrated with the previously obtained jointspace forces. Collectively, these forces serve as input control torques in the robot dynamic relation where final force resolution is performed. The joint space obstacle avoidance is performed as shown in the previous section and detailed in [5]. In task space, the obstacle force on the link is formulated in two parts, one generates the task-space force and the other the torque for the given link. To compute the link force component, the link is abstracted to its center of mass and the obstacle force for the center of mass is then computed in Cartesian space, as has been done for the point robot. The obs- tacle force is then computed as: Next, the obstacle torque is computed. This torque, the Modified Magnetic Torque is computed in a somewhat analogous fashion through the following relation: where w represents the angular velocity of the link, s represents the link axis, U the linear velocity due to the orientational component, and I' denotes the Modified Magnetic Torque Field, the angular analog of the MMF . The M M T F and the obstacle torque has similar electro-dynamic connotation as the MMF , however, in implementation, we have yet again, departed from the classical electro-magnetic mathematical definitions. Rather than visualizing the robot link as a point charge, as has been done in classical potential field methods and earlier in this paper in the development of the M M F , here the link is treated as a dipole and derivations of r o b s derive from the interaction of the dipole moment with the obstacle torque field. Eq. 8 constitutes a contraction mapping of the tensor I?. The cross product terms in Eq. 9 may be computed as outlined in Sec. 3. While the tensor form is necessarily important for higher dimensional spaces, the cross product form may be retained for classical Cartesian space development. The rationale for the above mathematical structure will be briefly outlined. The considerations governing the M M T F equations here are similar to those that went into formulating the MMF forces. Ideally, we would like to preserve link configurations in which the link lies parallel to the obstacle surface (i. e. where r o b s = sTn = 0) and reorient those in which the link lies along the surface normal. Towards that end, the sTn term is important in that this term is zero for every link configuration that lies along the surface and is only non-zero when the link axis is oriented towards the surface. Additionally, a torque expression that ensures that the work done by that torque will always be zero is desired i.e. r such that W = w.7 = 0, as will be shown to be important in the brief outline of the Lyapunov Energy analysis perform in the next paragraph. The (U x (li x s ) ) x w term in the definition of I' ensures that this requirement on the obstacle torque is met. Multiplying the dyads in Eq. 9 by the vector s causes the contraction of the tensor B, and yields the above vector, (li x s ) x w. The presence of the . x w term, this term is guaranteed to be orthogonal to U, and hence ensures that the work done by this obstacle torque is zero. To show that this choice of the obstacle torque preserves the convergence properties of this method (see [ 5 ] ) a Lyapunov candidate function of the form V = p X M T x + U ( x ) , or more verbosely, $ (XTXl + qTq) + U(x). The state velocity vector has been decomposed into the linear and angular components. The state vector x = [xl,4] where xl denotes the linear position vector, and q, the angular position quaternion. Furthermore, using the unit rotation quaternion representation, q = -($ @ q) and q = @ q + $ @ ($ @ q), where $ = [w,O] is the vector quaternion form of w and 8 represents the quaternion product, the convergence analysis is performed in this generalized position-orientation space. Further detail on the quaternion analysis may be found in [6]. The time derivative of the Lyapunov function yields 9 = M (XTxl + q'q) + VUTx, + VUTq. The rate of change of Lyapunov energy can be represented as i, = x:(-vU(xi) - k2Xl - BXl) + qT(-vU(q) - k 2 q f ( T o b s @ q - $ @ ($ 8 9))) + vU(Xl)Txi + vU(q)Tq (10) where Tabs is the quaternion form of r o b s , given by Tabs = [ r o b s , 01. Since r o b s is defined to be either zero (when s I n) or else normal to w , and may be given by the relation r o b s = (Q x w ) when not zero, the time rate of change of the Lyapunov function, upon resolution of the quaternion relations, becomes simply i, = -k2X?Xl - k2qTq 5 0 which is inherently negative semi-definite. Using the LaSalle Invariance Principle, strict negative definiteness can be shown. 5 Result of Dynamic Control on Puma560 using MMF Methods The governing robot dynamic equation is given by the relation: M ( 0 ) 8 +C(6,0)6 +k(O) = r (11) where M represents the mass matrix, C , the matrix of Coriolis and centripetal forces, k, the gravity vector and 0 the vector of joint angles, r is the applied joint force. The M M F control scheme outlined in this paper generates the set of r that will be applied to the dynamic control equation. The resulting joint positions and velocities represents the motion of the robot. In this section, an example of a robot navigating in the space of obstacles - both task space obstacles as well as Cartesian space obstacles - and required to obtain a certain goal configuration, is presented. The planner control is effected in the following fashion. The joint space obstacles (joint limits) are generated thus: upper joint limit 1 corresponds to a surface at [&,O, . . .O] and with surface normal [--I, 0 , . . .O]. Correspondingly, the surface vectors for this surface are setup as [O, 1,O.. .O], [O, 0,1, . . .O] , . . . [O, 0 . . . I] with accurate assignments for the sign of the surface vectors to ensure closed loops around the joint space boundary. This done, the joint space forces are computed using the relations Fattr = -kl(O - Od) (12) Fdamp = -m) (13) = -azo (14) Next the Cartesian space obstacle forces are computed. The Cartesian space force and torque are computed for each of the N-links of the robot. F:::t = Xzo(X:om x B:om) (15) ,xart - T T N obs - ( Xz=O(n(v (lz .)) (16) Now the generalized force vector is obtained by stacking the force and torque terms: (17) which is transformed through the generalized Jacobian matrix into joint space yielding the resultant relation: 7- = Faitr + Fdamp + FZS + JTFS,Er (18) Now by appending gravity compensation to this T , it is applied as the control to Eq. 11 Although parameter adjustment and tuning are not mandatory for convergence, the robot motion plan will be correlated with the parameters used for the control inputs. The parameters used affect the inertia in the control system. For instance, the larger the proportional gain in the attractive force, the steeper a potential well it sets up and hence the robot slides down it with correspondingly greater energy. A shallow well, on the other hand results in very straight lined paths, where the robot heads straight for the goal, but navigation around the obstacle becomes very exaggerated. The resulting task space paths are shown in the associated figures. In this problem, the objective or the desired configuration was stipulated at @, = [67.5, -45,176.4, -35.5,33,200]. The joint limits were the standard joint limits of a Puma560. and the initial configuration was given by 00 = [-75.6, -15,91.5,143, -59.7,112.3]. Task space obstacles were vertical walls located at: Wall config. Centroid Normal Vertical [0.05,0.4,0.6] [0, -1,Ol Horizontal [0.55,0.025,1.25] [O,O, -11 The robot starts with its tip very close to both, the vertical wall in X and the Joint4 joint limit. To get to the goal, without colliding with the walls or going through its limit, the robot, increases its elbow angle (dropping the forearm) but lifting the shoulder joint. To navigate the facing wall, the robot lifts its entire arm to the tool, curving up to avoid the wall, lifting the shoulder a t the same time. The presence of the short ceiling flattens the trajectory, leaving the robot having to pull out from the ceiling before it can adequately pull up to cross the second enclosing wall to the goal. The robot approaches the second vertical wall but has to approach very close to it to avoid both, its Joint3 singularity as well as the first vertical wall. Small \u201cbobbles\u201d are seen in the elbow and tip paths as the action of the M M F manifests its self strongly at this point due to the proximity of the robot to the obstacle surfaces. Removing the horizontal wall results in a much smoother and natural looking trajectory, whereby the robot tip first falls toward the floor as the forearm falls and the robot base turns toward the goal; the elbow and tip then smoothly curve up and over the second vertical wall. The corresponding joint space trajectory during this navigation are shown in Fig. 9 Joint 1 is most encumbered in this move. The robot starts off fairly close to its joint1 lower limit and has to further approach it to navigate the walls. In nearing the goal, it approaches very close to its other limit and the characteristic \u201cbobble\u201d is seen in the joint space trajectory at the highest points in the joint path arc. Vertical [0.75,0.0,0.85] [ - l , O , O ] 6 Conclusions In this paper, we reviewed the concept of the Modified Magnetic Field to robot motion planning and control in an obstacle field. The treatments in both Cartesian space and configuration space were highlighted. The fundamental idea is based on the electrodynamic principle, where a magnetic component originates from the presence of fictitious current elements wrapped around each obstacle. Extension of the planning algorithm to a linked manipulator was then presented where the objective was to navigate both joint space and Cartesian space constraints. The al- gorithm was successfully able to negotiate the constraints. Since the forces generated by the MMF can be analytically computed, the algorithm has also been implemented as a real-time feedback controller. References [I] J.C.Latombe, Robot Motion Planning. 101 Philip Drive, Assinippi Park, Norwell, MA 02061: Kluwer Academic Publishers, 1991. [2] 0. Khatib, \u201cReal-time obstacle avoidance for manipulators and mobile robots,\u201d Proc. of the IEEE Internat? Conf. on Robotics and Automation, pp. 500-505, 1985. [3] D. E. Koditschek, \u201cExact robot navigation by means of potential functions: Some topologi- cal considerations,\u2019\u2019 Proc. of the IEEE Intemat \u2019I Conf. on Robotics and Automation, pp. 1-6, 1987. [4] K. J.O. and K. P.K., \u201cReal-time obstacle avoidance using harmonic potential functions,\u2019\u2019 IEEE Ransuctions of Robotics and Automation, vol. 8, pp. 338-349, Jun. 1992. [5] L. Singh and H. Stephanou, \u201cA collision-free, realtime motion planning with guaranteed convergence using analytical circulation fields,\u201d Submitted IEEE Int? Conf. on Robotics and Automation, 1996. [6] L. Singh and H. Stephanou, \u201cTask-based servoing in vector-quaternion space,\u201d Proc. of the IEEE Internat? Conf. on Robotics and Automation, vol. 25, pp. 100-110, May 1995."
        ]
    },
    {
        "image_filename": "designv11_11_0003346_j.jsg.2004.07.005-Figure19-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003346_j.jsg.2004.07.005-Figure19-1.png",
        "caption": "Fig. 19. Geometrical construction for Eqs. (1), (2), (9), (17)\u2013(19) and (48).",
        "texts": [
            " This \u2018excess length\u2019 in the foreland may provide the proper triggering factor for second-order folding and faulting, and pressure solution cleavages that are commonly found at the toe of shallow foreland structures. Application of model predictions to natural thrust-related anticlines validates the usefulness of the proposed geometrical and analytical solution. We gratefully acknowledge constructive criticism and advice from D.A. Medwedeff, N. Woodward and an anonymous reviewer, which helped us to significantly improve an early version of the manuscript. f1 Z \u00f0a2 Kb1\u00de=2 (1) hb Za2 Kb1 (2) After migration across the axial surface g1, the triangle ABL (Fig. 19a) becomes A 0BL (Fig. 19b). In order to preserve line length, AB must equal A 0B: ABZ sin\u00f090Cf1 Ka1\u00de\u2020\u00bdAL=sin\u00f0a1\u00de (3) A0BZ sin\u00f090Cf1 Ka2\u00de\u2020\u00bdAL=sin\u00f0b1\u00de (4) By comparing Eqs. (3) and (4) we obtain: cos\u00f0f1 Ka2\u00de=sin\u00f0b1\u00deZ cos\u00f0f1 Ka1\u00de=sin\u00f0a1\u00de (5) cos(f1Ka2) can also be expressed as cos(f1Cb1), and Eq. (5) becomes: cos\u00f0f1 Cb1\u00de=sin\u00f0b1\u00de Z \u00bdcos\u00f0f1\u00de\u2020cos\u00f0a1\u00deCsin\u00f0f1\u00de\u2020sin\u00f0a1\u00de =sin\u00f0a1\u00de (6) Eq. (6) can also be written as: \u00bdcos\u00f0f1\u00de\u2020cos\u00f0b1\u00deKsin\u00f0f1\u00de\u2020sin\u00f0b1\u00de =sin\u00f0b1\u00de Z cos\u00f0f1\u00de\u2020cot\u00f0a1\u00deCsin\u00f0f1\u00de (7) Simplifying and rearranging: cot\u00f0a1\u00deZ cot\u00f0b1\u00deK2tan\u00f0f2\u00de (8) Substituting Eq. (1) into Eq. (8): cot\u00f0a1\u00deZ cot\u00f0b1\u00deK2tan\u00bd\u00f0a2 Kb1\u00de=2 (9) During shortening, the shape of polygon ABCDEFG (Fig. 19a) modifies to A 0BCDEF 0G 0H (Fig. 19b). Line length preservation imposes: EFCFGZEF0 CF0G0 CG0H (10) EFZABCCD\u2020tan\u00f0f1\u00de (11) FGZCD\u2020cot\u00f0a2\u00de (12) EF0 ZABKCD\u2020tan\u00f0f1\u00de (13) F0G0 ZCD\u2020d1 (14) G0HZCD\u2020cot\u00f0b2\u00de (15) Substituting Eqs. (11)\u2013(15) into Eq. (10) and simplify- ing: d1 Ccot\u00f0b2\u00deK2tan\u00f0f1\u00deZ cot\u00f0a2\u00de (16) d1 Z b2 Kb1 (17) Substituting Eqs. (17) and (1) into Eq. (16) we obtain: cot\u00f0b2\u00deCb2 Z cot\u00f0a2\u00deKcot\u00f0a1\u00deCcot\u00f0b1\u00deCb1 (18) hc Za2 Kb2 (19) After translation onto the upper ramp, triangle ABC becomes the polygon ABC 0D (Fig. 20). Line length preservation requires that: BCZBC0 CC0D (20) BCZAB\u2020cot\u00f0b2 or b1\u00de (21) being either b2 (Step I) or b1 (Step II) the hanging wall central ramp cut-off angles: BC0 ZAB\u2020\u00f0d2 or d 0 1\u00de (22) where either d2 (Step I) or d01 (Step II) are the apical angles of the circular sector pinned at the central ramp upper inflection point: C0DZAB\u2020cot\u00f0b3 or b 0 1\u00de (23) being b3 (Step I) or b 0 1 (Step II) the forelimb or the CP 0 panel cutoff angle",
            " Equations 42 and 43 (see Fig. 20a and b) h0 c Z b0 1 Ka3 (42) hf Z b3 Ka3 (43) d01 Cd02 Z d1 Cd2 (44) Substituting Eqs. (18), (25a) and (25b) into Eq. (44) and simplifying: d 0 2 Z b3 Kb 0 1 (45) A.9. Equations 48, 52a and 52b (see Figs. 19 and 20) The relationships between the total shortening along the lower ramp (S1) and its partitioning in the central (S2) and upper (S3) ramps are described by Eqs. (48), (52a) and (52b). In particular, when the amount of slip along the lower ramp (S1) is LA (Fig. 19), the amount of slip along the central ramp (S2) is LA 0 and the following equations are verified: LBZ S1\u2020sin\u00f0a1\u00de=cos\u00f0f1\u00de (46) S2=sin\u00bd180K \u00f090Cf1 Ka2\u00deKb1 ZLB=sin\u00f0b1\u00de (47) Substituting Eq. (46) into Eq. (47) and simplifying we obtain: S2 Z S1\u2020sin\u00f0a1\u00de=sin\u00f0b1\u00de (48) which relates the amount of shortening along the lower and central ramps. When the incremental shortening along the central ramp (S2) equals AC (Fig. 20), the amount of slip along the upper ramp (S3) is AD: ABZ S2=sin\u00f0b2; b1\u00de (49) S3 ZAB=sin\u00f0b3; b 0 1\u00de (50) Substituting Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002997_j.mechmachtheory.2004.02.005-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002997_j.mechmachtheory.2004.02.005-Figure4-1.png",
        "caption": "Fig. 4. Scheme of tooth profile errors.",
        "texts": [
            " (3) The distance between the two points can be given by: e\u00f0zk\u00de \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0x2 x20\u00de2 \u00fe \u00f0y2 y20\u00de2 q ; (4) For another section zk\u00fe1, given zk \u00bc zk\u00fe1, return to step (2), continue the above steps. Thus, we can calculate the axial errors along the axis of gear 2. Tooth profile errors can be defined by the deviation between the practical tooth profile and theoretical profile when the deviation is zero between the tooth profile curve and the involute curve on the pitch circle. As shown in Fig. 4, for a section of gear 2, line PA is tangent to the base circle, and the line PA intersects the tooth profile of gear 2 at the point B. Thus the deviation between the two lengths of line PA and PB is known as tooth profile error. The calculation procedure of tooth profile errors is : (1) The section of the gear 2 can be determined by the equation z2 \u00bc z20 \u00bc zk (zk is the z-coordinate of section k), then /0 can be obtained by the equations as follows: x22 \u00fe y22 \u00bc r2m \u00f0x2 x20\u00de2 \u00fe \u00f0y2 y20\u00de2 \u00bc 0 z2 \u00bc zk U \u00bc 0 9>= >; where rm is the radius of reference circle (mm)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000810_s0924-0136(02)00356-4-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000810_s0924-0136(02)00356-4-Figure6-1.png",
        "caption": "Fig. 6. Schematic illustration of wheel rolling.",
        "texts": [
            " The effectiveness of the dense regions in covering the areas of greatest strain rate can be seen in Fig. 5, in which the effective strain rate distribution during the process is shown. The resulting mesh was made up of 1620 nodes. The process took place over 40 revolutions at a variable feed rate, this required 4800 deformation increments and took approximately 3 weeks runtime. The wheel rolling process differs from conventional ring rolling due to the lack of a central mandrel, the use of profiled axial rolls, and the presence of idle pressure rolls. The configuration is illustrated in Fig. 6. These differences meant that a modified version of the rolling simulation program was required. In particular, the need for mandrel speed calculation was replaced by the need to handle the interfaces between the pressure rolls and the workpiece. Given the results shown in Section 3.2, it was considered best to determine pressure roll velocities in the same way as was used for mandrel speed, and apply a full friction model at each interface. In addition, the presence of the pressure rolls meant that the dense mesh region on that side of the wheel needed to be extended to cover the entire region in close proximity to the pressure and edge rollers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001242_s0020-7462(01)00052-x-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001242_s0020-7462(01)00052-x-Figure1-1.png",
        "caption": "Fig. 1. Actual position of vibrating pendulum, displacements with reference to the rigid shadow con.guration.",
        "texts": [
            " To describe the surface forces, we use the Lagrangian (Tre3tz) stress vector t(n)R at the surface SR with normal nR in the reference position. Inertial forces are included in the body forces b for the sake of brevity. The .rst Piola\u2013Kirchho3 stress tensor produced by the body and surface forces is TR = (Grad p)S , where p is the actual position vector, and S denotes the symmetric second Piola\u2013 Kirchho3 stress tensor. Eq. (2.1) is applied to the following benchmark problem: A 7exible elasto-plastic beam is .xed in space at one of its ends by means of a hinged rigid support. The other end of the beam is considered to be free, see Fig. 1. This elasto-plastic pendulum is released from an initial position, is subjected to the action of its own weight, and eventually rotates and performs vibrations. In the following, we consider plane motions of the pendulum only. It is the scope of the present contribution to study the in7uence of the elasto-plastic vibrations upon the rotation of the pendulum. Eq. (2.1) would allow to use a reference con.guration .xed in space. A .xed reference con.guration has been suggested by Simo and Vu-Quoc [15] for elastic beams in order to avoid the non-linear inertial coupling of the 7exible and the rigid-body degrees-of-freedom",
            " It is oriented towards the tip of the actual con.guration of the pendulum and is characterized by means of a co-rotated cartesian coordinate system in the plane of motion with base vectors (ex; ez). The coordinate transverse to the shadow con.guration is denoted by z, and x is the axial coordinate. The coordinate perpendicular to the plane of motion will be denoted by y. Later on, solutions for a hinged\u2013hinged elastic shadow beam will be used. The co-rotated straight reference position of the hinged\u2013hinged beam is also sketched in Fig. 1. With respect to the co-rotated system, the .rst Piola\u2013Kirchho3 stress tensor reads TR = t(x)R \u2297 ex + t(z)R \u2297 ez; (2.2) where \u2297 denotes the dyadic vector product. It has been demonstrated in Ref. [12] that the volume integral at the right-hand side of Eq. (2.1) can be replaced by\u222b B TR: Grad p\u0302 dVR = \u222b L 0 p\u0302Io \u00b7NR dx + \u222b L 0 !\u0302I \u00b7MR dx + \u222b L 0 !\u0302 \u00b7 (pIo \u00d7NR) dx: (2.3) The reference length of the beam is L. Note the abbreviation ()I = @()=@x. An admissible virtual position of the beam axis is denoted by p\u0302o = (x+ u\u0302)ex+ w\u0302ez, where w denotes the de7ection of the beam axis relative to the shadow con",
            " A short account on the so-called geometric sti3ening e3ect can be found in Ref. [17]. The weight of the pendulum, Rbext = Rg (sin\u2019ex + cos\u2019ez), is considered as the only imposed body force. Its virtual virial follows to\u222b B Rbext \u00b7 p\u0302 dVR = \u222b L 0 RgAR[(x + u\u0302) sin\u2019+ w\u0302 cos\u2019] dx: (2.12) In Eq. (2.12), the axis z=0 of the beam has been identi.ed with the centroids of the cross-sections of the beam. The beam is considered to be homogeneous. The rotation of the shadow reference con.guration is denoted by \u2019, see Fig. 1. The vector of inertial forces is approximately identi.ed with the acceleration vector a of the axis in an inertial frame: binert =\u2212 a=\u2212 (aguid + arel + acor): (2.13) Rotatory inertia has been neglected, which is appropriate for slender beams. Using a co-rotated reference con.guration, a in Eq. (2.13) is subdivided into three parts. The \u201cguided\u201d acceleration is aguid = (\u2212x\u2019\u03072 \u2212 w U\u2019 \u2212 u\u2019\u03072)ex +(x U\u2019+ u U\u2019 \u2212 w\u2019\u03072)ez; (2.14) the relative acceleration becomes arel = Uuex + Uwez (2.15) and the Coriolis part of the acceleration is acor =\u2212 2w\u0307\u2019\u0307ex + 2u\u0307\u2019\u0307ez (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000753_mchj.1997.1540-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000753_mchj.1997.1540-Figure3-1.png",
        "caption": "FIG. 3. The voltammograms of DA redox at PNR/CFME at different scan rates. Scan rate (from inner to outer), 10, 20, 50, 100, 200 mV/s. Solution, BPBS (pH 7.4). CDA \u00c5 3.0 1 1005 mol/L.",
        "texts": [
            "5 1 1005 mol/L DA; (d) (b) / 1.5 1 1005 mol/L DA. HO\u00a9 \u00a9CH\u00a4CH\u00a4NH\u00a4 1 2e 1 2H1. \u00a9CH\u00a4CH\u00a4NH\u00a4 O O (DA) HO\u00a9 At carbon fiber microelectrodes, DA did not have an apparent redox reaction in the potential range 00.3\u20130.6 V and BPBS (Fig. 2b). The CFME and PNR/CFME did not have an apparent electrode reaction also in the same potential range and solutions (Figs. 2a and 2c). But using the PNR/CFMEs, a pair of redox peaks was obtained when DA was added in BPBS and in the same potential range with Epa \u00c5 0.224 V and Epc \u00c5 0.110 V (Fig. 2d). Figure 3 shows the voltamograms at different scan rates. The oxidation peak currents (ipa) are linear with n1/2 in the range 10\u2013200 mV/s with a linear correlation coefficient of Y \u00c5 0.998, but the reduction peak currents are linear ah10$$1540 03-03-98 13:10:28 micas AP: MCH FIG. 4. The i\u2013t1/2 curves of potential step experiments. (a) A PNR/CFME inserted in 5.0 1 1005 mol/ L DA immediately. (b) A PNR/CFME immersed in 5.0 1 1005 mol/L DA for 24 h. Potential step from 00.3 to 0.6 V. with n in the same range of potential scan rate with Y \u00c5 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003088_tmag.2005.844840-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003088_tmag.2005.844840-Figure2-1.png",
        "caption": "Fig. 2. TLRM with closed magnetic system.",
        "texts": [
            " The stack of the silicon sheets of the rotor\u2019s moving core (runner) is formed and placed in the runner tube with internal diameter of cm. Thus, the gap with air permeability between the winding wires and the ferromagnetic core is mm. The weight of the runner is 1.05 kg. Because such motors are used at low speed, the eddy-current effects in the moving core can be neglected [4]. The variants of the stator with closed magnetic system have also been considered in this work. A simplified form of a closed magnetic system is shown in Fig. 2. The external part of the closed system consists of a laminated ferromagnetic cylinder and disks. The cylinder surrounding the stator coils forms not only the magnetic shield (screen), but also a part of the magnetic circuit. Two disks exclude the magnetic flux from outside the stator. They are fixed at the left and right ends of the stator. Due to very small gaps between the disks and the external ferromagnetic body, and lamination of the parts, we can consider the stator magnetic circuit as a solid iron without eddy currents [10]",
            " The variant is slightly worse (with regard to magnetic properties) than that assembled from U-shaped sheets, but more convenient for manufacturing. Each package of the sheets contains the air gaps between the stack sheets, and this technique can be fully adapted to grain-oriented silicon steel, which is used in a transformer magnetic circuit [10]. Thus, the eddy currents in the stator magnetic circuit can be omitted in the considerations. Similarly, in Section II we assumed that the stator of the closed magnetic circuit is composed of the cylinder (corpus) and two disks (Fig. 2). We also neglected the air gaps between the parts. In the simulations, we assumed that the thickness of the laminated external cylinder and the two disks are the same (Fig. 8). The air gaps of 2 mm long between the stator ferromagnetic circuit and the runner are included. To obtain the static and dynamic characteristics, the magnetic field analyses must be performed. The nonlinear \u2013 curve of the ferromagnetic material has been taken for the field analysis [12]. The calculations have been executed for parametric changes of the current value and the thickness of the stator circuit (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001551_robot.1996.503859-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001551_robot.1996.503859-Figure2-1.png",
        "caption": "Figure 2: Trajectory in non-Euclidean space",
        "texts": [
            " The Euler parameters are defined as a quaternion and are represented by a point on the surface of 4-dimension unit hypersphere S 3 . The Euler parameters E , namely, orientation from the standard orientation is expressed by the rotation axis n and the rotation angle 6 about the axis as follows: E = { cos g } \u20ac S 3 sin gn Note that the orientation space is a non-Euclidean space S'. Since we take U as generalized coordinates instead of q, our trajectory planning problem lies not in Euclidean space R6 but in a non-Euclidean space R3 x S 3 . as shown in Fig.2. Adopting the differential f o r m 191, the equation of motion of the whole system is obtained as 71 9 where x = ( ',\" ) is the generalized coordinates, and (3) Y is the matrix relating the end-effector velocity ti to the satellite orientation velocity \u20ac 0 , and I is an identity matrix. 3 Planning the Spiral Motion 3.1 Single-Turn Spiral Motion We derive the formula of closed brajectory motion that results in an arbitrary change of satellite orientation, by using the differential form and the Lie bracket"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.29-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.29-1.png",
        "caption": "Figure 3.29 Example of large rim with spokes flywheel. The cast steel rim is in two parts joined by shrink fit rings. The cast iron hub is also reinforced by shrink fit rings. The steel spokes are bolted at both ends. Note the tie bar to relieve the centrifugal stresses due to the mass of the connections between the two parts of the rim. The flywheel is from a rolling mill, and has a maximum peripheral speed of 62 m/s. (From F. Rotscher, 'Maschinenelemente', Springer, Berlin, 1929)",
        "texts": [
            " 28 S te el p la te p re st re ss ed f ly w he el (a ) s ec tio n of t he r ot or (b ) c irc um fe re nt ia l st re ss p at te rn . ( C le rk [ 77 -1 6] ) H CD CD CD p re st re ss in g Isotropic flywheels 103 possible of the rotor mass in the rim. A system of spokes can be used in order to connect the rim to the central hub, obtaining a radius of inertia which is close to the outer radius. Some examples of ancient rotors of this type have been shown in Chapter 1. A good example of large rim-with-spokes flywheel is shown in Figure 3.29. In rim-with-spokes rotors, strong bending moments can be present in the rim as a consequence of different radial displacements of the rim and of the spokes under the centrifugal field. The stress analysis in such a complex structure is difficult, particularly as the presence of irregularities has to be taken into account. Only numerical calculations using at least a two-dimensional method can yield satisfactory results. There is, however, a traditional simplified approach consisting of subdividing the structure in its main elements\u2014namely, some beams for the spokes, some curved beams for the rim and a central disc for the hub",
            " The maximum tensile bending stress at point B takes the following value: 1 * \" ' \" r l (3.139) 1 Sr|_2 tan{q>/2) \u00abo(l+/r/S, It can, however, be necessary to check that the stress expressed by equation (3.139) is really the maximum tensile stress due to bending in any particular case. The stresses due to bending are then to be added to the ones directly due to the centrifugal loads. A computer program for rim-with-spokes flywheels is given in Appendix 5. An example of calculation based on the flywheel illustrated in Figure 3.29 is also shown. If rim-with-spokes rotors have to deliver high powers they can be dangerously loaded by the inertial forces due to the angular acceleration. The accelerating torque applied to the rim by the spokes can be considered as evenly distributed between them. The force each spoke exerts at its tip in circumferential direction is then: d(D I FC~J\u2014 Nrr = P/rrNo> (3.140) The spokes can be considered as beams clamped in correspondence to the spoke-hub connection. The rotation of their tip section is, however, partially inhibited by the presence of the rim and the problem is not easily solved"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001624_robot.1996.506582-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001624_robot.1996.506582-Figure10-1.png",
        "caption": "Figure 10: Distal link collision avoidance",
        "texts": [
            " the third finger can exert a force so that a rotation The projection of the axis A, that is, the projection of the fingertips of the grasping fingers, is taken as the origin of W . Let W1 be the region where condition (1) is satisfied and W2 be the region where conditions (1) and (2) ;%re satisfied. Clearly W C W2 E W,. Appeiiidix A examines conditions (2) and (3). They depend on the orientation of an edge. We often explicitly describe the orientation dependency as Wz(a) and W(a) where a is the angle of the outer normal of an edge (see also Fig.10 in Appendix A for a). Condition (3) also depends on the coefficient of friction between the finger and the object. It is desirable to compute as much as possible offline before an actual manipulation takes place to reduce computational time. Since Wz is independent of coefficieiit of friction but dependent of the orientation of an edge, we calculate Wz(a) for all sampled angles of the outer normal of an edge of sin object about the axis A takes place. aj = (27r/Mff)j, j = 0,. . . , Mff - 1 (1) This paper calculates the workspace W(aJ) numerically rather than analytically since it is easier to check conditiolis (1) and (2) numerically",
            " Iberall \u201cDexterous Robot Hands,\u201d Springer-verlag, 1990 J. M. Maccarthy, \u201cIntroduction to Theoretical Kinematics,\u2019\u2019 ch.4, MIT Press, 1990 pp.269-279, 1989 Conditions (2) and (3) Condition (2): Collision avoidance The distal link is most likely to interfere with the object. This paper considers only its collision with the edge on which it exerts a force. The condition that the distal link does not interfere with the edge is given by If2 - CrLl > n/2 (16) where CYL is the angle of the distal link from the x-axis (see Fig.10). slip is substantially pure rotational. Hence we assume that when 1 > 10 =(given constant), the slip is pure rotational where I is the distance from the axis A to the line of the action of f \u2019. The hatched region in Fig.11 is the region of the fingertip of the third finger where the rotation takes place about the axis A. Let n R and nL be the outer normals of right and left edges of the friction cone, respectively. The hatched region is given by nRTx > 10, or, nLTx > lo B Numerical method for calculating workspace 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002070_j.ast.2004.03.005-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002070_j.ast.2004.03.005-Figure1-1.png",
        "caption": "Fig. 1. A flexible spacecraft model.",
        "texts": [
            " The inherent output feedback architecture is maintained by dealing with reaction torque that is directly created by the motion of flexible appendages. Both single-axis and three-axis slew maneuvers are discussed independently. Simulation results are presented to demonstrate the performances of the proposed control law. In particular, the simulation results are used to highlight the advantages which are given by reaction torque feedback in conjunction with the original predictive control command. The model spacecraft presented in Fig. 1 consists of a center rigid body with two flexible structures attached. The flexible structures represent on-board structural elements. Each structure has a mass element at the tip with negligible rotary mass inertia. The flexible structures are assumed to be identical in geometric and material properties. The center body structure is assumed to be perfectly symmetric with homogeneous material property. The appendages are attached to the middle points, located at l0 from the center, of the sides of the center body"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001912_tcst.2002.801879-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001912_tcst.2002.801879-Figure2-1.png",
        "caption": "Fig. 2. APGM top view, illustrating yaw angle ( ) relative to the current velocity vector (V ).",
        "texts": [
            " Third, their research did not consider the need for efficient real-time motion planning necessary for effective RCS reduction in dynamic radar threat environments. These and other deficiencies motivated the research described in this paper. Preliminary investigations demonstrated that it is possible to reduce the observed peak and/or aggregate RCS of an APGM during straight and level flight by specifying a single degree of freedom. The first of these investigations focused upon the intelligent specification of bank angle (Fig. 1), while the second showed how RCS reduction could be achieved through the intelligent specification of yaw angle (Fig. 2). The goal of the research described in this paper was to build upon these previous results by demonstrating the feasibility of combining route planning with the intelligent specification of APGM yaw angle and bank angle in a manner that significantly reduces the aggregate and/or peak RCS observed by any enemy radar located in a region of interest. This extraordinarily difficult problem may be thought of as a search through the space defined by the cross product of three parameters: 1) set of possible ingress routes from the current position of the APGM to the position of the target; 1063-6536/02$17"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001735_s0020-7683(01)00198-6-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001735_s0020-7683(01)00198-6-Figure1-1.png",
        "caption": "Fig. 1. Flat punch with square edge and rounding.",
        "texts": [
            " The pressure and the Muskhelishvili potential of the latter have the form p\u00f0a; x\u00de \u00bc Z a s\u00bcx p0\u00f0s\u00deds p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x\u00f0s x\u00de p ; /p\u00f0a;w\u00de \u00bc Z a s\u00bc0 ip0\u00f0s\u00deds 2p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi w\u00f0w s\u00de p : \u00f06\u00de Eq. (6) shows that the integrand of the pressure has a weak singularity at x \u00bc s, which can easily be integrated. Further, the pressure has a singularity of the order x 1=2 at x \u00bc 0. The displacement at the point x ! 0 of the elastic plane has a vertical slope, which requires a square edge at the origin (Fig. 1). The contact condition for a punch with the profile z1\u00f0x\u00de is illustrated in Fig. 1 uz\u00f0a; x\u00de \u00bc uz\u00f0a; 0\u00de z1\u00f0x\u00de; for x6 a; contact > uz\u00f0a; 0\u00de z1\u00f0x\u00de; for xP a; separation \u00f07\u00de Superposition of displacements (4) and insertion in Eq. (7) gives an integral equation for the differential forces p0\u00f0s\u00de z1\u00f0x\u00de \u00bc A p Z x s\u00bc0 p0\u00f0s\u00de ln 2x s s 0 @ \u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f02x s\u00de2 s2 1 s 1 Ads; 06 x6 a: \u00f08\u00de oz1\u00f0x\u00de ox \u00bc A p Z x s\u00bc0 p0\u00f0s\u00dedsffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x\u00f0x s\u00de p ; 06 x6 a: \u00f09\u00de Eq. (9) is an Abel integral equation and can be inverted p0\u00f0s\u00de \u00bc 1 A o os Z s x\u00bc0 ffiffiffiffiffiffiffiffiffiffi x s x r oz ox dx; 06 s6 a: \u00f010\u00de The partial derivative o=os in Eqs",
            " Thus, the validity of Coulomb\u2019s inequalities is a direct consequence of the method of superposition of flat rigid punches. In a series of publications (Ciavarella et al., 1998a,b), a Chebyshev expansion has been used for the Muskhelishvili potential of a symmetric flat rounded punch, and a wedge with rounded tip. This potential is useful for the interior stress field, and a simple analytical solution in closed form is derived below. The mentioned publications have been discussed in J\u20acager (1999b, 2001a). For the special case of a singular flat punch with a rounded edge (Fig. 1), which has a square edge at the origin and a rounding at the other contact end, the gap z1\u00f0r\u00de between the surfaces in undeformed contact has the form z1\u00f0x\u00de \u00bc H x b \u00f0x b\u00de2 2Rc ; for 06 x6 a; H\u00f0x\u00de \u00bc 0; x < 1 1; xP 1 \u00f014\u00de Insertion of Eq. (14) in Eq. (10) gives 2ARcp0\u00f0s\u00de \u00bc H s b 3 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b\u00f0s b\u00de p( \u00fe \u00f03s 2b\u00de arccos ffiffiffi b s r ) : \u00f015\u00de The pressure p\u00f0a; x\u00de in Eq. (6) can be evaluated with Eq. (15) pARcp1\u00f0a; x\u00de \u00bc ffiffiffiffiffiffiffiffiffiffiffi a x x r \u00f0a \" \u00fe 2x 2b\u00de arccos ffiffiffi b a r \u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b\u00f0a b\u00de p # \u00fe \u00f0b x\u00de ln ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b\u00f0a x\u00de p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x\u00f0a b\u00de p 2 a b xj j : \u00f016\u00de The normal force is the integral of differential forces p0\u00f0s\u00de P1\u00f0x\u00de \u00bc Z a s\u00bc0 p0\u00f0s\u00deds \u00bc 2ARc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b\u00f0a b\u00de p 3 2 a ( b \u00fe 3 2 a2 2ba arccos ffiffiffi b a r ) \u00f017\u00de with the coordinates x and z",
            "0 fp ffiffiffiffiffi ax p p1\u00f0a; x\u00deg \u00bc a \u00f0a 2b\u00de arccos ffiffiffiffiffiffiffi b=a p \u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b\u00f0a b\u00de p ; \u00f025\u00de p3\u00f0a; x\u00de \u00bc p1\u00f0a; x\u00de \u00fe p1\u00f0a; a x\u00de p03 pARc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x\u00f0a x\u00de p ; \u00f026\u00de /p3\u00f0a;w\u00de \u00bc /p1\u00f0a;w\u00de /p1\u00f0a; a w\u00de ip03 2pARc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi w\u00f0w a\u00de p : \u00f027\u00de Numerical comparison shows that Eq. (26) is identical with Schubert\u2019s formula (20) and (21) in Schubert (1942). The solutions (26) and (27) for a symmetric flat rounded punch (Fig. 3) have been derived with an alternative symmetric superposition method in J\u20acager (2001b). A non-symmetric superposition of two punches with the flat regions b1 and b2 in Fig. 1 is straightforward, i.e. the limit p xp1\u00f0a; b1; x\u00de for x ! 0 must be identical with the limit p\u00f0a x\u00dep1\u00f0a; b2; a x\u00de for x ! a. This gives a non-linear equation for b2 and b1, as a function of the contact length a, such that a flat punch with two square edges (3) can be subtracted. It is necessary that the punches have complete contact on the whole contact area and that both singularities are equivalent. The resulting punch of this superposition has a flat region of the length b \u00bc b1 \u00fe b2 a, such that the dependent variables b1 and b2 can be eliminated for a given contact length a"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000227_s0167-8922(98)80083-7-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000227_s0167-8922(98)80083-7-Figure2-1.png",
        "caption": "Figure 2. Idealised bi-Gaussian roughness height distribution (horizontal axis on a",
        "texts": [
            " The location of the knee-point on the scaled bearing fraction curve indicates an effective truncation depth. cumulative normal distribution scale) The following quantitative treatment expands on the descriptive work of Malburg and Raja [18]. The hi-linear form of the scaled bearing fraction curve obtained from profilometry on specimens prepared by The development of a simplified mathematical description of worn surface topography, is facilitated by referring to an idealised representation of a typical bi-!inear scaled bearing fraction curve (Fig. 2). Each straight line segment may be considered as representing part of a normal distribution. Each such distribution is characterised by its standard deviation and its mean. The standard deviation is given by the magnitude of the= gradient of the relevant line segment, whilst the mean is the height value at which the straight line segment crosses the 50% (or zero) line. It is convenient to define the datum plane for the surface at the mean of the \"upper\" ordinate height distribution. One may also obtain the mean, <z~>, of the lower, large-scale roughness along with the height, zk, of the knee-point in the curve"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003897_cdc.2005.1583096-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003897_cdc.2005.1583096-Figure1-1.png",
        "caption": "Fig. 1. PVTOL aircraft.",
        "texts": [
            " Using standard aeronautic conventions the equations of motion are given by y\u0308 = u1 sin \u03d5 \u2212 \u03b5u2 cos \u03d5, z\u0308 = \u2212u1 cos \u03d5 \u2212 \u03b5u2 sin \u03d5 + g, \u03d5\u0308 = u2. (1) The aircraft state is given by the position (y, z) of the center of gravity, the roll angle \u03d5 and the respective velocities y\u0307, z\u0307 and \u03d5\u0307. The control inputs u1 and u2 are respectively the vertical thrust force and the rolling moment. The rolling moment u2 generates also a lateral force because the lift forces are not perpendicular to the wings, \u03b5 is the coupling coefficient. Finally g is the acceleration of gravity. In fig. 1 the PVTOL aircraft with the reference system and the inputs is shown. If in system (1) we pose \u03b5 = 0, we obtain the equation of a simplified model with no coupling between rolling moment and lateral force. This is a desired condition from a pilot perspective, because it allows to tackle two different control tasks with decoupled inputs, i.e. thrust for the altitude control and roll moment for the direction. The simplified system can be exactly linearized (with no zero dynamics) introducing u1 and u\u03071 as new states and 0-7803-9568-9/05/$20"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000909_tsmc.1995.7102305-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000909_tsmc.1995.7102305-Figure4-1.png",
        "caption": "Fig. 4. Contour map for /NEC (solid) and /SUF (dashed) for m's typical of those determined from numerical technique. Function have common 0-contours over appreciable range, but case is not conservative.",
        "texts": [
            " A few cases fail to converge to an answer in a preset number of iterations and are discarded. In the rest of the trials, the procedure converges and tangent 0-value level curves of /NEC and /SUF are found but they are not conservative cases. These trials show that the 0-value level curves of both functions either thread through the nodes vertically as does case b', or horizontally as does case a', or diagonally as does case c'. Except when the results are those of (27), in no case do /NEC and /SUF thread the nodes in a consistent way. For example, in Fig. 4 the two functions have a common 0-value level curve over an appreciable range, yet because one function threads the nodes vertically and the other horizontally, they cannot be further perturbed into a conservative case. Fig. 5 shows a case where both curves thread the nodes vertically but the curves are tangent where the one curve is reversed, so again the curves cannot be adjusted to a conservative case. In all cases examined these types of mismatches in pattern occur. The conclusion of our numerical search is that there are no conservative solutions except for the very limited form of M that generates the same locked joint configurations as shown by Shamir and Yomdin"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000956_iros.1994.407471-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000956_iros.1994.407471-Figure2-1.png",
        "caption": "Fig. 2 Model of non-holonomic vehicle with camera Fig. 3 Model of camera system",
        "texts": [
            " Then we present how to construct control input based on the visual servoing concept. Finally results of computer simulation are shown to discuss of the effectiveness of our method. Moreover we apply the method to our actual experimental system. 2 Modeling In this section, we present kinematic models of the vehicle and the camera system. 2.1 Vehicle Kinematics Suppose that the vehicle can move only on a 2D plane and that its configuration is described in position (z ,y) and orientation 8 as shown in Fig. 2. The motion of vehicle is controlled by the linear velocity V and the angular velocity Cl. In this paper these velocities are assumed to track a command perfectly. The non-holonomic kinematics of the vehicle is represented as Suppose that a camera is mounted on the vehicle with offset 2 away from the center of vehicle and can rotate about the vertical axis which goes through the center of lense. For simplicity the optical axis is assumed to be on horizontal plane. The configuration of camera in the world coordinate frame (5 ti 0) is expressed by - = z+zcose g - = y+zsine (2) e = @ + P where p is the pan angle of the camera relative to the centerline of vehicle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002464_bf03258690-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002464_bf03258690-Figure1-1.png",
        "caption": "Figure 1. Original USBM induction slag crucible.s",
        "texts": [
            " In addition, other promising methods for titanium and zirconium melting, such as Rototrode, electron beam, and plasma arc melting, have high power requirements and capital costS.4 Recent technology addresses some of the factors which make titanium and zirconium expensive to manufacture. A significant technological break through was made by the UB. Bureau of Mines (USBM)5,6 with the development of the \"InductionSlag\"* melting process. USBM INDUCTION SLAG PROCESS Induction-slag melting was developed by USBM, Albany, Oregon, in the 1970sas a technique which permitted unalloyed titanium to be induction melted. Figure 1 shows USBM's original induction-slag crucible assembly. This assembly consists of four hollow copper quadrants brazed to a copper baseplate. Both the quadrants and baseplate contain internal passageways for cooling water. In addition, a high temperature refractory cement is packed between the quadrants. This crucible is installed in a vacuum furnace chamber, and an induction coil circles the OD of the crucible. This initial design could melt about eight pounds (3.6 kg) of titanium. For melting, a titanium or zirconium charge is placed in the crucible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002730_tmag.1987.1065248-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002730_tmag.1987.1065248-Figure3-1.png",
        "caption": "Figure 3 Flux density waveforms with peak values of 1.5 Tesla when 10% third harmonic flux",
        "texts": [
            " There is a great similarity between these two materials and several others tested showing that the deterioration factor was virtually independent of composition or texture over the range of non-oriented full processed and unannealed materials investigated. Increasing the percentage of harmonic flux 0-90\u00b0 out of phase with the fundamental component increases the D.F. The greatest increase occurs when the 3rd harmonic is in phase with 0018-9464/87/0900-3217$01.0001987 IEEE 3218 the fundamental. At high phase differences there is a reduction in loss shown up as a D.F. less than unity. This occurs because to maintain constant peak flux as the phase angle increases the fundamental component must be reduced. Figure 3 illustrates this point by reference to the harmonic content of two waveforms each with a peak value of 1.5T. In the one case the fundamental component is 1.66T and in the other case it is 1.36T so the effect of the first harmonic in the waveform would be very different in each case. As the magnitude of the harmonic component increases, the fundamental must again be reduced but the loss attributable to the increasing 3rd harmonic has a far larger effect on the total loss. 100 9; OF drd. HARMONIC FLUX",
            " The deterioration of iron loss due to 3rd harmonic distortion in the 3% silicon iron material is shown in Figure 4. The minor loop limit indicates the conditions under which minor loops would start to become present in the B-H loop of the material under test. This condition would cause some measuring problems so the region was avoided. The rapidly increasing effect of the 3rd harmonic flux is particularly noticeable when it was close to being in phase with the fundamental as would be expected from consideration of Figure 3. The effect of this phase angle on the total loss of a non-oriented sample magnetised at 1.5T, 50Hz is shown in Figure 5. Figure 6 shows the actual loss in non-oriented 3% silicon iron magnetised at 1.OT with the 3rd harmonic 40' and 180' out of phase with the fundamental component. The more harmful effect of the lower phase difference is clearly visible. Table 1 summarises the variation of deterioration factors of the fundamental and third harmonic components of loss in a range of materials at l"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003831_tnb.2005.850476-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003831_tnb.2005.850476-Figure3-1.png",
        "caption": "Fig. 3. Photograph of the fabricated ring-type interdigitated microelectrodes, the auxiliary electrode, and the reference electrode.",
        "texts": [
            " Second, the baked Shipley 1818 is exposed under UV light (300\u2013460-nm wavelength, 7 mJ/cm ) for 10 s, and consequently is immersed in chlorobenzene for 45 s. After immersion, dry the sample in the 120 C oven for 30 s. Third, the sample is developed for 1 min and dried. Fourth, Ti/Au (100 /1000 ) layer is deposited on the patterned sample surface. Fifth, the deposited sample is dipped into acetone for liftoff. Finally, Ag and AgCl are sequentially electroplated on one Ti/Au electrode using Silver Cy-less solution (Technic, Inc) and 0.1 M KCl solution to form the reference electrode. The fabricated device is shown in Fig. 3. The ring-type IDA nanoelectrodes with 275 pairs of fingers are fabricated using e-beam lithography liftoff technique [23]. PMMA (Microchem, 495 K) with a 300-nm thickness is spin-coated at the oxidized silicon surface, and then the nanopatterns are exposed by e-beam (Raith 150 e-beam lithography system). After the development of the exposed PMMA, Ti/Au (100 /1000 ) layer is deposited on the patterned sample surface, and then the deposited sample is dipped into acetone for liftoff. After the fabrication of the IDA nanoelectrodes, the counter microelectrode (gold) and the reference microelectrode (silver/silver chloride), are further made on the oxidized silicon surface by the optical lithography liftoff technique and electroplating technique as described in the fabrication of the IDA microelectrodes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003750_05698190500225334-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003750_05698190500225334-Figure1-1.png",
        "caption": "Fig. 1\u2014Asperity shape.",
        "texts": [
            " This assumption is valid for low to moderate values of contact pressure, which happens to also be the case when elastic interaction dominates. The statistical values of asperity height distribution and the average asperity summit radius are two important parameters in the representation of a rough surface. The statistical representation of an asperity is a quadratic asperity shape, given by the following equation: y = f (\u03c1) = \u03c12 2\u03b2 [1] where \u03b2 is the average radius of curvature of the peaks as shown in Fig. 1. Two asperities on two mating surfaces are considered: An asperity of height z1 on surface S1 and an asperity of height z2 on surface S2. Figure 2 shows the scenario of two asperities in contact. Figure 2(a) illustrates the case when two asperities just touch, while Fig. 2(b) shows the interference between two asperities. The horizontal distance between the two vertical central lines of the two asperities is defined as the radial distance r , and d denotes the separation of the mean planes of the asperity peaks of the two surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000600_ac0203037-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000600_ac0203037-Figure1-1.png",
        "caption": "Figure 1. (a) Experimental setup for the measurement of the magnetophoretic velocity of a microparticle in liquid under a high-gradient magnetic field. The inhomogeneous magnetic field was generated with a superconducting magnet and two iron pole pieces. (b) Configuration of optical devices and pole pieces. The capillary was inserted between the pole pieces. The pole piece was 5 \u00d7 10 \u00d7 1 mm, and the gap between the two pole pieces was 300 \u00b5m.",
        "texts": [
            " A 10-\u00b5L portion of the equilibrated organic phase was added to 5 mL of the equilibrated aqueous phase and was sonicated for 5 min to prepare organic droplets with a diameter of \u223c4-10 \u00b5m. TTA and TOPO were purchased from Wako Pure Industries (Tokyo, Japan). These were used as received. The water was purified by a Milli-Q system (Millipore, Bedford, U.K.). The concentration of Mn(II) in the equilibrated aqueous phase was determined by an atomic absorption spectrometer (AA-6200, Shimadzu, Kyoto, Japan) to calculate the concentration in the organic phase. Experimental Setup. Figure 1 illustrates the apparatus that was used in this study. The helium-free superconducting magnet (JMTD-10T100HH1, JMT, Japan), which had a room temperature bore of 100-mm diameter and could generate a high magnetic field up to 10 T, was used. The square glass capillary cell (Polymicro Technologies, Phoenix, AZ), which had a 100 \u00d7 100 \u00b5m inner section and a 300 \u00d7 300 \u00b5m outer section, was set between the two iron pole pieces, the sizes of which were 5 \u00d7 10 \u00d7 1 mm. The capillary cell and the pole pieces were fixed to the cell holder that was positioned at the place in the bore where the magnetic field was the most homogeneous and the strongest"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001248_1.2826898-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001248_1.2826898-Figure3-1.png",
        "caption": "Fig. 3 The \"double butterfly\" eight-bar linkage. The linkage has mobility one, but does not possess any four-bar circuits. Like all mobility one eight-bars it has three closures, all of which produce five member circuits.",
        "texts": [
            " Unfortunately this well ordered picture is disrupted both by the situation in which the driving joint is not in the four-bar cell, as discussed above, and by the eight-bar case that does not have a four-bar circuit. It is demonstrated below that this configuration has either 16 or 18 solutions, depending on the choice of driving joint. 390 / Vol. 118, SEPTEMBER 1996 Transactions of the ASME Copyright \u00a9 1996 by ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 06/17/2015 Terms of Use: http://asme.org/terms 2 Geometric Arguments The eight-bar configuration that does not contain any fourbar cells but which has mobility one is shown in Fig. 3. Analysis of the topology of this Unkage indicates that both the joints that connect two ternary members {E and F) are topologically equivalent. Also, all the remaining joints connect one binary and one ternary member. They can also be demonstrated to be topologically equivalent. Thus there are only two choices of driving joint to be considered. It is easily shown that the linkage has 18 possible assembly configurations when driven via joint E. If the value of the joint angle at E is specified, that joint can be regarded as being fixed in that position",
            " The 18 real configurations of a butterfly linkage that is composed of two rhombic four-bars for a specific position of joint E are shown in Figs. 5(a) through S{d). This conclusion, reached above by a purely geometric argu ment, is confirmed below by numerical solution using the poly nomial continuation method. When properly used, this tech nique can be used to find all solutions of a system of polynomial equations of unknown order, and hence can determine the order of the system (Morgan, 1987). The second case, that in which the linkage is driven by a joint connecting a binary and a ternary member, such as joint A in Fig. 3, is not so amenable to geometric solution. However, the polynomial continuation technique indicates that the order of the system is 16 in this case. This solution is also treated below. It should be noted here that the solutions to the second case can be viewed as all the intersections of the coupler curve of a Stephenson-I six bar with a circle. In Fig. 3, if joint A is the driver then the location of link AB is known. The position solution can be treated as the intersections of the coupler curve of the Stephenson-I six bar BCDEHGFK\u2014where K is the cou pler point\u2014with a circle centered at J that has a radius equal to the length of link JK. Coupler curves of six bars have been studied by Primrose et al. (1967) and they have reported that the equation of the Stephenson-I coupler curve is \"circular\" and has a degree of 14. This result seems to suggest that the number of solutions of the problem at hand must be 14 rather than 16",
            " 3 Numerical Solution Here, the position kinematics problem of the butterfly linkage is addressed with respect to the two distinct choices of driving joint as was discussed above. The loop equations are reduced to a set of six quadratics in six unknowns (overall degree of 64) for each of the two cases. Numerical examples are then solved using the continuation technique to solve the resulting polynomial systems, and, in each case, all the solutions to the position kinematics problem are obtained. (a) Joint E as Driving Joint. Referring to Fig. 3, mem ber 3, a triangle comprised of the three edges a^, b^ and c^, is considered to be driven relative to member 1 about joint E. The butterfly linkage consists of three five-bar loops. Therefore, a total of 15 angles, 0, through ^15, have to be identified to deter mine the position of the mechanism. The angle of joint E, 8s, is the input. Given 5\u0302 and the other linkage parameters, the position kinematics problem involves solving for the other four teen di's. The fourteen equations required to solve this are ob tained from the nine loop closure equations (three for each fivebar loop), and the five additional constraints arising from the five joints that are common to two of the three five-bar loops",
            " This implies that the mechanism can have a maximum of eigh teen real solutions when driven by a joint connecting two ternary links. A numerical example is listed below. This example led to eighteen finite solutions, four of which were real. Example 1 The linkage parameters for this example are: a, = 82.0, c, = 75.0, az = 150.0, 03 = 34.0, b^ = 59.0, a^ = 39.0, bn = 48.0, Og = 34.0, b^ = 57.0, /3, = 137.5\u00b0, 77 = 134.0\u00b0, 78 = 120.0\u00b0. The input angle is assumed to be 0^ = 142.0. The eighteen solutions are listed in Table 1. (b) Joint A as Driving Joint. Referring to Fig. 3, joint A connects members 1 and 2. In this analysis, the angle of joint A, 01, is the input. The basic loop equations and constraints listed in Eqs. (1) through (14) are also valid for this case. The only difference is that the angle &i, is assumed to be known instead of 0^. Equations (15) through (20) can be directly used here since both the angles 0i and 0s are still present in these equations. The only difference in the present case is that 05 should now be eliminated from Eqs. (15) through (20) instead of ^1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003178_s0022-0728(81)80373-7-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003178_s0022-0728(81)80373-7-Figure4-1.png",
        "caption": "Fig. 4. Percentages of the different sequences as a function of pH. Conditions as in Fig. 3.",
        "texts": [
            " Let us first consider the four-member square scheme at pH 1, when pKa~\" = 2, and pKa2 ---- 12 (Fig. 2). With the help of the equations derived above, we can calculate the percentages indicated in Fig. 3, for example for ke~ -- ke2. We deduce from this graph that we have 9.1% of the sequence A - A H + - A H \" (H+e) and 90.9% of the sequence AH + -AH\" (e). If we carry out the same analysis at different pH values (Table 1), we see that there is no ambiguity as to the reaction sequences, which are shown in Fig. 4. The situation becomes more complex when the interval between pKa~ and pK~ is smaller. If, for example, pKaj = 5 and pK~ = 9, there is no ambiguity for pH < 3.5 or pH > 10.5 (again for kel ---- ke2 ) (Table 2). However, at pH 6, for example, the percentages are those indicated in Fig. 5. This scheme can be interpreted by saying that we have 9% of a A-A~-AH\" (ell +) sequence, 82% of a A - A H + - A H \" (H+e) sequence and 9% of the A H + - A H \" (e) sequence. There is, however, an infinity of other conceivable arrangements, such as 9% for the path A H + - A - A ~ - A H \" ( - H + e H ) and 91% for the path A - A H + - A H \" (H + e) or 5% for AH + -AH\" (e), 4% for AH +-A-A~-AH\" ( - H + eH +), 86% for A - A H + - A H \" (H+e) and 5% for A-A~-AH\" (ell+)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001935_63.136258-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001935_63.136258-Figure4-1.png",
        "caption": "Fig. 4. (a) Loci of U and U* and error vector E. (b) Definition of r-6 coordinate.",
        "texts": [
            " As U corresponds to a stator flux vector when induction motors are driven, the method is also referred to as flux-controlled PWM in many reports [4]-[6]. A typical vector locus when the quasi-circular locus method is employed is illustrated in Fig. 3, where $ denotes the phase angle of the output voltage and \u201c0\u201d mark indicates that a zero vector is output. The selection of V, and adjustment of its time width are conducted at every sampling interval, AT(samp1ing angle A$ = w A Tin Fig. 3). One sampling interval is enlarged in Fig. 4(a), where the dotted curve shows the U* locus and the solid line shows the U locus. The U locus is adjusted so that U co- 0885-8993192$03.00 0 1992 IEEE I IWAJI AND FUKUDA: A PULSE FREQUENCY MODULATED PWM INVERTER ~ 405 80C196 U Fig. 2. Seven kinds of voltage vectors. Fig. 3 . Quasi-circular locus method incides with U* at the beginning (point P ) and end (point Q) instants of every sampling interval. In the A T period, one zero vector, V7, and two nonzero vectors, VI and Vz, are used as shown in the figure. B. Performance Index Introduce the error vector as E = U - U*. (4) If E is represented in the r-4 coordinate, which rotates with the reference vector U* [4]-[6] as shown in Fig. 4 , it is resolved into two perpendicular components: E = E , + jc,. ( 5 ) Define the performance index for the mth sampling period as to + A T 10 + A T Jm = IEI2dt = j ( E ; + E ; ) dt IO 0 = J,, + Jm,. (6) Then the total performance index is obtained by integrating Jm over a complete cycle as pNAT N J = J (EI2dt = C J,,, m = I N = (Jmr + Jm,) = J , + J,. (7) m = l J corresponds to the distortion factor of the output current [ 11 or the loss factor that represents the amount of copper loss [8] and has a close correlation to magnetic noises of driven motors [2], [6]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002201_j.triboint.2004.07.025-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002201_j.triboint.2004.07.025-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of two contact rollers.",
        "texts": [
            " But if the working frequency becomes higher, sliding velocity will occur. In automotives, the one way clutch in electric generator moves with very high sliding speed and small rolling speed, so the slide\u2013 roll ratio is nearly 2. In this paper, however, the tribo- characteristics are mainly discussed using the results obtained under condition where the slide\u2013roll ratio equals to 1.0, though the results of slide\u2013roll ratios 0, 1.0, and 2.0 are compared. Two infinitely long steel rollers in slide\u2013roll motion are shown in Fig. 1. The reciprocating motion is given by oscillating the two rollers sinusoidally about their shafts oa and ob. The oscillating angles of the two rollers are ha and hb, respectively. The equivalent radius of curvature is defined as 1 R \u00bc 1 Ra \u00fe 1 Rb \u00f01\u00de The velocities of the two surfaces are ua \u00bc Lxsin\u00f0xt\u00de=2 ub \u00bc DsLxsin\u00f0xt\u00de=6 \u00f02\u00de where Ds is a switch which changes according to slide\u2013 roll ratio Ds \u00bc 3:0\u00f0R \u00bc 0\u00de 1:0\u00f0R \u00bc 1:0\u00de 0\u00f0R \u00bc 2:0\u00de 8< : \u00f03\u00de For such a TEHL line contact problem, a general- ized Reynolds equation proposed by Yang and Wen [20] is adopted @ @x q g e h3 @p @x \u00bc 6ua @\u00f0~qah\u00de @x \u00fe 6ub @\u00f0~qbh\u00de @x \u00fe 12 @\u00f0qeh\u00de @t \u00f04\u00de where \u00f0q=g\u00dee \u00bc 12\u00f0geq0 e=g 0 e q00 e \u00de; ~qa \u00bc 2\u00f0qe q0 ege\u00de; ~qb \u00bc 2q0 ege qe \u00bc \u00f01=h\u00de \u00f0h 0 q dz; q0 e \u00bc \u00f01=h2\u00de \u00f0h 0 q \u00f0z 0 1=g dz0 dz; q00 e \u00bc \u00f01=h3\u00de \u00f0h 0 q \u00f0z 0 z0=g dz0 dz ge \u00bc h= \u00f0h 0 1=g dz; g0e \u00bc h2 \u00f0h 0 z=g dz In the above expressions, g is an equivalent viscosity for the Ree\u2013Eyring flow model used in the analysis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001563_a:1008185917537-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001563_a:1008185917537-Figure2-1.png",
        "caption": "Figure 2. Model for active dual-wheel caster with offset.",
        "texts": [
            " However, it is not necessary that the wheel mechanism utilized for the robot has a holonomic property. We first consider the conventional two-independent driving wheel mechanism as shown in Figure 1. In this mechanism, only the forward velocity Vx can be generated instantaneously, but the side velocity in the center of the steering axis can not be induced, because the steering axis is arranged in the center of its axle. It is obvious that this mechanism has only one-degree of freedom motion ability. Figure 2 shows the active dual-wheel caster assembly mechanism with offset steering axis used in this study. This mechanism can generate not only the forward velocity Vx in the center of steering axis, but also the side velocity Vy caused by the angular velocity difference of the left- and right-wheels, because the passive steering axis is arranged in the front of the axle. It is clear that this mechanism has two-degrees of freedom motion ability. Now, we consider the difference between the single-wheel caster mechanism proposed by Wada et al",
            " For the single-wheel caster depicted in the left-hand side of the figure, the forward velocity Vx is generated directly by the wheel rotation and the side velocity Vy is induced directly by the rotational torque caused by the driving motor arranged on the steering axis. On the other hand, for the dual-wheel caster, the forward velocity Vx is generated by an averaged translational velocity of the left- and right-wheels and the side velocity Vy is induced by the rotational torque caused by the angular velocity difference of the left- and right-wheels. Now we consider the model of active dual-wheel caster shown in Figure 2. It is assumed that the absolute coordinate system (O0,X0, Y0) as a movement space of dual-wheel caster is fixed in the plane and that the moving coordinate system (On,Xn, Yn) is fixed on the steering center of dual-wheel caster. Here, the Xn-coordinate is set so that it has the same direction as the front of the axle. Let \u03c60 denote the angle between X0- and Xn-coordinates, and the position vector of steering axis with respect to the absolute coordinate system be defined as s0 = [x0 y0]T. When defining the state variable for the dual-wheel caster as x0 = [x0 y0]T and the input variable as u0 = [\u03c9l \u03c9r]T, the kinematic model of the dual-wheel caster is given by x\u03070 = B0u0, (1) \u03c6\u03070 = r b (\u03c9r \u2212 \u03c9l), (2) where \u03c9l and \u03c9r are the angular velocities of the left- and right-wheels toward direction of the vector x\u03070, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001528_ias.1998.732256-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001528_ias.1998.732256-Figure1-1.png",
        "caption": "Fig. 1 Stationary and synchronous frames.",
        "texts": [
            " A table of slot torque ripple compensating currents with respect to rotor position has been developed off-line [6] and used in the controller. This on- and off-line combination of torque ripple minimization technique has a good balance between real-time calculation and operating performance. The effect of parameter variation on deadbeat controller perfommnce and torque ripple minimization is studied by simulation. 11. PMSM MODEL A PMSM can be conventionally modeled in the stationary (ap) and synchronous(dq) reference frames as shown in the Fig. 1. The abc and ap reference frames are fixed in stator. Abc windings have 120 degrees spatial angle differences. The a-axis is in line with the a-phase and p-axis leads a-axis by 90 degrees of spatial angle. The dq reference frame is locked with rotor. The d-axis is aligned to the magnet flux direction and q-axis lags the d-axis by 90 degrees of spatial angle. The rotor position is used to regulate the stator currents so that the 0-7803-4943-1/98/$10.00 0 1998 IEEE 35 current frequency is always in synchronism with the rotor",
            " (Dotted line is real k, ), (b) q aitis current error, and (c) d axis current error. response of the torque constant. Figs. 9b and 9c show the current errors between the reference model and the motor. The ripples in d-axis current error caused the ripples in resistance estimation. 5.2 Torque ripple minimization: The phase back-emf in a PMSM is not sinusoidal in nature. Fig. 10a shows the simulated slot torque ripple for the 23 slots in the stator of a PMSM with non-ideal rotor flux distribution. The a-phase back-enlfat 10 rads and rated torque is shown in Fig. lob. Fig. 1 l a shows the speed response with the rotor flux torque ripple minimization after 0.6 seconds. Before 0.6 seconds, the torque coinstant and the stator resistance are detuned to 130% of their off-line measurements. The stator winding inductance is, however, accurately modeled. The reference speed is 10 rads. Fig.llb shows the slot ripple minimization effect. Fig.12a shows the speed response when both the rotor flux ripple and slot ripple are compensated after 0.6 seconds. As in the previous case, the torque constant and the stator resistance are 130% detuned of their off-line nieasurenients before 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002639_s0263574700003611-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002639_s0263574700003611-Figure3-1.png",
        "caption": "Fig. 3. Simplified transmission.",
        "texts": [
            " Another approach is possible: we neglect the deformations of some elements. For instance, if the torsion of shaft 1 is neglected then qm = q\", and the sum of equations (4) and (5) will describe the dynamics of the motor-reducer assembly: + Jr)qm = CMi - Prw/N - Bcq m (16) The joint index \"/\" is omitted. In this way the number of generalized coordinates is reduced by one. 3. SIMPLIFIED MATRIX MODEL Let us make the following simplifications. The transmission in joint \"j\", j = 1, . . . , n, consists of the elements shown in Figure 3. Shaft 1 is considered Elastic transmissions 65 rigid {qf = q\") and hence the effective reducer inertia is added to the rotor inertia. Shaft 3 is also rigid and the inertia of the pair of gears can be added to that of the segment. Thus, the torsion is concentrated in the reducer and shaft 2. Let Kj and dy be the equivalent torsion and damping constants for these two elements. The dynamics of the motor is described by (3) and (16). Since the shaft 3 is rigid, then qf/nt- = q, and Pf = Pj. Equation (9) now becomes i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002427_50009-5-Figure7.38-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002427_50009-5-Figure7.38-1.png",
        "caption": "FIGURE 7.38 (a) The magnetic polarization v e c t o r Jp can be made to describe a circular locus at constant angular velocity dOi/dt in a non-isotropic lamination by applying a suitable rotating field H0(t) whose modulus and angular velocity can be determined as a function of time by means of 2D digital feedback. (b) Twophase and three-phase exciting fields provide the same rotational fields when they are related by Eq. (7.44).",
        "texts": [
            " Under normal conditions, coupling between Jy(t) and Jx(t) should be taken into account. One way to do so is by introducing in the iterative algorithms used for the generation of the suitable supply currents ix(t) and iy(t), the experimental relationships Jy(t)--f(iy(t), ix(t)) and Jx(t)=f(iy(t), ix(t)), which can be approximately obtained by an initial testing essay with sinusoidal 90 ~ phase shifted voltages impressed at the input of the magnetizing circuit [7.125]. actually be carried out in the following way. Let us consider, as in Fig. 7.38a, the polarization vector Jp, which is to be set in rotation at constant angular velocity dOI/dt, describing a circular locus of radius Jp. If at the start a uniformly rotating field of modulus Ha is applied by generating the sinusoidal field components Hay(t) = Ha cos 2vrft and Hax(t) = Ha sin 2\"rrft, a vector Ja(t) will be obtained. This will not describe, as eventually required, a circular locus at constant speed. The deviation from the ideal behavior will depend on the degree of magnetic anisotropy and the value of the demagnetizing coefficient of the employed specimen. At a given instant of time, the relationship between field and polarization can be represented as shown in Fig. 7.38a, where the actual polarization Ja differs from the desired polarization Jp by the error vector &J. In order to remove this error, the field H0 = Ha q- AH should be applied. We can arrive at it by iteration, where the correction term &H is progressively updated through increasingly better information on the Jp(Ha) relationship. After a first essay with the circular field Ha, the values taken by Jy(0j), Jx(0j), Hay(0j), and Hax(~) in correspondence with a reasonably high number N of equispaced angles 0j, distributed over the whole period, are calculated and stored",
            " In addition, no special difficulties arise on passing from circular to elliptical loci. The foregoing discussion has considered a two-phase system, but it has been noted that three-phase setups might sometimes be preferred for 2D testing of highly anisotropic laminations. This only implies a transformation of the computed field components Hay(t) and Hax(t) in the equivalent triplet Hi(t) = Hay(t)~1.5; H2(t) = I-I~x(t)/x/3- Hay(t)~3; (7.44) H3(t) = -Hax( t ) /~ /3 - Hay(t)/3 as schematically shown in Fig. 7.38b, and in the corresponding threephase currents i 1 (t),/2(t), and/3(t). It should be stressed again that we do not directly drive these currents, but we supply the voltages UG: (t), UG2(t), and UG3(t) (Fig. 7.39). We can relate currents and voltages by writing, for each supply channel, the primary circuit equation. We take into account in this equation that the inductance of the magnetizing yoke Ly is normally very large and very little influenced by the presence of the test specimen. It is also constant because the yoke is always kept far from saturation and is affected by a large demagnetizing coefficient, and we can reasonably assume that supply current and field in the gap are proportional"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001056_robot.1998.680759-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001056_robot.1998.680759-Figure1-1.png",
        "caption": "Figure 1: A planar 3-finger grasp on a polygon (a) and the friction sector (b).",
        "texts": [
            " The combination nuniber is clearly reduced to 0 ( N 3 ) . It, should be noted that the combination number is also O ( n 2 ) since N = 2n. 4 Computing All Force-Closure This section addresses a more challenging problem of computing all n - h g e r force-closure grasps on a polygonal object. Suppose that the object\u2019s sides to be grasped by the fingers have been specified. The cases are also considered when multiple fingers are located on same side. Suppose that finger i is in a contact with a side AB (Figure 1). Denote the position vector of the endpoint, A by ri and the direct,ion vector of the side by vect,or s i , To represent the grasp point p; on the side, a scalar parameter ui is introduced so that pi = ri + siu;. 0 5; U ; 5 la where l i denotes the length of the side AB. The n parameters 7 ~ i define ail n-dimensional space. The two primitive contact, wrenches at the contact point are represented by Grasps ( 5 ) (6) The parameter ui is constrained by It should be not,ed t,hat ,the moment, depends linearly on thc pararnet,er 71,i and the forces are con"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002509_j.jfranklin.2004.12.001-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002509_j.jfranklin.2004.12.001-Figure1-1.png",
        "caption": "Fig. 1. Kinematical scheme of DDArm manipulator.",
        "texts": [
            " The DDArm is characterized by the following set of manipulator parameters [15]: * link masses: m1 \u00bc 19:67 kg;m2 \u00bc 53:01 kg;m3 \u00bc 67:13kg; * link inertias: Jxx1 \u00bc 0:1825kgm2; Jxx2 \u00bc 3:8384kgm2; Jxx3 \u00bc 23:1568kgm2; Jxy1 \u00bc Jxy2 \u00bc Jxy3 \u00bc 0 kgm2; Jxz1 \u00bc 0:0166kgm2; Jxz2 \u00bc 0 kgm2; Jxz3 \u00bc 0:3145kgm2; Jyy1 \u00bc 0:4560kgm2; Jyy2 \u00bc 3:6062kgm2; Jyy3 \u00bc 20:4472kgm2; Jyz1 \u00bc 0 kgm2; Jyz2 \u00bc 0:0709kgm2; Jyz3 \u00bc 1:2948kgm2; Jzz1 \u00bc 0:3900kgm2; Jzz2 \u00bc 0:6807kgm2; Jzz3 \u00bc 0:7418kgm2; *distance: axis of rotation\u2014mass center: px1 \u00bc 0:0158m; py2 \u00bc 0:0643m; py3 \u00bc 0:0362m; pz1 \u00bc 0:0166m; pz2 \u00bc 0:1480m; pz3 \u00bc 0:5337m; * length of link: l2 \u00bc 0:462m; * angle a: a1 \u00bc a2 \u00bc 90 ; a3 \u00bc 0 : The kinematic scheme is shown in Fig. 1. The following fifth-order polynomial was chosen for tracking: initial points yi1 \u00bc 7=6 p\u00bdrad ; yi2 \u00bc 269:1=180 p\u00bdrad ; yi3 \u00bc 5=9 p\u00bdrad ; and final points yf 1 \u00bc 2=9 p\u00bdrad ; yf 2 \u00bc 19:1=180 p\u00bdrad ; yf 3 \u00bc 5=6 p\u00bdrad ; with time duration tf \u00bc 1:3\u00bds : The maximal value of joint velocity is j_ykmaxj \u00bc 6:2933\u00bdrad=s for each link, and the maximal acceleration j\u20acykmaxj \u00bc 14:9063\u00bdrad=s2 ; k \u00bc 1; 2; 3: Starting points were different from initial points D \u00bc \u00fe0:2;\u00fe0:2;\u00fe0:2; respectively. All simulations (realized in MATLAB/SIMULINK environment) were performed using the fourthorder Runge\u2013Kutta formula with a fixed step size of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002444_s0080-8784(04)80016-4-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002444_s0080-8784(04)80016-4-Figure4-1.png",
        "caption": "FIG. 4. Block diagram of a FIA system with electrochemical detection using a thin-layer flow cell.",
        "texts": [],
        "surrounding_texts": [
            "Greg M. Swain DEPARTMENT OF CHEMISTRY, MICHIGAN STATE UNIVERSITY, EAST LANSING, MI 48824, USA"
        ]
    },
    {
        "image_filename": "designv11_11_0003631_01.mss.0000230211.60957.2e-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003631_01.mss.0000230211.60957.2e-Figure2-1.png",
        "caption": "FIGURE 2\u2014Angular conventions used for leg angle at touch-down, and hip and knee angle at touch-down and take-off.",
        "texts": [
            " Kinematic variables were then calculated for TD and TO on each step and from TDboard to TOboard. These included center-of-mass height (%HCM), horizontal and vertical velocity at each step, hip angle, knee angle, and leg angle at TD. The height of the center of mass obtained for each athlete was normalized to her estimated height. The hip and knee angles were defined as the included angles between shoulder, hip and knee, and hip, knee, and ankle, respectively. The leg angle was defined as the angle made by the line joining the center of mass and the ankle to the vertical (Fig. 2). The maximum possible error associated with sampling at 50 Hz for each key variable was determined in the following way. Data for three of the athletes were analyzed TABLE 1. Maximum error attributable to sampling frequency used. TDboard TOboard $ HCM (m) $ Horizontal Velocity (mIsj1) $ Vertical Velocity (mIsj1) $ Hip Angle (-) $ Knee Angle (-) $ HCM (m) $ Horizontal Velocity (mIsj1) $ Vertical Velocity (mIsj1) $ Hip Angle (-) $ Knee Angle (-) Athlete 1 TT 0 0 0.1 7 0 0.03 0.1 0 10 2 Athlete 2 TF 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001358_s0094-114x(03)00090-9-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001358_s0094-114x(03)00090-9-Figure9-1.png",
        "caption": "Fig. 9. Assembly modes of the triad with one internal prismatic joint.",
        "texts": [
            " The coefficients of the polynomial equations (36) and (37) are calculated and the extraneous roots are eliminated. The solving of the final sixth order polynomial leads to four real roots and two complex roots (see Table 2) for the input data here considered. For each real value of the displacement s, using back substitution, the coordinates of the internal revolute joints B (see Table 2), C and E are calculated. The corresponding four assembly modes of the triad with one internal prismatic joint are illustrated in Fig. 9. The procedure proposed in Section 4 for the position analysis of the triad with one internal and one external prismatic joint (see Fig. 6) is applied in the third numerical example. The input data of the triad are given in the left part of the Table 3. By solving the sixth order polynomial equation, four real roots and two complex roots are obtained (Table 3). For each real value of the displacement s, the coordinates of the internal revolute joints B (see Table 3) and E are calculated. Finally, the displacement s1 is determined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003096_anie.199010531-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003096_anie.199010531-Figure4-1.png",
        "caption": "Fig. 4. Time course of NADH formation at carbon electrodes modified as described in Figure 3. Electrode surface: 1 cm2 (glassy carbon), potential: - 407 mV vs. NHE, 6 mL oxygen-free catholyte (TRIS/HCI buffer, 0.1 M, pH 7.0); 18 pmol NAD. (a)-(I) as in Fig. 3). Bioluminescence-NADH test: 250 pL potassium phosphate buffer (25 mM, pH 7.0) contained 25 pmol dithiothreitol. 1.25 pg luciferase EC 1.14.14.3.9.5 mU flavin mononucleotide (FMN) oxidoreductase EC 1.6.8.1, 0.6 pmol FMN, 10 pg TRITON X-100, 5 pmol myristinaldehyde, 150 pmol NAD, and 50 pL sample. Apparatus: BIOLUMAT LB 9500T, Berthold, D-7547 Wildbad (FRG).",
        "texts": [
            "r61 By varying the sequence of the immobilization steps for viologen and VAPOR, differently coated electrode surfaces can be prepared (Fig. 3). The electrodes were tested as cathodes in po- tentiostatically-controlled, electrochemical cells as shown in Scheme 1 . All experiments were carried out with strict exclusion of oxygen; anolyte and catholyte were therefore separated by a diaphragm. The initial rate of NADH formation was determined by the bioluminescence method ['I using a calibration curve (Fig. 4). The following conclusions can be drawn: 1) all electrodes without VAPOR (a, b) or without mediator (c, d) show no NADH formation (measured values in the region of that of the blank). 2) Monomolecular layers of VAPOR on a cathode with viologen layer reduce NAD to NADH (e-g). 3) In the case of electrodes modified with DAPV and coated with a multilayer of enzyme (h), the enzyme Layers reachable by the substrate no longer have ample electronic contact with the electrode. 4) If, however, DAPV is covalently incorporated in the enzyme layer in the case of such an electrode, a modified electrode (i) is formed which reduces NAD to biologically active NADH)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000239_02678299508036629-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000239_02678299508036629-Figure4-1.png",
        "caption": "Figure 4. Director orientation angle in rectangular coordinates.",
        "texts": [
            " However, intuitively it is evident that there should be two solutions where the sum of torques is zero. The solution with = 90\" seems to represent the physical situation in capillary flow, and the axial behaviour should be quite similar in channel flow. Therefore, due to the added complexity of this problem, we shall bypass the question of stability and assume that p = 90\", to see if the resulting predicted orientation profile qualitatively matches observed fibre textures. The out-of-plane angle, [, will be allowed to vary with x and y, as shown in figure 4. The director components are as follows: n = sin[(x,y) (34) rsc:l The x-, y- , and z-components of the conservation of linear momentum are (35 ) az, ax, a T x - + __ + __ = 0, ax ay az (37) After evaluation of the viscous stress tensor, the x- and y- components vanish, while the z-component is given by (\"5 avz a t a v j + (a5 - CI') cos(2i) - -+ - ~ ax ay ay ax a2v, + [(as - a2) cos2 [ + a4] - ax? + [(a5 - a') sin' i + a41 - a2vz - 2 (f) = O . (38) ay2 D ow nl oa de d by [ M ic hi ga n St at e U ni ve rs ity ] at 1 7: 57 1 1 Fe br ua ry 2 01 5 Orientation X a ni2 \u2019Y 0 h Figure 5",
            " Partial solutions to problem represented in figure 5. The x-, y-, and z-components of the balance of torques are a 2 i a2[ -+-=o, a 2 ay2 K Z O . (39) The above z-component contains only the angle, [, as a dependent variable. Furthermore, it takes the familiar form of the Laplace equation. Therefore, we only need to specify the appropriate boundary conditions to obtain a solution for [ across the flow field. First, taking advantage of the symmetry of the flow system, we will consider only one quadrant from figure 4. For convenience, we will shift the origin midway along one edge. Examination of the case of flow between infinite parallel plates with an out-of-plane director (directly analogous to capillary flow) indicates that the director should tend to orient parallel to the walls of the channel. This corresponds to a perpendicular alignment of the long molecular axes with respect to the solid boundaries. The formulation of the problem is depicted in figure 5, where the dashes within the flow field represent the long molecular axes (disk edges)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003169_iecon.2003.1280230-FigureI-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003169_iecon.2003.1280230-FigureI-1.png",
        "caption": "Figure I. The conmller and rotor refcrcnce frmcs.",
        "texts": [
            " The equation of motion of the system is 0-7803-7906-3/03/$17.00 02003 IEEE. 1239 where J is the total moment of inertia and T, is the load torque. In sensorless control, the rotor position angle 0, is estimated based on knowledge of the stator current and voltage. The d-axis of the controller's reference frame is fixed to the estimated rotor position angle 0,. Due to estimation errors, there may he a non-zero error angle E = 8, - 0, between the d-axes of the rotor and controller reference frames, as depicted in Fig. I . The proposed control method is a variant of a method previously applied in sensorless control of induction motors [IO]. An ac test signal with rms cment I:d and varying at a low angular frequency w, , i.e., ifd(t) = cos(w,t) (7) is superimposed on the d-component i,\"d of the stator current in the controller's reference frame. In the rotor reference frame, the test signal appears to have both d- and q-components given by icd ( t ) = i$ ( t ) cos E i,(t) = i$(t)sin E (8) The current component iq(t) causes the electromagnetic torque to show a response (9) Combining (6) and (9) and assuming constant load torque, the response in the speed will be Tec(f) = --u$,i:d("
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002301_a:1023275502000-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002301_a:1023275502000-Figure3-1.png",
        "caption": "Figure 3. The snakeboard model.",
        "texts": [
            " The left multiplication of the Lie group G = S 1 on Q, *:G\u00d7Q\u2192 Q, *(a, (\u03b8, r2, r3)) = (a + \u03b8, r2, r3) leaves invariant this mechanical system. The snakeboard. The snakeboard [31, 38] is a variant of the skateboard in which the passive wheel assemblies can pivot freely about a vertical axis. By coupling the twisting of the human torso with the appropriate turning of the wheels (where the turning is controlled by the rider\u2019s foot movement), the rider can generate a snake-like locomotion pattern without having to kick off the ground. A model is shown in Figure 3. We make the simplifying assumption that the front and rear wheel axles move through equal and opposite rotations [6, 39], which eliminates terms in the derivations below and does not affect the essential features of the problem. A momentum wheel rotates about a vertical axis through the center of mass, simulating the motion of a human torso. The position and orientation of the snakeboard is determined by the coordinates of the center of mass (x, y) and its orientation \u03b8 . The shape variables are (\u03c8, \u03c6), so the configuration space is Q = SE(2) \u00d7 S 1 \u00d7 S 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003719_j.cma.2004.07.044-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003719_j.cma.2004.07.044-Figure2-1.png",
        "caption": "Fig. 2 corres",
        "texts": [
            " Note that the remaining compression is uniaxial everywhere, but it is not everywhere in the same direction, therefore it has to be treated separately in the different parts of the domain. The procedure just described corresponds to the Gioia\u2013Ortiz approximation [56]. In the next sections we refine this construction, showing how the remaining uniaxial compression in the orthogonal direction can be relaxed. Uniaxial compression in a flat domain can be relaxed by means of a cylindrical deformation containing smooth fine-scale oscillations, as illustrated in Fig. 2. If the oscillation scale is fine enough, it is possible to insert a small-energy boundary layer to achieve Dirichlet boundary conditions and/or to patch together oscillations with different orientations. To give a precise construction of the oscillatory map we choose a smooth curve c : R ! R2 which is parameterized by arc length (i.e. jc 0j = 1 everywhere) and satisfies c\u00f0t \u00fe 1\u00de \u00bc c\u00f0t\u00de \u00fe 1 0 (see e.g. Fig. 2a). It is easy to see that the function c can be chosen so that the distance from a straight line is controlled by ponding deformation wp. and analogous bounds on the first and second derivatives, much as in the analysis of Euler buckling of compressed rods. Given a period p > 0 to be chosen later, we set wp\u00f0x\u00de \u00bc x1 pc1\u00f0x2=p\u00de pc2\u00f0x2=p\u00de 0 B@ 1 CA; where we assumed for definiteness that the uniaxial compression is in the x2 direction. The resulting deformation is illustrated in Fig. 2b. The map wp achieves on average the uniaxial compression F \u00bc 1 0 0 1 0 0 0 B@ 1 CA in the sense that the average over one period of wp(x) Fx vanishes. In addition, it is crucial that wp has exactly zero stretching energy, i.e. $wp 2 O(2,3) everywhere. Moreover, we have the bounds jwp\u00f0x\u00de Fxj 6 cp 1=2 ; jrwp\u00f0x\u00de F j 6 c 1=2 ; jr2wp\u00f0x\u00dej 6 c 1=2 p : The energy per unit area is proportional to h2 */p 2, and is entirely determined from the bending term in I2D. Such oscillatory maps do not, however, satisfy the affine Dirichlet boundary condition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003264_j.jmatprotec.2004.01.030-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003264_j.jmatprotec.2004.01.030-Figure1-1.png",
        "caption": "Fig. 1. FE meshing model.",
        "texts": [
            " The stiffness excitation and error excitation were computed using an \u201cinhouse\u201d developed analysis system. MCAE software\u2014SDRC I-DEAS was used to analyse the dynamic characteristics by the Lanczos approach. The housing of a speed-increase gearbox is designed to be a casting and it is rather complicated where some stiffing shoulders, bearing holes and holes for bolt connection, etc. are positioned. Before the finite element model is created it is necessary to simplify the actual structure. The finite element model of the gearbox auto-generated using a free meshing method [3] is shown in Fig. 1. There are 176216 tetrahedral solid elements and 62546 nodes altogether in this model. According to vibration theory, gear transmission is simplified as a vibration system with concentrated parameters, 0924-0136/$ \u2013 see front matter \u00a9 2004 Published by Elsevier B.V. doi:10.1016/j.jmatprotec.2004.01.030 shown in Fig. 2 (A: driven gear; B: driven gear). The dynamic differential equation is as follows: mx\u0308+ cx\u0307+ k(t)[x+ xs + e(t)] = ps (1) where m is the equivalent mass matrix, c the damping coefficient matrix, k(t) the gear meshing stiffness matrix, x a dynamic displacement vector, xs a static relative displacement vector, ps a static load vector, and e(t) is a gear integrate error vector",
            " The Lanczos method is a new one and is better than other two procedures. It is a fast procedure and its input requirements for the user are also less. There are some methods for system dynamic response solution in finite element analysis: the mode superposition method, the state space method, immediate integration, etc. In SDRC I-DEAS the mode superposition method is widely used for solving the problem of dynamic response. Constrained modal analysis was carried out for the gearbox for which the finite element model was created (Fig. 1). The first 10 orders of natural frequencies are given in Table 1. The mode superposition method was applied to analyze the dynamic response of the speed-increase gearbox system [7]. Before the analysis, excitation force should be applied to the gear teeth. There are 28 sorts of excitation functions. The first 20 level mode results were selected to initiate the response analysis, so that the vibration response in the time-domain at a random point of the speed-increase gearbox was obtained. The response in the frequency-domain was obtained through FFT analysis by means of which the root-mean square values of displacement, velocity and acceleration were computed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001505_1.1401015-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001505_1.1401015-Figure1-1.png",
        "caption": "Fig. 1 Schematic of noncontacting mechanical face seal",
        "texts": [
            " However, because a closed form solution is not available, the perturbation here is carried one level deeper, and more parameters are being investigated to increase the confidence in drawing meaningful conclusions. The solution technique here is similar to the work by Green and Barnsby @11#. However, the rotor and stator forcing misalignments add a significant change to the formulation of the problem. For completeness some definitions are repeated, but emphasis is given to the steady-state analysis. The kinematics of a mechanical seal having a flexibly mounted stator configuration is shown in Fig. 1. The rotating seal seat ~rotor! is rigidly mounted to the rotating shaft. The flexibly supported seal ring ~stator! is attempting to track the misaligned rotor. The rotor misalignment is represented by a tilt gr measured between the out-normal to its plane and the axis of shaft rotation. Similarly, the stator may have prior to final attachment to the rotor, an initial misalignment, gsi , measured with respect to the axis of shaft rotation. At rest, and with zero pressure differential, the stator is pressed against the rotor by supporting springs",
            " The tilt vector go is the relative misalignment g in the special case when gsl50, so using Eqs. ~1\u20132! gives 152 \u00d5 Vol. 124, JANUARY 2002 rom: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Term gW o5gW sr2gW r . (3) The equations of motion of the flexibly mounted stator are ~see Green and Etsion @9,10#!: I~ g\u0308s2c\u03072gs!5M x (4) I~ c\u0308gs12c\u0307g\u0307s!5M y (5) mZ\u03085FZ , (6) where M x and M y are, respectively, the moments acting on the stator about axes x and y of a coordinate system xyz which whirls at a rate c\u0307 within an inertial system XYZ ~see Fig. 1!. The tilt vector gW s takes place about axis x of the rotating system, positioned by an angle c with respect to the inertial axis X. The moments M x and M y as well as the axial force Fz consist of contributions from both the flexible support and the fluid film. The support moments and force are M sx5Ks~gs cos c2gs!2Dsg\u0307s (7) M sy52Ksgsi sin c2Dsc\u0307gs (8) FsZ52KsZZ2DsZZ\u0307 , (9) where KsZ and DsZ are, respectively, the axial stiffness and damping coefficients of the support. Note here that the term gsi in Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001563_a:1008185917537-Figure16-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001563_a:1008185917537-Figure16-1.png",
        "caption": "Figure 16. Coordinates of 3D joystick.",
        "texts": [
            " Photographs were taken by exposing these trajectories in the experiments. Crank, circular, and sine curve trajectories of the robot are shown in Figure 15. All trajectories were tracked by the translational motion without any rotational motion. These results show that the mobile robot possesses the three-degrees of freedom mobility and the holonomic property. To consider an application of this omnidirectional mobile robot to a powered wheelchair, the experiment controlling the prototype robot was conducted by using a 3D joystick as an input device. As shown in Figure 16, the joystick that can detect the rotational angles of three axes of X,Y , and R (rotation) was used to change the reference velocity of the robot, x\u0307r , according to the output response of the joystick. Here, the maximum input values of the reference velocities were set as |x\u0307r | = 0.05 m/s, |y\u0307r | = 0.05 m/s and |\u03c6\u0307r | = 0.1 rad/s. A simulator was constructed in order to illustrate the effectiveness of this control system using a joystick before proceeding to the experiment by the computer control to the prototype robot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001079_s0020-7683(00)00151-7-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001079_s0020-7683(00)00151-7-Figure2-1.png",
        "caption": "Fig. 2. Experimental apparatus.",
        "texts": [
            " Unless the computed solution agrees with the known boundary conditions at the other end of the membrane z L0 l0; r L0 1 , the initial unknown conditions ~u and ~v are adjusted using the Newton\u00b1Raphson method, and the process is repeated until the assumed initial conditions yield, within speci\u00aeed tolerances, a solution that agrees with the known boundary conditions at the end of the integration interval. Two pairs of aluminium rings were fabricated to hold the two edges of the cylindrical membrane, as shown in Fig. 2a. These two rings are attached to the metal frame shown in Fig. 2b in such a way that the cylindrical membrane can be stretched in the axial direction, as seen in Fig. 3. The membrane is \u00aelled with water through the upper hollow ring. The two rings are connected by a shaft, which can be rotated as a rigid body. The cylindrical membrane used in these experiments is an isotropic, homogeneous rubber membrane of undeformed radius A 1:62 cm and thickness H 0:005 cm. The elastic material constants were obtained comparing the experimental and numerical solutions for the membrane under traction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002713_iros.2004.1389556-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002713_iros.2004.1389556-Figure2-1.png",
        "caption": "Fig. 2. Model of humanoid mba",
        "texts": [],
        "surrounding_texts": [
            "Procoedlngs of 2004 IEEEIRSl Inbmatlonal Conference on Intelligent Robots and Systems September 28 -October 2,2004, Sendal, Japan\nMobile Manipulation of Humanoid Robots -Control Method for CoM Position with External Force-\nTomohito Takubo*, Kenji Inoue*, Kotaro Sakata*, Yasnshi Mae** and Tatsuo Ami* * Department of Systems Innovation Graduate School of Engineering Science, Osaka University\n1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan Department of Human and Artificial\n** Intelligence Systems Faculty of Engineering,University of Fukui 9-1, Bunkyo 3-Chome, Fukui, Fukui 910-8507, Japan\nEmail: takubo@sys.es.osaka-u.ac.jp\nAbshncl-Mobile manipulation control metbod for humanoid robots provides gwd manipulability and stability on manipulation tasks. This method leads whole body motion and locomotion, when Le manipulator tip trajectory is decided. For the dexterous manipulation, the mbot has to cope with L e unexpected forees ading to the bands. By assuming the statical balance, we define the projection of the CoM as \u201dComplement Zem Moment Point(CZMP)\u201d, when the extemal forces ad to the end-elledom. We propose to use the CZMF\u2019 for the modification control of CoM with balancing control. The method is implemented to the mobile manipulation control method and the effectiveness is con6med by the experimental results.\nI. INTRODUCTION Humanoid robots are expected to do some tasks together with or instead of human assistants. If humanoid robots canied out dexterous manipulation as human does, they were used in many places which human lives in. Such human being\u2019s dexterous manipulation have been studied at some laboratories[l], [Z], [31, 141. These studies focus manipulation skill for the industrial manipulator. In recent years, some dynamic simulator are developed and the generated pattems for robots are verified correctly and easily on the simulator[5], 161, (71. There are some study of control method about whole body balancing and d e g coordination considering the stability for humanoid robots using dynamic simulator[8], [91, [lo]. They focus the balancing control for humanoid robots. We consider the dexterous manipulations is important factor for the humanoid robots since it will be used in the human life space such as offices, home, construction industry, transportation industry, etc.\nWe focus manipulation tasks for humanoid robots and suggested some control schemes[ll], [12]. Human works mainly u\u2019sing their arms and their whole body is positioned for dexterous manipulations. According to such a human behavior, we consider humanoid robots should decide body positiodposture and ledarm motions following manipulation tasks. We propose this integrated motion control method as \u201dMobile Manipulation\u201d control. It determines the fwthold which provide good working condition keeping high ability of the arms to perform the tasks and stability based on the ZMP for humanoid robots. This control scheme focus not a locomotion but a manipulation for which the whole body is controlled.\n.\nIn this paper, we deal with an implementation \u201dMobile Manipulation\u201d to the real robot and a balancing control when the external force acts to the end-effectors. There are many programs to experiment on real robot such as unexpected forces occuring from the collision with environments or other objects. Thus, we have to consider states of the robot, sensing the collision and whole body balance. First, we consider a manipulation task based on \u201dMobile Manipulation\u201d for humanoid robots in Section 2. In Section 3, we explain the scheme controlling whole body motion which satisfies stability and the desired motion of the end-effectors. Section 4 explains the ZMP m d c a t i o n controller which guarantees the desired CoM trajectory when the extemal forces acted end-effectors. Dynamic simulations and experiments on real robot IIRp2 show that the proposed methods can cany out the manipulation task with collision of the object in Section 5 .\n0 -7803446~04$20 .00 WOO4 IEEE 1180",
            "11. MOBILE MANIPULATION CONTROL FOR HUMANOID ROBOTS\nIn this section, we explain \"Mobile Manipulation\" control scheme for humanoid robots. The \"Mobile Manipulation\" control decides the next foothold considering the band motion, orientation, manipulability and stability of the humanoid robot. Fig. 1 shows the concept of the control scheme. The \"Mobile Manipulation\" control outline is described as follows.\n1) The manipulator tip positions and postures are given by desired trajectory for performing an objective manipulation task with two hands. 2) An evaluation function consisting of manipulability of the arm and stability of the whole body is defined. Stability is evaluated using static zero moment point. Humanoid robot satisfies the desired motion of the manipulator as well as its balance constraints. 3) If the new double legs support state is better than that of the current one, the robot begins to step. 4) In the both of single leg and double legs support state, the robot controls its whole body to optimize the evaluation.\nWe define the evaluation function for the robot judges whether it steps or not as follow.\n(1) K, U, = (r. - r d T T ( r s - r s d )\nwhere rB E R3 is current shoulder position, E R3 is desired shoulder position and K, E R3y3 is the coefficient matrix which bas fixed positive number; U, is to be minimized. We use the shoulder position, without using the manipulability measure for the evaluation. The desired rad calculated by\n(2)\nwhere red is desired manipulator tip position and lesd is desired position of the shoulder from the manipulator tip. Considering the rsd and red. the next foothold is calculated. The definition of the foothold in a horizontal plane is described in detail in our previous study[ll].\nIn this method, we only direct manipulator tip position or velocity, the locomotion and whole body motion are controlled automatically in consideration of the stability and manipulability, and the application will he used in various fields of the work using hands, such as reaching operation to subjects.\n111. WHOLE BODY MOTION GENERATION To control a humanoid robot that has the same sue as a human for the various tasks of manipulator and the whole body motions, we should control each joints considering each body parameters. Using the robot parameters, we can control the each joints considering the whole body momentum and angular momentum by the momentum control scheme[l3].\nNow, we describe a method of generating stable whole body motions which satisfy the desired trajectory of the manipulator tip positions. C B , C F ~ , C E ~ (2=1,2) are defined as the frame fixed on the body, feet and end-effectors respectivelypig.\nrsd = red - l ead\n2). The humanoid robot has 30 DOE which includes two manipulators with 6 DOF, two legs with 6 DOF, a waist with 2 DOF, a bead with 2 DOF and two fingers with 1 DOE T B ,\na ~ , r F i . am. rEi, a ~ i ( =1,2) are the position and angular vector from world frame Cw to each frame origin. When O F $ , BE, (k1.2) are the each leg and manipulator joint angles, the velocity of the each frame origin are calculated by\n( tF' ) = ( E O E ) ( 2 ) + J ~ i d p ~ , (3) a F i\nwhere E is indentity matrix, JF~, J E ~ (k1.2) are Jacobian matrix for each legs and arms, rBFi,rBEi are the vector from the origin of the body frameCB to the origin of each frame. is an operator as cross product. When the desired velocities of the body frame are known, the target joint angular velocities for which the manipulator tip pursues a desired trajectory in the world frame are calculated as follow.\nOFi = JFf [ ( iFi ) - ( E -iBFi ) ( 6 )} (5)\nbm=J&:{( a E i !E' ) - ( E -iBEi ) ( !& )} (6)\n&Fi O E\nwhere J-' denote the generalized inverse of the Jacobian matrix. The linear momentum P and angular momentum L of the whole mechanism can be given by\nWe define 0 has 26 DOF including two arms, two legs and waist joints. M, H are the inertia matrices of which joint velocity affects the total h e a r momentum and angular momentum of the robot. With (3),(4) and (7) equations, we can calculate the velocities of the body frame ig, &B and",
            "(i)\n(:) =\nthe joints velocities of the waist joints 8, that realize the reference momentum, P,,?, L,f and the reference velocities for the controlled legs and arms +pt. &pir +E;, &E; (k1.2) as the least square solution by\n= A'S( ( )\nrBsub\nBWsub\nRg. 3. Simple model with ertemal force to the manipulator, +(E-AfA) ( OBmb ) (8)\nFirst, we assume the simple model of humanoid robot acted external forces at the manipulator tip as Fig. 3. C F . C E and C c are each represented to a certain point inside the support polygon, the end-effector and the CoM frame. If the external force acted to the end-effectors, the humanoid robot should control the whole body to achieve desired manipulation tasks. Since the reference linear and angular momentum are.required -$( ::)JG!<(: -fi$) in (8) equation, we calculate the difference between current and desired CoM position from the external forces to define -$( Ez)J;i<( : - * F T i ) the required momentum. From Fig. 3, the linear and angular momentum equations, P F , LF at CF are described as follows. A = S ( E : g:) i ) (7\n(10)\nwhere ME(. HE;. M F ~ , HF;, Mw and Hw are inertia mahices of which each m s , legs and waist affect linear and angular momentum. 7jL is total mass of @nanoid robot. + is an operator as pseudo inverse matrix. I is moment of inertia with CoM. S is selection matrix which chooses control direction. 1'Bsub. Oigaub and Owsub in (8) equation are subtask using redundancy of the body joints. We can specify the target velocity, if redundancy remains after carrying out first task, P,,f and L,,f, humanoid robot carries out sub-task so as to control a redundant manipulator. With the target velocities of the waist calculated by the (8) equation, the target angular velocities of the armsflegs are calculated using ( 5 ) and (6) equations that satisfies the velocities of the desired manipulator tips and legs in world frame and the generated angles are passed to the joint servo controller of the robot.\nIn implementing a momentum conml to the \"Mobile Manipulation\" control, the motion of the CoM position is substituted for a motion of the waist. The vertical motion of the waist is achieved by the impedance control with CoM height. The CoM position starts to move vertical direction, when the manipulator tip position is over the boundary of the work area.\nIV. MODIFICATION 01: THE TARGET COM MOTION In this section, we discuss the target CoM motion for which calculate the reference momentum to generate the stable whole body motion using \"Momentum Control\" described in former secsion.\n(11) TF + TE - TFCfig - PFEFE=LF\nwhere FF, FE, T F , ~g are measured force and torque at CF and C E , rFc and T F E are vector from CF to C c and C E . g is a gravity acceleration vector. The momentum(PF,LF) at CF and the momentum(P,L) at CC are concerned as follows.\nFF +FE - mg=Pp\nFrom (1 1) and (12) equations, the ZMP on the leg frame is represented as follows.\nZ M P z = ( L y - T F C z P z - TEz + T F C s m g z f TFEzFEz +rFEzpEz)/(pa - FE* + f i g = ) (13)\nZMPy = (Ly - T F C z P y - TEy + T F C y m g z + T F E y F E z\n+ T F E ~ F E ~ ) I ( P ~ - FE^ + f i g , ) (14)\nThese equations show we can manipulate the ZMP of the humanoid robot by controlling the linear and angular momentum P and L around the CoM.\nFrom (11) and (12) equations, we assume P and L are zero as the humanoid robot balances with external forces. The vector rFE is decided from manipulability and joint limits based on \"Mobile Manipulation\" control. With desired ZMP, ZMP,d and ZMP,d are described from (13) and"
        ]
    },
    {
        "image_filename": "designv11_11_0001332_s0925-4005(96)02008-4-FigureI-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001332_s0925-4005(96)02008-4-FigureI-1.png",
        "caption": "Fig. I. (A) Schematic representation of the ISCOM and the membrane covered thin-film electrodes. (B) Co-extraction-mechanism for ISCOM, M z+ and A- are the cation and anion, respectively, L is the ionophore, LpM z+ is the cation-ionophore-complex and MLpA z the associated ion F;ir within the membrane. KML and KML A represent the equilibrium constants for the complex-formation and ion-pair-association, respectively and PA the anion partition between the aqueous and membrane phase.",
        "texts": [],
        "surrounding_texts": [
            "The solvent polymeric membranes were prepared according to Ref. [5] by using 2-5 wt% ionophore, 60- 65 wt% plasticiser and 30-35 wt% PVC. The membranes were deposited directly on the transducer by using a dipcoating technique. Thus ion sensitive membranes having a thickness <1/~m were obtained. For conditioning, 10 -2 M solutions of the respective alkalinitrate were used. The ISCOM were stored in the same solutions when no measurements were performed. !. 1.3. Conductometric measurements The ISCOM were operated by using a.c. input voltage Uin with a frequency of 1 kHz and r.m.s amplitude of UinrmS = 100 mV. The voltage drop/-/out at a loading resistance R L = 1 kf~ was used as the sensor output signal, and a lock-in amplifier, EG&G 5209, was used to measure the real part Uo, t which is proportional to the sensitive membrane conductance Gm. The measured ISCOM admittance was independent of/.]in rms until at least Ui, rms = 1 V. 1.2. Results and discussion Typical examples of the calibrations curves for Li +-, K +-, NH4 +- and Ca2+-ISCOM are shown in Fig. 2. In general the ISCOM calibration curves have a sigmoidal shape due to the association-dissociation equilibrium between ionic species in the plasticised polymeric membrane. The ISCOM studied work reversibly and have response times of several seconds (for membrane-thickness -1 ~m) and operational stability of several weeks with occasional re-calibration. The detection limits and the dynamic range are comparable with those for conventional ion-selective sensors. The response characteristics of the ISCOM studied are collected in Table 1. ISCOM prepared with membranes without an ionophore showed no sensitivity at all. Fig. 3 presents a series of repeated measurements of physiological relevant K+-concentrations with a K +- ISCOM. The reproducibility of the sensor response is Table I Response characteristics for pH, Li +-, K +-, NH4 +- and Ca2+-ISCOM K+.ISCOM Ca2+-ISCOM NH4+-ISCOM Li+-ISCOM pH Ionophore Valinomycin ETH 5234 Dynamic range 10 - 5 - 10 -1 M 5 x 10 - 7 - 10 -! M Detection limit 5 x 10 -6 M 10 -7 M Response time < 1 s < 1 s Reproducibility <2% <2% Lifetime Several weeks Several weeks Nonactin DOPP ETH 1907 10 \"5- 10 -I M 10 .-4- 10 -! M 3-9 5 x iO-6M 10-4M - <2 s <!0 s <5 s <2% <2% <2% Several weeks Several weeks Several weeks better than 5%. The selectivity of any ion.selective sensor is one of its most important characteristics as this property often determines whether a sensor may be used in a particular application. Due to '-e different operational principles of ISCOM and ISE, the selectivity patterns of both differ substantially even if comparable membrane compositions are used [3]. The standard ISCOM demonstrates practically relevant selectivities against interfering ions common for biomedical and environmental applications. For example, the selectivity coefficient for K +- and Ca2+-ISCOM with respect to Na + is less than 10 -s. In Table 2 the determined conductometric selectivity coefficients (definition of log/ t con analogous to log K p\u00b0t [5]) for K +- and Ca2+-ISCOM are summarised and compared with the values required for measurements in blood. In this particular case, the ISCOM se!ectivities are comparable with the best selectivities achievable for ISE [5] and fulfil the requirements for a clinical application. The results concerning the performance of ISCOM for heavy metal ions (Hg 2+, C d 2+, etc.) will be presented elsewhere. CalNO3)2. 2. Ion-selective voltammetric electrodes (ISVE) For the on-site determination of ionic substances, reliable disposable sensors are of increasing interest. In the last few years, disposable sensors based on potentiometric ion-selective electrodes have been developed. Due to the logarithmic relationship between ion activity and measured potential, potentiometric ion determination suffers from comparatively large errors. The application of a technique providing a linear relationship between ion concentration and signal on liquid membrane electrodes is a proper way to improve the determination of ionic substances. Thus voltammetric techniques applied to membranes based on plasticised PVC meet these requirements and have led to the development of ion-selective voltammetric electrodes (ISVE). Voltammetric investigations at the interface between an aqueous and a polymer gel phase were most often carried out using nitrobenzene as the organic phase [6,7]. PVC-gel formation was also used in the development of amperometric sensors for ammonia [8] and urea [9]. In this paper the development of a test strip suitable for the voltammetric detection of ions is described and experimental data for the determination of nitrate are given. The commonly used liquid contact was replaced by a solid contact and special fabrication technologies opened the route to the production of suitable sensors at low cost. The principle is based on the determination of iontransfer currents across the interface between two immiscible electrolyte solutions (ITIES) [10]. The distribution of ions between two phases can be manipulated by the application of a potential different from the equilibrium potential value. The equilibrium of ion distribution is investigated using potentiometric methods\u00b0 Applying voltammetric methods, the disturbance of the equilibrium leads to current flow caused by redistribution of ions across the interface between the aqueous phase and the membrane. Processes controlled by diffusion (reversible processes) can serve for analytical purposes. Under suitable conditions and in a certain potential range (potential window), the ITIES can be described as an ideally polarizable electrode. Ions with a transfer potential within this range can be determined."
        ]
    },
    {
        "image_filename": "designv11_11_0002927_j.enzmictec.2004.11.016-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002927_j.enzmictec.2004.11.016-Figure1-1.png",
        "caption": "Fig. 1. Design of mini- (A) and micro-immobilization (B) test cells for immobilization and characterization of the PCP type electrode.",
        "texts": [
            "1 M KCl, pH 7; subseuently referred to as EFC buffer). .2. Electrode and cell fabrication To accommodate different carbon types and immobilizaion techniques, two types of electrodes (and test cells to ouse them) were fabricated. The first used porous pyrolytic arbon paper (PCP) as the carbon support, while the second sed packed graphite columns (PGC). The porous pyrolytic arbon paper electrodes were composed of 50 mm \u00d7 3 mm orous PCP strips (Marketech Intl., WA, USA) imbedded into a septum sealed screw cap (Fig. 1). Immersion area (geometric) was 0.18 cm2. Electrical connection was made via a zinc foil strip crimped to the end of the PCP strip and sealed into place with epoxy resin. This design made the electrodes transferable to different sealed vessels with the same screw cap acceptor. To conserve enzyme during immobilization and dynamic potentiometry tests, a \u201cmicro-immobilization\u201d vessel that could accept the same screw cap and possessed a lower port for the miniature Ag/AgCl reference electrode (BAS, West Lafayette, IN, USA) was employed (Fig. 1). Gas sparging was provided through a needle pierced through the upper (screw cap) septum. Thereafter, during dc polarization tests, the electrode was housed in a larger 35 ml \u201cmini-cell\u201d that was purged with hydrogen or nitrogen via a sparging tube. Mixing (300 rpm) was provided by use of a 1\u2032\u2032 magnetic stirrer placed at the bottom of the cell. In both cases, the reference electrode (RE) was a miniature Ag/AgCl type, while the counter electrode (CE) was a 25 mm \u00d7 4.5 mm strip of platinum foil (Alfa Aesar, MA, USA)",
            " dc polarization Potentiostatic dc polarization was used to characterize the performance of the electrodes (with or without enzyme) in a three-electrode configuration. The enzyme and its electrode support as a working electrode (WE) were held at a constant polarization potential against the reference electrode (RE), and current flowing from the WE to platinum counter electrode (CE) was monitored. Measured current was taken after the potential step on the electrode was imposed and stabilized for 1 h. For the PCP type electrode, a standard three-electrode configuration in a sealed 35-ml test cell (mini-cell) was used for electrochemical measurements (Fig. 1). The cell was continuously flushed with nitrogen or hydrogen as required and stirring was conducted via a 1\u2032\u2032 magnetic stirrer at 300 rpm. The counter electrode was made with a 5 mm \u00d7 5 mm (immersion area) platinum foil strip pretreated by immersion into 5 M HCl for 5 min. For the PGC electrode, the entire cell was filled with degassed electrolyte (3 ml), in order to allow contact with the platinum counter electrode (Fig. 2). 2 i 1 w t c i i v d a 2 a o p t t d p b t g e t b f o yme addition port"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002001_1.1649662-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002001_1.1649662-Figure1-1.png",
        "caption": "FIGURE 1. Sketch of a Terrestrial Bucket Wheel Excavator.",
        "texts": [
            " This will require the excavation of granular material and preparation of the material (principally controlling the grain size) for introduction into a reactor where the material can be heated. Thus, the first step in the process is one of excavation and transfer of material to the reactor. As the concentrations of volatiles are generally low, in the case of typical lunar regolith, extremely low, efficient excavation is required. Our studies are aimed at the development of a class of excavators known as bucket wheel excavators (Figure 1) that are widely used on Earth for removing overburden on coal seams and similar tasks. The bucket wheel excavator is a continuous excavation device, which allows high rates of removal of material compared to the mass of the system. Material excavated by the bucket wheel can be carried to the processing stage in several ways. It could contain a hopper that received the excavated material and, when the hopper was filled, move to a dumping spot where material would be delivered to the reactor. This would minimize the number of systems to be developed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000765_s0043-1648(02)00108-4-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000765_s0043-1648(02)00108-4-Figure9-1.png",
        "caption": "Fig. 9. (a) Load form of the rail and (b) FE mesh of rail.",
        "texts": [
            " But the crossed influences between the loads and the deformations on the left and right wheels are not so small, and should be not ignored in such situation that there is a big difference between the lateral loads on the treads of the left and right side wheels. Under the conditions of no flange action and equal vertical loads on the left and right wheels, lateral creep forces of the left and right wheels are not quite different [17]. So the average of the deformations, before the lateral load of 45 kN, shown in Fig. 8 will be used in the numerical analysis. Fig. 9a is a solid model of FEM for the calculation of turnover deformation of the rail. Displacements of sleepers and ballast are neglected. The length of calculation of the rail is 2.725 m, which spans five sleepers. Fig. 9b is the mesh of the rail. Fasteners and rubber pads between a sleeper and rails are replaced with springs of equivalent stiffness. It is assumed that stiffness of the springs in the longitudinal and lateral directions is the same. Values of stiffness of the springs are selected as, \u221e, 2.94 \u00d7 107 N/m [13], 7.8 \u00d7 107 N/m [14,15] in the FEM analysis. Fig. 10 shows the turnover deformations of the rail against lateral loads, with combined action of vertical and lateral loads. Numbers 1\u20133 in the legend in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002591_0094-114x(85)90040-0-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002591_0094-114x(85)90040-0-Figure8-1.png",
        "caption": "Fig. 8. Gear tooth form.",
        "texts": [
            " At this point three separate arrays have been generated to describe the right root bottom, eqn (15): the right fillet, eqn (20): and the right side involute portion of the tooth, eqn (7/. The exact points of demarcation between the three curves are also known. The description of this right side of the tooth is in a coordinate frame on the gear blank with its origin at the gear center and its X-axis projected through the pitch point on the right side involute surface. This axis makes an angle a with the tooth 358 B. HEFENG et al. centerline. The angle a, as shown in Fig. 8, is related to the tooth thickness at the pitch circle by Pc _ ~ = a = 4 R 4 R P d 2\"-N\" (22) The description of the three tooth sections can now be rotated through the angle a to produce the description of the section in the fourth coordinate f rame-- re la t ive to the tooth centerline: The left side of the tooth can now be generated by reversing the right array and changing the signs of the Y array elements. The sum of these two arrays completely defines the profile of a single rack form generated involute tooth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002266_ijmee.31.2.5-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002266_ijmee.31.2.5-Figure1-1.png",
        "caption": "Fig. 1 A schematic for derivation of eqn (6).",
        "texts": [
            " Since the aim of this paper is to treat the relationship between curvature and bending moment with a tutorial approach, not all the literature associated with this subject will be cited here. Consider an in-plane loaded uniform beam with coinciding shear centerline and centroidal line. The curvature of a planar curve is defined as follows: (2) where q is the slope angle of the tangent at any point on the elastic curve, and s is the arc length of the curve measured from an arbitrary starting point (see Fig. 1). It is well known from differential calculus [15] that (3) and (4)d d d d d dx x y y x x= +( ) = + \u00ca \u00cb \u02c6 \u00af \u00c8 \u00ce\u00cd \u02d8 \u02da\u0307 2 2 1 2 2 1 2 1 tan q = d d y x k q = d ds at HEC Montreal on July 10, 2015ijj.sagepub.comDownloaded from Differentiating eqn (3) and solving for dq provides (5) The purpose of rewriting these relationships, which can easily be found in any standard calculus book, is to attract attention to the fact that the x variable here denotes the abscissa of any point of the curve in its final position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002112_jf00081a003-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002112_jf00081a003-Figure1-1.png",
        "caption": "Figure 1. Inhibition of enzymic and nonenzymic membrane lipid peroxidation by ceruloplasmin (CP): 0, enzymic system [membranea (0.5 mg of protein/mL), NADPH (0.4 mM), ADP (0.4 mM), FeC13 (0.01 mM at pH 7.3)]; A, nonenzymic system [membranes (1 mg of protein/mL), ascorbic acid (0.2 mM), FeC13 (0.01 mM), at pH 7.01; 0, enzymic and nonenzymic systems in the presence of 10 units of ceruloplasmin.",
        "texts": [
            " Thiobarbituric acid reactive substances were determined in model systems by a procedure of Bidlack et al. (1973) and in muscle tissues by a method developed by Witte et al. (1970) and calculated as malonodialdehyde (MDA) using an extinction coefficient of e532 = 1.55 X lo5 M m-l (Buege and Aust, 1978). The results are means of triplicates of one microsomal preparation; in the figures, each bar (I) denotes the standard deviation. RESULTS AND DISCUSSION Membranal lipid peroxidation initiated by an enzymic ADP-Fe or by nonenzymic iron redox cycle systems was inhibited by ceruloplasmin (Figure 1). Enzymic microsomal NADPH and ADP-Fe-dependent lipid peroxidation were found in our model system to derive from a hydroxyl radical site-specific attack or by ferryl ions uninhibitable by hydroxyl radicals scavengers (Hazan, 1986). Similarly, it was found that membranal lipid peroxidation stimulated by iron redox cycle seems to be derived from hydroxyl radical site-specific attack or from ferryl ions uninhibitable by hydroxyl radicals scavengers (Kanner and Harel, 1985). I t seems that in both systems the stimulation of lipid peroxidation was also derived from the catalytic reduction of hydroperoxides to free radicals by ferrous ions generated by NADPH cytochrome 450 reductase and ascorbic acid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000615_rnc.4590050410-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000615_rnc.4590050410-Figure6-1.png",
        "caption": "Figure 6. A three-axle system with kingpin hitch",
        "texts": [
            " Although the class of systems that are covered by the above results is quite large, the same techniques do not extend to trailer systems where the hitch point is not at the axle, but at some offset distance. It has been shown that a car towing one offset trailer can be converted into Goursat normal form (equivalently, is differentially flat); see References 16 and 21 for two different sets of coordinates which achieve this transformation. The firetruck with one offset trailer can also be converted into extended Goursat form as was shown in Reference 3. However, a simple three-axle system with both hitches offset, such as that sketched in Figure 6, does not satisfy the necessary and sufficient conditions for conversion to Goursat form (equivalently, is not differentially flat). This is a system with three constraints in five variables and is an example of the type of generic situation considered by Cartan in Reference 4. Path planning for such a system remains an open problem. REFERENCES 1. R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmidt and P. A. Griffiths, Exterior Diferential Systems, Springer-Verlag, New York, 1991. 2. L. Bushnell, D"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000858_cta.4490220606-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000858_cta.4490220606-Figure12-1.png",
        "caption": "Figure 12. Two congruent minor loops",
        "texts": [
            " Thus, keeping the same range of variation of 2 and taking two different pairs ( f i 3 , f i 4 ) (within the limits both of the compatibility of the state vectors with the circuit and of their reachability) will result in two minor loops with identical geometrical characteristics, the only difference being the vertical shift term originated by the constant difference in charge. This congruence property of minor loops is obviously a general feature of the model. A minor loop congruent with that shown in Figure 1 1 can be obtained by starting from the point P3 of the limit ascending branch for values of 6 within the same range [ -1,2]. Here the pair (C3, C4) becomes (0, - l ) , so that the charge shift term between the two loops amounts to 3 . Both loops are presented in Figure 12 for comparison. Among the variety of models of static hysteresis, the classical phenomenological Preisach model, together with its various generalizations and extensions, is surely the most important and the most popular. For this reason, it is interesting to consider it as a term for a comparison with our model and to outline the main results of the comparison. To this end, we shall briefly recall the basic concepts of Preisach\u2019s model. The symbolism will be kept as close as possible to that used in our model for ease of reference"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001563_a:1008185917537-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001563_a:1008185917537-Figure12-1.png",
        "caption": "Figure 12. View of omnidirectional mobile robot platform.",
        "texts": [
            " The actual view of active dual-wheel caster assembly mechanism is shown in Figure 11. The specifications were as follows: r = 0.05 m, s = 0.075 m, b = 0.26 m. The width of the wheel was 0.04 m, the DC motor was used as an actuator. Torque was transmitted by the gear between the motor and wheel. Furthermore, to take the balance of assembly or robot, a passive free caster was arranged on the front of steering axis of each assembly as an auxiliary wheel. The view of the prototype of the omnidirectional mobile robot with two active dual-wheel caster mechanisms is shown in Figure 12, in which two casters are arranged in the front and rear. The distance between the steering axis of each dualwheel caster and the c.g. of the robot was 0.4 m, and the length, width and height of the platform were 1.1, 0.6, 0.34 m, respectively. Encoder was installed on each driving wheel, and the position and posture of the omnidirectional mobile robot could be estimated by the dead-reckoning. Furthermore, to measure the posture of the dual-wheel caster, an encoder was installed on the steering axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001400_10402009208982083-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001400_10402009208982083-Figure8-1.png",
        "caption": "Fig. 8-Typical tinlte element meshes-radlal and parallel groove geometries.",
        "texts": [
            " [3] is obtained by multiplying the latter with any arbitrary trial firnction w and integrating the product over the domain CiAncll, as given below, The trial function w is so chosen as to assume a zero value on the boundaries rAB and TcD (see Fig. 3), on which pressures are specified. Thus, Applying Green's theorem on Eq. [23] and using Eq. [24], one obtains The domain CiAscD is discretized with nodes and elements. The typical finite element grids for parallel and radial groove seal faces are shown in Fig. 8. For the finite element method of solution, the grid lines need not follow coordinate lines. However, the lines of discontinuity, e.g. the land/groove~junctions, may preferably be grid lines. Isoparametric bilinear quadrilateral element is chosen here. The pressure over an element is defined by its nodal pres- D ow nl oa de d by [ D ea ki n U ni ve rs ity L ib ra ry ] at 0 5: 14 1 5 M ar ch 2 01 5 sure fii and the appropriate shape functions Ni (13), (16). 'I'hus. 'I'he linear shape function N , for each node is chosen such that its value is unityat that node and zero at the other nodes",
            " The hydrodynamic effectiveness is defined here to be the excess opening force generated due to the hydrodynamic action, over the corresponding hydrostatic force (in absence of any motion) divided by the latter. The higher the compressibility number A is, the higher will be the hydrodynamic effectiveness, where A is defined as Follows: A typical mesh with 7 radial lines and 9 circumferential lines on a radial groove sector (for both FD and FE), and a parallel groove sector (for EE only) are presented in Fig. 8. A convergence study was made with respect to mesh size for both methods. Based on the results of the convergence study, 10 radial and 150 circumferential (75 over land and 75 over groove) lines, with uniform spacing, were selected for subsequent runs. Although high density uniform mesh is chosen here, a judicious scheme of non-uniform grid lines with much less overall mesh density may be more economical for actual design optimization runs without cornprornisiag accuracy. One such example is to choose fine meshing near the two circumferential hundaries and the radial lines of discontinuity, and coarse meshing elsewhere"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001916_(sici)1098-237x(200001)84:1<27::aid-sce3>3.0.co;2-8-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001916_(sici)1098-237x(200001)84:1<27::aid-sce3>3.0.co;2-8-Figure1-1.png",
        "caption": "Figure 1. The educational hot-air balloon and its gas burner system.",
        "texts": [
            " Accordingly, hot-air balloons are used as the focal point for studying various subjects in physics, such as the effect of temperature on balloon raising (Haugland, 1991) and the measurement of air resistance acting on a sphere (Greenwood, Hanna, & Milton, 1986). A passenger-carrying hot-air balloon is very large, approximately 8 meters in diameter by 20 meters in height, and quite 30 BARAK AND RAZ short standard long Top of RH Base of RH Top of test Base of text expensive. Thus, an educational hot-air balloon with dimensions and cost suited to schools\u2019 budgetary constraints was developed. Figure 1 indicates that the height of the balloon is 8 meters. An electronic control system for heating the air by means of a gas burner is placed in the basket. The source of energy is a 1.5-kilogram butane gas cylinder. The maximum load is 15 kilograms. The system is activated by means of radio remote control. The hot-air balloon program allocates to a central project all 6 hours/week for science and technology, during an entire school year. Pupils learn a variety of high-level subjects in physics and technology",
            " The flame in the burner was large at first, and gradually decreased in size. As a result, the balloon remained airborne for only several minutes before falling. The pupils suggested a number of solutions, such as: using an electric heat supply; attaching mirrors to make use of solar energy; and simultaneous use of several cylinders. After several failed attempts, a creative solution was found: the gas cylinder was fixed upside-down with piping attached to the balloon in a spiral fashion from bottom to top, as illustrated in Figure 1. The ratio between the surface area of the copper piping and the volume of the gas contained therein is much greater than that in the gas cylinder. The requisite heat energy for evaporating the gas was absorbed more efficiently from the atmosphere. The temperature of the copper pipe was somewhat reduced, but the gas cylinder itself hardly cooled down at all. In this way, good gas flow was achieved during combustion. Although the pupils knew all the scientific principles for the solution, significant ground had to be covered to find the optimal technological solution within the given limitations of equipment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003320_j.vibspec.2005.01.001-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003320_j.vibspec.2005.01.001-Figure5-1.png",
        "caption": "Fig. 5. The most possible orientation of isonicotinic aci",
        "texts": [
            "5 V 410 419 430 431 433 430 Out-of-plane ring vibration 663 666 666 666 Ring breathing 710 683 684 684 685 g(CH) 826 850 848 848 846 847 Out-of-plane ring vibration 870 1028 1007 1010 1011 1012 1010 Ring breathing 1060 1060 1062 1063 1060 b(CH) 1093 1092 1094 1097 b(CH) 1142 1153 1153 1153 1148 1148 b(CN) 1211 1202 1200 1200 b(CH) 1239 1225 1221 1222 1218 1218 n(C-sub) 1315 n(C\u2013O)s 1336 1337 b(CH) 1382 1381 1383 1378 1378 n(COO )s 1496 1496 1496 n(CC, CN) 1574 1574 1574 n(CC) 1609 1608 1608 1608 1608 n(CC) 1639 1639 n(CC) 1698 n(C O)s acid, in which all assigned to C\u2013N bending bands are very strong, the same vibrational bands (1153 and 1476 cm 1) are relatively weak yet. Therefore, it is indicated that the adsorption of isonicotinic acid takes place only through carboxyl group, as is shown in Fig. 5a. It is interesting that with the potential negative shifting from 0.1 V to 0.5 V, most bands\u2019 relative intensities change obviously, quite differently compared to the finding in picolinic acid. And partial vibration frequencies are shifted about 3\u201310 cm 1, indicating that the interaction between isonicotinic acid molecules and the silver surfaces is strong and SERS signals are very sensitive to the electrode potential. It is notable that there are two exceptions at the varying of in-plane and outplane vibrations with the shifting of potential",
            " The discussion about the orientation of the isonicotinic acid molecules to the silver surface has been made by applying the results of \u2018\u2018surface selection rules\u2019\u2019 in the in-plane and out-of-plane d on Ag electrode at 0.1 V (a) and 0.4 V (b). vibrations. Therefore, according to these observations mentioned above in Fig. 4, it is thought that isonicotinic acid is adsorbed on to the silver surface with its molecular plane lying flat and that both the carboxylate and the nitrogen atom interact with the surface when the potential is varied to 0.4 V, as is shown in Fig. 5b. The SERS signal disappears on Ag surfaces at about 0.9 V due to the potential-driven desorption or the occurrence of hydrogen evolution at the surface. The potential-dependent SERS spectra of nicotinic acid molecules adsorbed onto roughened Ag electrodes are Fig. 7. The most possible orientation of nicotinic aci presented in Fig. 6. As is shown that bands of moderate to strong intensity around 1033 cm 1 (ring breathing), 1535 cm 1, 1600 cm 1 and 1633 cm 1 (C\u2013C stretching), 1387 cm 1 (COO symmetric stretching), all assigned to inplane vibration modes, when the electrode potential is at 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001525_5.301683-Figure16-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001525_5.301683-Figure16-1.png",
        "caption": "Fig. 16. Schematic representation of conventional ac machines. (a) Induction machine. (b) Synchronous machine. @s = 1 magnetic field rotating with respect to the stator, @T = 1 magnetic field of the rotor, rotating at I), with respect to the rotor in (a) and stationary with respect to the rotor in (b).",
        "texts": [],
        "surrounding_texts": [
            "converters (C2), ac/dc converters (G3), and acJac converters (C4).\n111. MOTION CONTROL LOADS FOR CONVERTERS\nControl, machines, and drives are being discussed in other contributions in this issue, so that machines and drives are only briefly reviewed here-especially to appreciate the impact they have as loads on the converters. From the subsequent discussion it will also follow that the type of effect the machine as load has on the converter is connected to the type of electrical machine and its operation.\nA. Controllable Electromechanical Conversion To approach the application of power converters to the control of electrical machines systematically, an approach based upon the revolving field theory is taken, and an attempt to unify the different electromechanical energy conversion processes is subsequently presented [ 111.\nIn any multiphase electrical machine the stator windings build a magnetic field revolving at an angular speed\nQ s = w:q\nwhere\nw, = pif,\nand fs is the stator supply frequency and 2q the number of magnetic poles. If the rotor of the machine also carries some multiphase electrical excitation, the rotor magnetic field would be revolving at an angular speed\n0, = w;q\nwith respect to the rotor itself, which runs at an angular speed 0, with respect to the stator. As continuous conversion of electrical into mechanical energy will only occur when the rotor and the stator magnetic fields rotate at the same angular speed, i.e., when the two \"magnets\" line up, the following relationship may be written:\nw s / s - w r / s = Q m .\nIf it is now furthermore supposed that the machine develops a torque Tg in its air gap between rotor and stator, it may be written that\nTgw,/q - Tgw?-/q = TgQm\nPg - P, = P,.\nor in the form of a power relationship\nIn this relationship, Pg represents the energy that flows from the stator into the air gap of the machine, P, the energy that flows into the rotor electric circuits from the air gap, and P, the mechanical power that leaves the machine via its mechanical port.\nNow consider the different types of electrical machines in terms of this angular frequency condition. For a synchronous machine the rotor is excited by either dc or a permanent magnetic field, so that\nw, = 0\na, = w:q.\nFor an induction machine, the above frequency condition is automatically obeyed, as the difference in speed of the stator magnetic field and the rotor mechanical speed is the\nVAN WYK: POWER ELECTRONIC CONVERTERS FOR MOTION CONTROL 1177",
            "cause of the induced frequency on the rotor. For a dc machine in its conventional form, the application of this relation is also interesting. As its stator is excited by dc (field excitation), the following relation is obtained:\n-w;q = cl,.\nThis naturally indicates that the rotor field of a dc machine is rotating backward with exactly the same speed that the rotor is rotating forward, so that the net effect is a rotor magnetic field stationary in space to line u p with the stationary magnetic field produced by the field winding on the stator.\nThus a general law for electrical machines has been illustrated, i.e., that in any rotating electrical machine at least one of either the rotor or the stator must cany an altemating current. In induction and synchronous machines the multiphase altemating current is applied to the stator windings, whereas in a dc machine the multiphase alternating current is supplied to the rotor by means of the commutator-an ingenious mechanical frequency converter and the exact mechanical counterpart of the electronic switching inverter. This is also the reason why, as will be shown subsequently, the dc machine remains such an attractive machine in variable-speed electrical drives. It is only necessary to control the applied dc voltage-the machine automatically adapts its own frequency via the commutator. Figures 16 and 17 illustrate these concepts, from which it follows why induction and synchronous machines are essentially constant-speed machines, whereas the dc machine is directly suited to variable-speed drives. Figure 17(b) shows an inverted dc machine, where the stator carries the commutator. In the past, some O F these types of variable-speed drives have in fact been built [104], but have not met with success, owing to the intricacies of the mechanical commutator and brush arrangement when fixed to the stator windings. It will be shown, however, that what the most modem electrical variable-speed drives with electronic switching converters attempt, is just to emulate this old idea by replacing the mechanical commutator with an electronic inverter. A close investigation indicates, in fact, that this inverted dc machine is a multiphase synchronous machine; with variable frequency supplied to its stator windings via the mechanical commutator (MFC). The feedback of R, from the rotor shaft to the stationary mechanical commutator sees to the observance of the frequency condition as previously discussed.\nFrom the above discussion it is clear that in the case of dc machines, the power electronic converter will only be required to condition the average value of the voltage iipplied to the machine as controlled variable. No other requirement than an acceptable current ripple follows from this, leading to a requirement for the switching frequency of the converter given by the total circuit inductance-including the armature inductance of the dc machine. However, in the case of motion control systems with ac machines it will become clear subsequently that both fundamental frequency and voltage amplitude are controlled variables, posing much\n4\n+ I. . . . - h . . - . - . . .\nDC MACHINE\n(a) ;m$ -\nmore complications to the power electronic converter than in the case of a dc commutator machine.\nB. Systematics of Converter-Fed Drives for Motion Control Modem electrical variable-speed drives for motion control form a small part of all the solutions that have been suggested for this problem in the past. Systems to be discussed are those that are of the most practical interest today, and therefore the discussion does not attempt to be all inclusive. For an encyclopedic discussion covering most of the possiblities for variable-speed drives that had been realized or are realizable, refer to [218]. The present discussion is consequently limited to:\n1178 PROCEEDINGS OF THE IEEE, VOL. 82, NO. 8, AUGUST 1994",
            "i) Variable-speed drives with armature voltage control of dc machines by controlled rectifiers.\nii) Variable-speed drives with variable stator frequency control of synchronous and induction machines by inverters. iii) Variable-speed drives with variable slip control of induction machines by switching converters for amplitude conditioning.\n1 ) Variable-Speed Drives with Armature Voltage Control of dc Machines: The two types of armature voltage control systems most widely found at present are shown in Fig. 18. Although it has not been shown, both of these systems may also operate with field control. As a controlled rectifier is able to allow energy flow in two directions, while maintaining current flow in one direction, the system as shown in Fig. 18(a) will be able to operate in the first two quadrants of the torque-speed plane. If operation in quadrants I11 and IV is desired, the field connections should be reversed, or a second antiparallel controlled rectifier should be provided, as shown dotted in the figure. Although these solutions differ very much in their operational characteristics, it would be beyond the limits of the present aims to discuss them.\nLow-loss control of variable-speed drives fed from dc busbars, such as traction equipment with overhead wire systems and battery-fed drives, may be achieved by means of force commutated chopper controllers. As shown in Fig. 18(b), these units operate on a pulse-modulation principle, the drive being capable of operating in the first quadrant of the torque-speed plane. Both the direction of power flow and current flow through the chopper are unidirectional, limiting operation only to the first quadrant of the torque-speed plane. Regenerative braking (operation in quadrant IV) can be obtained by adding a second force commutated chopper in antiparallel, shown dotted, or by reconnecting the existing chopper by multiple contactor switching. If the dc busbar cannot accept regenerative energy, resistors should be brought in by contactor across the input to limit the voltage rise in the dc link.\n2 ) Variable-Speed Drives with Variable Stator Frequency: Variation of stator frequency of a synchronous machine or a squirrel-cage induction machine changes the speed of rotation of the magnetic field in the air gap and therefore also the output speed of the mechanical drive shaft. Some particulars of these types of systems are shown in Fig. 19.\nThe inverter converts the dc input to variable-frequency three-phase output. This means that the system may be fed from a dc busbar, such as in overhead dc traction systems or battery vehicles (as also indicated for force-commutated chopper circuits). Using either a controlled or uncontrolled rectifier, the intermediary dc voltage may also be obtained from a three-phase supply system. The amplitude control of the multiphase ac output of the inverter may either be done by pulsewidth modulation in the inverter itself, or by controlling the rectifier to control the intermediary dc voltage. Choosing between these two methods affects the behavior and characteristics of the drive fundamentally.\nBoth the induction machine drive and the synchronous machine drive are automatically regenerative, because inverter circuits allow current and power in two directions. Reversing the rotation of the drive also presents no problem, because this means changing the phase rotation of the ouput\nVAN WYK: POWER ELECTRONIC CONVERTERS FOR MOTION CONTROL 1179"
        ]
    },
    {
        "image_filename": "designv11_11_0002531_rspa.2004.1439-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002531_rspa.2004.1439-Figure8-1.png",
        "caption": "Figure 8. A set of four hinged cubes used to show the mobility of a ring of four tetrahedra: the relationship between the four cubes and the four tetrahedra is shown in figure 7. I shows the D2d bifurcation configuration: two mechanism paths emerge. Relative rotation (a) about one pair of collinear hinges leads from the D2d configuration I, through a sequence of C2v configurations (not shown) to the standard setting II; here the hinges have D2h symmetry. Alternatively, relative rotation (b) about the other pair of collinear hinges leads to a distinct D2h standard setting III.",
        "texts": [
            " Much of the previous analysis applies in this case, although the equivalence of the symmetry results is obscured by differences in notation for Abelian and non-Abelian groups. Proc. R. Soc. A (2005) The case NZ4 has one obvious difference from the larger rings in that there is a bifurcation in the path followed by the mechanism. This is most clearly revealed by starting, not at the standard (in this case D2h) configuration, but at the alternative high-symmetry point, the D2d arrangement of four tetrahedra. Figure 7 shows the D2d arrangement of four \u2018skinny\u2019 tetrahedra, and its equivalence to a set of four cubes. Figure 8 illustrates the bifurcation of the Proc. R. Soc. A (2005) mechanism of the four-ring. Relative rotation (a) about one pair of collinear hinges leads from the D2d configuration I, through a sequence of C2v configurations (not shown) to the standard setting II; here the hinges have D2h symmetry. Alternatively, relative rotation (b) about the other pair of collinear hinges leads to a distinct D2h standard setting III. Each of the paths (a) and (b) are theoretically continuous, crossing at I, although when the ring is realized with the cubic blocks shown in the figure, steric clashes prevent continuation of the paths through the high symmetry point; this would not be the case with suitably skinny bodies"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001436_j.wear.2003.10.004-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001436_j.wear.2003.10.004-Figure2-1.png",
        "caption": "Fig. 2. Development of the concept of sharpness for conical and \u2018realistic\u2019 asperities.",
        "texts": [
            " Sharpness is a measure of the capacity of a body to cause material removal in another body by virtue of its shape alone\u2014it is the central concept in this work and is developed for both abrasive particles and surfaces. The most elementary measure of sharpness is given by the angle-of-attack of the (hypothetical) conical asperity [6]. The regular nature of the cone implies that the ratio (\u03bb) of the projected penetration and groove areas is a constant. In notation consistent with [1,7], the projected penetration area is typically represented by \u2126, and the groove area by \u039b\u2014their definition is explained by reference to the asperities shown in Fig. 2. The quantities \u2126 and \u039b are proportionally related to the load acting on each asperity and the wear rate induced by the asperity, respectively. The parallel drawn between asperity shape and the abrasion parameters load and wear rate is reasonable for the most common conditions associated with two-body abrasion. Extreme conditions can lead to significant divergences from the linear model, but generally, the monotonicity of the relationships indicate that increasing sharpness yields increasing wear rate",
            " By informal convention, those bodies possessing diameters smaller than 1 mm are referred to as particles. Fragmented particles are brittle, but generally much harder than the bodies they abrade. Their shape is therefore preserved under the severe stresses which cause the preferential attrition of the softer surface by plastic deformation and/or fracture. Fragmentation is a complex phenomenon that does not yield particles with cone-like asperities [8]. The continuously varying relationship between \u2126 and \u039b for an arbitrary asperity is shown in Fig. 2 and is called the groove function. Consistent with previous definitions, it is indicative of wear rate as a function of load. Sharpness is developed in its simplest form when given a single asperity with predetermined orientation and traversal direction, as shown in Fig. 2. This represents just one of the many events that contribute to wear in two-body abrasion. It naturally follows that, in order to estimate wear rate, it is necessary to determine the average sharpness of a large number of asperities, belonging either to particles (i.e. radial asperity distribution) or surfaces (i.e. planar asperity distribution). Each orientation of an irregular particle can be considered as a single asperity and reduced to the case illustrated in Fig. 2. Abrasive systems governed by multiple random interactions between the particle and the wearing surface require a statistical treatment of particle shape. Assuming that all orientations are equally likely to participate in abrasion, then it is possible to identify an asperity possessing average shape that is representative of the entire particle sample. In theory, if a particle is considered as a closed set in Euclidean 3-space, then its average shape is obtained by systematically averaging the groove functions over the domain of all possible orientations, as illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003070_j.mechmachtheory.2004.11.006-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003070_j.mechmachtheory.2004.11.006-Figure3-1.png",
        "caption": "Fig. 3. (a) The top platform and (b) the base platform.",
        "texts": [
            " Similarly, the movable frame C has its origin on plane c, with its Yc-axis passing through the midpoint of c1c2 and Zc-axis being normal to plane c. Leg cylinders are numbered from 1 to 6, base cylinders from 7 to 9, and the top cylinders from 10 to 12, as shown in Fig. 2. All the cylinders can be actuated whenever required. For example, leg cylinders are used to manipulate the object whereas the base and top cylinders are used only when the adjustment has to be made for an object of different shape and size. Fig. 3 shows schematic diagram of the base and top platforms in detail. The paper is organized as follows: Sections 2 and 3 provide the inverse and forward kinematics algorithms, respectively, whereas Section 4 gives the results of a numerical example. Finally, conclusions are given in Section 5. In the present kinematic analyses, it is assumed that the Dodekapod will be used as a positioning and gripping device. Keeping this in mind, the inverse kinematics problem of the Dodekapod can be stated as follows: Given the position and orientation of the top platform and the positions of the top mobile knots which depend on the object to be gripped, determine the lengths of all the cylinders. For any given gripping application, the top platform need to be positioned and orientated. The position and orientation of the top platform for this purpose can be described by defining a position vector tbc x y z\u00bd T, and rotation matrix Rb c from frame C to frame B. The positions of the top mobile knots which are defined by their distances from the center of the top platform (shown as at, bt and ct in Fig. 3a), are dictated by the shape and size of the object to be gripped. So, input to our inverse kinematics problem are tbc , R b c , at, bt and ct. The other three degree of freedom of the Dodekapod in terms of the positions of the base mobile knots defined by their distances from the center of bottom platform, namely, a, b, and c in Fig. 3b are redundant resulting in infinite number of solutions to the inverse kinematics problem. In order to have a finite number of solutions, the method proposed here starts with assuming an initial configuration for the base mobile knots (a, b, and c). Problem of finding the leg lengths for this assumed configuration of the base mobile knots is equivalent to that of a general 6\u20136 Stewart platform inverse kinematics problem for which solutions have been proposed [6,8,9]. The feasibility of a solution in this case is first checked and if there is no feasible solution for the assumed configuration of the base mobile knots, the positions of the base mobile knots are changed",
            " (ii) Knowing a, b, and c, compute coordinates of each mobile knot. (iii) Solve for leg lengths by solving the inverse kinematics problem of the 6\u20136 Stewart platform. (iv) Verify the feasibility of the solutions, and change the position of the base mobile knots if necessary, till a feasible solution is found. The initial position of the base mobile knots can be taken as the positions to which they adapt to when the three base cylinders are at their minimum or maximum lengths. That is, l7, l8 and l9 are assumed to be known. From the geometry of Fig. 3b, note that a1p \u00bc a6r; a3q \u00bc a2p; a5r \u00bc a4q \u00f01\u00de which can be expressed in terms of the values, a, b, c, and s of Fig. 3b, as shown in Eq. (A1) of Appendix A. Now, using the \u2018\u2018sine rules\u2019\u2019 given in Eqs. (A2)\u2013(A4), we get six linear transcendental equations in six variables, i.e., a1p, a3q, a5r, and /1, /2, /3, as indicated in Fig. 3b. We shall now eliminate the variables, /1, /2, and /3, using the following relations: /1 \u00bc ArcCsc 2l7ffiffiffi 3 p a3q ; /2 \u00bc ArcCsc 2l8ffiffiffi 3 p a5r /3 \u00bc ArcCsc 2l9ffiffiffi 3 p a1p where ArcCsc(\u00c6) implies Cosec 1(\u00c6). Substituting the values of /1, /2, and /3 in Eqs. (A2)\u2013(A4), we get three equations in three variables, a1p, a3q and a5r, which are as follows: ffiffiffi 3 p 2 a1pCsc p 3 ArcCsc 2l7ffiffiffi 3 p a3q \u00bc l7 \u00f02\u00de ffiffiffi 3 p 2 a3qCsc p 3 ArcCsc 2l8ffiffiffi 3 p a5r \u00bc l8 \u00f03\u00de ffiffiffi 3 p 2 a5rCsc p 3 ArcCsc 2l9ffiffiffi 3 p a1p \u00bc l9 \u00f04\u00de where Csc(\u00c6) stands for Cosec(\u00c6)",
            " Knowing the geometry of the base and top platforms, we can solve for the inverse kinematics of the Dodekapod to determine its cylinder lengths for a specific position and orientation of the top platform, and the required positions of the top mobile knots. Initially, the lengths of the base cylinders are either minimum or maximum depending on which one adopts for the initial positions of the base mobile knots. However, during iterations of finding a feasible solution, the positions of the base mobile knots are changed, which can be determined using the following cosine rules (Fig. 3b): l7 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L2 a \u00fe L2 b 2LaLb cos 2p 3 a b s \u00f05\u00de l8 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L2 b \u00fe L2 c 2LbLc cos 2p 3 b c s \u00f06\u00de l9 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L2 a \u00fe L2 c 2LaLc cos 2p 3 c a s \u00f07\u00de where La, Lb, and Lc are defined as La ffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe a2 p ; Lb ffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe b2 p \u00f08\u00de Lc ffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe c2 p \u00f09\u00de and tan a \u00bc s a ; tanb \u00bc s b ; tan c \u00bc s c Similarly, referring to Fig. 3a, the lengths of top cylinders are obtained from: l10 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L2 at \u00fe L2 bt 2LatLbt cos 2p 3 at bt s \u00f010\u00de l11 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L2 bt \u00fe L2 ct 2LbtLct cos 2p 3 bt ct s \u00f011\u00de l12 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L2 at \u00fe L2 ct 2LatLct cos 2p 3 ct at s \u00f012\u00de where Lat, Lbt, Lct, and tanat, tanbt, and tanct, are defined similar to Eqs",
            " Similar to inverse kinematics, the forward kinematics has also been solved using a hierarchical method. First, the positions of the mobile knots which are not affected by the leg-lengths are determined. Then the coordinates of all the attachment points are calculated using the relations developed while solving the inverse kinematics, i.e., Eqs. (A5)\u2013(A7). The position of base mobile knots can be determined using Eqs. (2)\u2013(4). Similar equations for the top mobile knots can be derived, which are given as follows: Referring to Fig. 3a, where points c1, . . .,c6 coincide with points d1, . . .,d6, ffiffiffi 3 p 2 c2ptCsc p 3 ArcCsc 2l10ffiffiffi 3 p c4q \u00bc l10 \u00f022\u00de ffiffiffi 3 p 2 c4qtCsc p 3 ArcCsc 2l11ffiffiffi 3 p c6r \u00bc l11 \u00f023\u00de ffiffiffi 3 p 2 c6rtCsc p 3 ArcCsc 2l12ffiffiffi 3 p c2p \u00bc l12 \u00f024\u00de Eqs. (22)\u2013(24) can be solved for c2pt, c4qt, and c6rt, and then at, bt and ct can be calculated similar to a, b, c of Eq. (A1) using Eq. (A8). A rotation matrix is orthogonal, i.e., \u00f0Rb c\u00de T Rb c \u00bc 13 3\u201313\u00b73 being the 3 \u00b7 3 identity matrix",
            " Authors acknowledge the support provided by the DAAD (German Academic Exchange Program) to the first author during 1999\u20132000 to carry out the research at the Technical University, Berlin, Germany, under the DAAD-IITs collaboration. Besides the help from Mr. Kiran Kolluru, an M. Tech student at IIT Delhi, to re-draw the figures and re-write the equations during the preparation of the final manuscript is duly acknowledged. In this appendix, some useful geometric expressions are provided which are essential for the inverse and forward kinematic analyses of the Dodekapod at hand. From Fig. 3b, a \u00bc a1p \u00fe s tan p 6 b \u00bc a3q\u00fe s tan p 6 c \u00bc a5r \u00fe s tan p 6 9= ; \u00f0A1\u00de whereas the \u2018\u2018sine rules\u2019\u2019 provides, l7 sin 2p 3 \u00bc a3q sin/1 \u00bc a1p sin p 3 /1 \u00f0A2\u00de l8 sin 2p 3 \u00bc a5r sin/2 \u00bc a3q sin p 3 /2 \u00f0A3\u00de l9 sin 2p 3 \u00bc a1p sin/3 \u00bc a5r sin p 3 /3 \u00f0A4\u00de Moreover, the coordinates of the six base mobile knots (Fig. 3b) are given as xa1 \u00bc s ya1 \u00bc a xa2 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe b2 p cos p 6 b ya2 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe b2 p sin p 6 b xa3 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe b2 p cos p 6 \u00fe b ya3 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe b2 p sin p 6 \u00fe b xa4 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe c2 p cos p 6 \u00fe c ya4 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe c2 p sin p 6 \u00fe c xa5 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe c2 p cos p 6 c ya5 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe c2 p sin p 6 c ya6 \u00bc axa6 \u00bc a 9>>>>>>>>>>>>>= >>>>>>>>>>>>>; \u00f0A5\u00de Similarly, the coordinates of the base mobile knots in plane b can be expressed from Fig",
            " 4 as xb1 \u00bc xa1 \u00fe q yb1 \u00bc ya1 \u00fe p xb2 \u00bc xa2 r cos p 6 \u00fe k yb2 \u00bc ya2 r sin p 6 \u00fe k xb3 \u00bc xa3 r cos p 6 k yb3 \u00bc ya3 r sin p 6 k xb4 \u00bc xa4 \u00fe r cos p 6 k yb4 \u00bc ya4 r sin p 6 k xb5 \u00bc xa5 \u00fe r cos p 6 \u00fe k yb5 \u00bc ya5 r sin p 6 \u00fe k xb6 \u00bc xa6 q yb6 \u00bc ya6 \u00fe p 9>>>>>>>>>>>= >>>>>>>>>>>; \u00f0A6\u00de The coordinates of the top mobile platform in plane c are then given by xc1 \u00bc xd1 \u00fe q yc1 \u00bc yd1 \u00fe p xc2 \u00bc xd2 \u00fe q yc2 \u00bc yd2 \u00fe p xc3 \u00bc xd3 r cos p 6 \u00fe k yc3 \u00bc yd3 r sin p 6 \u00fe k xc4 \u00bc xd4 r cos p 6 k yc4 \u00bc yd4 r sin p 6 k xc5 \u00bc xd5 \u00fe r cos p 6 k yc5 \u00bc yd5 r sin p 6 k yc6 \u00bc yd6 r sin p 6 \u00fe k xc6 \u00bc xd6 \u00fe r cos p 6 \u00fe k 9>>>>>>>>>>= >>>>>>>>>>; \u00f0A7\u00de where p, q, and r are shown in Fig. 4. Finally, from Fig. 3a the following relations are obtained: at \u00bc c2pt \u00fe st tan p 6 bt \u00bc c4qt \u00fe st tan p 6 ct \u00bc c6rt \u00fe st tan p 6 9>= >; \u00f0A8\u00de [1] G. Spur, E. Uhlmann, M. Seibt, A new type of gripping system with parallel kinematics, Prod. Eng. V/2 (1965) 61\u2013 64. [2] P. Bande, Programming of DODEKAPOD: A Parallel Manipulator, M. Tech Project Report, IIT Delhi, April 2000. [3] D. Stewart, A platform with 6 degree of freedom, Proc. Inst. Mech. Engrs. 180 (Part 1, No. 15) (1965) 371\u2013386. [4] V.E. Gough, Contribution to discussion to papers on research in automobile stability and control and in tyre performance, by Cornell Staff, Proc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002997_j.mechmachtheory.2004.02.005-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002997_j.mechmachtheory.2004.02.005-Figure1-1.png",
        "caption": "Fig. 1. Scheme of new type of beveloid gear pair.",
        "texts": [
            " The method to calculate the tooth profile errors and axial errors has been obtained in the paper. All the work will be helpful to other fields such as the stiffness calculation, backlash, efficiency of transmission, relative normal curvature and generation methods of beveloid gears. Finally, this paper has finished the simulation of the new type of noninvolute beveloid gears by applying the CAD system, Pro/Engineer. The motion coordinate systems r1 \u00bc \u00bdo; i*1; J * 1; k * 1 and r2 \u00bc \u00bdo; i*2; J * 2; k * 2 , as shown in Fig. 1, are attached to the involute beveloid gear (gear 1 in short) and to the tooth profile (gear 2 in short) of the gear which is conjugated with gear 1, respectively. r10 \u00bc \u00bdO10;~i10;~j10;~k10 and r20 \u00bc \u00bdO20;~i20;~j20;~k20 are the original coordinate systems of gear 1 and gear 2, respectively. The conversion relationship of all the coordinate systems is shown in Fig. 2. Thus the coordinate transition matrix can be expressed as follows: M21 \u00bc cosu1 cosu2 sinu1 sinu2 cosd sinu1 cosu2 \u00fe cosu1 sinu2 cosd sinu2 sind cosu1 sinu2 sinu1 cosu2 cosd sinu1 sinu2 \u00fe cosu1 cosu2 cosd cosu2 sind sinu1 sind cosu1 sind cosd 2 4 3 5 \u00f01\u00de where d is the shaft angle between gear 1 and gear 2; u1 and u2 are the rotation angles of gear 1 and gear 2, respectively",
            " (3) can be determined as viewed from the large end of the beveloid gear. For example, for the right profile l is positive, for the left profile l is negative. According to differential geometry, the unit normal of profile P 1 at a point is n* \u00bc o r*1 ol o r*1 oh o r*1 ol o r*1 oh \u00bc cos bb1 sin\u00f0l \u00fe h\u00de i*1 cos bb1 cos\u00f0l \u00fe h\u00de j*1 \u00fe sin bb1k * 1 \u00f04\u00de The relative velocity at the contact point between gears 1 and 2 is given by v*\u00f012\u00de \u00bc dn * dt x* \u00f02\u00de n * \u00fe x* \u00f012\u00de r*1 \u00f05\u00de where n * is the vector O2O1 ! , as shown in Fig. 1, ~n \u00bc~0; x *\u00f012\u00de is the relative angular velocity between gears 1 and 2, x* \u00f012\u00de \u00bc ~x\u00f01\u00de x* \u00f02\u00de (1/s). According to Eq. (1), by using the coordinate conversion, the expression (5) can be given by v* \u00f012\u00de \u00bc x* \u00f012\u00de r*1 \u00bc f x2ph cosu1 sin d \u00fe rb1\u00f0x1 \u00fe x2 cos d\u00de\u00bdsin\u00f0l \u00fe h\u00de l cos\u00f0l \u00fe h\u00de g~i1 \u00fe f x2ph sinu1 sin d rb1\u00f0x1 \u00fe x2 cos d\u00de\u00bdcos\u00f0l \u00fe h\u00de \u00fe l sin\u00f0l \u00fe h\u00de g~j1 \u00fe frb1x2 sinu1 sin d\u00bdsin\u00f0l \u00fe h\u00de l cos\u00f0l \u00fe h\u00de \u00fe rb1x2 cosu1 sin d\u00bdcos\u00f0l \u00fe h\u00de \u00fe l sin\u00f0l \u00fe h\u00de g~k1 \u00f06\u00de The conjugate motion must satisfy the engagement equation [6]: U \u00bc n* v*\u00f012\u00de \u00bc 0 \u00f07\u00de Substituting Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003146_1-84628-214-4-Figure1.4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003146_1-84628-214-4-Figure1.4-1.png",
        "caption": "Fig. 1.4. The h-alloc command extends the memory, so that the program of the child organism can be stored. Later, on h-divide, the program is split into two parts, one of which turns into the child organism.",
        "texts": [
            " If there are instructions left between the write head and the end of the memory, these instructions are discarded, so that only the part of the memory from the beginning to the position of the read head remains after the divide. 1 Avida 15 In most natural asexual organisms, the process of division results in organisms literally splitting in half, effectively creating two offspring. As such, the default behavior of Avida is to reset the state of the parent\u2019s CPU after the divide, turning it back into the state it was in when it was first born. In other words, all registers and stacks are cleared, and all heads are positioned at the beginning of the memory. The allocation and division cycle is illustrated in Fig. 1.4. Not all h-divide commands that an organism issues lead necessarily to the creation of an offspring organism. There are a number of conditions that have to be satisfied; otherwise the command will fail. Failure of a command means essentially that the command is ignored, while a counter keeping track of the number of failed commands in an organism is increased. It is possible to configure Avida to punish organisms with failed commands. The following conditions are in place: An h-divide fails if either the parent or the offspring would have less than 10 instructions, the parent has not allocated memory, less than half of the parent was executed, less than half of the offspring\u2019s memory was copied into, or the offspring would be too small or to large (as defined by the experimenter)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000615_rnc.4590050410-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000615_rnc.4590050410-Figure5-1.png",
        "caption": "Figure 5. A five-axle trailer system with the first and third axles steerable. This is the only configuration of the fiveaxle system with two steering wheels which does not satisfy the conditions for converting to extended Goursat normal form without prolongation",
        "texts": [
            " A singularity also occurs when the angle between two adjacent axles is equal to n/2; at this point, some of the codistributions in the derived flag will lose rank. The derived flag is not defined at these points; nor is the transformation. The methods described herein will not work for controlling the multi-steering trailer system when the trailers must go through such a jack-knifed configuration. Example 3. Five-axle, one-three steering Proposition 10 has the first and third axles steerable, as shown in Figure 5 . The only instance of the five-axle trailer system which satisfies neither Theorem 9 nor The constraints are that each axle roll without slipping: o' = sin 8' dx' - cos 8' dy' i = 1,2 ,3 a'=sin rp'dxi-cos r)jdA j = 1,2 The Pfaffian system is I= ( a ' , o', a', o', w 3 } , and a complement to the system is given by (d q5 I , d @', dx3}. By Lemma 6, the derived flag has the form 1 1 I = (a , U , a2,02,w3} I = (1) {U1, 02, 03} b3} (2) I = (3) I = (01 THE MULTI-STEERING N-TRAILER SYSTEM 363 In order to have {Z(\u2019), JC} integrable, x must be dx3 (mod 03)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003836_nme.1620180404-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003836_nme.1620180404-Figure3-1.png",
        "caption": "Figure 3. Example 2: (a) structure; (b) element ordering and front configuration--open arrow denotes general front motion, last assembled element shown shaded",
        "texts": [
            " The stiffness equation for the \u2018unconstrained\u2019 structure is The constraint condition of equal u2 and u g is The stiffness equation (7) is then and its solution 526 J. BARLOW The master variables from equation (8a) are ii(==u* = u g ) = ([l, 11 k / 2 )-'[l, 13 0-0 [ 0 1 [Q-01 = 2 Q - k and the remaining displacement (8b) 1 2Q Q 2 ' K K u\" (=u* )=o+- -=- which is the true solution. Note that the load applied to the constraint member (Figure 2b) is given by equation (9) as U T = U,Z * = 0 - 0 - k f 2 2 Q / K = -Q [Us,] LO1 [01 0 1 [ Ql Example 2 An application of the method in substructure analysis is now demonstrated. The substructure A of Figure 3(a) has 48 nodes in the circumferential direction and 5 nodes in the axial direction with 6 degrees-of-freedom per node. Its total degrees-of-freedom are 1,440 with 288 variables on the boundary with substructure B. The adjoining substructure B is modelled using Fourier term axisymmetric shell elements and the boundary variables are given in terms of 44 Fourier coefficients. It i s required to reduce the 1,440 variables in A to its boundary values, in terms of the coefficients of substructure B, in order to synthesize the two structures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000213_978-1-4419-8710-5-Figure5.6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000213_978-1-4419-8710-5-Figure5.6-1.png",
        "caption": "Figure 5.6. Conventional Active-Input Current Mil ror, (a) bipolar and (b) MOS versions",
        "texts": [
            " These structures assure that Collector (or Drain) voltages of input and output transistors are the same: the output transistors are the current source transistors Q1 or Q2 of Fig. 5.4(a) whose Collectors will be connected to voltage Vs. Consequently, the use of this current mirror to generate the Emitter voltage of all synaptic current sources eliminates the Early voltage effect , which is very high for minimum size lateral bipolars [Arreguit, 1989]. 124 ADAPTIVE RESONANCE THEORY MICROCHIPS The advantages of the Emitter/Source driven active input current mirrors of Fig. 5.5 over the conventional active input current mirror, shown in Fig. 5.6 are: 1. As mentioned earlier, it allows to share the Base voltage (in the bipolar case) for all current mirrors on the same chip, independently of the current value to be mirrored. This fact allows all current mirrors to share their Base diffusion (or well), which yields a much higher density layout. mirror input stage (voltage amplifier and transistor Min) for the MOS ver sions in Fig. 5.5(b) and Fig. 5.6(b), assuming the differential input voltage amplifier can be modeled by a single pole behavior (gm1, gol and Cp1 ). Ca pacitance Cp models the parasitic capacitor at the input node of the mirrors and gm2, g02, Cgd2 are small signal parameters for transistor Min. For the conventional structure (Fil?;. 5.7(b)) the resulting characteristics equation is 8 2 [Cp1 Cp + Cgd2(Cp1 + Cp)] + 8[gol(Cp + Cgd2 ) + g02(Cp1 + Cgd2 )+ +Cgd2 (gm2 - gm1)] + [golg02 + gm1gm2] = 0 (5.12) By reducing I u, gm2 and g02 are made smaller, and may make the 8 coefficient negative, introducing instability and the need for compensation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000383_10402009408983294-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000383_10402009408983294-Figure1-1.png",
        "caption": "Fig. 1-Statlc and dynamic test diagram. Fig. 2-Adjustable frame.",
        "texts": [
            " A new type of hydrostatic and hybrid bearing test rig has been set up for static and dynamic tests of journal bearings with automatic collection and management of the test data. TEST RIG The test shaft (50 mm in diameter) is supported by two h'igh-stiffness hydrostatic bearing blocks with the loaded test bearing in the middle of the shaft. During rotation of the shaft, the test bearing is free to translate and swing under the static load and finally locate at an equilibrium position, with a certain eccentricity and attitude angle to the shaft. The instrumentation diagram for the test is shown in Fig. 1. The key approach of static load testing of a bearing is to measure the pressure and thickness distribution in the oil film by means of a micro pressure transducer and a displacement transducer, buried in the shaft perpendicularly to each other. Since a smaller probe more accurately measures the local film pressure, a micro transducer only 2 mm in diameter was employed. Signals from the rotating shaft were brought out to the stationary signal conditioning equipment by slip rings which were fitted at the end of the shaft",
            " For this reason the misalignment jig employed the principles that a taut wire had low lateral stiffness compared to the longitudinal stiffness, and that a plane was identified by three points. Therefore, the misalignment of the test bearing could be slightly adjusted in the horizontal and vertical planes with an adjustable frame fixed to a taut wire, shown in Fig. 2. In order to minimize interfering signals, in dynamic load tests, signals were transferred from the time domain to the frequency domain. As shown in Fig. 1, under and behind the test bearing electromagnetic exciters each applied an exciting force to the test bearing in the horizontal and vertical direction alternately. The exciting force and its corresponding absolute and relative displacements of the shaft and test bearing were then collected by transducers for input to a digital analyzer simultaneously in order to obtain the frequency responses. Four stiffness coefficients and four D ow nl oa de d by [ C ar ne gi e M el lo n U ni ve rs ity ] at 2 0: 48 1 6 O ct ob er 2 01 4 Experimental Investigation of Hybrid Bearings 287 damping coefficients of oil film were then easily evaluated from Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002848_0020-7462(84)90034-9-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002848_0020-7462(84)90034-9-Figure3-1.png",
        "caption": "Fig. 3. Deformed configuration of totally wrinkled membrane.",
        "texts": [
            " 2w/s' in 42o ~,/,,, v /s in0o + sin4) Thus for a given P (or F), 42o and ~bl can be evaluated using equations (12) and (13) as a result of which the shape of the wrinkled region is determined as /1 sin(/) F R o S ' sin42 d42 r(42) = F R o + -\" h ( 4 2 ) - .. . (14) N sin420 2\\/sin42o -e,,,\\/sin(/)o + sin~ Singularities in equations (1 3) and (14) (at -420) are handled during the integration process, unless 42o = ~z/2. In stating the boundary conditions (10), it was assumed that the membrane is flee to deform into the shape depicted in Fig. 2. If the initial central angle of the membrane is rio (see Fig. 3) the above relations will be applicable until the angle qS~, denoting the slope of the tangent of the deformed membrane at the support, reaches the central angle value rio. When (h, = [~o and under increasing load the following conditions must be met r((/;i ) - Ro sinfio. (1 5) Introducing equation (1 5) in to the boundary conditions and rearranging the inextensibility condition, one arrives at a new relation fiom which the values of (ho and (/)~ can be found sin&l sine/fo = - 1 (16) sin&c, 1 \"'2 f: -,I,~ dO [~o = ~ ~ ( 1 7 1 2\\, sin42(~ "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001700_1.1636193-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001700_1.1636193-Figure4-1.png",
        "caption": "Fig. 4 Hoop",
        "texts": [
            " is a standard dry friction model @7# in which m denotes the associated kinetic coefficient of fric- DECEMBER 2003, Vol. 125 \u00d5 531 003 by ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F tion. The equations governing the motion of the ball will be numerically integrated in time. During contact with the backboard, the basketball will either slide or roll. The dry friction model accurately predicts the motion of the basketball during roll, as well as during sliding ~see Appendix 2!. Contact With the Hoop. Now consider the contact between the basketball and the hoop ~see Fig. 4!. When the basketball is in contact with the hoop, the use of any one of the popular coordinate systems, i.e., rectangular, polar, tangential-normal, and spherical @7#, is cumbersome. It proves advantageous to develop a customized coordinate system for the contact with the hoop. The customized coordinate system is referred to here as the hoop coordinate system. Using the hoop coordinate system, the position vector C of the basketball is expressed as: rC5xi1yj1zk5rnun1rfuf , rn5R2uH2RH cos f , (5) rf5RH sin f , where uH denotes the compressive displacement of the basketball"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002297_robot.1998.680701-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002297_robot.1998.680701-Figure1-1.png",
        "caption": "Fig. 1: Enveloping grasp of multiple objects",
        "texts": [
            " 7711- tler siich a condition: they discussed several graspiiig issues, such as the stability of grasp; the analysis of contact force, the planning for manipulating an object, and so forth. In this paper; we relax tlie of single object, and discuss how to grasp multiple 01)- jects by a multifingered hand. Suppose that a multifingered hand is grasping two ohjects by the finger tip grasp. Intuitively, we can imagine that it is difficult for siich system to keep a stable grasp and the system will easily fkil in grasping for a sinal1 disturbance. On the other hand, suppose that a multifingered hand is grasping two objects by enveloping grasp, as shown in Fig.1. It seems that the enveloping grasp can achieve this task even more easily than the finger tip grasp. We can find another advantage for enveloping two objects by a multifingered hand. Suppose that the friction between an object and the link surface is very significant. Under such a condition, since it is hard to lift up the object by slipping over the link surface, we have to provide an alternative scheme based on rolling contact. In siich a case: one finger continuously pushes the object so tliat it may be rolled 1113 over the siirface of the other fingers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003678_00022660510597223-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003678_00022660510597223-Figure1-1.png",
        "caption": "Figure 1 System of axes considered for a plane in flight",
        "texts": [
            " Several authors have derived different models for airplanes (Roskam, 1995a; Seckel, 1964; Blakelock, 1965; Dole, 1984; Bryson, 1994; Fuerza Aerea de Chile, 1987; Roskam, 1995b; Van Sickle, 1965). A plane in flight is a system of six degrees of freedom. The equations describing the plane dynamic behavior are three force equations, three momentum equations, and a seventh equation relating the kinetic energy (Roskam, 1995b). If we consider a coordinate system of perpendicular axes rotating with angular velocity ~v as shown in Figure 1, the equations describing the movement are: ~F \u00bc m \u203a ~V \u203at \u00fe ~v \u00a3 ~V ! where ~V is the velocity of the center of gravity with respect to the rotating axes and m represents the mass of the body. Furthermore the momentum balance equation is: ~M \u00bc \u203a ~H \u203at \u00fe ~v \u00a3 ~V where ~H represents the kinetic moment of the body with respect to the rotating axes. The orthogonal systems used to describe the plane behavior are the terrestrial axes (coordinate system X0Y0Z0) and rotating axes (coordinate system XYZ). We will assume that the plane total mass and mass distribution remain constant. This is a reasonable assumption for mass that changes less than 5 percent within the first 30-60 s of flight, with respect to the fuel consumption. We apply Newton\u2019s second law to a wing profile over the non-inertial rotating axes XYZ (Figure 1), characterizing each vector component on the coordinate axes system (as shown in Figure 2). Noting that the inertia moment Ixy \u00bc Iyz \u00bc 0; because of the plane symmetry in the XZ plane, we obtain the following linear and angular momentum equations (Roskam, 1995b) . Scalar equations of linear momentum m\u00f0 _U 2 VR \u00fe WQ\u00de \u00bc mgx \u00fe FAx \u00fe FTx m\u00f0 _Y 2 UR \u00fe WP\u00de \u00bc mgy \u00fe FAy \u00fe FTy m\u00f0 _W 2 UQ \u00fe VP\u00de \u00bc mgz \u00fe FAz \u00fe FTz . Scalar equations of angular momentum _PIxx 2 _RIxz 2 IxzPQ \u00fe \u00f0Izz 2 Iyy\u00deRQ \u00bc LA \u00fe LT _QIyy \u00fe \u00f0Ixx 2 Izz\u00dePR \u00fe Ixz\u00f0P2 2 R2\u00de \u00bc MA \u00fe MT _RIzz 2 _PIxz \u00fe \u00f0Iyy 2 Ixx\u00dePQ \u00fe IxzQR \u00bc NA \u00fe NT where I denotes the moment of inertia"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001993_s003320010001-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001993_s003320010001-Figure8-1.png",
        "caption": "Fig. 8. The spring-loaded inverted pendulum (SLIP) monoped is dynamically equivalent to the SLSK monoped when there is no mass as the knee (m0 = 0).",
        "texts": [
            " Although X Hpert is nonintegrable and the spring potential, U , is not prescribed at all, h1 U closely approximates the results of numerically integrating trajectories of X Hpert from stance bottom states (where the leg spring is maximally compressed) to flight apex states (where the body\u2019s vertical height is greatest) for all instances we have examined when U is a convex function (i.e., the spring resists compression with a nonnegative stiffness). For example, when we take the potential function of (47), UT H K (qr ) = k 2 ( arccos [ q2 r \u2212 l2 1 \u2212 l2 2 2l1l2 ] \u2212 arccos [ q2 rl \u2212 l2 1 \u2212 l2 2 2l1l2 ])2 , resulting from a torsional Hooke\u2019s law spring at the \u201cknee\u201d of the slightly more zoomorphic leg (see Appendix B) of Figure 8, we produce with (1) and (2) a map that takes the cubic cell of bottom states shown in Figure 7(a) into a twisted volume of apex states similar to that of Figure 7(b). The bottom state cube of Figure 7(a) contains leg lengths in the range rb \u2208 [0.75, 0.975] m, angular momentum in the range p\u03b8b \u2208 [1.5, 6.5] kg m2 rad/s, and spring potential energy in the range U (rb) \u2208 [2.5, 7.5] kg m2/s2, and we shall use it throughout the paper as a means of comparing approximants, since it results in a typical range of human gaits: hopping heights in the range ya \u2208 [0",
            " The SLIP monoped operates in two distinct dynamical phases, depending on whether it is on the ground or in the air. Section 2 introduces the Hamiltonian dynamics of both phases. The first question addressed is the importance of the spring law. While virtually all successful running robots to date have adopted the revolute-prismatic kinematics of the SLIP monoped, biomechanists have heretofore adopted this model [5] only in analogy to the more biologically valid revolute-revolute kinematics, the toe and knee depicted in Figure 8. Thus, while it is straightforward to express a given spring law in one or another set of coordinates, it is equally clear that simple expressions in one set will yield very complex expressions in the other, and vice versa. More fundamentally, actuation technology in robotics is incredibly diverse, and the form and function of animal muscles is similarly varied. We seek a mode of analysis that does not commit to any specific spring form. Any physically interesting SLIP spring potential law must be repulsive in nature",
            " This question is more than academic, since other spring laws appear prominently in the running literature. For example, the familiar Hooke\u2019s law spring is used extensively by the biomechanists in their running studies [4], [5], [8], and it also accurately models the springs used in Buehler\u2019s running machines [15], [31]. In an attempt to address this question, we introduce two different spring models, a SLIP Hooke\u2019s Law Spring, UH (qr ) = k 2 (rl \u2212 qr ) 2 and DUH (qr ) = \u2212k(rl \u2212 qr ), (16) and a \u201cTorsional Hooke\u2019s Law\u201d pulled back from the \u201cknee\u201d of the revolute-revolute leg shown in Figure 8. The potential and force law for this spring, which are derived more thoroughly in Appendix B, are given by UT H K (qr ) = k 2 ( arccos [ q2 r \u2212 l2 1 \u2212 l2 2 2l1l2 ] \u2212 arccos [ q2 rl \u2212 l2 1 \u2212 l2 2 2l1l2 ])2 and DUT H K (qr ) = \u22122qr k (arccos [ q2 r \u2212l2 1\u2212l2 2 2l1l2 ]\u2212 arccos [ q2 rl\u2212l2 1\u2212l2 2 2l1l2 ])\u221a 4l2 1l2 2 \u2212 (q2 r \u2212 l2 1 \u2212 l2 2) 2 . (17) To compare the Air Spring solution to those of the other springs, we numerically integrate the unperturbed stance dynamics from bottom (pr = 0) to liftoff (qr = qrl) for a large number of initial (bottom) conditions for both of these Hooke\u2019s law springs",
            " However, one can easily see that the set of bottom conditions for which (37) is violated will be a \u201cthin\u201d set and therefore unlikely to occur. While bearing strong resemblance to the physical construction of many running robots [32], [15], the SLIP leg bears little resemblance to animal legs, since they generally have revolute, not prismatic, joints. To begin to make the connection to more biologically plausible models, we introduce the simplest physical correlate, the revolute-revolute leg with a spring at the knee, shown in Figure 8. This leg will be referred to as the SLSK (Spring-Loaded Small Knee) leg. In the case of negligible leg (knee) mass, there is a change of coordinates\u2014an isometry, in fact\u2014between the SLIP and SLSK leg motions.14 As Figure 8 suggests, for any SLSK spring, there is a well-defined SLIP spring and vice versa (the two are related, of course, through the transposed jacobian of the isometry), such that SLSK motion from any initial condition can be read off the motion of the SLIP mapped back through the isometry (assuming appropriately chosen SLIP initial conditions). Since all properties of interest are invariant under change of coordinates, and since the isometry can be written in closed form, it follows that we can derive the same insights from either leg model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001033_a:1009832426396-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001033_a:1009832426396-Figure4-1.png",
        "caption": "Figure 4. Slider crank mechanism with one flexible body.",
        "texts": [
            " In order to obtain the acceleration level constraint, one can differentiate Equations (7) and (8) twice with respect to time to yield (Ci q)flex q\u0308i = \u2212((Ci q)flex q\u0307i) q q\u0307i = (Qi c)flex =  Ai ((\u0303u\u0304 i \u03c9\u0304) \u00d7 \u03c9\u0304)\u2212 2 Ai \u02dc(8i R p\u0307if ) \u03c9\u0304 fT H1 g + 2 fTH2 g + fTH3 g + fTH4 g gT H1 h + 2 gTH2 h + gTH3 h + gTH4 h fT H1 h + 2 fTH2 h + fTH3 h + fTH4 h  , (14) where \u03c9\u0304 is the angular velocity with respect to the body reference frame and the generalized velocity vector q\u0307 is q\u0307 = [R\u0307i T \u03c9\u0304i T p\u0307i Tf r\u0307i+1 T \u03c9\u0304i+1 T ]T and H1 k = \u02dc\u0304\u03c9i \u02dc\u0304\u03c9i Ai T Ai+1 k H2 k = \u02dc\u0304\u03c9i Ai T Ai+1 k\u0303 \u02dc\u0304\u03c9i+1 H3 k = Ai T Ai+1 \u02dc\u0304\u03c9i+1 \u02dc\u0304\u03c9i+1 k H4 k = ( \u02dc(8i \u03b8 p\u0307if ) Ai f Ai,i+1 k) \u00d7 (8i \u03b8 p\u0307if )  , k = g, h. (15) Even though the proposed method is applicable to a general system consisting of many flexible bodies, a slider crank mechanism with one flexible body (Figure 4a) is used to show the impact of the proposed method on the equations of motion. An equivalent virtual system, modeled by using the rigid virtual bodies proposed in this investigation, is shown in Figure 4b. The augmented equations of motion for the system are obtained by using the general form of equations of motion as [11][ M Cq T Cq 0 ] [ q\u0308 \u03bb ] = [ Qe +Qv +Qs Qc ] , (16) where M is the mass matrix of the system. Non-singularity of the coefficient matrix of Equation (16) is proved in the following subsection. The q\u0308 consists of translational acceleration for rigid and flexible bodies, angular acceleration, and modal acceleration for the flexible body. The \u03bb is the vector of Lagrange multipliers and Qs , Qv, and Qe are the strain energy terms, velocity induced forces, and externally applied forces, and the vector Qc absorbs terms that are quadratic in the velocities, defined clearly by Shabana [11]. The mass matrix for the system in Figure 4a is M =  M1 f 0 M2 r 0 M3 r  , (17) where Mf and Mr are the mass matrices for a flexible body and for a rigid body, as M1 f =  mrr symmetric m\u03b8r m\u03b8\u03b8 mf r mf \u03b8 mff  (6+nf )\u00d7(6+nf ) , Mk r = [ mk rr 0 0 mk \u03b8\u03b8 ] 6\u00d76 , k = 2, 3 (18) and nf is the number of modal coordinates. The conventional constraint Jacobian matrix (Cq)c of the slider crank mechanism with flexible crank is (Cq)c =  (C01 q )flex,c (C12 q )flex,c (C23 q )joint (C30 q )joint  , (19) where (Cq)flex,c is the constraint Jacobian matrix of the flexible joint obtained by the conventional method [11]. The mass matrix for the system in Figure 4b is M =  M1 v M2 f 0 M3 v 0 M4 r M5 r  , (20) where the mass matrix for virtual body, Mv, the mass matrix for flexible body, Mf , and the mass matrix for rigid body, Mr , are Mk v = [ 0 ]6\u00d76, k = 1, 3, M2 f =  mrr symmetric m\u03b8r m\u03b8\u03b8 mf r mf \u03b8 mff  (6+nf )\u00d7(6+nf ) , Mk r = [ mk rr 0 0 mk \u03b8\u03b8 ] 6\u00d76 , k = 4, 5. (21) The proposed constraint Jacobian matrix (Cq)p of the slider crank mechanism with flexible crank is (Cq)p =  (C01 q )joint (C12 q )flex,p (C23 q )flex,p (C34 q )joint (C45 q )joint (C50 q )joint  , (22) where (Cq)flex,p is the constraint Jacobian matrix of the flexible body joint obtained by the proposed method",
            " This mixed formulation can be very effective if a set of basic joint and force modules have already been developed and more modules for the flexible bodies need to be added. Dynamic analysis of a flexible slider crank mechanism and a flexible pendulum mechanism is presented in order to validate the results from the proposed method. The example problems are solved by using both the proposed method and the nonlinear approach developed by Simo and Vu-Quoc [6]. The system consists of two rigid bodies and one flexible body, as shown in Figure 4a constant acceleration is imposed on the joint between the ground and the body 1 as a driving constraint. Length, cross sectional area, and area moment of inertia of the elastic crank are 0.4 m, 0.0018 m2, and 1.215\u00d710\u22127 m4, respectively. The crank is modeled by using 10 two-dimensional elastic beam elements of equal length. The material mass density of the beam is 5540.0 kg/m3 and its Young\u2019s modulus is 1.0 \u00d7 109 N/m2. Vibration analysis of the crank is carried out by an FEA program. Since the crank is driven by the driving constraint, the fixed-free boundary condition is used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003084_s00422-005-0008-x-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003084_s00422-005-0008-x-Figure5-1.png",
        "caption": "Fig. 5 A locomoting robot",
        "texts": [
            "1 Internal and External Configuration Variables Applying the spinal fields paradigm to locomotion requires a formalization of the distinction between internal and external variables. We follow the same approach given in (Bloch et al. 1996) and (Ostrowski 1999), distinguishing the configuration variables of a locomoting robot into two classes. A first set of variables, g \u2208 G, describes the position of the robot in terms of the displacement between a coordinate frame attached to the robot and an inertial reference frame (Fig. 5). Typically, the set of displacements is chosen to be SE(m) with m \u2264 3 or one of its subsets. The second class of variables, r \u2208 M , defines the internal configuration, or shape, of the mechanism (Fig. 5); M takes the name of shape space and is required to be a manifold. The total configuration space is therefore Q = G\u00d7M . 3 Notice that some regions of the output space are outside the convex hull formed by z1 f , z2 f , z3 f . Points outside the convex hull can be reached only choosing negative combinators. The choice of negative coefficients does not affect stability: positivity of combinators is a sufficient condition (see Note 6) for the stability of the linear combination of stabilizing force fields"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003859_iros.1989.637921-Figure15-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003859_iros.1989.637921-Figure15-1.png",
        "caption": "Figure 15: Sett ing of mobile and objec t cells.",
        "texts": [
            " In docked s t a t e , t h e communication is done through COMBUS connected by 14 pin-connector.(see Fig.14) Transmitting and receiving are done by DI/DO G Experimental rcsul ts . The communication experiments are made based 0x1 t h e communication protocol. 6.1 Expcrimcntai r c s u l t s of communication in t h e undockcd state. 'IWo of t h e purposes of communication are cell identification and automatic measurement of re la t ive distance and angle. realized. Three cells are arranged as shown in Fig.15 and t h e communication between master cell(cel1 0 ) a n d s l a v e ce l l ( ce l1 1 ) is achieved. Figure 16 shows t h e communication sequence as shown on a computer monitor. In Fig.16, t h e communication statements are shown as comments and t h e numbers to t h e l e f t of t h e comments mean communication s t e p as follows. 0-0: Decision of master cell's address and desired cells function. 0-0: A l l cells except communication master c e l l Adjust t h e i r sensors t o sender cell. 0-0 : The communication sequence is done in order "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000761_b000550i-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000761_b000550i-Figure5-1.png",
        "caption": "Fig. 5 Schematic diagram of the needle biosensor for glucose.",
        "texts": [
            " Other effects of heparin on the enzyme kinetics and stability cannot be ruled out. The lower sensitivity observed in the presence of heparin is not of concern in view of the favorable signal-to-noise characteristics [e.g., Fig. 1 and 3(B)]. Since the primary application of the electropolymeric entrapment of heparin is for fabricating implantable glucose biosensors, we examined the concept in connection with a miniaturized needle electrode. This configuration relied on the incorporation of GOx within a carbon paste microelectrode of 250 mm diameter (Fig. 5), while using the PPD for entrapping the heparin and excluding potential interferences. Fig. 6 demonstrates the transient response of the needle electrode to alternate exposures to flowing 4 3 1023 and 1 3 1022 M glucose solutions. Both the bare (A) and PPD-coated (B) carbon paste microelectrodes display significant ( > 50%) current suppressions following a 60 min exposure to whole blood (a vs. b). In contrast, a similar exposure of the heparinized biosensor has a negligible effect on its response (a vs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000615_rnc.4590050410-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000615_rnc.4590050410-Figure3-1.png",
        "caption": "Figure 3. A sketch of the firetruck, with steering wheels on the front and back axles",
        "texts": [
            " + nk-, is needed to convert the system Some specific multi-steering mobile robot systems will be examined to show how the Pfaffian systems generated by the rolling without slipping constraints can be converted into extended Goursat normal form. The examples were chosen so that the general form of the transformation into Goursat form can be seen. + nk-2. into extended Goursat normal form. Example 1 . Two, three, or four axles It is a simple exercise in combinatorics to check that all of the possible configurations with two or three axles and one, two or three steering wheels satisfy the conditions of Theorem 9. Note particularly the firetruck e ~ a m p l e , ~ sketched in Figure 3, which corresponds to n = 1. In addition, it can be shown that all except one configuration of a system with four axles will satisfy the conditions of Theorem 9. The exception is m = 2, two steerable axles, two passive axles, alternating. That is, the first and third axles are steerable, and the second and fourth axles are passive. This situation would arise if a car were towing another car and both of the cars had drivers at the steering wheels. This example satisfies Proposition 10, and thus can be converted into Goursat form without prolongation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003209_j.jsv.2004.12.011-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003209_j.jsv.2004.12.011-Figure2-1.png",
        "caption": "Fig. 2. Outline of loading systems and sensors\u2019 locations.",
        "texts": [
            " The shaft is driven by an 80 kW AC motor (1) through a gear box (3) and a flexible bar coupling (2). The rotational frequency can be adjusted by an infinitely variable transmission controller and can reach 60Hz (3600 rev/min). The transmission ratio of the gear box is 2.8. Two separate oil supply systems are used to feed the lubricant into the gear box (3) and test bearing (13). The lubricant is turbine oil 22#, kinetic viscosity 48:65 10 3 Pa s at 20 1C and 28:25 10 3 Pa s at 30 1C. It can be seen from Figs. 2 and 3 that two electric exciters compose the dynamic load system (Fig. 2-1). They are placed perpendicular to each other at 451 to the horizontal pointing to the geometric center of the test bearing. Each of the exciters is manipulated by an individual controller and driver system. The exciters can generate sinusoidal forces up to 1.5 kN in two directions simultaneously. And they are connected to the bearing housing by thin-walled tubular connecters. The pressure sensors (Fig. 2-2), which mount in the middle of connecters, are used to measure the excitation forces. The oil-film forces in the experimental rig are analyzed in Fig. 4. Note that f 3 is the static load on the bearing, which is induced by pneumatic loading system; f 1 and f 2 are dynamic loads, which are generated by two exciters. In Fig. 4(a), the X and Y are absolute movement coordinates of the bearing housing. In Fig. 4(b), the x1 and y1 are relative movement coordinates of the rotor. The oil-film forces can be calculated from the following equations: f X \u00bc f 1 cos 45 f 2 cos 45 \u00fe m \u20acX , f Y \u00bc f 1 sin 45 \u00fe f 2 sin 45 \u00fe f 3 mg \u00fe m \u20acY , (2) where f 1; f 2; and f 3 can be measured from pressure sensors in the test rig",
            " It should be pointed out that the static component of load f 3; i.e., f 30; is dominant, and the dynamic component ~f 3 which results from the pneumatic loading system is trivial. In the process of computing the dynamic oil-film force ~f Y ; the tiny dynamic component ~f 3 is taken into account. The detailed calculation procedure and data acquisition techniques are discussed in the next section. Displacement sensors and force sensors are employed to acquire testing data. The positions of these sensors are shown in Fig. 2. Six eddy current sensors (Tsinghua 8500) are used to measure displacements. Four of them (12 and 15) are installed on the test bearing housing at both ends of the test bearing to measure the relative displacements between the bearing and the journal in the horizontal and vertical directions \u00f0x1; y1\u00de: The other two (3 and 13) are installed on the framework to measure the absolute displacements of bearing housing in the horizontal and vertical directions \u00f0X ;Y \u00de: A pressure sensor (17, GKCT15-1A) is positioned under the top splint to measure the pneumatic load \u00f0f 3\u00de: Another two pressure sensors (2, GKCT15-2C) are connected to the exciters to measure dynamic loads (f 1 and f 2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001358_s0094-114x(03)00090-9-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001358_s0094-114x(03)00090-9-Figure4-1.png",
        "caption": "Fig. 4. Triad with one external prismatic joint.",
        "texts": [
            " In the present paper four kinematic models of the Assur group with one, two and three prismatic joints are investigated. In all cases, using a successive elimination procedure, a final polynomial equation in one unknown is obtained. Since the degree of freedom of the Assur group is zero, it is a statically determinate structure. In order to solve the position analysis of the Assur group with one external prismatic joint, without loss of generality, a local Cartesian coordinate system, with origin the joint A, and x-axis from A to D is chosen (Fig. 4). The position of the external revolute joints A\u00f00; 0\u00de and D\u00f0d; 0\u00de and of the auxiliary point F \u00f0xF ; yF \u00de situated on sliding direction of the external prismatic joint are known, as well as the length of links and the angles a and h. The distance d1 from the joint E to sliding direction is also given. The position of the triad links is described by a small number of parameters, such as the coordinates of the internal joint B\u00f0x; y\u00de and the displacement s, in order to obtain a small number of equations and unknowns",
            " (1), a final polynomial equation of sixth order with only variable s is derived: X6 i\u00bc0 Hisi \u00bc 0 \u00f024\u00de which is free from extraneous roots and whose coefficients Hi (i \u00bc 0; 1; . . . ; 6) depend only on the Assur-group data. Eq. (24) provides six solutions for s in the complex field. For every root sr (r \u00bc 1; . . . ; 6), the coordinates of the internal joints B, C, E are determined. The real solutions correspond to the assembly modes of the triad. The order of the polynomial equation (24) is minimal. This is confirmed by the following consideration: For a given position of the external joints A, D and G of the triad (Fig. 4), the internal joint E lies on the tricircular sextic curve of the four-bar mechanism ABCD of the RRRR type [2]. Also E belongs to the straight line parallel to the sliding direction of the external prismatic joint and located at distance d1. The point E is the intersection point of the sextic curve with a straight line. This intersection contains at most six real intersection points and therefore the maximum number of the assembly modes of the triad is six. The number of real solutions can be reduced to four, two or zero, depending on the links lengths and the position of the external joints of the triad",
            " The point B3 is the intersection point of the second order curve with a straight line and two real intersection points exist at most. Therefore the maximum number of the assembly modes of the triad with three external prismatic joints is two. Finally, using Eqs. (55) and (56) the coordinates of the internal joints B1, B2 and B3 are calculated. In this section the proposed procedures are applied to corresponding numerical examples. The method presented in Section 2 is applied in the first numerical example for the triad with one external prismatic joint (see Fig. 4). The geometrical data, the position of the external joint D and of the auxiliary point F of this triad are given in the left part of the Table 1. For the specific geometry here considered, the coefficients of Eq. (24) are calculated and the following sixth order polynomial equation with parameter s is obtained: 7:23424s6 \u00fe 0:315365s5 0:0181185s4 \u00fe 0:0535636s3 \u00fe 0:0109935s2 0:0000497313s 0:0000137254 \u00bc 0 The roots of the above polynomial equation are determined numerically. The six solutions for this polynomial are inserted in the Table 1, where two real roots and four complex roots are obtained for the specific geometry here considered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002297_robot.1998.680701-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002297_robot.1998.680701-Figure4-1.png",
        "caption": "Fig. 4: Definition of the project,ioli plane",
        "texts": [
            " 0 0 0 0 0 1 0 -B2YCzly 0 0 1 B2ZC21y - 0 1 BlZCOl-, 0 -1 - -B2ZCOly B2 0 0 1 0 - B l y C o , - , -1 0 Ycoly From this results, we can say that tAe matrices B , ~ ( z , U ) . and B 1 2 ( 2 , ~ ) are alrnost identical to the zero matrices since all components are either exactly zero or extremely srna,ll values. On t,lie other hand, the matrices Bzl (z, U ) and Bol (2: U ) incliidc enough large coinponents. Tli~is, theorem 1 eiisiircs that object, 2 can keep rolling condition at both contact points while object 1 cannot. 6 Condition for Lifting up 111 this section, we consider wlictlm two objects ca,n be lifted iip by a simple pushing rriot,ion(Fig.l). As shown in Fig.4; the common ta,ngent,ial plane of two objects are defined a,s n. The plane which is normal to 11 and tangent to the gravity vector is defined as I?. We consider the motion of the objects projected on r. The rolling condition is assumed to be satisfied at each contact point. The kinematic relationship between the objects projected on r is shown in Fig5 where the suffix y denotes a vector on the two dimensional plane I?. For simplicity we assume that an object contacts with one finger at one point or that contact points between an object and fingers are overlapped when they are projected on I7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000707_s1359-6462(98)00173-0-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000707_s1359-6462(98)00173-0-Figure1-1.png",
        "caption": "Figure 1. Schematic diagram comparing the structure of polycrystalline and \u201cbamboo\u201d fibres. Formation of a \u201cbamboo\u201d structure eliminates triple junctions isolating contributions to mechanical properties from grain boundaries [ref. 15, 16].",
        "texts": [
            " Grain boundaries were subsequently classified using Brandon\u2019s criterion [27] for the maximum permissible deviation from the CSL relationships. ASTM Type V dogbone tensile specimens and 1mm 3 1 mm 3 10cm \u201cpolycrystalline\u201d fibres were electro-discharge machined separately from material containing the lowest and highest frequency of \u201cspecial\u201d grain boundaries. Fibres of each material were also electrochemically thinned to a diameter of 100mm, representing one-half of the nominal grain size, as depicted schematically in Figure 1. Fibres were electrothinned in a 10% (by vol.) perchloric acid in methyl hydrate solution at 240\u00b0C using an applied voltage of 40V for approximately 5 min. Twelve replicate samples of each geometry were tensile tested to failure at room temperature according to ASTM E8 using an elongation rate of 1mm/min with a nominal gauge length of 51mm [28]. Strain-at-failure, yield stress at 0.2% offset, and ultimate tensile strength (UTS) were evaluated for the Type V sample geometry and compared between materials representing extremes in low-S CSL grain boundary fractions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002010_cdc.1991.261601-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002010_cdc.1991.261601-Figure1-1.png",
        "caption": "Figure 1: Description of the DolphinSK vehicle.",
        "texts": [
            " Finally, in Section 4 we evaluate the performance of the controller on a full nonlinear model of the vehicle. 2 A Model for an AUV The model of a thruster propelled AUV that we use in this paper is described in [lo], to which the reader is referred for complete details (see also [3] and [la] for standard nomenclature). For sake of clarity, the model is briefly described below. 2.1 The Dynamics of a Thruster Propelled AUV Let {A} denote an inertial frame, and let {B} denote a body coordinate frame that is fixed with respect to the vehicle (see fig.1). We introduce the following notation: P = (pz, p,, pz)\u2019position of the origin of {B} expressed in {A}; U = (U=, uy, tiz)\u2019linear velocity of the origin of {B} relative to {A}, expressed in {E}; U - Linear acceleration of the origin of B relative to {A), expressed in {B); R = (U=, U,, w,)\u2019-.rotational velocity of {B) relative to {A), expressed in {B}; R - rotational acceleration of {B) relative to {A}, expressed in {B); R - rotatioq matrix which describes the orientation of {E} relative to {A}; R - timederivative of the rotation matrix R; SO(3) - Lie group of 3 x 3 unitary matrices",
            "3 Sensor Dynamics The following sensors are available to measure A, R, U , and P (see [lo] for technical details and sensor modelling): A - roll and pitch are obtained from two pendulums, and yaw is available from a directional gyrocompass; R - roll, pitch and yaw rates are directly available from rate-gyros; U - linear velocities are obtained from a three axis Doppler sensor; P - linear positions are estimated by combining the information that is provided by a long base line acoustic positioning system, together with the linear velocity vector U and linear accelerations given by three accelerometers. 2.4 Nonlinear Model Implementation The model described was integrated in the control suite M A T R I X x \u2019 , and tailored for the thruster propelled DOLPHIN 3K vehicle described in [9], for which a complete set of hydrodynamic parameters is available (See fig.1 for a description of the geometry of the vehicle). The input-output structure of the model is depicted in fig.2, where we introduce some notation that will be used in the sequel: U = ($a) xa, y.1 za, 0,)\u2019 is the input actuator vector that consists of $a (differential command in thrusters 1 and 2), x, (symmetric command in thrusters 1 and 2), yo (differential command in thrusters 3 and 4), z, (sym- metric command in thrusters 5 and 6), 0, (differential command in thrusters 5 and 6). The water speed UW is a constant perturbation that is specified in the simulation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002315_robot.1993.291875-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002315_robot.1993.291875-Figure4-1.png",
        "caption": "Figure 4: A manipulator-base system",
        "texts": [
            " For example, if we consider a manipulator on a base that is powered by two independently driven, coaxial wheels, the generalized velocities are the manipulator 'oint velocities, the angular velocity of the base and the linear com onent of the velocity of a suitable point (say the mi&oint of the axle) on the base alon the perpendicular to the axle. We can model the whejs with a prismatic joint perpendicular to the axle and a revolute joint perpendicular to the plane of the platform through the midpoint of the axle. Thus we have a serial chain consisting of revolute and prismatic joints which can be modeled according to Sections 2 and 3. We consider a simple example of a planar three degree-of-freedom manipulator with revolute joints mounted on a wheeled base as shown in Figure 4. The base is geometrically similar to the LABMATE (Transitions Research Corporation) mobile platform. I t has two driving wheels on an axis which passes through the vehicle's geometric center as shown in Figure 3. They are powered by D.C. motors. The platform has four passive wheels (castors) on each corner. The platform's position is uniquely specified by the position of its geometric center (z,y) and the angle of orientation q5 as shown in Figure 4. The manipulator joint angles are given by \\k l , \\ E 2 and \\k3. Thus the six generalized coordinates are: q = [ E y dJ \\Er1 *2 %IT The end-effector position and orientation is specified by the Cartesian coordinates X, Y, and 0 as shown in Figure 4. E'rom the kinematics of the wheeled system the nonholonomic constraint corresponds to: A(q) = [ - s in(4) cos(4) 0 0 0 01 The objective is to decompose the end-effector twist, SE, into joint rates and Section 3 offers a general method to fulfill this goal. There are other considerations to keep in mind, especially when selecting the stiffnesses in the W matrix: 1. By making all the joints equally stiff 2. By makin we obtain the well-known Moore-Penrose pseudo inverse solution [8]. the manipulator joints more compliant than the pfatform's freedoms, we can synthesize a behavior in which the platform res onds more sluggishly than the manipulator",
            " This is because r is not the Jacobian matrix of a kinematic function f ( q ) [l]. One way to proceed is by imposing additional constraints on the nonholomic system so that the resulting sustem is holonomic. Thus the additional constraints, say, B(q)dq = 0, must be such the resulting Pffafian form: is integrable. For example B(q) = [0 0 11 (the platform can only translate) or B(q) = [(% - Rsinq5) ($ + Rcosq5)l (the platform can only move in an elliptical trajectory) are possible constraints. 6 Results Computer Simulation In Figure 4,the lengths are: lo = l.Om, 11 = 0.75m, 12 = 0.75m, and 13 = 0.25m. Consider a trajectory (3.54, 3.54,$)T. Two types of stiffness matrices are considered. First we examine the case in which the oints on the base are made stiffer while the manipuiator joints are more compliant. Here the weights are: Wz=50N.sec/m, WY=50N.sec/m, We= 25 N.sec/rad, W*1= 10 N.sec/rad, Wq2= 5 N.sec/rad, and Wq3= 2 N.sec/rad. In the second case we consider uniform weights so that the stiffness are all unity: W, = Wy = 1 N"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002343_acc.2004.1383814-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002343_acc.2004.1383814-Figure3-1.png",
        "caption": "Figure 3 -Formation Geometry",
        "texts": [
            "6913, C,& - 0.2681. Lateral-Directional Aerodvnamic derivatives: Cy0 = 0.0208, C, = 0.3073, Cy, = 0.8345, Cy, = -1.0777, cy&=o.2115, cy&=-O.4466, ~ 1 ~ = - 0 . 0 0 1 6 , c,b=-O.O453, Clp = -0.2260, C , = 0.0994, CIa = -0.0543, C,w = 0.0175, C.,=O, Cnb=0.0546, Cw=-0.1106, C,=-0.2629,Cn~= -0.0228, Cnw = -0.0638. From a geometric point of view the formation flight control problem can be naturally decomposed into two independent problems: a level plane tracking problem and a vertical plane tracking problem. Figure 3 shows the level plane formation geometry. All trajectory measurements, i.e., leaderhingman position and velocity, are defined with respect to a pre-defined EarthFixed Reference x -0 - y plane and are measured by the on-board GPSs. The pre-defined formation geometric parameters are the forward clearance f, and lateral clearance I , , The forward distance error f and lateral distance error I can be calculated from the trajectory measurements and formation geometric parameters using the relationships: (6) (7) v, ( x , -xw 1- VI"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001516_iros.1997.649040-Figure13-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001516_iros.1997.649040-Figure13-1.png",
        "caption": "Figure 13: Throwing area and phase portrait",
        "texts": [
            "56m as an example, B l r is restricted to the region between the two curves given by equation (23) shown in Figure 12. Then defining &=0.50m, &=0.03m, elr is restricted to the limit represented by the dotted lines shown in Figure 12 as a necessary condition. When the gripper is thrown in the (I3) 174 that satisfies equations (24) and (25), the gripper can approach the target and catch it. Next, the area of the solutions of 01, that satisfy equations (22)-(2.5) is shown as the shadowed portion in Figure 13. When the gripper is thrown in the case that B,, and 61, take values in this area, the gripper can approach the target and catch it, so we call this area TA (Throwing Area}. Next, we put the phase portrait shown in Figure 5 on TA in Figure 13, and investigate the longest time in the part of the elliptic orbit that is contained in TA. If we define this time and the length of the major axis of the elliptic orbit as t,[sec] and 81,. respectively, then the relationship between t , and 8 1 ~ is as shown in Figure 14. 5 Conclusions Considering the error of throwing timing, a larger t,,, is more effective for the time delay of throwing the gripper. Since t,,, becomes maximum when Blm =0.37rad in Figure 14, we can select the elliptic orbit whose major axis length is 0.37rad in Figure 13. We can choose the throwing point on the elliptic orbit as point A in Figure 15 in consideration of the time delay of the throwing command data. In this paper, a casting manipulator consisting of an unformed flexible link of variable length was proposed for enlarging the work space of a robot. For this manipulator, we first proposed a method of generating the desired swing motion for throwing the gripper by choosing a timepefiodx input for the second joint based on the error between the current amplitude and the desired amplitude"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000710_mech-34246-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000710_mech-34246-Figure3-1.png",
        "caption": "Figure 3a. The Locus of the Instant Center ++95I .",
        "texts": [
            " The next step is to convert the two five-bar linkages (i.e., links 1, 2, 3, 4, and +5 and links 1, *5 , 6, 7, and 8) into two four-bar linkages by instantaneously freezing binary links +5 and *5 . The absolute instant centers for the coupler links 3 and 3 loaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/02/2016 Term 7, denoted as +5 13I and *5 17I in Figures 3a and 3b, can be obtained from the Aronhold-Kennedy theorem. Draw a line through the instant center ++95I parallel to the line ++ BI 5 13 , see Figure 3a. This line represents the locus of ++95I for all possible directions of the path tangent of link +9 (an analytical proof is presented in the appendix). Similarly, draw a line through the instant center **95I parallel to the line *5 17 * BI , see Figure 3b. This line represents the locus of **95I for all possible directions of the path tangent of link *9 . Therefore, the point of intersection of these two lines is the instant center 59I , henceforth denoted as point Q, as shown in Figure 4a. Since the ground pivot 5O is the instant center 15I then the path tangent of point Q is perpendicular to the line QO5 as shown in Figure 4b. Note that the velocity of the coupler point B of the double butterfly linkage is equal to the velocity of point Q. Therefore, the line through point B parallel to the line QO5 is the path normal of point B",
            " The remaining instant centers of the linkage can now be obtained from the Aronhold-Kennedy theorem. Copyright \u00a9 2002 by ASME s of Use: http://www.asme.org/about-asme/terms-of-use Downlo 4 aded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/02/2016 Term 1. Find the point of intersection of link 4 (or link 4 extended) with the line through 5O that is parallel to link 2. Through this point, draw a line parallel to the line between point B and the point of intersection of links 2 and 4. (See Figure 3a). 2. Find the point of intersection of link 6 (or link 6 extended) with the line through 5O that is parallel to link 8. Through this point, draw a line parallel to the line between point B and the point of intersection of links 6 and 8. (See Figure 3b). 3. The point of intersection of the two lines, in steps 1 and 2, is the instant center 59I . (See Figure 4a). 4. Draw a line through coupler point B parallel to the line 559OI . The intersection of this line with link 2 (or link 2 extended) is the instant center 13I , and the intersection of this line with link 8 (or link 8 extended) is the instant center 17I . (See Figure 4b). Copyright \u00a9 2002 by ASME s of Use: http://www.asme.org/about-asme/terms-of-use Down Consider the double butterfly linkage shown in Figure 5 with the link dimensions as tabulated in Table 1 (the link lengths are specified to the nearest 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000808_20.582604-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000808_20.582604-Figure2-1.png",
        "caption": "Fig. 2 Finite Element Mesh",
        "texts": [],
        "surrounding_texts": [
            "1719\n4\nNow, the total current density Jt is\nx=x+z (12) --b\nwhere Js: source current density, x: eddy current density. Eddy current density is\n(13)\nwhere D : electric conductivity, p: electric scalar potential. From (5) to (13), we obtain the governing equation of our system as followings.\n-V?[-c$-+V 1 d x p ) = - J, -.. (14) P dt\nAssuming that the end effect of the core lamination ends and end leakage reactance of stator end coil are ignored, the magnetic vector potential and electric current density are\n\u2018d= ~ ( x , Y, t)e, J = J(x , Y- t) e,\nP = P I z+ Po\n--.+ (15)\n(16)\n(17)\n4 +\nrespectively. Electric scalar potential is\nwhich means that p is linearly variant to axial direction. Thus 2D form of (14) is\n(18)\nC. Stator circuit equation\nOur problem is the voltage source problem. External voltage source is connected extemally to the FE analysis region. For this case stator equivalent circuit equation is as follows.\nV(t)=l? I( t )+L (19)\n(20)\nwhere h\u2019? L , C : extemally connected resistance, inductance and capacitance to the FEM model, respective1 y. V( t) : external voltage source, I( t) : stator current nt :ne motor, V :.I,\u2019: external capacitance voltage, O ( t ) : magnetic flux linking the stator\ndo d - - winding. From 7 = N x $ A . dl , (19) is changed\nto\n(21)\nR. Rotor circuit equation\nBy Kirchhoff\u2019s current law, rotor bar current and endring ciirrent are coupled as follows.\nwhere [D ] : matrix which determines the relation between bar current I , and endring current I,.\n[I ,] =[Dl V , I , (22)\nFrom Kirchhoff\u2019s voltage law, 2 Ye [~,l=-[DlI:dVl (23)\nwhere re : resistance of the endring connecting adjacent two bars, L! V : potential difference between both ends of rotor bar. The potential difference is\n(24) A v= - d z\nwhere I is core lamination length. The bar current is\nwhere S , is the cross-sectional area From (22) to (as), rotor circuit equation\nE. Heat constant::\nFrom the fact ihat \u2019heat resistance\n(25)\nof rotor bar. is\n(26)\nd RNL= -, AA the\nequivalent heat conductivity 1 following relation., is calculated from the\n(27)\nwhere dq is the thickness of lhe equivalent layer. We consider the turlbulent effect in calculating the equivalent conductivity of the air gap[8]. Heat convection coefficient h is calculated from the following formula.\nwhere Q, b are exlperim~ental constants and z, is fluid velocity.\n(28) h=a.v 6\nF. Loss calculation\nWe consider 1st and 2nd copper loss and core losses. Y e stray load 10-s and the mechanical loss are given as typical values in many small size motors from the textbook[9]. Stator and rotor copper loss is W, = 3 IiR,, W, == 3 IiRZ , respectively. The core loss\nis calculated from B-Loss curve.\nIl . NUMERICAL RESULTS\nFig.l is our computation model. It shows one pole of the 3.7kW 4 pole motor. In heat conduction problem, Neumann boundary cundilion is applied to the left side and to the righit side of the model. Mixed boundary condition is given to the upper side i.e. fin surface in Fig.1. The model has three equivalent layers. First, there is an equivalent contact layer with 1 [mml thickness between stator core and stator",
            "1720\nand b=0.6. F'ig.2 shows FE mesh of the model. Number of elements is 9747. Most of the elements lie in near the rotor bar. Fig.3 shows the heat source distribution. 'The values at several points in the motor are shown in Table IJI. Fig.4 shows equithermal line distribution. Most of the lines lo on rotor bar gap, air gap and stator insulation. This tells us that temperature decades down very suddenly at these regions. Fig.5 shows the temperature variation along the straight line AB in Fig.4. shows the lemperature variation along the connecting the two points C and D.\nframe. The equivalent thickness of the layer was calculated by (27). There is an equivalent slot insulation layer with 1 [\"I thickness. In stator slot\nit consists of slot insulator, insulation varnish and air between slot insulators and winding conductors. Finally we introduce rotor bar gap layer with 0.15 h\"m thickness. There exists a gap which arise from manufacturing process between rotor bar and rotor core. Table I is the specification of our TEFC cage rotor type induction motor. Table II shows heat conductivities of each region of the model. Heat convection coefficient h is 50 from (281, where a=14",
            "1721\nFig.4 Equithermal line distribution\nI 74411\ni\nF i g 5 'Temperature variation along the line AB in Fig.4\n45 RO 75 W 105 1PO 135 P.N~PLE [DEOREE]\nFig.B Temperature variation along the arc CD in Fig.4\nhr. CONCLUSION\nIn this paper we showed the method to estimate more accurately t h e temperature of the induction motor with distributed heat sources using 2D FEM including 3D effect. Through the numerical results, it is easy to understand the heat flow in the motor,\nREFERENCES\n111 DSarkar, P.K.Mi&herjee and S.K.Sen, \"Approximate Analysis of Steady !State Heat Conduction in an Induction Motor\", IEEE Trans. on EC, Vol. 8, No. 1,\nMarch 1992 [21 A.F.Armor, \"Transient, thee dimensional finite-element\nanalysis of heat f Low in turbine-generator rotors\", IEEE\nTrans. on PAS, Vol. PAS-99, No. 3, May/Jun. 1980 C31 A.F.Armor and M.V.K.Chari, \"Heat flow in the stator\ncore of large turbine-generators, by the method of three dimensional finite elements ( Part I : Analysis by scalar potential formulation)\", IEEE Trans, on PAS, Vol.\nPAS-95, NO. 5, Sep./Oct. 1976 [41 A.F.Armor and M.V.K.Chari, \"Heat flow in the stator\ncore of large turbine-glenerators, by the method of three dimensional finite elements ( Part I7 : Temperature distribution in thle stator iron)\", BEE Trans. on PAS,\nVol. PAS-95, No. 5, Sep./Oct. 1976 [51 C.C.Chan, L.Yan, P.Chen, ZWang and K.T.Chau,\n\"Analysis of Electromagnetic and thermal fields for induction motors\", IEEE Trans. on EC, Vol. 9, No. 1,\nMarch 1994 161 T.Kitamori and J.Kataoka, \"Evaluation of Temperature\nRise in Totally IZnclos,ed Fan-Cooled Induction Motor\",\nNational Techniccil Report, Vol. 17, No. 4, AUG. 1971 [71 G.Champenois, D.Roye and D.S.Zhu, Electric Muchines\nand Power S y s t e m , Taylor & Francis, 1994, 22:355- 359.\n[8l Hatziathanassiou V., X ypteras J. and Archontoulakis G., \"FEM coupled electro-thermal calculation on electrical machines\", ICEM'94, Faris, France, 1994\n[91 J.C.Andreas, Energy-Efficient Electric motors, Marcel Dekker, Inc.,1992"
        ]
    },
    {
        "image_filename": "designv11_11_0003678_00022660510597223-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003678_00022660510597223-Figure4-1.png",
        "caption": "Figure 4 Example of a disturbed flight condition in straight and horizontal motion",
        "texts": [
            " A stable steady-state flight can be defined as one in which all movement variables remain constant with respect to the XYZ coordinate system. This implies ~V_P \u00bc 0 and ~v_\u00bc 0: Three typical stable-steady state flight conditions are (Roskam, 1995b) 1 straight and horizontal motion; 2 coordinated turning; and 3 upward and downward motion. A disturbed steady-state flight is defined as one in which all movement variables can be described relative to the stablesteady state flight condition, as shown in Figure 4. In this paper our interest is in the disturbed state flight condition. Figure 3 Plane orientation with respect to Euler\u2019s angles Control of longitudinal movement of a plane Manuel A. Duarte-Mermoud et al. Volume 77 \u00b7 Number 3 \u00b7 2005 \u00b7 199\u2013213 D ow nl oa de d by U ni ve rs ity o f M as sa ch us et ts A m he rs t A t 0 3: 32 3 0 M ar ch 2 01 6 (P T ) The disturbed movement, force and momentum variables will be defined as the difference between its absolute value and its steady-state value. We will use the disturbed variables instead of the variable absolute value"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002334_robot.2001.932993-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002334_robot.2001.932993-Figure7-1.png",
        "caption": "Figure 7: Relationship between finger's motion and contact force",
        "texts": [
            " Journal of Robotics Research, Vol. 18, No. 9, pp. 951-958, (1999). Appendix A: Frictionless Grasp From Eq. (15), we have Then Vuct and Vu,, are formulated a b [VU,, Vuc , ] = - [ Vh,, Vh,, J ah,, dh,, Considering initial conditions yields 1 V u c i / o & i K f i f z i - (&ai + K f i ) k z i Substituting the above equations into VSyiiO and V6,ilo yields In a similar way, we have Appendix B: Eq. (21) The term 2 represents relationship between contact position and contact force. This relation is illustrated in Fig. 7. Hence, we have the following three conditions. (a) if IC, > O , I C ~ > 0 then - (b) if K~ < O , ~ i f > 0 then - I > 0, (c) if ducz 0 > 0, I C ~ < 0 then ~ where From these conditions, kzi and fxz are restricted to In a similar way, from *, I;,, and f x z are restricted to duct Appendix C: Frictional Grasp In frictional case, the first and the second derivatives of U,., uCi is given by Then the derivative of d X z , dYz, and 6,i are derived as If Eqs. (30) and/or (31) are not satisfied, the grasp is unstable, and eigenvalues of the hessian Hitz are infinity (,vfm = -CO)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.3-1.png",
        "caption": "Figure 3.3 Systems of reference and basic geometrical parameters",
        "texts": [
            " The calculation of the stress distribution in the general tri-dimensional case cannot be performed in closed form, even in the simplest cases. It is, however, possible to use numerical methods and, in particular, any tri-dimensional finite element routine is generally applicable to the stress analysis of flywheels. In the case of rotating discs, particularly if relatively thin and built using composite material laminates, there are some points to be considered. The stress distribution is usually close to a plane stress state, at least in the inside of the disc, or better, on the plane of symmetry, if it exists. With reference to Figure 3.3, the axial stress az is far smaller than circumferential and radial stresses ac and <rr. The shear stresses in the reference system r, c, z are often very small, i.e. the system is not too far from being the principal one for stresses. This, however, does not mean that the normal stress oz and all shear stresses can be neglected. Actually the strength of the material in z direction and the shear strength can be far lower than the strength in r and c directions, and the Rotor stress analysis 59 axial stress can be the most dangerous one, even if it is small"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002427_50009-5-Figure7.11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002427_50009-5-Figure7.11-1.png",
        "caption": "FIGURE 7.11 The PTB horizontal-type magnetizer for the 2D testing of soft magnetic laminations (upside and cross-sectional views) [7.44]. The laminated double yoke can provide either rotational or unidirectional field in the gap, according to the programmed time dependence of the current flowing in the exciting windings. The sample is an 80 x 80 r e_ In 2 square, placed at the center of the double yoke and separated from it by a narrow (---1 mm) air-gap. The induction and the field are detected upon a 20 mm wide area, where both quantities achieve acceptable homogeneity. The two orthogonal B-coils are threaded through holes of 0.5 mm diameter. The corresponding multi-turn H-coils are wound on a thin former and placed on the lower sample surface. A couple of crossed RogowskiChattock coils can also be employed in place of the fiat H-coils.",
        "texts": [
            " It is, therefore, not surprising that intercomparison exercises have shown poor reproducibility of the measurements under rotational fields [7.41]. Basically, the RSST magnetizers can be distinguished for the type of supply used (two- or three-phase), the type of yoke (vertical/horizontal, simple/double), and the specimen shape (square/ circular, with or without air gap, cross-shaped, etc.). The whole subject has been discussed quite extensively in the recent literature, especially in a series of lively workshops devoted also to some general problems regarding measurements in soft magnetic materials [7.42, 7.43]. Figure 7.11 provides a schematic view of the horizontal-type RSST magnetizer developed at PTB [7.44]. An alternating/rotating field is applied, by suitably p rog ramming phase and ampl i tude of the currents circulating in the magnet iz ing windings , to a square specimen of 80 m m side, which is placed exactly in the mid-plane of the gap and is separated from the apex of the wedge-shaped pole faces by a narrow air-gap (~-1 mm). The two 332 CHAPTER 7 Characterization of Soft Magnetic Materials components of the induction in the sample are detected by means of two orthogonal few-turn windings, which are threaded through 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000710_mech-34246-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000710_mech-34246-Figure5-1.png",
        "caption": "Figure 5. Notation for the Angular Displacements.",
        "texts": [
            " The point of intersection of the two lines, in steps 1 and 2, is the instant center 59I . (See Figure 4a). 4. Draw a line through coupler point B parallel to the line 559OI . The intersection of this line with link 2 (or link 2 extended) is the instant center 13I , and the intersection of this line with link 8 (or link 8 extended) is the instant center 17I . (See Figure 4b). Copyright \u00a9 2002 by ASME s of Use: http://www.asme.org/about-asme/terms-of-use Down Consider the double butterfly linkage shown in Figure 5 with the link dimensions as tabulated in Table 1 (the link lengths are specified to the nearest 0.01 cm). For the chosen position of the input link 2 (i.e., 1352 =\u03b8 counterclockwise from the horizontal axis), the position solution of the linkage is obtained from a vector loop analysis and a MATLAB computer program (Waldron and Sreenivasan, 1996; and Hasan, 1999). The results of the angular position of each link are included in Table 1. The linkage was drawn to scale using AutoCAD and the joint angles were specified to the nearest 01"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002625_s0003-4975(10)61832-2-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002625_s0003-4975(10)61832-2-Figure2-1.png",
        "caption": "Fig 2 . Intramyocardial pH unit. Lower drawing illustrates circular base, which may be utilized as a sewing ring. Upper drawing illustrates 10.0-mm width of ring, 5.0-mm length of pH and temperature sensors, and perpendicular exit of sensors from opposite points on the base. Outside diameter of temperature and pH sensors is 0.6 mm.",
        "texts": [
            " Animal Care All animals received humane care in compliance with the \u201dPrinciples of Laboratory Animal Care\u201d formulated by the National Society for Medical Research and the \u201dGuide for the Care and Use of Laboratory Animals\u201d prepared by the National Academy of Sciences and published by the National Institutes of Health (NIH Publication No. 80-23, revised 1978). Intramyocardial p H and Temperature A new miniature myocardial transducer was designed by us for the continuous and simultaneous measurement of interstitial myocardial pH and temperature (Fig 2). The transducer unit incorporates a circular base and two sensors. The circular base has perforations for attachment of the unit to the epicardial surface by sutures. Two sensors (pH and temperature) exit the circular base at right angles from opposite points on the ring, thereby minimizing rotary, vertical, and horizontal instability when properly positioned on the heart. The sensor needles have an outside diameter of 0.6 mm and a length of 5.0 mm. The pH sensor incorporates fiberoptic technology and is based on the work of Goldstein and colleagues [7, 81"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002471_10255840310001637266-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002471_10255840310001637266-Figure1-1.png",
        "caption": "FIGURE 1 (a) The assumed barrel shape of the ligament before stretching with e \u00bc 0:5 mm: (b) Ligament shape after stretching to the parabolic length (dimensions are in mm).",
        "texts": [
            " The third mechanism is also examined with the finite element method, being the effect of osmotic pressure [2] which would cause the unloaded ligament to swell and have an initial barrel shape. Mechanism 1 The effect of the initial curvatures of the fibres was studied by calculating the difference in volumes between barrels and cylinders. A barrel shaped ligament represents a ligament with parabolic curved fibres. As the ligament stretches the curved fibres are assumed to straighten initially without extension in their length (Fig. 1) until the barrel shape becomes a cylinder with a slightly longer height. The volume change corresponding to the straightening of the fibres is calculated. A decrease in volume would indicate exudation of fluid. The mathematical model was 12 mm high and 2 mm in diameter at the ends, with a barrel-shape giving a maximum diameter at the centre of \u00f02 \u00fe 2e\u00de: The value of the eccentricity of the parabola (e) was changed from 0.5 to 0.1 mm in step of 0.1 mm. The diameter of the ends of the ligament is maintained at 2 mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001911_015-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001911_015-Figure1-1.png",
        "caption": "Figure 1. Possible phases in the plane (D, 8 ) in the limit d-a. C1 denotes the crumpled phase where self-avoidance is irrelevant. CZ is a swollen crumpled phase with v=ZDIS. In addition, C3 with Y = (4 - D)/2 corresponds to the crumpling transition and exists only in the region where F2 and C2 coexist. FI is a flat phase with anomalous roughening and Fz a Rat phase with normal roughening.",
        "texts": [
            " The q2 term has a negative coefficient - r because repulsion between the monomers pushes each of them away from the plane of the membrane. This does not mean, however, that the membrane is unstable, because the elastic term ,yq2 compensates for it. In the flat phase ,y = r, and more generally ,y 2 r. One easily sees that Ss,(q) = s,(q) - rq2 is always positive, guaranteeing the stability. Similarly the q4 term in the expansion (9c) is positive because self-avoidance is unfavourable to bent configurations. We now list the possible phases when D and S are vaned. Their domain of existence is represented in figure 1. We restrict ourselves to 6 > D (the case S < D leads to a super-stretched flat phase or to an instability as discussed in [9]). Let us first consider the case C = 0. Then there are three possible isotropic phases: Crumpled 1 , for which T(q) - q2, e.g. ,y > r. This implies from (76) that U = ( 2 - D) /2 , which itself is possible from (9) only above a critical \u2018dimension\u2019 when 6 > S,(D) where S C ( D ) = 4 D / ( 2 - D ) corresponds to twice the fractal dimension of a single crumpled membrane (above which intersections are irrelevant)",
            " This regime corresponds to a crumpled phase where self-avoidance is relevant with a non-trivial exponent. It generalizes the result of des Cloizeaux [ll] for the polymer. This regime corresponds to case (96) above and thus is possible only when S,,(D) < 8 < &(D) where 6,,(D) =4D/(4- D). Note that this is twice the fractal dimension of the network at the crumpling transition to this order. Furfhermore this regime is possible only for U < 1 or equivalently 6 > 2 D , since otherwise the momentum integral in (7c) diverges. Thus, as represented on figure 1, for D < 2 this phase is bounded by the line 6 = 2 D , below which the only solution is a flat phase (see below), and for D > 2 by the line 6 = S,,(D). The amplitude is where Crumpled3, for which r(q) - q4 (also ,y = r). This implies from (2.8) that Y = (4- D)/Z. This regime also corresponds to a crumpled phase where self-avoidance is relevant, but with a different exponent than the other one. In this phase the bending energy L474 Letter to the Editor dominates the fluctuations and the effective bending rigidity is x4 d D X 4 ",
            " Although the physics of long-range interactions is different this might provide some insight into the short-range problem as well. Note that for D = 2 , S = 3 we find v ' = f (numerical simulations [3] with short-range selfavoidance give U' = 0.65). We found that short-range repulsion also leads to non-trivial solutions. Fluctuation calculations leading to higher-order l i d corrections [8] might thus give interesting information. One can anticipate that the flat phases be stabilized, thus moving the line D = D,, = 2 figure 1 to the left. I thank D R Nelson for discussions. This work was supported by NSF grant DMS9100383. Nore added. The present results, interpreted as in a variational method for shon-range self-avoidance ( 6 being the dimension). are in surprisingly good agreement with recent numerical simulations of D = 2 membranes in high dimensions by Crest [13]. The agreement is better than for the polymer D = I [ I l l , and much better than for the Flow value for membranes [ 2 ] . The measurcd value vm from simulations, the value vp predicted here and the Flow value vs are: f o r S = 3 : \",, ,=I"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002414_027836403128965277-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002414_027836403128965277-Figure1-1.png",
        "caption": "Fig. 1. Robot fork truck motivation. Based on the location of the load, a trajectory must be generated which ends precisely in front of, and aligned with, the fork holes. The curvature and speed must also be zero at the terminal point. Although the pallet is to the left of the truck, it must turn initially to the right to achieve the goal posture.",
        "texts": [
            " While computing trajectories is a complicated matter, there are many situations for which nothing less will solve the problem. Due to dynamics, limited curvature, and underactuation, a vehicle often has few options for how it travels over the space immediately in front of it. The key to achieving a relatively arbitrary posture is to think about doing so well before getting there, and to do so based on precise understanding of the above limitations. One of the motivations for our work on this problem is the application of robot fork trucks handling pallets in factories, as illustrated in Figure 1. Pallets can only be picked up when addressed from a posture which places the fork tips at the fork holes with the right heading and with zero curvature. In our application, a vision system determines where the fork holes are, so the goal posture may not be known until limited space requires an aggressive maneuver to address the load correctly. In the event that the fork holes are located after traveling past the point where a feasible capture motion exists, it still may be valuable to optimize the terminal posture error based on the fact that the holes are often much larger than the forks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003051_acc.2005.1470426-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003051_acc.2005.1470426-Figure3-1.png",
        "caption": "Figure 3 \u2013 Horizontal formation geometry",
        "texts": [
            " Since flight paths mostly lie on a horizontal plane, (and since gravitational force is perpendicular to such plane), a formation flight control problem can be naturally decomposed into two (almost) independent problems: horizontal (planar) tracking and a vertical tracking. Note that position and velocity of both leader and follower are expressed with respect to a pre-defined earth-fixed reference frame and are measured by the on-board GPSs. The pre-defined formation geometric parameters are the forward clearance fc and lateral clearance lc. (Figure 3) The forward distance error f and lateral distance error l can be calculated from positions and velocities using the following formulas: ( ) ( ) ( ) ( ) sin cos cos sin L L cL L L cL lx xl fy yf \u03c7 \u03c7 \u03c7 \u03c7 \u2212 \u2212 = \u2212 \u2212 (9) where \u03c7L is the azimuth angle for the leader: ( ) 2 2 cos Lx L Lx Ly V V V \u03c7 = + , and ( ) 2 2 sin Ly L Lx Ly V V V \u03c7 = + (10) Note that the 2 by 2 matrix in (9) is simply a rotation matrix that rotates the error from an earth fixed reference frame to a reference frame oriented as the velocity of the leader"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001321_s0013-7944(03)00050-x-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001321_s0013-7944(03)00050-x-Figure5-1.png",
        "caption": "Fig. 5. Gear test piece.",
        "texts": [
            " The test piece was loaded by axial loading with the ratio DF \u00bc Fmax=Fmin \u00bc 0:1, at the room temperature and with 50 Hz frequency. Thermal treatment of the test piece was the same as that of the gears. From the previous tests on three point test piece made of the same material and with the same heat treatment we obtained basic fracture mechanics properties of this material for long cracks [10]. (b) Non-standard test piece for determination of fracture parameters of gears. This type of test piece was gear test pieces developed during previous researches [10]. A test piece together with the testing device is shown in Fig. 5. We assumed that cracks would start in the critical cross section, i.e., the cross section with maximal tensile stress, which proved to be correct on the basis of previous researches and theoretical findings. The arrangement of the individual measuring instruments is shown in Fig. 5. As we wanted to observe particularly initiation and propagation of short cracks and to determine the conditions occurring in this case [6] (stresses, strains, moment of beginning of fracture etc.), we used mixed experimental methods: photo elastic method, method of measuring of stress/strain by means of strain gauges, replica technique for determination of prevailing initials and measuring of micro cracks by means of crack gauges. The a.m. methods were combined as follows: \u2022 photo elastic examination with strain and crack gauges, \u2022 strain and crack gauges and \u2022 gauges with replica method",
            " After 210 103 the test was stopped and final impressions were made. All impressions were made in critical cross section at the point of maximum tensile stress. In the end we made ground section from the test piece on which we observed the process of occurrence of cracks and their size. For measuring the crack lengths greater than approximately 0.2 mm we used crack gauges made by Measurement Group Vishay Type TK-09-CPB02-005. The measuring gauges were glued to gear test pieces at approximately 0.11\u201302 mm from the edge as shown in Fig. 5. By means of the gauge and x\u2013y plotter we recorded the crack growth from the initial value to the size of 2.6 mm in ten steps. By means of these measurements we obtained the a\u2013N curve. On the basis of this diagram and measurements of short crack lengths we made the diagram da=dN\u2013a and diagram da=dN\u2013DZ. We loaded and relieved the gear test piece with fixed strain gauges from 0\u2013114 kN and measured deformations in the critical cross section of the gear tooth. On the basis of deformations we calculated the stress and residual stress, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003825_j.finel.2005.08.001-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003825_j.finel.2005.08.001-Figure10-1.png",
        "caption": "Fig. 10. Determination of the adapted flexibilities.",
        "texts": [
            " The total working force in the bolt Fb is Fb = Q + Sp2 Sp + Sb Fe (5) with the total flexibility of the part Sp = Sp1 + Sp2. (6) What complicates the computation is that the part flexibility is not uniformly distributed across the thickness. In fact, the image of the compressed zone under the head of bolt, up to the mating plane, appears as a volume approaching the shape of a truncated cone (Fig. 9). To fairly accurate the real situation, an appropriate algorithm is used to calculate the flexibility of a compressed part. Part could be made by two or multiple partitions. Considering a two parts partition case (Fig. 10), the methodology is as follows: 1. Calculate Ap cross-section by improved Rasmussen\u2019s formulation [14], then total part flexibility Ap \u21d2 Sp = Lp ApEp . (7) 2. Calculate Ap1 cross-section by improved Rasmussen\u2019s formulation [14] and the corresponding flexibility, characterized by L1 length Ap1 \u21d2 Sp1 = L1 Ap1Ep . (8) 3. Calculate the lower part flexibility Sp2 = Sp \u2212 Sp1. (9) 4. Calculate Ap2 obtained from Sp2, as equivalent cross-section of the lower segment. The lower part can be partitioned into as many segments as necessary, without repeating the algorithm since it is sufficient to preserve constant the sum of the elements flexibilities (Sp2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000524_ft9959104321-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000524_ft9959104321-Figure9-1.png",
        "caption": "Fig. 9 Band structure diagram and electronic transitions in (a) neutral polymer, and oxidised polymer with (b) polaron and (c) bipolaron states",
        "texts": [
            " In this case polymerization is limited by the diffusion of Cu2+ to the site of pyrrole monomers, since there is insufficient room for pyrrole to diffuse past the polymer, and also by charge movement along the polymer chains. Thiophene may interact too strongly with the lattice to allow diffusion of polymer units at a rate fast enough to detect in our experiments. The number of spins produced per uc is around 0.01-0.02 for pyrrole and 0.03-0.04 for thiophene (Table 3) which sug- The electronic transitions in conducting polymers are normally discussed in terms of the band structure diagram shown in Fig. 9.7,10,31,41 The neutral polymer possesses two electronic bands: the valence band, which is filled, and the conduction band, which is empty. The lowest-energy optical transition is the band gap transition h u g , Fig. 9(a). Oxidative doping of the polymer leads to the formation of two types of charges, polarons and bipolarons. At low oxidative doping levels, two new electronic levels appear within the gap which arise from the formation of a polaron (radical monocation). This gives rise to the three electronic transitions 2hu0, hal, h a , , Fig. 9(b), notation of Caspar et a!.\" At higher doping levels, the unpaired electron occupying the polaron level in the band gap is removed, leading to formation of a bipolaron (molecular dication). With the removal of this electron, both of the levels within the band gap are unoccupied, so that the transition 2hu0 from the singly occupied polaron level to the unoccupied polaron level can no longer occur. For polythiophene, the band gap transition h o g occurs at 2.1 eV, and the transitions 2kw0 and ho, have been measured at 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001005_0165-0114(94)00225-v-Figure15-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001005_0165-0114(94)00225-v-Figure15-1.png",
        "caption": "Fig. 15. Behavior of the mean of a fuzzy state vector in the phase space.",
        "texts": [
            " Sliding mode with boundary layer To avoid drastic changes of the control output control law (30) is changed into u = - K sat(s/~), (37) where sat(s/~) has already been explained in Eq. (15). Within the boundary layer from Eqs. (37) and (27) follows formally the filter equation K + ~ s = G (38) for G = 2~ - 5i d + d + d +f(S:,x, t) as a fuzzy input of the \"filter\". Taking the means of s, ~ and G we obtain the filter equation ~+Kg=d with the solution g(t)=e-~'otr/~)dr[go--f i '~(t)eJ'o'(K/~)dtdt '] . Eq. (40) describes the behavior of the mean g of the fuzzy set s approaching the line g = ~ . ~ + e = 0 . Fig. 15 shows the two approaching components regarding Eqs. (35) and (40). (39) (40) (41) 326 R. Palm, D. Driankov / Fuzzy Sets and Systems 70 (1995) 315-335 Following Eq. (15) the control law (37) still provides a fuzzy control output which does not make sense for the input of a plant. Therefore, the fuzzy control law (37) is changed into the crisp control law u = - K sat(defuzz(s)/~) = - K sat(g/~). (42) Tp,ec = T~ec + O = (2a + O), (43) where O = ~/2 is the ~-component of the width of the boundary layer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003346_j.jsg.2004.07.005-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003346_j.jsg.2004.07.005-Figure4-1.png",
        "caption": "Fig. 4. Labelling convention for the mathematical modelling of curvilinear fault-bend folding. See text for details.",
        "texts": [
            " Hanging wall motion above a thrust fault articulated in three straight ramp segments where the central one is the steepest (Fig. 3), produces an anticlinal fold geometry consisting of seven panels named hinterland panel (HL), backlimb panel (BP), inner circular panel (BP 0), crestal panel (CP), outer circular panel (FP 0), forelimb panel (FP) and foreland panel (FL). Folding is produced by translation of the hanging wall above the three ramp sectors, respectively named the lower, central and upper ramp. Adjacent rock panels are separated by straight (g1\u2013g6) and parabolic (g7 and g8) hinges (Fig. 4): the shape of the latter is imposed by the adoption of circular sectors and varies with increasing displacement. The across strike length of parabolic hinges depends on the fault shape, on the thickness of the hanging wall, and on the amount of slip (Fig. 4). Hinge g1, is pinned at the lower inflection point of the central footwall ramp (I1) and bisects the angle between HL and BP panels. Hinge g2 is pinned at the stratigraphic elevation (Sc1) of the central hanging wall ramp lower inflection point (C1) and is perpendicular to layering in the BP panel. For small amounts of displacement (Step I, Fig. 3a), g1 and g2 join at point C2 from which hinge g7 originates. Hinge g3 is pinned at C1 and hinge g4 is pinned at the upper inflection point of the central footwall ramp (I2), as well as g5. The latter is perpendicular to bedding in the FP panel. Hinge g6 is pinned at the stratigraphic elevation (Sc3) of the central hanging wall ramp upper inflection point (C3) and bisects the angle between FP and FL. Hinges g5 and g6 joint at point C4 from which hinge g8 originates. When the entire central hanging wall ramp is translated onto the upper footwall ramp (Step II, Fig. 3d), two new straight hinges originate and bound panel CP 0 (Fig. 4b): g0 3 is pinned at the upper inflection point of the central footwall ramp, while g0 4 is pinned at C1 and migrates with it (Fig. 4b). The footwall cut-off angles in the lower, central and upper ramp are named a1, a2 and a3, respectively (Fig. 4a). The hanging wall cut-off angles are a1 in the HL panel, b1 in the BP panel, b2 in the CP panel, b3 in the FP panel and b4 in the FL panel. The inter-hinge angle g1^g2 is f1 and g5^g6 is f2. The angles at the apexes of BP 0 and FP 0 are d1 and d2, respectively. The backlimb, crest, and forelimb dip are hb, hc and hf, respectively. During Step II, the angular parameters are preserved unvaried except for d1, d2, b1 and hc that become d01, d 0 2, b 0 1 and h0 c, respectively (Fig. 4b). Linear parameters include the amount of slip along the lower (S1), central (S2) and upper ramp (S3), and the length of the central ramp (R). The adoption of circular hinge sectors (e.g. Julivert and Arboleya, 1984; Rafini and Mercier, 2002) to geometrically model fault-bend anticlines (Rich, 1934), produces an overall fold shape resembling that of the kink-style folding. Circular sectors pinned at the fault surface replace straight axial surfaces characterising the backlimb\u2013crest and crest\u2013 forelimb transition in the kink-style model (Fig",
            " The central ramp hanging wall cutoff angle (b2 or b1, depending on fault displacement) is then entered in graph (c) to obtain the upper ramp hanging wall cutoff angle (b3 or b0 1). When the available data are the backlimb dip (hb), the forelimb dip (hf), and the crestal dip in step II (h0 c), the hanging wall (a1, a2 and a3) and the footwall (b1, b2 and b3) cutoff angles are provided in graphs (a), (b) and (d). The geometric construction of the step I configuration starts from a2, that is obtained by linking the curvature centres of the two circular hinge sectors (Fig. 4a). The backlimb dip (hb) and a2 are entered into Eq. (2) to obtain b1; a2 and b1 are then entered in graph (b) to obtain a1 and b2. Once b2, a2 and the forelimb dip (hf) are known, graph (d) provides the solution for b3. Finally, a3 is obtained from Eq. (43). The geometric construction of the step II configuration starts from a3, which is obtained by linking the curvature centres of the two circular hinge sectors (Fig. 4b). Entering a3, hf and h0 c into Eqs. (42) and (43) provides b0 1 and b3, respectively. Entering b0 1, h 0 c and hb in graph (a) provides b1. Once b1 and hb are known, the solution for a2 is given by Eq. (2); a2 and b1 can be entered in graph (b) to obtain a1 and b2. The geometrical construction of the simple step construction (Fig. 7) requires one to know either the backlimb or forelimb dip, which are univocally related (Fig. 12). For small amounts of displacement, (i.e. when g7 and g8 axial surfaces still occur), the dip of the ramp (corresponding to hb) can be obtained by linking the curvature centre of the two circular hinge sectors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001964_robot.1997.614291-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001964_robot.1997.614291-Figure3-1.png",
        "caption": "Figure 3: Showing virtual link forces created by the artificial magnetic field",
        "texts": [
            " Now select any 2-d skew-symmetric matrix with eigenvalues f i , find its eigenvectors and the last two eigenvectors of our MMF matrix is now known in terms of the 2 known basis vectors scaled by the components of the 2-d eigenvectors just found for the known 2-d matrix. Now, the eigenvalues and the eigenvectors are known and the computation of B may be computed. 4 Computing the Obstacle Fields and Forces for a Linked Manipulator An outline of the computation of the obstacle forces for a linked manipulator navigating in a Cartesian or task space are presented herein. Consider the situation shown in Fig. 3. The joint space obstacle forces are generated in joint space and joint limit avoidance is performed by treating each limit or singularity as an obstacle and computing the resulting set of forces as described earlier. Subsequently, task space motion planning is performed whereby the obstacle forces and torques are computed for the task space obstacles. These task space forces and torques are then transformed back to joint space through the manipulator Jacobian, where they are integrated with the previously obtained jointspace forces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000981_rnc.4590030203-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000981_rnc.4590030203-Figure2-1.png",
        "caption": "Figure 2. The qualitative expected behaviour of the solution to objective (b)",
        "texts": [
            " Starting from the instant t = f 1 , the behaviour of trajectories of system (14) in the plane (SI, E) is similar; the variable SI, starting from zero becomes less negative than - [p / (cn + p)] I E(t1) I and then it becomes zero again at r = c2. Meanwhile E changes sign (sign[E(tl)] = -sign[E(f2)]) still remaining, in absolute value, less then I E ( t l ) I where I E(t2) 1 < I E(t1) I < 1 E(t0) I. This particular behaviour, decreasing for the values 1 E(tk) I , persists for the following time intervals (22,231 , (t3, ?4] , . . ., ( t k , t k + I 1 , . . . (see Figure 2). This specific time evolution of b and E will be achieved by the piecewise continuous virtual control input p and therefore through the continuous control signal u. In the case of the first objective, the practicability of the procedure is guaranteed by the following first theorem. Theorem 1 inequalities: Given a second order system (14) with starting conditions (15), which satisfies the P > cn, E(O) > 0 choose an input p which satisfies the following conditions: (a) until the instant t = to > 0, the first instant when SI = 0: p is continuous and satisfies the inequalities: where A is the fixed constant (17) and 6 is any fixed positive constant satisfying the ASYMPTOTIC LINEARIZATION 93 following inequality: (b) starting from the instant t = to: (b"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003784_1.1829070-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003784_1.1829070-Figure6-1.png",
        "caption": "Fig. 6 \u201ea\u2026 A ten-bar linkage with revolute and prismatic joints. \u201eb\u2026 A two-degree-of-freedom nine-bar linkage. \u201ec\u2026 The first arbitrary choice of the instant center I14 . \u201ed\u2026 The second arbitrary choice of the instant center I14 . \u201ee\u2026 The secondary instant center I13 .",
        "texts": [
            " Foster and Pennock @12# show how to find the secondary instant centers of the double flier eight-bar linkage graphically, using a method similar to the techniques that are presented here. Therefore, due to the additional contributions of this paper, the secondary instant centers of all 16 eight-bar linkages can now be located from purely graphical techniques. Example 3. A Ten-Bar Linkage With Prismatic Joints. To illustrate the fact that the two methods presented in Sec. 3 are also valid for linkages with prismatic joints, consider the indeterminate ten-bar linkage shown in Fig. 6~a!. Links 2 and 9 are in pure translation relative to the ground link and link 6 is constrained to translate along the moving link 4. Therefore, the primary instant centers I19 , I46 , and I12 all lie at infinity along the lines shown in Figs. 6~b! and 6~e!. Note that this linkage has no four-bar loops; therefore, there are no secondary instant centers that can be found using the Aronhold\u2013Kennedy theorem. The first method will be used to locate the secondary instant center for the coupler link 3; i.e., I13 . The first step is to remove link 2 which results in the two-degree-of-freedom nine-bar linkage shown in Fig. 6~b!. Note that the instant center I14 must lie on the line connecting the instant centers I15 and I45 . Select an arbitrary point on this line as the first choice for I14 , denoted as I14 1 , as shown in Fig. 6~c!. Then the location of the instant center I13 1 can be obtained as follows: ~i! locate I16 1 at the intersection of the two lines I14 1 I46 and I17I67 ; ~ii! locate I18 1 at the intersection of the two lines I16 1 I68 and I19I89 ; ~iii! locate I48 1 at the intersection of the two rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 02/26/20 lines I14 1 I18 1 and I46I68 ; ~iv! locate I38 1 at the intersection of the two lines I34I48 1 and I3-10I8-10 ; and finally ~v! locate I13 1 at the intersection of the two lines I14 1 I34 and I18 1 I38 1 . Now select a different point on the locus of I14 as the second choice of the instant center I14 , denoted as I14 2 , as shown in Fig. 6~d!. Then find the instant center I13 2 using a procedure similar to steps ~i!\u2013~v!. Then draw a line passing through I13 1 and I13 2 which is the locus of I13 as shown in Fig. 6~e!. Finally, replace link 2 to restore the original ten-bar linkage. The instant center I13 is the point of intersection of the locus of I13 with the line I12I23 , as shown in the figure. The remaining instant centers can now be obtained from the Aronhold\u2013Kennedy theorem. Note that for some indeterminate linkages, links i and j must be chosen carefully in order to guarantee that all of the secondary instant centers can be located from the methods presented in this paper. For purpose of illustration consider the third example presented above"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002767_978-3-642-71015-5-Figure4.15-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002767_978-3-642-71015-5-Figure4.15-1.png",
        "caption": "Fig. 4.15. Integration path in u '+ i v I plane Fig. 4.16. Transformation of path of integration in a+ iP plane",
        "texts": [
            "91) We introduce the notation s' =s+ 2: ' -!l' = - (2:)' <: (4.3.92) Hence Further, we resort to the transformation which introduces, through the auxiliary notation s ,= U '+ i v ~ the elliptic coordinates a, p, namely u I = -.0 cos a cosh P '} . Vi = .Qsinasinhp (4.3.95) the values -rc<a<rc, P>O. With the requirement VS'2- .02 lim = + 1 s'-+oo s' in mind, we obtain VS ,2 _.Q2= +i.Qsiny. Now what is the path of integration of (4.3.93) in the plane a, P? (4.3.96) (4.3.97) (4.3.98) In order to answer this question, we resort to Fig. 4.15 and to (4.3.94,95); thus, if a = - (rc/2) and P decreases from P--+ 00 to p--+e (where, in turn, e--+O), the path - 00 < v' < 0 is traced in the u', v'-plane. Keeping now e fixed, and varying a between the limits - rc < a < - rc/2, we obtain the path 0 < u' < .0. The lower half (AB) of the integration contour 210 4. Electromagnetic Induction: Transient Phenomena - Stationary Configuration in the u', v'-plane is therefore represented by the path A'B' (Fig. 4.16) in the a, p-plane. Similarly, the contour CD transforms into C'D'",
            "Q2}<0 only for these values of a. The closed contour of Fig. 4.17 comprises no singu larities; hence, according to Cauchy's theorem, we obtain f (x, t) = 0; t < (xl c) . b) t> (xl c). Instead of 0, we define in this case x tanhx= ct and obtain (4.3.101) (4.3.102) 4.3 Field Switching in the Presence of Superconducting Material 211 Convergence for P-+ 00 is now ensured for cos a > 0, i.e. for the interval - nl2 < a < nl2 (Fig. 4.18). The direction of the original path of integration is traced in Fig. 4.15; reversing this direction, we obtain the path traced in 212 4. Electromagnetic Induction: Transient Phenomena - Stationary Configuration t>xlc. (4.3.107) or, finally, resorting to Sommerfeld's integral representation [4.14] f(x, t) = exp [ - (0/2 eo) t] Jo(i aV t2_ x 21 c2) = exp [ - (al2eo) t] Jo(i V(0/2eo)2- (c! Ai\u00b7 Vt 2- x 21 c2), t > xl c. (4.3.108) Hence, see (4.3.89,90), Ez = - Va V(al2eo)2- (c! Aiexp[ - (al2eo)t] xlc Vt 2-x21c2 x[-iJ j (iV(al2eo)2-(c!AiVt 2-x2Ic 2\u00bb), t>xlc, (4.3.109) H y = VaVeol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001248_1.2826898-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001248_1.2826898-Figure1-1.png",
        "caption": "Fig. 1 The Stevenson six-bar discussed in the text. When driven via joint OA this linkage has four solutions for any specified value of OA. When driven via joint Oc it has six solutions for any given value of 0c > as is demonstrated in Fig. 2.",
        "texts": [
            " In instances when the four-bar circuit does not include the base of the mechanism it is necessary to invert the mechanism. Also, in instances in which the linkage is to be driven by a joint which is not included in the four-bar circuit, it is necessary to use interpolation to find output angles or positions correspond ing to a given driver angle. What is not usually appreciated is that driving the linkage in this manner also changes the number of solutions. A simple Stevenson six-bar, as shown in Fig. 1, has four solutions if OA or OB is considered to be the driving joint, but six if Oc is the driving joint. If OA is the driving joint, there are two possible positions of the dyad OBBA for any given value of 9A. Hence there are two possible positions for point D. For any given position of point D there are two possible positions of the dyad OQCD. Hence there is a total of 2^ solu tions. This is characteristic of solution by dyadic decomposition with the linkage driven by a crank of the four-bar cell"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003256_j.jsv.2004.06.029-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003256_j.jsv.2004.06.029-Figure5-1.png",
        "caption": "Fig. 5. Computational model of the rotor system.",
        "texts": [
            " In this work, bearings with weak nonlinearity spring characteristics, as shown in Fig. 1, are considered. In this case the bearing restoring forces are usually modeled by the third power of the displacement, so that the bearing forces can be expressed, including linear damping characteristics, as [10,11] f bu \u00bc K1u \u00fe K3u3 \u00fe C _u; f bv \u00bc K1v \u00fe K3v3 \u00fe C _v; (14) where K1 and K3 are the linear and nonlinear stiffness coefficients and C is the linear damping coefficient. These and other coefficients of the rotor are shown in Fig. 5 and the numerical values of the bearing parameters used in the simulations are listed in Tables 1 and 2. Assuming S \u00bc s1 s2 s3 s4 8>>< >>: 9>>= >>; u v _u _v 8>>< >>: 9>>= >>; (15) and combine Eqs. (9)\u2013(13), the equations of motion can be rewritten as _S \u00bc _s1 _s2 _s3 _s4 8>>< >>: 9>>= >>; \u00bc s3 s4 1 M meO2 cos\u00f0Ot \u00fe j0\u00de \u00fe K1s1 6EI L3 s1 \u00fe K3s31 \u00fe Cs3 n o 1 M meO2 sin\u00f0Ot \u00fe j0\u00de \u00fe K1s2 6EI L3 s2 \u00fe K3s32 \u00fe Cs4 n o 8>>>< >>>: 9>>>= >>>; : (16) The fourth-order Runge\u2013Kutta method is used for the solution of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002614_0301-679x(87)90094-6-Figure13-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002614_0301-679x(87)90094-6-Figure13-1.png",
        "caption": "Fig 13 Orientation vectors r~, r2, r and contact surface o f conventional oil seals. Ml = 0.33, N~/No = 0.04, u = 4.5 x 10 -2 m s -1",
        "texts": [
            " Exper imenta l results and discussion Classification of the sealing condition by statistical microgeometry parameters First, by applying digital image processing, the topography of contact surfaces of oil seals under dynamic dry contact conditions between the seal and the glass shaft surface was expressed for conventional seals by a group of contour lines. Next, a variety of these patterns was analysed statistically to estimate the parameters M~ and N1/No together with orientation vectors, r, rj and ?-2. Fig 13 shows a typical example of the contact surface of a conventional oil seal. From this statistical analysis of the dynamic behaviour of conventional oil seals under dry conditions at a shaft speed of 10 r rain -1 , the relationship l arg?- I< 7r/36 is satisfied with regard to the direction of the orientation vectorS, T R IBO L O G Y i n t e r n a t i o n a l 95 Nakamura - sealing mechanism o f rotary shaft l ip-type seals dition Specimen A - I Sealing condition Sealing M I (Dry condition) O. 14 j J N I /No(Dry condition) 0 ",
            "-> 0 on all of the non-leaking oil seals and, conversely, arg7 < 0 on all of the leaking all seals. On the other hand, [~ I approaches zero when N~/No is increased. 7is considered, therefore, to be an unsatisfactory factor in classifying clearly the sealing condition. Effective information, however, will be given to clarify the sealing mechanism by the fact that the various elements of orientation become evident when N1/No approaches zero, and that ?- will be divided into two factors, r~, rz as shown in Fig 13 which satisfy the relationship [ arg r l I - I arg ?-2 f and 171J --~ I ? - 2 [. Next, a study was conducted to clarify the sealing condition by using the parameters, M1 and NI/NO. The result is shown in Fig 14. From this figure, it becomes clear that classification of the sealing condition is possible by using M1 and NI/No, and that the non-leaking condition will be established only by oil seals which maintain M~ and NI/No in the region Sa in Fig 14. 96 Apr i l 87 Vol 20 No 2 of the triple interlines among oil, air and contact surface of the oil seal with lubrication at the shaft speed of 100 r min -1 at the same place where M1 and N1/No were measured",
            " The flow of the oil film is observed only in the area of the convergent gap region adjacent to the ridges (microasperities). With a divergent gap, however, the flow of the film will be obstructed as a result of cavitation. Therefore, the description of sealing phenomena will be satisfied only when considering the flow adjacent to the convergent gap along ridges. Fig 28 shows the phenomena explained above. TR I BO LOGY international 99 Nakamura - sealing mechanism o f rotary shaft l ip-type seals Also, according to the experimental result shown in Fig 13, the relationship I arg?-~ I ~- [ arg?-2 I will be obtained for conventional oil seals. Therefore, the relationship 0~ - 0 : = 0 will be established. Eq (7) can now be expressed as follows: Q a [h2( t ) -h i (t)] u sin0 (8) The adequacy of the proposed basic structure of contact surfaces has already been confirmed by the experiment in\" which model seal II was used. Based on this fact, the relationship Q/> 0 must be established in oil seals with the basic structure of contact surfaces which satisfy the sealing condition shown in Fig 27"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000856_s0039-9140(02)00314-4-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000856_s0039-9140(02)00314-4-Figure1-1.png",
        "caption": "Fig. 1. Side view of the flow-through cell. (1) Inlet of sample with 0.8 mm i.d. PTFE tubing; (2) flow divisor with 0.5 mm i.d.; (3) polyethylene tubing with 0.5 mm i.d.; (4) glass capillary of the SMDE; (5) o-ring; (6) mercury drop with 0.46 mm of radius; and (7) outlet of sample and used Hg (1.5 mm i.d.) to the conventional 10 ml electrochemical glass cell.",
        "texts": [
            " Data acquisition was performed with the model 270/250 RESEARCH ELECTROCHEMISTRY Software from EG&G (Princeton, NJ, USA) using differential pulse mode of potential scanning and current sampling. Solutions were driven to the electrochemical flow cell using an Alitea XV peristaltic pump fitted out with Pharmed\u2020 pump tubing of 0.8 mm i.d. All other connections were made of 0.8 mm i.d. polytetrafluoroethylene (PTFE) tubing. The flow channel from the sampling tube to the electrochemical cell was 40 cm long, including the pump tubing. The flow cell was constructed with a cylinder of acrylic and tightly fitted to the capillary tubing of the SMDE using an o-ring, according to Fig. 1. Two small holes with 0.5 mm i.d. were drilled in the cell to drive the sample solution in opposite directions toward the mercury drop surface. In the bottom of the flow cell, another hole was drilled to allow the output of the sample solution. This hole works also as drain for the mercury drops that are dislodged after each analysis, avoiding its accumulation inside the flow cell, which could affect the geometry and flow patterns in the vicinity of mercury drop working electrode. The division of the flow is previously made in a small T-acrylic piece mounted inside the conventional glass cell, according to Fig",
            " No modifications on the SMDE PAR 303 are necessary, so that the instrument can be operated either under flow conditions, or under batch conditions using the commercial glass cells, requiring for this only the disconnection of the flow cell from the capillary tubing. The reference and auxiliary electrodes are the same ones connected to the commercial nylon block of the SMDE, immersed in the solution contained in the glass cell. The electric contact of the electrodes is made through the hole by which the solution flows out the cell (Fig. 1). The same hole works as a path to the dislodged Hg drops, which accumulate in the bottom of the glass cell, without changing the flow cell weight and flow patterns in its interior. The flow cell configuration and its mass of only 1.1 g, allows one to work for long periods without causing damages to the capillary tubing and with low frequency needs for maintaining, cleaning and re-calibration. The division of the flow enlarges the electrode area that receives directly the sample flow in the wall jet configuration, increasing the sensitivity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003404_j.snb.2004.12.037-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003404_j.snb.2004.12.037-Figure3-1.png",
        "caption": "Fig. 3. Scheme of the CO gas sensor.",
        "texts": [
            " After that, the l-cysteine self-assembled Pt disk lectrode was dipped into 1 ml nano-Au colloid for 12 h at \u25e6C. Au particles bind strongly to the surface by covalent onding with the polymer function groups NH2 and SH 10] to form the nano-Au modified Pt disk electrode. Finally, nano-Au colloid modified Pt disk microelectrode was stored in doubly distilled water prior to use. Fig. 2, which was referenced according to literature [7], shows the process of modification nano-Au Pt disk microelectrode. 2.4. Preparation of the CO gas sensor Fig. 3 shows the structure of the CO gas sensor, which is similar to the structure of the traditional Clark-type gas sensor. It had a nano-Au colloid modified Pt disk microelectrode as working electrode, Ag/AgCl electrode as reference electrode, a Pt wire electrode as counter electrode and selective permeable porous film (polyethylene) in contact with the gas-containing atmosphere. 3. Results and discussion 3.1. Catalytic oxidation CO with nano-Au modified Pt disk microelectrode The CV responses of CO in 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002534_s10800-004-1700-6-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002534_s10800-004-1700-6-Figure1-1.png",
        "caption": "Fig. 1. Equipment and electrochemical cell. (1) Luggin capillary; (2) counter electrode; (3) separator; (4) flow distributor; (5) porous cathode; (6) current feeder; (7) electrical contacts; (8) electrolyte inlet and outlet.",
        "texts": [
            " The authors also observed a current reduction in voltammograms taken after some cycles and concluded that this reduction could be connected with polypyrrole degradation or with aluminium oxide formation. In this work, the ability of RVC, polypyrrole and polyaniline to reduce Cr(VI) to Cr(III) in a flow cell was investigated and compared. Two different operating conditions were studied: open and closed circuit conditions. The reaction rate and the stability of the conducting polymer were evaluated. The reduction of Cr(VI) was performed in a flow cell (Figure 1). The working electrode/cathode was a 60 ppi RVC (Electrosynthesis Company) 3D mesh (0.7 cm 1.0 cm 3.0 cm) coated with either polyaniline (PANI) or polypyrrole (PPY) films. A vitreous carbon plate was connected to the cathode to act as a current feeder. The counter electrode/anode was a Ti/ RuO2 DSA plate (De Nora). A polyethylene mesh, covered with a polyamide fabric, was positioned between the anode and the cathode in order to avoid short circuits. Potential control was achieved using an Autolab PGSTAT30 potentiostat (Eco Chemie)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001964_robot.1997.614291-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001964_robot.1997.614291-Figure4-1.png",
        "caption": "Figure 4: Start configuration of robot",
        "texts": [],
        "surrounding_texts": [
            "In this section, the MMF method is bricfly summarizcd. While conventional potential field methods are derived from principles of electrostatics, the Modified Magnetic Field method is derived from electrodynamical considerations. The obstacle forces are obtained from a current based formalism. This distinction and the methods of their computation are briefly summarized in this section and shown in greater detail in [ 5 ] . The conventional attractive potential field form is used to represent the field setup by the attractor: where -kattr is some positive constant used to represent the intensity of the force field and x is the location of the operating point with respect to the goal location Xd. A damping force is used to damp out oscillations that accrue from the specification of the above attractive field and is given in the following form. where x represents the velocity of the robot. The damping field force is a non-conservative force that tends to oppose the motion of the system. The definition of the obstacle field and force is the key innovation of the MMF method. The basis of the MMF is a set of virtual closed current loops enclosing the obstacle. These virtual current loops generate virtual forces that are termed the Modified Magnetic Field . The obstacle force and field are defined by the following relations: Fobs = X x B (3) (4) where B represents the obstacle field, the MMF , and Fobs represents the obstacle force due to this field. Again, x represents the robot velocity, x the unit velocity vector, l represents the direction of the current loop enclosing the obstacle face and p represents the magnitude of the perpendicular distance of the robot from the given obstacle face. The obstacle field definition is similar in structure to the conventional electro-magnetic Magnetic field, however, the structure of the M M F is somewhat different from that of the classical Magnetic field. Using the redefined Eq. 4 B improves the behavior of the control law, resulting in less convoluted paths, than the classical form. This is shown in Fig. 2. Rather than spiral endlessly, the M M F field has some preferred directions such that motions in those directions remain unaffected while others are turned into those directions. 3 Domain Extension of the MMP The form introduced for the obstacle force has been delineated in terms of the vector cross product operation. To address planning in higher dimensional spaces such as configuration or task spaces, the definition needs to be extended to consistently and exactly address force generation. Towards this end, we use the tensor notation to compute the B = B x . = C,(l,x)X) x . (5) term so that the computation of the corresponding obstacle force Fobs becomes a tensor reduction operation with the robot velocity, as Fobs = -BX. In this section, we briefly recount the computation of B for any given obstacle surface and robot velocity given that the form selected for the MMF was given by B = We also discuss the computation of the obstacle forces and torques applied to a robotic link. Previously, we presented control forces that applied to a point robot - whether operating in Cartesian or in joint space. Here we extend the definition of the obstacle force to apply to linked manipulators. The method of computing the B tensor is briefly summarized for its relevance to the next section. Let the n-dimensional obstacle surface be characterized by a minimal set of n orthonormal vectors: 1 surface normal and (n-1) surface vectors. The B tensor matrix is then computed from these vectors. Given that Fobs = x x B or Fobs = -Bx using new notation, it follows that x.(Bx) = 0 from the scalar triple product result. Now this must be true for all x, including those velocity directions that are parallel to the eigenvectors of B. $ in Eq. 4. P For x = [,[ E [EV set ofB] . 1 1 [ 1 1 2 = o (6) To satisfy this requirement, either X g = 0 or llE112 = 0. Skew-symmetric matrices meet these criteria since the roots of skew-symmetric matrices are either zero or strictly imaginary. Now, if X g = 0, then Fobs = AB . = 0 which is exactly the desired behavior if the robot velocity runs parallel to the surface. However, if the robot velocity runs along the surface normal the 1 1 [ 1 1 2 = 0 solution is used, which corresponds to an imaginary root. To choose a real 13 with 2 complex conjugate pairs (to ensure realness of a), select any (n - 2) of the surface vectors as the B eigenvectors with eigenvalues of 0, and choose f~ as the two remaining eigenvalues. Eigenvectors for these last two values are constrained to lie in the plane of the surface normal direction and the last (n-1)th surface vector. Now select any 2-d skew-symmetric matrix with eigenvalues f i , find its eigenvectors and the last two eigenvectors of our MMF matrix is now known in terms of the 2 known basis vectors scaled by the components of the 2-d eigenvectors just found for the known 2-d matrix. Now, the eigenvalues and the eigenvectors are known and the computation of B may be computed. 4 Computing the Obstacle Fields and Forces for a Linked Manipulator An outline of the computation of the obstacle forces for a linked manipulator navigating in a Cartesian or task space are presented herein. Consider the situation shown in Fig. 3. The joint space obstacle forces are generated in joint space and joint limit avoidance is performed by treating each limit or singularity as an obstacle and computing the resulting set of forces as described earlier. Subsequently, task space motion planning is performed whereby the obstacle forces and torques are computed for the task space obstacles. These task space forces and torques are then transformed back to joint space through the manipulator Jacobian, where they are integrated with the previously obtained jointspace forces. Collectively, these forces serve as input control torques in the robot dynamic relation where final force resolution is performed. The joint space obstacle avoidance is performed as shown in the previous section and detailed in [5]. In task space, the obstacle force on the link is formulated in two parts, one generates the task-space force and the other the torque for the given link. To compute the link force component, the link is abstracted to its center of mass and the obstacle force for the center of mass is then computed in Cartesian space, as has been done for the point robot. The obs- tacle force is then computed as: Next, the obstacle torque is computed. This torque, the Modified Magnetic Torque is computed in a somewhat analogous fashion through the following relation: where w represents the angular velocity of the link, s represents the link axis, U the linear velocity due to the orientational component, and I' denotes the Modified Magnetic Torque Field, the angular analog of the MMF . The M M T F and the obstacle torque has similar electro-dynamic connotation as the MMF , however, in implementation, we have yet again, departed from the classical electro-magnetic mathematical definitions. Rather than visualizing the robot link as a point charge, as has been done in classical potential field methods and earlier in this paper in the development of the M M F , here the link is treated as a dipole and derivations of r o b s derive from the interaction of the dipole moment with the obstacle torque field. Eq. 8 constitutes a contraction mapping of the tensor I?. The cross product terms in Eq. 9 may be computed as outlined in Sec. 3. While the tensor form is necessarily important for higher dimensional spaces, the cross product form may be retained for classical Cartesian space development. The rationale for the above mathematical structure will be briefly outlined. The considerations governing the M M T F equations here are similar to those that went into formulating the MMF forces. Ideally, we would like to preserve link configurations in which the link lies parallel to the obstacle surface (i. e. where r o b s = sTn = 0) and reorient those in which the link lies along the surface normal. Towards that end, the sTn term is important in that this term is zero for every link configuration that lies along the surface and is only non-zero when the link axis is oriented towards the surface. Additionally, a torque expression that ensures that the work done by that torque will always be zero is desired i.e. r such that W = w.7 = 0, as will be shown to be important in the brief outline of the Lyapunov Energy analysis perform in the next paragraph. The (U x (li x s ) ) x w term in the definition of I' ensures that this requirement on the obstacle torque is met. Multiplying the dyads in Eq. 9 by the vector s causes the contraction of the tensor B, and yields the above vector, (li x s ) x w. The presence of the . x w term, this term is guaranteed to be orthogonal to U, and hence ensures that the work done by this obstacle torque is zero. To show that this choice of the obstacle torque preserves the convergence properties of this method (see [ 5 ] ) a Lyapunov candidate function of the form V = p X M T x + U ( x ) , or more verbosely, $ (XTXl + qTq) + U(x). The state velocity vector has been decomposed into the linear and angular components. The state vector x = [xl,4] where xl denotes the linear position vector, and q, the angular position quaternion. Furthermore, using the unit rotation quaternion representation, q = -($ @ q) and q = @ q + $ @ ($ @ q), where $ = [w,O] is the vector quaternion form of w and 8 represents the quaternion product, the convergence analysis is performed in this generalized position-orientation space. Further detail on the quaternion analysis may be found in [6]. The time derivative of the Lyapunov function yields 9 = M (XTxl + q'q) + VUTx, + VUTq. The rate of change of Lyapunov energy can be represented as i, = x:(-vU(xi) - k2Xl - BXl) + qT(-vU(q) - k 2 q f ( T o b s @ q - $ @ ($ 8 9))) + vU(Xl)Txi + vU(q)Tq (10) where Tabs is the quaternion form of r o b s , given by Tabs = [ r o b s , 01. Since r o b s is defined to be either zero (when s I n) or else normal to w , and may be given by the relation r o b s = (Q x w ) when not zero, the time rate of change of the Lyapunov function, upon resolution of the quaternion relations, becomes simply i, = -k2X?Xl - k2qTq 5 0 which is inherently negative semi-definite. Using the LaSalle Invariance Principle, strict negative definiteness can be shown. 5 Result of Dynamic Control on Puma560 using MMF Methods The governing robot dynamic equation is given by the relation: M ( 0 ) 8 +C(6,0)6 +k(O) = r (11) where M represents the mass matrix, C , the matrix of Coriolis and centripetal forces, k, the gravity vector and 0 the vector of joint angles, r is the applied joint force. The M M F control scheme outlined in this paper generates the set of r that will be applied to the dynamic control equation. The resulting joint positions and velocities represents the motion of the robot. In this section, an example of a robot navigating in the space of obstacles - both task space obstacles as well as Cartesian space obstacles - and required to obtain a certain goal configuration, is presented. The planner control is effected in the following fashion. The joint space obstacles (joint limits) are generated thus: upper joint limit 1 corresponds to a surface at [&,O, . . .O] and with surface normal [--I, 0 , . . .O]. Correspondingly, the surface vectors for this surface are setup as [O, 1,O.. .O], [O, 0,1, . . .O] , . . . [O, 0 . . . I] with accurate assignments for the sign of the surface vectors to ensure closed loops around the joint space boundary. This done, the joint space forces are computed using the relations Fattr = -kl(O - Od) (12) Fdamp = -m) (13) = -azo (14) Next the Cartesian space obstacle forces are computed. The Cartesian space force and torque are computed for each of the N-links of the robot. F:::t = Xzo(X:om x B:om) (15) ,xart - T T N obs - ( Xz=O(n(v (lz .)) (16) Now the generalized force vector is obtained by stacking the force and torque terms: (17) which is transformed through the generalized Jacobian matrix into joint space yielding the resultant relation: 7- = Faitr + Fdamp + FZS + JTFS,Er (18) Now by appending gravity compensation to this T , it is applied as the control to Eq. 11 Although parameter adjustment and tuning are not mandatory for convergence, the robot motion plan will be correlated with the parameters used for the control inputs. The parameters used affect the inertia in the control system. For instance, the larger the proportional gain in the attractive force, the steeper a potential well it sets up and hence the robot slides down it with correspondingly greater energy. A shallow well, on the other hand results in very straight lined paths, where the robot heads straight for the goal, but navigation around the obstacle becomes very exaggerated. The resulting task space paths are shown in the associated figures. In this problem, the objective or the desired configuration was stipulated at @, = [67.5, -45,176.4, -35.5,33,200]. The joint limits were the standard joint limits of a Puma560. and the initial configuration was given by 00 = [-75.6, -15,91.5,143, -59.7,112.3]. Task space obstacles were vertical walls located at: Wall config. Centroid Normal Vertical [0.05,0.4,0.6] [0, -1,Ol Horizontal [0.55,0.025,1.25] [O,O, -11 The robot starts with its tip very close to both, the vertical wall in X and the Joint4 joint limit. To get to the goal, without colliding with the walls or going through its limit, the robot, increases its elbow angle (dropping the forearm) but lifting the shoulder joint. To navigate the facing wall, the robot lifts its entire arm to the tool, curving up to avoid the wall, lifting the shoulder a t the same time. The presence of the short ceiling flattens the trajectory, leaving the robot having to pull out from the ceiling before it can adequately pull up to cross the second enclosing wall to the goal. The robot approaches the second vertical wall but has to approach very close to it to avoid both, its Joint3 singularity as well as the first vertical wall. Small \u201cbobbles\u201d are seen in the elbow and tip paths as the action of the M M F manifests its self strongly at this point due to the proximity of the robot to the obstacle surfaces. Removing the horizontal wall results in a much smoother and natural looking trajectory, whereby the robot tip first falls toward the floor as the forearm falls and the robot base turns toward the goal; the elbow and tip then smoothly curve up and over the second vertical wall. The corresponding joint space trajectory during this navigation are shown in Fig. 9 Joint 1 is most encumbered in this move. The robot starts off fairly close to its joint1 lower limit and has to further approach it to navigate the walls. In nearing the goal, it approaches very close to its other limit and the characteristic \u201cbobble\u201d is seen in the joint space trajectory at the highest points in the joint path arc. Vertical [0.75,0.0,0.85] [ - l , O , O ] 6 Conclusions In this paper, we reviewed the concept of the Modified Magnetic Field to robot motion planning and control in an obstacle field. The treatments in both Cartesian space and configuration space were highlighted. The fundamental idea is based on the electrodynamic principle, where a magnetic component originates from the presence of fictitious current elements wrapped around each obstacle. Extension of the planning algorithm to a linked manipulator was then presented where the objective was to navigate both joint space and Cartesian space constraints. The al- gorithm was successfully able to negotiate the constraints. Since the forces generated by the MMF can be analytically computed, the algorithm has also been implemented as a real-time feedback controller. References [I] J.C.Latombe, Robot Motion Planning. 101 Philip Drive, Assinippi Park, Norwell, MA 02061: Kluwer Academic Publishers, 1991. [2] 0. Khatib, \u201cReal-time obstacle avoidance for manipulators and mobile robots,\u201d Proc. of the IEEE Internat? Conf. on Robotics and Automation, pp. 500-505, 1985. [3] D. E. Koditschek, \u201cExact robot navigation by means of potential functions: Some topologi- cal considerations,\u2019\u2019 Proc. of the IEEE Intemat \u2019I Conf. on Robotics and Automation, pp. 1-6, 1987. [4] K. J.O. and K. P.K., \u201cReal-time obstacle avoidance using harmonic potential functions,\u2019\u2019 IEEE Ransuctions of Robotics and Automation, vol. 8, pp. 338-349, Jun. 1992. [5] L. Singh and H. Stephanou, \u201cA collision-free, realtime motion planning with guaranteed convergence using analytical circulation fields,\u201d Submitted IEEE Int? Conf. on Robotics and Automation, 1996. [6] L. Singh and H. Stephanou, \u201cTask-based servoing in vector-quaternion space,\u201d Proc. of the IEEE Internat? Conf. on Robotics and Automation, vol. 25, pp. 100-110, May 1995."
        ]
    },
    {
        "image_filename": "designv11_11_0003846_robot.2005.1570351-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003846_robot.2005.1570351-Figure3-1.png",
        "caption": "Fig. 3 Moment of inertia about C.M.",
        "texts": [],
        "surrounding_texts": [
            "OF OBJECT G D\u00b1DF2L [ [[p(l) i(2)lX [[F(2N1) -F(2N)]X[P(2N-1) (2N) T DF2 = [Ff 2)-Ff22) ... [[f2 )-f2)]X (19) (20) (21) From the obtained G, the corresponding C.M. line can be described as x = (Pf -G) + tx lplPA (22) where, x is a point on the C.M. line, and tx is an unknown coefficient about the distance from point C to point x. Hereafter, for convenience, we denote the above G, Pfi, Pf2, P and point C as G1, Pfii, Pf21, Pi and Cl, where subscript \"1\" means 1st time pushing operation. After estimating G1, the finger will be put on another object side for another pushing operation, and the straight motion direction will be changed within 20\u00b0 1600. Thereby, G2 for another C.M. line can be estimated, where subscript \"2\" is used for the 2nd time pushing operation. Since the intersection of G1 and G2 is the C.M. of the object, we have: P1 ~~~P2(Pf11-G1)+tgl i (Pf12-G2)+tg2 * (23)Pd ~P2~ Here, tgl, tg2 are unknown coefficients about the distance respectively from points C1, C2 to C.M. position PG and are obtained from (23) as [ tgl 1 F P1 P2 1 [ tg2 j [ Pll IP2fJ [(Pf 11 - Pf12) - (G1 - G2)] (24) Accordingly, by substituting the obtained tgl, tg2 to (22), the C.M. position PG can be estimated as PG = 2 1=l [(Pfli - Gi) + tgi (25) If we perform n (n > 2) pushing operations with different directions, the C.M. position PG can be estimated with well accuracy as P0 =Z%E= [(Pfli -Gi)+tgi Pi . (26) When an object is rotated with angle 0 by two robot fingers, the relation between the moment of inertia IG about C.M. and the moment NG around C.M. can be represented as TIG = NG, (27) Here, let us denote the coordinates of fingertip 1 and fingertip 2 on a frame whose origin is set at C.M., by GR1, GR2, the distance from C.M to the Coulombfrictional resultant FC by Rcg, the distance from C.M to the viscosity-frictional resultant F, by Rag. Thus, the moment around C.M. NG will be NG = Ffi X GR1 + Ff2 X GR2 + FC x Rcg + yP x Ra9g. (28) From (27) and (28), there is IG0 = Ffi x GR1 +Ff2 X GR2 +FC x Rcg +P xRa, (29) where, Ff1, Ff2 are obtained from fingertip force sensors, 0, 0 are from the variations of fingertip position, GR1, GR2 are from the obtained C.M. positions. The unknown parameters are IG, FC, Rcg and aR,g. By changing angular acceleration 0, 2 equations based on (29) can be obtained as TJO(1) =F(1) + F()xGR2 +F41) x Rcg + P (1) x -yR-,g, I 0(2) = F(2l) X GR1 +F(f2) X GR2(2). (2)Ic6~2) fl f2GR +4F2) x Rcg + i,x2)x ygR (30) (31) Since F41) and F42) are the same, we have: IG[0(1)- 0(2)] = [F -l) Fr2)] x GR1 + [Ffi2)-FF2)] x GR2 + [P(l) _- (2)1 X] RxgR (32) so that only IG, -yRag are unknown. For the 2 unknown parameters, we take 4 equations based on (29) respectively with different angular accelerations. From the differences between the equations, we have: F0(1)_ (2)X IG[[P(l)-P(2)] F 1 L (3)-(4P ]X [ F[F11 F(21)] X GR1 + [F(2)-F(2)] X GR21 [ 1)-F(41)] x GR1 + [F(3)-F(4)] X GR2 1 (33) Therefore, the moment of inertia around C.M. IG can be obtained by IG 1_ (l) [[P) iP ]X]1 L -L[(3) - [[P(3)_-P(4)]X] J F[() - F(2)] X GR1 + [F(2) - F(2)] X GR2 1 L[F(31)-F(41)] X GR1 + [F(3)_F(4)] X GR2 ( (34) By taking 2N (N > 2) equations based on (29) with different angular accelerations, from the differences between the equations, 1G, -yRa can be estimated with well accuracy as [ R]G D+P[DF1 x GR1 + DF2 x GR2], (35) Dp [(1) (2)] [0P [[. (l) .p(2)] ]xT [0(2N-1) _ (2N)] -T _[[P(2N-1) -P(2N)]X]T (36) DF1 = [ [[F(l) -F(21)]X]T [[(2N-1) _ (21N)]X]T ]T (7 DF2 =[[[F(l2)- F(22)]X]T .. [[F(2N-1) - F(2N)]X]T ](38) VI. VERIFICATION BY EXPERIMENTS We have done some experiments for verifying the validity of the proposed method. In the experiments, the object is a wooden box with sizes 200(mm)x150(mm) x I00(mm) in which 1(kg) and 0.5(kg) weights have been put. Pushing operations are performed by a 6 joints manipulator (Mitsubishi, MELFA RV-1A, Position repeatability: +/-0.02(mm)), on the effector of which two fingers with 6-dimensional fingertip-force sensors (BL Autotech, NANO 5/4 Sensor, Resolution: 3.3(gf)) are equipped as shown by Fig.4. There are unknown frictions among the fingertips, the object and its environment. The environment for the pushing operation is a level acrylic plane, and the frictions on the contact plane between environment and object are uniformity. In the experiments, the robot arm will put its two fingertips on an side of object and push the object within 5(mm). If the two fingers have sensed contact forces respectively, a C.M. line will be between the two fingertips so that the object can be pushed straightly or with a certain rotation. Otherwise, the fingers will move 5(mm) right or left along the side of object and push again till a C.M. line between the fingers is found. Then the fingertips will still adjust thier positions to make the difference between two fingertip forces as small as possible. After deciding the fingertip's position on the object, the finger will slowly push the object slowly straightly or rotatively with different accelerations or angular accelerations, to obtain the information on the forces, positions, velocities and accelerations of fingertips. Over 8 different accelerations are taken out in each experiment. TABLE I"
        ]
    },
    {
        "image_filename": "designv11_11_0003909_icsmc.2005.1571491-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003909_icsmc.2005.1571491-Figure2-1.png",
        "caption": "Figure 2. Representation of a static obstacle",
        "texts": [
            " This particular case is characterized by a special value for \u03b10i, that is \u03b10i = 0 (11) This value can be seen as an optimal value for \u03b10i, which results in a minimum time to reach the prey by robot Ri. The kinematics equations for this case are similar to the general case. In the case of the pure pursuit, propositions 1 and 2 state that the line of sight angle and the robot orientation angle track the prey orientation angle. The proof that the robot reaches the prey is obvious in this case. Static obstacles are modeled as circles. The obstacle avoidance mode is activated when an obstacle is detected within a given distance from the robot. We use a collision cone approach as shown in figure 2. The robot\u2019s deviates from its nominal path by changing the value of \u03b10i, but at the same time, the robot keeps \u03b10i \u2208 ( \u2212 \u03c0 2 , \u03c0 2 ) in order to accomplish the pursuit. The deviated pursuit control law allows the robots to reach the prey, but at the same time it can result in collision between robots. We suggest an algorithm for collision avoidance based on the collision cone principle discussed in various recent publications [19]. In our approach the robots are modeled as circles of radius d. We assume that all robots have the same size"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002629_pime_proc_1987_201_156_02-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002629_pime_proc_1987_201_156_02-Figure7-1.png",
        "caption": "Fig. 7 The measured dependence on pulley radius of F JF, at the linear slip limit (0) and the near-peak efficiency limit (m) for the raw-edged belts compared with theories (hatched regions)",
        "texts": [
            " It is of practical importance to know what is the largest torque that can be transmitted without incurring the penalty of much reduced efficiency. In the review of theories of the transition to skidding an underestimate of the torque was suggested to be that at which nonlinear speed loss commenced. The present experiments have shown that for F, + F , 2 100 N, FJF, at the start of non-linear slip was almost independent of F, + F,. Its dependence on pulley radius is shown for the rawedged belts in Fig. 7. Figure 7 also records the larger values of FJF, which correspond to the torques above which much reduced efficiencies. actually occur: these critical torques have been obtained from the raw-edged data in Fig. 4, for example 12 and 17 N m at F , + F , = 400 and 600 N with the 36 mm radius pulleys or 6 and 8 N m at the same belt tensions with the 21 mm radius pulleys. The hatched regions in Fig. 7 show Gerbert's predicted (8, 10) non-linear and weak non-linear limit values of F J F , . They are regions rather than lines because of experimental uncertainty in the belt deformation properties used in their calculation (see Table 1). It can be seen that the weak non-linear limit is a safe design limit for pulleys of a greater radius than 50 mm but it is not safe for the smaller pulleys. For the 21 mm pulleys the non-linear limit is just safe. Proc Instn Mech Engrs Vol201 No D1 at WEST VIRGINA UNIV on July 21, 2015pid",
            " Speed loss inversely dependent on total belt tension and R 2 may possibly arise from carcass shear and an arc of contact reducing with reduced belt tension, but it cannot be exactly modelled by analogy with flat belt behaviour. The large influence of pulley radius on torque and speed losses is seen in equations (26) and (27). Pulley radius also strongly influences the maximum tension ratio that Proc Instn Mech Engrs Vol 201 No D1 at WEST VIRGINA UNIV on July 21, 2015pid.sagepub.comDownloaded from 52 T H C CHILDS AND D COWBURN can be supported round a pulley without excessive power loss. This is shown in Fig. 7. The allowable tension ratio falls from more than the weak non-linear prediction when R = 51 mm to almost the non-linear limit when R = 21 mm. It has not yet been attempted in this study to predict this variation by extending the analysis of speed loss into the non-linear region. It is worth pointing out, however, that for R = 21 mm the limiting value of F J F , measured to equal 5 is not significantly different from the value of 4.8 predicted by the capstan formula [equation (3b)l for a flat belt with p = 0.5 and an arc of contact of a radians. The effective friction increase expected from wedging the belt in the pulley groove has been completely offset by the reduction caused by belt radial movement. It is commonly recommended in design guides (16, 17) that for a nominal contact arc of R radians, FJF, should not exceed 5, whatever the pulley radius. Figure 7 shows that this is extremely conservative for largeradii pulleys as far as efficiency is concerned. Finally, it is instructive briefly to extend the discussion to consider the matching of the raw-edged belt's power transmission capacity to the power requirements of a typical medium car alternator. Figure 12 shows the input power typically required for full output from a modern medium-sized (55 A) alternator (from private communication, Lucas CAV Limited, 1986). It also shows the power that can be transmitted by an AVlO raw-edged belt without excessive power loss, assuming an angle of wrap of 18W, F, + F, = 500 N, an alternator pulley radius of 30 mm and taking F J F , to equal 7 (from Fig. 7); driving between pulleys on fixed centres has been assumed (in contrast to the present experiments) and the loss of drive at high speed stems from centrifugal effects calculated for the belt's measured mass of 0.083 kg/m. In practice the angle of wrap on the alternator pulley is less than 180\"; a second belt transmission characteristic has been estimated for an Proc Instn Mech Engrs Vol201 No DI angle of wrap of 12W, assuming the maximum allowable FJF, to reduce with angle of wrap in proportion to F J F , at the linear slip limit",
            " Linear speed losses have also been found to depend on (gEZ/R\")'/' in addition to extension and radial compliance speed losses, as described in equation (27). Unexpectedly they increased as total belt tension decreased, also as shown in equation (27). This is possibly a result of reduced arc of contact at reduced total belt tension. The maximum tension ratio that could usefully be supported round an arc of contact of 7c radians also reduced with pulley radius, from 21 to 5, as the radius was reduced from 51 to 21 mm, as shown in Fig. 7. It is speculated (with some supporting evidence from testing more simple geometry flat belts) that the failure of current theories, particularly with small-radii pulleys and at low total belt tensions, is due to the fact that they ignore the warping and shearing of belt carcass sections. In the entry and exit regions this leads to torque loss and in the remainder of the contact arc it leads to speed loss. Further work is needed to develop these suggestions and to extend the applicability of equations (26) and (27) to power transmission between pulleys of unequal radius and to nominal arcs of contact less than n radians"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001499_20.877692-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001499_20.877692-Figure7-1.png",
        "caption": "Fig. 7. Acoustic mesh and Cartesian coordinates of the noise pressure measurements points",
        "texts": [
            "3 m from the source for illustration purposes). Fig. 6 shows the radiation efficiency as a function of the excitation frequencies, obtained applying the numerically calculated sound power radiated values in (2) and solving for . These radiation efficiency values are much more precise than the ones calculated using (3) because the electric motor is not a monopole source. Tables I, II, III and IV compares the calculated sound pressures levels with the measured ones at points 1, 2, 3 and 4 (shown in Fig. 7, which represents the acoustic mesh), respectively, for the 1250 Hz, 1500 Hz and 1750 Hz excitation frequencies, considering a distance of 1m from the source and for a rotor speed of 2500 rpm. Observing the Tables I and II one can notice that the sound pressure values obtained by BEM calculation and by measurements are relatively close at points 1 and 2 for the frequencies of 1250 Hz and 1750 Hz, however for the 1500 Hz frequency the measured values are much larger than the calculated ones. These elevated values are probably due to noise of aerodynamic origin as the turbulence effects, since for this frequency in particular important structural vibration peaks were not observed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003909_icsmc.2005.1571491-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003909_icsmc.2005.1571491-Figure4-1.png",
        "caption": "Figure 4. Velocity command and orientation command",
        "texts": [
            " The control law for the orientation angle of R\u2217 i is given by \u03b8\u0307i = \u2212k2 ( \u03b8i \u2212 \u03b8des i ) (13) where \u03b8des i is the desired orientation angle, and k2 is a real positive constant. The collision cone is built around the estimated point of collision, where this point becomes the center of a circle of radius 2d (as shown in figure 3) upon which the cone is constructed. The orientation angle for R\u2217 i is calculated so that the velocity vector of R\u2217 i is outside the cone. R\u2217 i can perform a right or left deviation (towards point A or B). We suggest that R\u2217 i turns towards the closest point to the other robot, which is point A in figure 4\u2013b. This is the final navigation mode, where the aim of the robots is to enclose the prey. Circle formation as well as other geometric forms formation was addressed in [10] based on geometrical rules. The problem here is more difficult since the aim is to form a circle around a moving object. This mode is activated for each robot separately when the robot reaches a point within a given distance from the prey (say l0). The circle enclosing the prey has l0 as radius. The circle formation is established in the following steps: 1",
            " Here, we illustrate the algorithms using simulation. In this example the prey moves with constant orientation angle, and vp = 2m/s. The initial position of the prey is (12, 12). The predators move with vi = 3m/s, i = 1, ..., N . The initial positions and the deviation angles for the robots are given in table 1. The paths traveled by the prey and the robots is shown in figure 5, where the capture task is accomplished successfully. The orientation angles for the prey and the robots are shown in figure 4, where it is easy to see that the angles \u03b8i (i = 1, ..., N) track \u03b8p with small deviation. In this paper we discussed the problem of modeling and controlling a hunting problem using a group of robots. The motion of the prey is not a priori known to the robots. We model the hunting problem using the relative equations of motion of the prey with respect to the robots. The control laws for the robots are decentralized and depend mainly on the motion of the prey. In the navigation-tracking mode, the robots use the deviated pursuit control law with different deviation angles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001551_robot.1996.503859-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001551_robot.1996.503859-Figure8-1.png",
        "caption": "Figure 8: Movements of the space robot (Au, = 0.5[m], without spiral motion)",
        "texts": [
            "5[m/s] in the positive x-axis direction with the satellite orientation maintained. The initial configuration and the desired trajectory are given in Fig.6, where the broken line stretched from the end-effector denotes the desired trajectory. X 0 :joints Figure 5: Structure of a space robot Figure 7 shows the satellite orientation variation in response to the end-effector desired trajectory without spiral motion. The solid, broken and chained line denotes the 3 vector elements of the Euler parameters in the order. Figure 8 shows the same motion every 0.2[s]. The results of the single-turn spiral motion are shown in Figs.9 through 11. In Fig.9, the solid line denotes xcoordinates variation of the end-effector. the broken and the chain line denotes y's and z's, respectively. The dotted lines denote the desired trajectories. Fig- ure 10 shows the satellite orientation variation. Figure 11 illustrates the motion every 0.2[s]. The Figs.12 through 14 correspond to the multiturn spiral motion when the spiral radius limit g d sets O"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002107_s0967-0661(03)00048-0-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002107_s0967-0661(03)00048-0-Figure1-1.png",
        "caption": "Fig. 1. Experimental device.",
        "texts": [
            " jBk\u00f0m\u00dej \u00bc 1 l 1 lk 1 Ak 1\u00f0m\u00de; Ak\u00f0m\u00de \u00bc lAk 1\u00f0m\u00de \u00fe jXk\u00f0m\u00dej A0\u00f0m\u00de \u00bc 0; B1\u00f0m\u00de \u00bc 0: ; \u00f06\u00de During the synthesis all the #Sk\u00f0m\u00de are at first transformed into #sk\u00f0n\u00de segments by the inverse Fourier transform. The time domain signal is then reconstituted by the sum of the segments respecting the superimposing used in analysis. #sk\u00f0n\u00de \u00bc XL m\u00bc0 #Sk\u00f0m\u00de:ei\u00f02p=M\u00denm; nA\u00bd0;M 1 ; \u00f07\u00de #s\u00f0n \u00fe kM=2\u00de \u00bc #sk 1\u00f0n \u00fe M=2\u00de; \u00f08\u00de nA\u00bd0;M 1 ; mA\u00bd0;L ; L \u00bc M 1 sha ; where sha is the Shanon factor, k \u00bc 2i (i integer), L the number of line spectrum. Let us consider the signal generated by a spalled bearing. This signal comes from vibratory measures made on a defective ball bearing tested in laboratory on a bench (Fig. 1). On the outer ring of this bearing a defect is made using an electric pen. The width of this defect is of 3mm, the repetition frequency of this defect is of 47.72Hz. A static charge of 100N is applied on the bearing, and the accelerometer is set on the outer ring as close as possible to the defect. The time domain signal (Fig. 2) is characterized by the presence of a periodic shock occurring as soon as one of the balls of the bearing is in contact with the defect and by the presence of a high-level noise"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000022_s0022-0728(99)00114-x-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000022_s0022-0728(99)00114-x-Figure3-1.png",
        "caption": "Fig. 3. Electrolytic cell for LAV.",
        "texts": [
            " LA voltammetric measurements were performed by using a potentiostat with potential and current responses of 5 ms (Huso, HECS 972) and a function generator (Huso, HECS 980). These two instruments and the Q-switching of the YAG laser were controlled by a personal computer. In this work, the current was sampled every 0.2 s throughout recording of the LA voltammogram, independent of the repetition frequency of the laser pulse, 0.5 Hz. A transient current\u2013time (I\u2013 t) curve after the laser pulse was observed with a digital oscilloscope (Tektronix 2440). A trigger signal to the oscilloscope was supplied from the Q-switching circuit of the YAG laser. Fig. 3 shows the electrolytic cell used. The cell was provided with an optical window through which the laser pulse was delivered to the electrode and a glass jacket in which thermostatic water was circulated. The working electrode was constructed by inserting a gold wire of 0.5 mm in diameter (Nilaco, 99.95%) into a glass tube and Fig. 4. Scanning microscopic images of a gold electrode surface after laser ablation (a) and the intact surface (b). The gold electrode was ablated in 1 M KCl solution at 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002299_027836402761393487-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002299_027836402761393487-Figure8-1.png",
        "caption": "Fig. 8. Robot system used for simulation.",
        "texts": [
            " By using the planned trajectory, we simulated the motion of the object. For this simulation, we used the software ADAMS (Mechanical Dynamic, Inc.) where the dynamic model can 2. The monotonicity is proved in the Appendix. at UNIV OF WISCONSIN MADISON on July 19, 2012ijr.sagepub.comDownloaded from automatically be constructed, and the simulation can be performed graphically if we assign a proper boundary condition for the points of contact. The 2 DOF manipulator used for the simulation is shown in Figure 8. For the simulation, we first calculated the desired joint trajectory corresponding to the planned trajectory of contact coordinates by using eq. (19). We stored the desired joint trajectory as an array, and made the manipulator to follow the desired joint trajectory. The results of this simulation are shown in Figures 10(a) and (b). Figure 10(a) shows the simulation result where the plate at the tip of the manipulator is moved in 36 sec. Figure 10(b) shows the result where the plate is moved in 360 sec"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001704_s0022-5193(03)00015-8-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001704_s0022-5193(03)00015-8-Figure3-1.png",
        "caption": "Fig. 3. Two-dimensional schematic of a predator with perception cone defined by semi-vertex angle a and contact radius R moving along a trajectory (shown as a long dashed line) at speed UR. After a time t it makes a change of direction as shown. If the predator\u2019s line of sight was permanently directed along is direction of motion, the perception volume it would map out would be basically a combination of two cylinders radius R sin(a) and length URt, plus two segments of a sphere of radius R at the end of each cylinder (although the volume of overlap must be ignored). However, if the predator is free to alter its line of sight after a time tsight, it can look away from its direction of motion. Then the perception volume mapped out would be made up of a series of \u2018ice cream\u2019 cones moving along the trajectory as shown.",
        "texts": [
            " (18) in the previous work would be to produce a small reduction, B2%, in the predicted encounter rates for the two sets of simulations labelled B2 and C2, an improvement in both cases. In this work the effects of making velocity changes at intermediate tS values, typically tS=0.2, 0.5, 1.0, 1.5, 2.0, 2.5 in addition to tS=N will be examined. The simulation results discussed earlier show that when aop/2 a predator can increase its encounter rate by changing direction rapidly, although the effect only manifests itself in the presence of the flow field. To visualize what is happening consider Fig. 3. The modelling ideas presented so far suppose that a predator travels, on average, with speed UR for some time t. In doing so Eqs. (8) and (A.1) suggest that the contact rate is proportional to the volume of a cylinder of radius R sin(a), length URt, (plus the spherical base of the cone) as shown. It then changes direction and maps out a new cylinder. By changing direction the total volume it can map out is reduced and so is the contact rate, as discussed earlier. However, the predator can also vary its line of sight after a time tsight, which is typically equal to tS (i",
            " Now if tsightot the volume mapped out is not a cylinder but, on average, that produced by tracing out a series of \u2018ice cream\u2019 cones at independent orientations to each other, with their vertices moving along the predator\u2019s trajectory. If tsight or a are sufficiently small, changing the line of sight in this way may map out a greater perception volume than is the case when the line of sight is directed along the predator\u2019s trajectory. Crucially this interpretation has two consequences. First, if a=p/2 changing the line of sight in this way can have no enhancement effect. In this instance the cylinder mapped out has radius R and the predator cannot look out beyond this distance in the way shown in Fig. 3. Second, if there is no flow tsight=tS=t by definition and the predator\u2019s line of sight is always constrained to lie along its direction of motion. Again there can be no enhancement effect, as the volume mapped out must be made up of series of cylinders. This explains the results shown in Table 5 columns 2 and 3 for a=p/2, and the no flow results mentioned earlier. In both cases changing direction served only to reduce the encounter rate, there being no enhancement. However, when a=p/3 the enhancement effect is starting to show up and by the time a=p/6 it is clearly dominating the encounter simulations",
            " The question that arises is it possible to modify the ideas outlined previously in order to take account of this effect. It would be preferable if any new ideas were relatively simple, and which would require no new independent parameters beyond those already specified, e.g. tsight or tS, tLC, R and a, and the scales UR and wU defined earlier. In what follows a combination of heuristic ideas, together with comparisons of the results of many kinematic simulations, will be used to design a model of encounter enhancement. Clearly Fig. 3 suggests that to estimate the enhancement effect one needs to estimate the volume mapped out as the predator changes its line of sight, i.e. by following a series of cones which periodically change their orientation after tsight and the trajectory they follow after a time t. Lacking the simple geometry of mapping out cylinders this is a much more complex problem which requires significant computer resources. One way around this difficulty is simply to say that by changing its line of sight in this way, the predator is effectively increasing it\u2019s field of perception",
            " By doing so they can raise the number of contacts made up close to the value perceived when sP=2, Fig. 6b. (This increase will be proportionately greater for smaller a values.) Here the predators can still maximise their encounter rates by reducing tS, but the enhancement effect is much reduced. This is because for larger sP the difference between tS and t is smaller, and hence, the correlation between line of sight and direction changes is increased. Consequently there is a reduction in the extra volume a predator can map out by changing its line of sight in the manner illustrated in Fig. 3. Finally in Fig. 6c there is no enhancement effect at low tS values. Indeed there is a reduction in the number of encounters, rather as one observes for the simulations with no flow field. Here the predators swimming dominates the turbulent motion, tSEt and line of sight and direction changes are closely correlated, allowing no scope for the enhancement effect to manifest itself. Note that the discrepancies between the model predictions and the simulations in Figs. 6b and c, largely arise from the differences in the two straight line results (dashed lines)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003209_j.jsv.2004.12.011-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003209_j.jsv.2004.12.011-Figure4-1.png",
        "caption": "Fig. 4. Analysis of oil-film forces of bearing. (a) Forces acted on the bearing, (b) oil-film forces acted on the journal.",
        "texts": [
            " They are placed perpendicular to each other at 451 to the horizontal pointing to the geometric center of the test bearing. Each of the exciters is manipulated by an individual controller and driver system. The exciters can generate sinusoidal forces up to 1.5 kN in two directions simultaneously. And they are connected to the bearing housing by thin-walled tubular connecters. The pressure sensors (Fig. 2-2), which mount in the middle of connecters, are used to measure the excitation forces. The oil-film forces in the experimental rig are analyzed in Fig. 4. Note that f 3 is the static load on the bearing, which is induced by pneumatic loading system; f 1 and f 2 are dynamic loads, which are generated by two exciters. In Fig. 4(a), the X and Y are absolute movement coordinates of the bearing housing. In Fig. 4(b), the x1 and y1 are relative movement coordinates of the rotor. The oil-film forces can be calculated from the following equations: f X \u00bc f 1 cos 45 f 2 cos 45 \u00fe m \u20acX , f Y \u00bc f 1 sin 45 \u00fe f 2 sin 45 \u00fe f 3 mg \u00fe m \u20acY , (2) where f 1; f 2; and f 3 can be measured from pressure sensors in the test rig. Each of f 1; f 2; f 3; f X ; and f Y can be divided into two components: the static f i0 and the dynamic ~f i (i \u00bc 1; 2; 3;X ; or Y). It should be pointed out that the static component of load f 3; i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002215_ajpa.10133-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002215_ajpa.10133-Figure7-1.png",
        "caption": "Fig. 7. Final 0.33 sec of contact during run C. Images are taken from alternate fields (2/60 sec intervals) and show decelerating force vectors, during which the arm flexes at the elbow. Grey circles allow qualitative assessment of extent of arm contraction.",
        "texts": [
            " Interestingly, there appears to be no attempt to \u201cdump\u201d energy by muscular means; body parts do not extend against tension (away from the center). This is in contrast to the situation for terrestrial animals, in which braking can involve considerable energy loss due to negative muscular work. In the gibbon also, , so shear forces at the handhold are not large, suggesting that energy is not dumped via torques at the shoulder joint that impose a forced lengthening of the pectoralis muscle. Instead, it appears that positive work is done, this time due to bending of the arm about the elbow (Fig. 7). The shoulder joint, along with the rest of the body, is pulled towards the handhold through active flexion of the elbow, \u201cworking\u201d against tension. Arm-flexing appears to require positive metabolic work, and acts to raise the overall energy of the brachiating system, both by raising the center of mass (potential energy) and by drawing the mass towards the handhold (which acts to increase the rotational velocity about the handhold, and so the kinetic energy of the mass). Run C provides an example of deceleration, but also of an addition to mechanical energy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003808_09544070jauto309-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003808_09544070jauto309-Figure8-1.png",
        "caption": "Fig. 8 Exploded image of the four-component redesign idea",
        "texts": [
            "2 Design idea I the fact that the first redesign, which made maximum It was not possible to generate a DFE graph for use of the design freedom offered by SLS, could not design idea I as it could not be disassembled. It was be subjected to a DFE analysis. The design freedom assumed that the entire product would be recycled that allows a multipart assembly to be built from a and, as it was manufactured from a single material, single component in a single material may have no separation of parts would be required. profound effects on future design for disassembly/ environment approaches. 4.3 Design idea II The comparison of both the financial and environ- mental impacts of the original product and the four-Figure 8 shows an exploded view of the four comcomponent redesign idea is shown in Fig. 10. Withponents that comprised design idea II. Table 3 shows the original product, the cost of dismantling all eleventhe disassembly sequence for design idea II. parts is approximately \u00a31.00, taking 140 s. However,The assessment shown in Fig. 9 is based on the with the four-component design idea it takes 40 s atsame assumption as the evaluation shown in Fig. 7 neutral cost and with zero environmental impact.that the profits of reusing the two zinc die-casting The financial line for the four-component designparts are \u00a30"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003645_1.1848530-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003645_1.1848530-Figure3-1.png",
        "caption": "FIG. 3. Principle of sensor operations.",
        "texts": [
            " In this control system, the height position is monitored and compared by imaging the melt pool with a CCD camera and employing a sensor. The image of melt pool appears with a certain angle form the deposition plane due to the movement of melt pool and the angle of the CDD camera. In order to maintain reference height, it is compared with the current height detected by the sensor. For instance, the sensors are not activated when the upper edge of the melt pool falls outside of the active area, as shown in Fig. 3. When the deposition level is higher than the reference value, the melt poll image falls into the detection range of the sensors, thereby the light triggers them, generating a voltage signal. As the voltage signal from the sensors triggers, that is, overdeposition occurs, laser control pulse is cut off, and the laser beam is turned off instantly. The beam remains off for a very shot time, and it depends on the pulse period of the TTL signal setup as shown in Fig. 2 and Fig. 6. Consequently, no more deposition is made at the same time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003976_1.3452904-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003976_1.3452904-Figure6-1.png",
        "caption": "Fig. 6 Selected shape of pressure and temperature transducers",
        "texts": [
            " In order to ensure the needed mechanical and electrical stability of the isolating layer between transducer and surface ex traordinary requirements regarding the surface finish of the test disks had to be fulfilled. Using a microfinishing treatment the fol lowing surface toughness could be established: 502 / OCTOBER 1976 Maximum roughness: R t '\" O.l!Lm (= cla = 0.03 !Lm) Table 2 contains details about the methods of measurement and about the transducers for measuring pressure, temperature, and film thickness in elastohydrodynamic contacts. Fig. 6 shows the shape of the transducers used for pressure and temperature measurements. The photograph of an actual pressure transducer is shown in Fig. 7. The measuring area with a width of about 10 !Lm and the large edge areas for soldering on the electrical contacts clearly can be distinguished. More details about the methods of measuring, the development and the production of these micro transducers have been published elsewhere [2} . The calibration of the pressure transducer was determined from Transactions of the ASME Downloaded From: http://tribology"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003719_j.cma.2004.07.044-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003719_j.cma.2004.07.044-Figure3-1.png",
        "caption": "Fig. 3. constru",
        "texts": [
            " The map wp achieves on average the uniaxial compression F \u00bc 1 0 0 1 0 0 0 B@ 1 CA in the sense that the average over one period of wp(x) Fx vanishes. In addition, it is crucial that wp has exactly zero stretching energy, i.e. $wp 2 O(2,3) everywhere. Moreover, we have the bounds jwp\u00f0x\u00de Fxj 6 cp 1=2 ; jrwp\u00f0x\u00de F j 6 c 1=2 ; jr2wp\u00f0x\u00dej 6 c 1=2 p : The energy per unit area is proportional to h2 */p 2, and is entirely determined from the bending term in I2D. Such oscillatory maps do not, however, satisfy the affine Dirichlet boundary condition. Therefore one inserts a boundary layer, as illustrated in Fig. 3. Precisely, we fix a small parameter n representing the width of the interpolation layer, and define w\u00f0x\u00de \u00bc h\u00f0x\u00dewp\u00f0x\u00de \u00fe \u00f01 h\u00f0x\u00de\u00deFx: Here h is a smooth interpolation function which equals zero outside x, one on all points inside x whose distance from the boundary is larger than n, and obeys the bounds 0 6 h 6 1, j$hj 6 c/n, j$2hj 6 c/n2 everywhere, for some constant c which depends only on the domain x. This generates a boundary layer whose area is controlled by n. There, the deformation gradient takes the form rw\u00f0x\u00de \u00bc rh\u00f0x\u00de\u00f0wp\u00f0x\u00de Fx\u00de \u00fe h\u00f0x\u00derwp\u00f0x\u00de \u00fe \u00f01 h\u00f0x\u00de\u00deF ; \u00f07\u00de and its stretching energy density is controlled by dist2 \u00f0rw;O\u00f02; 3\u00de\u00de \u2019 c 2 1\u00fe p4 n4 : To see this, observe that the second and third term in (7) correspond to an average between $wp 2 O(2,3) and F"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002653_1.7420-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002653_1.7420-Figure2-1.png",
        "caption": "Fig. 2 Three-vehicle formation.",
        "texts": [
            "7 42 0 where k1 = \u221a 1 + (tan \u03b4)2 \u2212 2 (15) k2 = \u221a 2 \u2212 1 \u2212 (tan \u03b4)2 (16) c1 = \u22121 \u2212 k1 + ( \u2212 tan \u03b4) tan(\u03b80/2) \u22121 + k1 + ( \u2212 tan \u03b4) tan(\u03b80/2) (17) c2 = arctan [\u22121 + ( \u2212 tan \u03b4) tan(\u03b80/2) k2 ] (18) and \u03b8(t0) = \u03b80. The solution defined by Eq. (11) converges to 2 arctan[(1 \u2212 k1)/( \u2212 tan \u03b4)] as t \u2192 \u221e. This value is independent of the initial condition \u03b80. The solution defined by Eq. (13) is periodic. We are interested in the solution given by Eq. (11). Note that condition (12) is automatically satisfied if \u2264 1 (i.e., the leader\u2019s turn radius is greater than or equal to the formation spacing). However for any there is \u03b4 for which the condition is satisfied. Figure 2 describes the geometry associated with one leader and two followers (F1 and F2). Applying the DDP approach, we note that follower 1 pursues the leader and follower 2 pursues follower 1. Following the described geometry, we find that r\u03071 = VL cos \u03b8 \u2212 VF1 cos \u03b41 (19) r\u03072 = VF1 cos(\u03b41 \u2212 \u03b5) \u2212 VF2 cos \u03b42 (20) \u03bb\u03071 = (1/r1) ( VL sin \u03b8 \u2212 VF1 sin \u03b41 ) (21) \u03bb\u03072 = (1/r2) [ VF1 sin(\u03b41 \u2212 \u03b5) \u2212 VF2 sin \u03b42 ] (22) The DDP approach requires that r\u03071 = r\u03072 = 0. Therefore, VF1 = VL cos \u03b8 cos \u03b41 (23) VF2 = VL cos \u03b8 cos(\u03b41 \u2212 \u03b5) cos \u03b41 cos \u03b42 (24) The angle \u03b5 between the lines F1 \u2212 L and F2 \u2212 F1 can be calculated as \u03b5 = \u03bb2 \u2212 \u03bb1 (25) Substituting Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002028_978-1-4613-9030-5_37-Figure37.8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002028_978-1-4613-9030-5_37-Figure37.8-1.png",
        "caption": "Figure 37.8: Diagram showing the trajectory of the center of mass during a running step of the McMahon and Cheng model (broken cUIVe). (From McMahon and Cheng (1990); reprinted with permission.)",
        "texts": [
            " When the ball is replaced by a linear leg spring with a mass on the top, the situation changes. As long as the motion is confined to hopping in place, force-plate records analyzed by either of the two me~ods will calculate a k\"\"ri equal to the linear spnng constant of the leg spring, kk' When for ward motion is included without ~hanging the stiffness of the leg spring, calculations for k will give a value higher than k,eg, vert 586 Multiple Muscle Systems. Part V: Lower Limbs in Cyclic/Propulsive Movements t 10(1 . COSAo) Figure 37.8 may be used to explain why this is true. The broken curve shows the trajectory of the center of mass during the contact phase of a run ning stride. The initial (and final) angle of the leg with respect to the vertical is a 0' and the initial (and final) length of the leg is 10 \u2022 The downward vertical displacement from the moment of contact until mid-step is t..y. If we call the ground reaction force at mid-step F max' then the vertical stiffness kvert isF mJt..y. The stiffness of the linear leg spring is given by F max divided by its entire change in length at mid-step, so that kl = F 1[/ (J - cos e ) eg ma:i 0 0 + t"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001755_elan.200302773-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001755_elan.200302773-Figure1-1.png",
        "caption": "Fig. 1. Schematic configuration of the flow-through electrochemical cell. Plexiglass blocks (A), cellulose acetate membrane (B), working electrodes (W1 copper-modified electrode, W2 gold electrode) (C), reference electrode (D), counter electrode (E), flow in (F) and flow out (G).",
        "texts": [
            " The working solution consisted of 50 mL of 1 mol L 1 HAc/0.1 mol L 1 Ac buffer 0.1 mol L 1 KI, pH 3.7. Starch was used as end point indicator in the titrations. The dual-band amperometric sensor was fabricated from a recordable CD, which is composed of a polycarbonate base, a photosensitive organic dye and a thin gold layer [19]. A small piece of this material (a slice of the CD) was used to fabricate 2 different electrodes, separated by a very thin stripe done in the gold layer as shown in the inset of Figure 1. Copper was electrodeposited in one of the sides by holding the potential at 0.10 V for 20 minutes in a 0.1 mol L 1 CuSO4 solution, originating the Au/Cu electrode. The design of the flow-through electrochemical cell is illustrated in Figure 1. The cell consisted of two Plexiglass blocks ((2.0 5.2 2.2 cm) and (1.1 5.2 2.2 cm)) separated by a cellulose acetate membrane (spacer, thickness 0.1 mm) containing a hole of 3.0 16.5 mm. The Au/Cu electrode was inserted below the cellulose acetate membrane and positioned in the region of the hole of the spacer, which defines the volume of the layer of liquid flowing in contact with both working electrodes (estimated as 5 L). The external contact of these electrodes was done by direct connection to the bipotentiostat"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003310_1.2400209-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003310_1.2400209-Figure10-1.png",
        "caption": "FIG. 10. A schematic sketch showing the placement of the vortices in the same-signed symmetric equilibrium in the case N=2.",
        "texts": [
            " Thus, a numerical algorithm is required to find these equilibria and this will not be attempted in this paper. However, for two special cases, one in which 1= 2= and the other in which 1=\u2212 2= , and in both of which the vortices are symmetrically located about the y axis, the task of finding equilibria is relatively easier and these will be now described. Consider now the special case of the above Hamiltonian vector field in which 1 = 2 = . Equilibrium configurations then exist in which the two symmetric vortex pairs are also symmetrically placed about the y axis. A schematic sketch is shown in Fig. 10. The equilibrium curve is given by \u2212 y\u0304*2 \u2212 1 + y\u0304*2 2 1 + y\u0304*2 4 \u2212 x\u0304*12 2 + y\u0304*2 + x\u0304*10 \u2212 2 + 4y\u0304*2 \u2212 6y\u0304*4 + x\u0304*8 4 + 9y\u0304*2 + 34y\u0304*4 \u2212 15y\u0304*6 + x\u0304*6 4 + 48y\u0304*2 + 24y\u0304*4 + 56y\u0304*6 \u2212 20y\u0304*8 \u2212 2x\u0304*2 1 + y\u0304*2 2 1 \u2212 8y\u0304*2 + 12y\u0304*4 \u2212 8y\u0304*6 + 3y\u0304*8 + x\u0304*4 \u2212 2 \u2212 7y\u0304*2 + 24y\u0304*4 + 14y\u0304*6 + 34y\u0304*8 \u2212 15y\u0304*10 = 0. 10 It should be noted that in the classical problem this equilibrium has been mentioned in the paper by Elcrat et al.23 The curves of 10 are shown in Fig. 11 and a list of representative values of x* /R and y* /R is given in Table I in Appendix D"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000336_s0045-7825(99)00371-0-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000336_s0045-7825(99)00371-0-Figure1-1.png",
        "caption": "Fig. 1. Discretization of an axisymmetric circular plate with radius a: (a) discretization m terms of constraints and discontinuity of loading, geometry and material; (b) equilibrium and grid of the ith element.",
        "texts": [],
        "surrounding_texts": [
            "Civan and Sliepcevich [25] to analyze a pool boiling problem in an irregular, two-dimensional geometry, then by Shu and Richards [26] to develop the multi-domain GDQ (generalized DQ) scheme for parallel computation. The QEM has been successfully used to perform static analyses of trusses and beams subjected to various loads [24] and free vibration analyses of thin plates [23]. However, it is inconvenient and not accurate enough for governing differential equations of fourth-order or higher-order, due to the introduction of the 6-grid arrangement, which uses two points to represent one end point in order to deal with double boundary conditions. Furthermore, the basic convergence characteristics of the QEM (or the multi-domain GDQ scheme) have not been extensively and systematically examined and clearly demonstrated, which erects a huge obstacle to its further utilization. In this paper, a new method, entitled the differential quadrature element method (DQEM), is proposed and applied to analyze the axisymmetric bending of moderately thick circular and annular plates based on the Mindlin plate theory with the shear deformation capability [27]. For this purpose, the annular and circular Mindlin plate elements of DQ are developed. The basic idea of the DQEM involves: (1) to divide the whole variable domain into several sub-domains (elements); (2) to form discretized element governing equations by applying the DQM to each element; and (3) to assemble all the discretized element governing equations into the overall characteristic equations, from which the solution of a problem is acquired. The basic convergence characteristics of the proposed method are carefully explored and illustrated with element refinement and element-grid refinement, and some general regulations and suggestions on element division and element-grid selection are made. A number of numerical examples, including patch loads, ring loads, stepped thickness and multiple component materials, are calculated to demonstrate high accuracy, wide applicability and simplicity of the proposed method. The DQEM is a hybrid of the domain decomposition technique and the DQM, like the QEM. The essential difference between the DQEM and the QEM is that there are two degrees of freedom at each grid point for axisymmetric plate problems in the DQEM, therefore, the (6-grid arrangement is no longer needed and no overlapping will occur when connecting intersecting elements."
        ]
    },
    {
        "image_filename": "designv11_11_0003819_rspa.2005.1452-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003819_rspa.2005.1452-Figure6-1.png",
        "caption": "Figure 6. Thermal contact resistance experimental set-up.",
        "texts": [
            " In such modelling, the relative movement (sliding) of interfaces can only be artificially included, since the user must define fixed nodes (that do not move), which will determine the direction of sliding. In practice, some relative movement of components is inevitable during assembling, which combined with gradual increase of clamp force makes the \u2018non-friction\u2019 approach the most suitable. For interface pressure and TCR measurements, the disc and wheel carrier were bolted to the very stiff spin rig adapter (see figure 6). This enabled simplified (\u2018rigid\u2019) but realistic modelling of the underside surface of the disc hat (see \u2018clamped\u2019 nodes in figure 2). To model the bolt clamp force, a continuous load was applied to 120 nodes under the bolt head on the surface of the wheel carrier (see bolt force, figure 2). At the symmetry planes of the model (368 apart), appropriate boundary conditions were introduced, ensuring nodes remained within these planes during loading. Figure 3 shows the contour plot of the ZZ stress component (perpendicular to the interface), representing interface pressure distribution",
            " Thermal contact resistance measurement (a) Experimental set-up The experimental part of the study was conducted using a specially developed spin rig (see Voller 2003). The rig has a simple, in-line arrangement of the disc/ wheel assembly, shaft with adapter, torque transducer, speed sensor and electric motor. The spin rig has been designed for measuring all modes of brake disc heat dissipation (convection, conduction and radiation) and disc airflow characteristics. Experiments have been conducted on the CV brake disc and wheel carrier assembly (see figure 1) installed on to the spin rig shaft, schematically shown in figure 6. For TCR measurements, the shaft did not rotate. The brake disc was heated using two hot air guns fitted to a heater box that shrouded the brake disc (not shown in figure 6). The heater box allowed hot air to flow over the surface of the disc providing uniform heating. The heating power could be controlled from 0 to 4 kW. The shaft adapter, disc and wheel carrier were insulated, as shown in figure 6, to prevent heat losses and ensure adequate heat flow. A thermal blanket placed over the test components and relatively low test temperatures (below 200 8C) further ensured very low thermal losses. For the worst case (maximum interface temperature), thermal losses have been calculated to be under 5% of the heat flow through the interface. The temperatures were measured in close proximity to the interface under steadystate conditions. Therefore, such relatively small losses were considered acceptable and no \u2018compensation\u2019 was introduced in processing the results",
            " Proc. R. Soc. A (2005) Pressure distribution investigation, conducted in \u00a77, indicated two distinctive areas, high pressure areas around the bolts, and low pressure areas between the bolts (see figure 3). Therefore, temperature distributions have been measured in these two areas, positions (1) and (2), as shown in figure 7 (note the heating box over the disc surface in figure 7a). At each position, four holes have been drilled into the disc and four into the carrier (in the radial direction, see figure 6). The axis of the first holes (closest to the interface) were 2 mm from the interface, with the remaining holes drilled every 4 mm. The hole diameter was sized to provide secure fitting of thermocouples. The hole depth was chosen to enable accurate measurement of temperature at the two distinctive areas (see figure 3). At each position, all eight holes were of the same depth. This was to ensure accurate radial position, providing measurement in the direction of conductive heat flow, minimizing the influence of any possible (despite insulation) convective or radiative heat dissipation",
            " A (2005) The temperatures were measured using K-type welded tip glass fibre insulated thermocouples. Heat sink compound was applied to the thermocouple head to evacuate air and improve the contact at the measurement points. The temperature readings were taken when steady-state conditions were reached, allowing the temperatures of thermocouple tip and the surrounding material to equalize. (b) Experimental procedure The fixing bolts were tightened to six torque levels (all bolts to the same torque), gradually increasing from 50 to 300 N m (as shown in table 1). The assembly was heated (see figure 6) with pre-set, constant power, until steadystate conditions were reached. By controlling the heating power, three temperatures levels were achieved, of approximately 70, 120 and 170 8C. The maximum temperature level (170 8C) can be considered to be relatively low, but it realistically represents service thermal loads in this region. All 16 temperatures were simultaneously logged. The criteria for reaching steady-state condition was set as a temperature change of less than 0.05 8C during 400 s. (c) Experimental results For illustration purposes, at position (2), figure 8 shows the average steadystate temperatures at the eight points, for the interface temperature level of approximately 70 8C"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001358_s0094-114x(03)00090-9-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001358_s0094-114x(03)00090-9-Figure5-1.png",
        "caption": "Fig. 5. Triad with one internal prismatic joint.",
        "texts": [
            " The number of real solutions can be reduced to four, two or zero, depending on the links lengths and the position of the external joints of the triad. The influence of the triad input data on the number of the real solutions can be investigated using basic theorems of algebraic geometry [13]. The same procedure can be applied for the other two kinds of Assur group of class 3 and order 3, where the external joint A or D is prismatic and the other joints are revolute. A similar procedure previously described can be used for the position analysis of the triad with one internal prismatic joint (Fig. 5). The local coordinate system, located at external joint A, is oriented such that AD, where D is the second external joint, coincidents with x-axis. The input data for the position analysis are the coordinates of the external joints A\u00f00; 0\u00de, D\u00f0d; 0\u00de and F \u00f0xF ; yF \u00de, the dimensions of each link as the lengths lAB, lBC, lCD and the distances d1 and d2. The constraint equations to be solved are given as: x2 \u00fe y2 \u00bc l2AB \u00f025\u00de \u00f0xC x\u00de2 \u00fe \u00f0yC y\u00de2 \u00bc l2BC \u00f026\u00de \u00f0xC d\u00de2 \u00fe y2C \u00bc l2CD \u00f027\u00de where the coordinates x and y of joint B and the displacement s are unknown",
            " (36) contains two extraneous roots, with a multiplicity of five, defined by the equation: F5\u00f0s\u00de \u00bc \u00f0s\u00fe r\u00de2 \u00fe d22 \u00bc 0 \u00f037\u00de Hence, a final sixth order polynomial equation in s, free of the extraneous roots, is obtained. This equation provides six solutions for s in the complex field. For every root sr (r \u00bc 1; . . . ; 6), the coordinates of the joints B, C, E are determined. The real solutions correspond to the assembly modes of the triad. The six order of the final polynomial equation in parameter s is minimal. This is confirmed using a similar consideration as at the previous triad: For a given position of the external joints A, D and F of the triad (Fig. 5), the internal joint C lies on the tricircular sextic curve of the four-bar mechanism ABEF of the RRPR type [2]. Also C belongs to the circle centered in D, of radius CD. C is the intersection point of the sextic curve with the circle and 12 intersection points exist at most. Due to the fact that this intersection contains two imaginary points as triples points, there will be at most six real intersection points. Therefore the maximum number of the assembly modes of the triad is six. The proposed method can be applied for the other two kinds of triad with one internal prismatic joint, where the internal joint B or C is prismatic and the other joints are revolute",
            " After that the coordinates of the internal joint E are calculated with the aid of Eqs. (4) and (5) while the coordinates of the internal joint C are obtained with Eqs. (16) and (17). The two configurations of the triad corresponding to the real solutions are presented in Fig. 8. Others input data of the triad can lead to six, four or zero real solutions. In the second example, using the procedure described in Section 3, the position analysis of a triad with one internal joint is considered (see Fig. 5). The geometrical data and the coordinates of the external joints A, D and F of this triad are inserted in the left part of the Table 2. The coefficients of the polynomial equations (36) and (37) are calculated and the extraneous roots are eliminated. The solving of the final sixth order polynomial leads to four real roots and two complex roots (see Table 2) for the input data here considered. For each real value of the displacement s, using back substitution, the coordinates of the internal revolute joints B (see Table 2), C and E are calculated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003089_tmag.2005.846230-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003089_tmag.2005.846230-Figure8-1.png",
        "caption": "Fig. 8. Flux variation under sinusoidal input.",
        "texts": [
            " Compared to the nonskewed model, the torque ripples of the skewed model even with a rectangular wave drive is smaller than the ripples of the nonskewed model with a sinusoidal wave drive. B. Iron Losses The iron loss increases as the frequency increases and this can be verified also by the simulation results. The iron loss at 2000 rpm is 47.8 W with a rectangular wave drive and 39.1 W with a sinusoidal wave drive. Compared to the sinusoidal wave drive, the iron loss of the rectangular wave drive is larger. This is due to the high harmonics that the rectangular waveform contains. Fig. 8 shows the location where the flux is calculated by FEM. a, b, c is placed on the stator and d, e, f on the rotor. The flux variations during the sinusoidal wave drive are shown in Figs. 9 and 10. The dashed line means and the solid line means . In the Fig. 10, axis is and axis is . At the part of rotor, the variance of the magnetic flux density is large in nonsinusoidal and the iron loss increases. In this paper, the characteristics of FRM was analyzed in respect of the torque ripple and iron loss"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000213_978-1-4419-8710-5-Figure7.1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000213_978-1-4419-8710-5-Figure7.1-1.png",
        "caption": "Figure 7.1. Schematic Representation of Physical Part",
        "texts": [
            " It can be used to monitor glucose concentration in diabetic people and control an insulin injector, working in a continuous manner. The device is composed of two parts: \u2022 A physical part which includes a laser diode, optical lenses, mirrors, beam splitters, holographic filters, and wavelength dispersion devices. \u2022 An electronic part including a charge couple device (CCD) image sensor and subsequent circuitry to read the sensed image and process it. Let us describe each part independently. Physical Part A simplified representation of the physical part of this device is shown in Fig. 7.1. It is based on the fact that when a monochromatic light of wavelength Ao impinges on a tissue sample (like for example, an ear lobe or a finger) Ra man scattering is produced. Raman scattering is such that the dispersed light coming out of the illuminated tissue contains wavelengths Ai whose values are shifted with respect to the incident light wavelength. The set of dispersed light beams with shifted wavelengths and their intensities represent a \"fingerprint\" of the biological substances and their concentrations in the exposed tissue. The device described by Ham and Cohen is intended for determining anhy drous D-glucose (C6 H 120 6 ) concentrations. Therefore, they have trimmed the physical part of the device to look at the Raman spectral lines characteristics for this substance. Glucose has a rich Raman spectrum with eight fundamental wavelengths. Table 7.1 shows the eight Raman wavelengths produced by this substance if the incident light wavelength is Ao = 780nm. In Fig. 7.1 a Laser diode generates a monochromatic light beam at Ao = 780nm. This beam is divided into two by a polarizing beam splitter. One of the resulting beams is directed to a wavelength dispersion device (A in Fig. 7.1) which deviates the beam according to its wavelength. The resulting dispersed light is sensed by the right half of the CCD array unit shown in Fig. 7.1. This is done for two reasons: (a) to monitor wavelength changes in the light source, and (b) to monitor the intensity of the incident light beam. Wavelength changes SOME POTENTIAL APPLICATIONS FOR ART MICROCHIPS 171 are monitored by detecting the position of the incident light on the right half of the CCD array, while intensity is monitored by adding all pixel intensities of the right half CCD array. The second beam going out of the polarizing beam splitter is directed (for example, through an optical fiber as shown in Fig. 7.1) to the skin tissue. Another optical fiber collects the light scattered by the tissue and directs it to a wavelength dispersion device (B in Fig. 7.1) after lens focusing and holographic notch filtering. The notch filter eliminates all light whose wavelength is equal to that of the laser source light. The light coming out of the wavelength dispersion device B is projected onto the left half of the CCD array unit. On this side of the CCD the intensity as a function of position (i.e., as a function of wavelength) is measured. The outputs of both halves of the CCD array unit are then processed by the electronic part of the system. The electronic part of the system performs basically the following processing: The output of the left half of the CCD array provides a spectrum like res ponse seA)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000660_bf02482438-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000660_bf02482438-Figure3-1.png",
        "caption": "Fig. 3. - a) The loops which are generated by a system of four equal linear springs and three pistons with equal friction, b) Major loop obtained with Preisach's model with four particles.",
        "texts": [
            " 2 is enclosed in an opaque container so that we are unaware of the positions of the individual pistons. The accessible ,,state~, variables of our system are therefore the applied force F = F1 and the overall deformation of the spring sequence Y = ~ Yk. For the sake of simplicity, let us further assume that spring elasticity is linear, and that all springs have the same elastic constant. (In fact, we may take this constant to be unity.) behaviour. What is really surprising is the capability of predicting realistic behaviour already with the very few series elements. As an example, fig. 3a) shows symmetric loops obtained by using a system of only four springs (and three friction pistons). By may of comparison, fig. 3b) shows how much cruder is the representation of a typical major loop obtained by using Preisach's model with only four particles. It is worth noting that the mechanical model of fig. 2, in spite of its simplicity, already shows non-local memory. Figure 4 depicts such a property for the simple model considered in fig. 3a). Indeed, for decreasing F, two different paths may issue from point P in fig. 4, depending on past history. One of them, PQ, is obtained if F is made to decrease monotonically from point A, i.e. by following the path A-G-P-Q. The other one, PR, is obtained if, again starting from A, F is first increased to B and then made to decrease, i.e. by following the path A-B-C-D-E-F-G-P-R. Notice further that the two alternative paths have a whole segment in common, G-P, before bifurcating. (Compare the discussion reported in [4]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001886_1.1396343-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001886_1.1396343-Figure2-1.png",
        "caption": "Fig. 2 Prototype adjustment test",
        "texts": [
            "org/ on 01/29/2016 Term Figure 1 shows a cross section of the inverse orientation form of the bearing with displacements greatly exaggerated for clarity. A rotor is supported via full film lubrication on a stationary central shaft. There are 4 separate hydrodynamic regions influenced by 4 adjustable cantilevered segments, 1, 2, 3, and 4, formed within the shaft and each supported by a tapered adjuster pin labeled \u2018\u2018A,\u2019\u2019 providing a radially stiff load path. The hydrodynamic conditions for each region could be changed by independent controlled adjustments of the segment shapes and positions, by position inputs to the tapered adjuster pins. Figure 2 shows a prototype version of the central shaft under test, with one pin in position and rotor absent. The effect of moving the adjuster pin was to lift ~or lower! the segment surface slightly in a controlled and continuous manner, thereby changing 002 by ASME JANUARY 2002, Vol. 124 \u00d5 203 s of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F the film shape and consequent hydrodynamic pressure field. Various alternative forms of adjustment have been devised for this and other orientations of the bearing system, but the method of imparting such adjustments is not particular to the principle of operation nor to the mathematical model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000308_s0020-7462(98)00001-8-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000308_s0020-7462(98)00001-8-Figure3-1.png",
        "caption": "Fig. 3. Sketches of (a) the bifurcation diagram and of the phase portraits for (b) p(p #3 and for (c) p'p #3 .",
        "texts": [
            " ) exists such that for k(k #3 there is a supercritical pitchfork bifurcation when p crosses the critical value p #3 , while for k'k #3 the pitchfork is subcritical. For a Winklertype reaction, i.e., for k 1 \"k 2 \") ) )\"0, we have k #3 :9.477 [8]. In this paper we will consider only the case k'k #3 , so that a subcritical pitchfork bifurcation always occurs. In this range of parameters, the bifurcation diagram, which is described by p(b)\" A 1 A 2 ! A 1 B 2 !B 1 A 2 (A 2 )2 b2! A 1 [A 2 C 2 !(B 2 )2]#A 2 (B 1 B 2 !C 1 A 2 ) (A 2 )3 b4# ) ) ) (12) is sketched in Fig. 3a. We note that, after an initial decreasing path, a saddle-node bifurcation will cause a change in the monotony, so that for \u2018\u2018large\u2019\u2019 values of b the path, according to the physical sense, increases. When p belongs to a neighborhood of p #3 , there are two different phase portraits which are qualitatively illustrated in Fig. 3b and c. When p(p #3 , there are two symmetric saddles which are connected by a heteroclinic loop which surrounds the stable trivial solution b\"0. The saddles also have homoclinic orbits which encircle two other centers, which appear for \u2018\u2018large\u2019\u2019 displacements. For p'p #3 , on the other hand, there are two symmetric centers which are divided by the trivial solution which becomes a saddle after bifurcation. We now add the dissipating term eabQ (t), which models the dampings (internal, external, etc",
            " It should, however, be noted that chaos in the Melnikov\u2019s sense means transverse intersection of a stable and unstable manifolds, which in turn assures the existence of an invariant hyperbolic Cantor set. This certainly produces chaotic transient, fractal basin boundaries [16] and\u2014by varying the parameters\u2014basin metamorphoses [17], but, in general, it is not sufficient to prove the existence of a chaotic attractor. This will be further discussed by means of numerical simulations in Section 4. According to the two phase portraits depicted in Fig. 3, the analysis of the chaotic dynamics is of course different if p(p #3 or p'p #3 . The main difference rests on the fact that in the former case there are two saddles and two different mechanisms of manifolds interserction, ensuing from perturbation of homoclinic and heteroclinic orbits. In the latter case, on the other hand, there is only one saddle and chaos may arise only as a consequence of perturbation of homoclinic orbit. 3.1. The case p(p #3 When the load is slightly less than the critical value, chaos may occur as a consequence of the perturbation of the two heteroclinic orbits as well as a consequence of the perturbation of the two (symmetric) homoclinic loops. For e sufficiently small it is possible to theoretically establish when this occurs. To employ the Melnikov\u2019s technique, we first compute the heteroclinic and the homoclinic orbits. By hypothesis, there are five equilibrium points for the unperturbed Eq. (10) (Fig. 3b), given by !b 2 , !b 1 , 0, b 1 \"S!B!JB2!4AC 2C , b 2 \"S!B#JB2!4AC 2C , (14) where 0(b 1 (b 2 are well-defined quantities because in the case considered A'0, B(0 and C'0. Eq. (13) can therefore be rewritten as b\u00ae #eabQ #Cb(b2!b2 1 )(b2!b2 2 )\"e f b cos('q). (15) If we define the parameters h\" b 2 b 1 \"S!B#JB2!4AC !B!JB2!4AC , c\"b2 1 J2C (h2!1), b\" 5!3h2 3h2!1 , (16) it is then possible to express the homoclinic and the heteroclinic orbits of the saddle b 1 in the form b )0. (t)\"$J2b 1 cosh(ct/2) Jb#cosh(ct) , (17a) b )%5 (t)\"$J2b 1 sinh (ct/2) J",
            " In this latter case, no qualitative difference exists with respect to the case of Fig. 4a. In the former case, on the other hand, a different succession of events occurs when the amplitude of excitation increases. It is now the heteroclinic bifurcation that initially takes place, so that we can say that in this range chaos should emerge in the middle of the phase space and then \u2018\u2018propagate\u2019\u2019 toward the exterior. 3.2. The case p'p #3 When the load is slightly greater than the critical value, chaos may occur as a consequence of homoclinic bifurcation [see Fig. 3c]. This scenario is substantially similar to that of a Duffing\u2019s equation with cubic non-linearities, which has been thoroughly studied [6, 7] and which is quite well understood [14, Section 4.5F). Consequently, the case treated in this section does not require special attention, and here we compute only the critical curve in the parameter space without providing a detailed analysis. When p crosses its critical values p #3 , the coefficient A in Eq. (13) becomes negative, while both B and C do not change in sign (B(0 and C'0). Eq. (13) can be rewritten as, b\u00ae #eabQ #Cb (b2#b2 1 )(b2!b2 2 )\"e f b cos('q), (21) where now b 1 \"SB#JB2!4AC 2C , b 2 \"S!B#JB2!4AC 2C . (22) Note that in Eq. (22) only the definition of b 1 has been changed with respect to Eq. (14), that b 2 'b 1 and that b 2 is again the abscissa of the stable center of the unperturbed equation [Fig. 3c]. The homoclinic solutions of Eq. (21) are b )0. (t)\"$2b 1 S h2b 1!h2 1 Jb#cosh(ct) , (23) where h\" b 2 b 1 \"S!B#JB2!4AC #B#JB2!4AC , c\"2b2 1 hJC, b\" (1!h2)J3 J(3h2#1) (3#h2) . (24) The Melnikov function is again given by Eq. (18) and the condition for chaos by Eq. (19), where b 4%1 (t) now stands for Eq. (23). The integrals which appear in Eq. (19) have been computed in closed form in Appendix A. Using expression (A.2), the condition for chaos becomes ac f ( 4nJ1!b2 2/J(1!b2) arctan J(1!b)/ (1#b)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000710_mech-34246-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000710_mech-34246-Figure1-1.png",
        "caption": "Figure 1b. Two Five-Bar Linkages.",
        "texts": [
            " This paper presents a purely graphical technique to find the absolute instant centers for the two coupler links of the double butterfly linkage. The remaining instant centers can then be obtained by inspection using the Aronhold-Kennedy theorem. The graphical technique is presented in Section 2. The procedure is based on a study of the velocity of the coupler point; i.e., the revolute joint connecting the two coupler links. Copyright \u00a9 2002 by ASME s of Use: http://www.asme.org/about-asme/terms-of-use Down Figure 1a. Schematic Drawing of Double Butterfly Linkage. The velocity of this point is unique, for a given input angular velocity, since the double butterfly linkage is a single degree of freedom linkage. A numerical example is presented in Section 3 to illustrate the velocity analysis of a double butterfly linkage using the graphical technique. Finally, some conclusions and suggestions for future research are presented in Section 4. A schematic drawing of the double butterfly linkage is shown in Figure 1a. Links 2 and 8, pinned to the ground (link 1 in this paper) at 2O and 8O , can be regarded as the input and the output links, respectively. The floating links 3 and 7 are referred to as the coupler links. The focus of the graphical procedure is to determine the path tangent and the path normal of the coupler point B. The path tangent will define the unique direction of the velocity of point B and the intersection of the path normal with link 2 (or link 2 extended) will locate the absolute instant center for link 3, henceforth denoted as 13I ",
            " Also, the intersection of the path normal with link 8 (or link 8 extended) will locate the absolute instant center for link 7, henceforth denoted as 17I . Recall that the goal of the graphical technique is to locate the absolute instant centers 13I and 17I . When this is accomplished then the remaining instant centers can be located using the Aronhold-Kennedy theorem. The first step in the graphical technique is to replace the ternary ground link 5 by two binary links, denoted as links +5 and *5 as shown in Figure 1b. The resulting nine-bar linkage has two degrees of freedom which means that the velocity of point B (i.e., the path tangent of point B) can be in any direction in the plane of the linkage. Therefore, disconnect links 3 and 7 at pin B and attach a slider, denoted as link +9 , to link 3 at pin 2 loaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/02/2016 Term +B (henceforth referred to as the instant center +39I ), see Figure 2a. Similarly, attach a slider, denoted as link *9 , to link 7 at pin *B (henceforth referred to as the instant center *79I ), see Figure 2b"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002334_robot.2001.932993-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002334_robot.2001.932993-Figure2-1.png",
        "caption": "Figure 2 : Difference of finger's displacement betweem 1D spring model and 2D spring model for frictionless 2D grasp",
        "texts": [
            " Montana [12], Shimoga [17], Xiong [21] discussed dyamamic stability of the grasp. 1.2 Frictionless Grasps When the hand grasps a cake of soap or a cube of ice, a coefficient of contact friction is small. Hence, it is important to analyze frictionless grasp stability. Refs. [4] [5] [6] [l4] also explored frcitionless grasp stability. Rimon and Burdick [15], Lin et al. [9] [lo] presented systematic approach. These papers used 1D spring model for representation of frictionlcss contact as a matter of course (Fig. 2). However, these papers did not consider that contact force act along the normal 0-7803-6475-9/01/$10.000 2001 IEEE 2466 direction, and tangential component of the contact force is equal to zero when the grasped object is displaced. Ref. [a] did not considered the effect of initial grasping force. To overcome the problems, Saha et al. [16] introduced 2D spring model as shown in Fig.2(b) and explicitly formulated the frictionless contact force. Then, more accurate evaluation of grasp stability was obtained. 1.3 Approach of this paper This paper discusses stability of 3D grasps, based on Ref. [16]. 3D spring model is introduced into frictionless 3D grasps. The frictionless contact force in 3D is explicitly forniulated. And grasp stability is determined by the potential cnergy method. From numerical examples, it is shown that there exists a region of contact force for stable grasp and an optimum contact force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002525_s0022-460x(85)80146-2-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002525_s0022-460x(85)80146-2-Figure7-1.png",
        "caption": "Figure 7. A meridionally symmetric mode for N = 0 with dominan t motion in circumferential direction ( M V = 3). (a) Half-section view; (b) side view.",
        "texts": [],
        "surrounding_texts": [
            "In the present study, a graphics software has been developed to display tire natural mode shapes in 3-D in order to interpret the eigenvectors generated by the free vibration analysis. To illustrate those mode shapes in an easy-to-visualize manner, it is imagined that a tire is cut along a meridional line and then opened up to become a rectangular plate. The two sides of the plate are either simply supported or fixed, depending on the tire boundary condition assumed at the wheel rim. The other two sides of the plate are free to move but the displacements at the corresponding positions must be compatible. As explained earlier, four modal numbers, N, MW, M U and MV, may be used, either in part or all together, to identify a mode shape. The circumferential wavenumber N indicates the number of-full harmonic variations around the tire circumference. The meridional wavenumbers MW, M U and M V designate the number of half waves in the transverse, meridional and circumferential displacements, respectively, along a bead-tobead meridional line. Figures 5(a) and (b) illustrate two meridionally symmetric mode shapes characterized by these four modal numbers. The mode shape in Figure 5(a) is dominated by transverse motion and the mode shape in Figure 5(b) is dominated by tangential motion. An odd number in M W and M V or an even number in M U signifies L. E. KUNG E T AI . . 338 a meridionally symmetric mode shape, as shown in Figures 5(a) and (b), while the opposite signifies a meridionally skew-symmetric mode shape. The 3-D graphical display software was then used to study the predicted natural mode shapes. Figures 6(a) and 7(a) display two major spin modes for N = 0. It is noted that the 3-D tire mode shapes presented in this paper are exceptionally enlarged for the purpose of illustration. Since the displacements ofthe two modes are in the circumferential direction, their side views, as shown in Figures 6(b) and 7(b), further illustrate the details of these mode shapes. In order to observe the N = 1 transverse mode shown in Figure 8(a), the same view with 90-degree rotation about the tire axis, as shown in Figure 8(b), appears to be quite informative. It is of interest to illustrate a natural mode shape composed of displacements in all the w, u and o directions. The side view of one of these mode shapes is shown in Figure 9(a), and a half-section view is shown in Figure 9(b). Since the present computer graphics software can plot the 3-D views for any mode shape from the various viewing angles, a more thorough understanding of the tire natural mode shapes can be achieved."
        ]
    },
    {
        "image_filename": "designv11_11_0001563_a:1008185917537-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001563_a:1008185917537-Figure6-1.png",
        "caption": "Figure 6. Robot model with two driving assemblies.",
        "texts": [
            " The reference trajectory was a straight line, whose gradient was 0 rad for the first 3 s, and \u03c0/3 rad for the rest. The purpose of the control was to ensure that the center of a dual-wheel caster steering axis follows this trajectory, and also that the posture of dual-wheel caster \u03c60 satisfies the line gradient. Simulation results are shown in Figures 4 and 5. From the control results, it is shown that the dual-wheel caster pursued the reference trajectory well. The omnidirectional mobile robot with two active dual-wheel caster mechanisms is shown in Figure 6. It is assumed that the absolute coordinate system (O,X, Y ) as a movement space of the mobile robot is fixed in the plane and that the moving coordinate system (Om,Xm, Ym) is fixed at the centre of gravity (c.g.) of the robot. Here, Xm-coordinate is set so that it has the same direction as the front of the robot. Let the coordinate of each dual-wheel caster a, b be defined as (Oi,Xi, Yi), i = a, b. \u03c6 denotes the angle between X- and Xm-coordinates (i.e., an azimuth of the robot). The position vector of the c"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003842_cdc.2006.376730-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003842_cdc.2006.376730-Figure1-1.png",
        "caption": "Fig. 1. Basic leader-follower setup.",
        "texts": [
            " VI is devoted to the simulation experiments. In Sect. VII the major contributions of the paper are summarized and future lines of research are highlighted. Notation. The following notations will be used. R + = {t \u2208 R | t \u2265 0}; \u2200 a, b \u2208 R, a \u2227 b = min{a, b}, a \u2228 b = max{a, b}; \u2200x, y \u2208 R n (n \u2265 1), \u3008x, y\u3009 = \u2211n i=1 xi yi, \u2016x\u2016 = \u221a \u3008x, x\u3009; \u2200x \u2208 R 2\\{0}, arg(x) = \u03b8, where \u03b8 \u2208 [0, 2\u03c0) and x = \u2016x\u2016(cos \u03b8, sin \u03b8)T ; \u2200 \u03b8 \u2208 R, \u03c4(\u03b8) = (cos \u03b8, sin \u03b8)T , \u03bd(\u03b8) = (\u2212 sin \u03b8, cos \u03b8)T . The leader-follower setup considered in this paper is presented in Fig. 1. It consists of a leader robot RL and a follower RF whose kinematics is described by the unicycle model x\u0307L = vL cos \u03b8L y\u0307L = vL sin \u03b8L \u03b8\u0307L = \u03c9L (1) 1-4244-0171-2/06/$20.00 \u00a92006 IEEE. 5992 and x\u0307F = vF cos \u03b8F y\u0307F = vF sin \u03b8F \u03b8\u0307F = \u03c9F (2) where the vectors L = (xL, yL), F = (xF , yF ) represent the position of the leader and respectively the follower. Analogously \u03b8L, \u03b8F are the orientation of the leader and follower with respect to the reference system (x, y). Finally, vL, vF and \u03c9L, \u03c9F are the linear and angular velocities of the robots. With reference to Fig. 1, consider the following. Definition 1: Set d > 0 and \u03c6 : |\u03c6| < \u03c0 2 ; the robots RL and RF make a (d, \u03c6)-formation, if, \u2200 t \u2265 0: \u2016L(t) \u2212 F (t)\u2016 = d (3) arg(L(t) \u2212 F (t)) \u2212 \u03b8F (t) = \u03c6 . (4) It is required that the velocities of the leader and the follower verify the following constraints: 0 < vL \u2264 VL \u2212K \u2264 \u03c9L/vL \u2264 K (5) 0 \u2264 vF \u2264 VF \u2212\u2126 \u2264 \u03c9F \u2264 \u2126 (6) lim inf t\u2192\u221e vF (t) > 0 where VL, VF , \u2126 \u2208 R + are the leader and follower maximum linear velocity and the follower maximum angular velocity, and K represents the leader trajectory maximum curvature (note that for a unicycle robot the instantaneous trajectory curvature is given by \u03c9L/vL)",
            " \u2022 the desired relative orientation of the follower with respect to the leader \u03c8d, is expressed in the leader reference frame. Note that \u03c1d and \u03c8d play the same role of d and \u03c6. Hereafter we will use the terms \u201ccentralized\u201d and \u201cdecentralized\u201d to refer respectively to the approach presented in [3] and our approach. These terms do not refer here to the control of the formation, as usual in the literature, but to the sensing system. In fact in our approach the relative angles between the leader and followers are referred to the follower frame (angle \u03c6 in Fig. 1), and can be measured, for instance, by on-board cameras mounted on each follower. On the other hand in [3] the angle variables used to control the formation are referred to the leader (angle \u03c8d in Fig. 3) and in general require a centralized sensing system to be measured. Centralized systems are usually cheaper but less reliable than decentralized ones. The formation control problem in [3] can be formalized in our geometric setting analogously to Problem 1, where, instead of (3) and (4), it is now required that \u03c1(t) = \u03c1d (21) \u03c8(t) = \u03c8d (22) hold for all t \u2264 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000507_027836499501400207-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000507_027836499501400207-Figure11-1.png",
        "caption": "Fig. 11. Ellipses governing the mcrpping from the pushing force f to the rod endpoint acceleration as for the pure dynamic case and different rod lengths. Also shown is the mapping from a friction cone to an acceleration cone for l= 1.",
        "texts": [
            " The matrix A\u2019 = STAS is symmetric and positive definite, indicating that F\u2019(p\u2019) = p\u2019rA\u2019p\u2019 - c2 is an ellipsoid in the new force space. The gradient of this sheared ellipsoid gives the acceleration in the primed system. For the slider, we construct the ellipsoid with torques measured about the contact point and intersect this ellipsoid with the plane of zero torque. The intersection is an ellipse with a major axis of half-length cB/2m aligned with the rod and a minor axis of half-length cp.J2iri/ J p2 + 12, where p is the (unit) radius of gyration (see Appendix). Figure 11 I shows the ellipses corresponding to different rod lengths and the mapping of a friction cone to an acceleration cone for the case l = 1. These ellipses provide a convenient visualization of the possibility of pulling and slip with infinite friction. 4.3. With Support Friction Finally we address a case where neither friction nor inertial forces can be neglected. In such a case neither the at The University of Iowa Libraries on June 8, 2015ijr.sagepub.comDownloaded from 180 velocity cone nor the acceleration cone is directly applicable, but it is still easy to construct examples where the initial motion involves pulling or slip with infinite friction",
            " For forces applied through the rod endpoint (x,, y) in E, we construct the ellipsoid F\u2019(p\u2019) for a reference frame E\u2019 located at this point. We intersect this ellipsoid with the plane of zero torque in ~\u2019 to get an ellipse. This ellipse is described by the 2 x 2 upper left submatrix of A\u2019: The major axis of the ellipse is in the direction (r, y) with half-length c,/2?n, and the minor axis is in the direction (-y, x) with half-length cp 2rn/(p2 + x2 + y2). The gradient of the ellipse at the applied force gives the linear acceleration of the point (~, y) (see Fig. 11). Acknowledgments We thank John Maddocks for an interesting discussion on infinite friction. Thanks also to the anonymous reviewers and the members of the Carnegie Mellon Manipulation Laboratory for their helpful comments. This work was supported by NSF grant IRI-9114208. References Alexander, J. C., and Maddocks, J. H. 1993. Bounds on the friction-dominated motion of a pushed object. Int. J. Rohot. Res. 12(3):231-248. at The University of Iowa Libraries on June 8, 2015ijr.sagepub.comDownloaded from 183 Baraff, D"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001005_0165-0114(94)00225-v-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001005_0165-0114(94)00225-v-Figure12-1.png",
        "caption": "Fig. 12. Lyapunov function regarding a fuzzy value s. Fig. 13. Forming ofA = I~+ qssgn(s).",
        "texts": [
            " Vector e is fuzzy since dis a fuzzy vector. For the sake of simplicity we set C = E (E is unity matrix). Further, let f ( x , t) be a nonlinear function of the state vector x and of time t. Now, we formulate s = (d/dt + 2) t ' - 1)e (19) with e = x + d - Xd, e is fuzzy scalar error, x is crisp scalar position, Xd is crisp scalar desired position, 2 is positive scalar value and s is scalar fuzzy value. With the help of the fuzzy value s, the cross product s x s and a subsequent projection (see Fig. 12) we define a fuzzy Lyapunov function v = \u00bds 2. (20) Further, let the condition for stability be R. Palm, D. Driankov / Fuzzy Sets and Systems 70 (1995) 315-335 323 12 <~ - qs sgn(s), (21) where r/is the crisp positive value. Condi t ion (21) means a decrease of energy within the system. The derivat ive of the fuzzy function V with respect to t ime can be ob ta ined with the help of the procedure of forming the derivative of a fuzzy values ment ioned above. The resulting fuzzy value 12 is added to the fuzzy value qs sgn(s) A = 12 + r/ssgn(s) (22) taking into account the cross p roduc t 12 x qs sgn(s) and its project ion on to the diagonal as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002875_s00170-004-2013-y-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002875_s00170-004-2013-y-Figure3-1.png",
        "caption": "Fig. 3. Model describing misalignment",
        "texts": [
            " Some experimental tests were also achieved to study the phenomenon of misalignment. Dewell and Mitchell [5] analysed the vibration frequencies for a misaligned metallic disk flexible coupling. Their experimental results, obtained by means of spectral analysis, show that all the theoretically predicted vibration frequencies actually appear with the 2\u00d7 and 4\u00d7 running speed. The present work is a survey of shaft misalignment adopting a theoretical. This model allows one to analyse a dynamic response of a misaligned shaft as well as reactions that affect bearings. Figure 3 shows the kinematical diagram of a mechanism that describes misalignment [6]. The mechanism model taken to represent misalignment in this study includes a motor shaft carried by the bearing supposed rigid and a rigid weighing receptor shaft carried by two elastic bearings and . The studied system is at two degrees of freedom. The first one \u03b1(t) corresponds to the angular misalignment and represents the small variations of the receptor shaft position around an imposed value \u03b1E . This is made possible by means of a pivot link which models the coupling"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001696_s004540010017-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001696_s004540010017-Figure5-1.png",
        "caption": "Fig. 5. A reduced form.",
        "texts": [
            " (If the supporting lines are parallel, we drop the centering requirement.) In the remainder of the elimination process, the disk translates along with the intersection of the supporting lines, acting like a finite-size vertex. Because the disk and its contents are infinitesimal, we are sure that no translating edge touches the disk unless it also touches the corresponding vertex in the original edge elimination process. The infinitesimal edge is hidden inside the disk and does not participate directly in the remainder of the elimination process. See Fig. 5. When the edge elimination process terminates, the reduced form of the polygon consists of a triangle with some microstructure at its vertices. Each vertex is contained in a disk, and the three disks are disjoint. If we look inside a disk, we see two infinite edges\u2014the ones that cross the disk boundary\u2014and a single finite edge joining them. The vertices where the finite edge joins the infinite edges have microstructure themselves: they are contained inside smaller disks that are disjoint from each other and completely inside the surrounding disk; each smaller disk contains recursively similar structures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000925_20.917621-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000925_20.917621-Figure12-1.png",
        "caption": "Fig. 12. Bearing parts.",
        "texts": [
            " Centrifugal force applied to the oil serves to prevent any oil leakage from the bearing. 3) The groove angle is 17 degrees. (This is stable zone of Fig. 6 and Left zone of Fig. 9). 4) It was conjectured that a radial herringbone groove pattern, with at least one side of the two sets of herringbone grooves designed to follow an asymmetrical pattern, (asymmetrical part length: 0.1\u20130.3 mm), for prevents outflow. For example, the lower half of the lower side herringbone groove is longer by 0.1 mm. Fig. 12 shows photograph of prototype high-speed hydrodynamic bearing divided into parts. Both ends of shaft are anchored by screws \u2022 Rotational speed: 20 000 r/min \u2022 Characteristic value: Radial run out of rotor hub: 2.5 m Radial NRRO: nm 0-p VII. SUMMARY The HDB design for high-speed HDDs is greatly assisted by consideration of groove design, bubble prevention, and optimal shaft form design. [1] H. Saito and T. Asada et al., \u201cHydrodynamic bearings and applied technologies,\u201d Matsushita Tech. Journal, vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003147_978-1-4612-1140-2_6-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003147_978-1-4612-1140-2_6-Figure6-1.png",
        "caption": "Figure 6. 7.6. The construction of an invariant set with large unstable thickness. (a) R\" n f\"(R\"); (b) r\"CRn) n Rn.",
        "texts": [
            " This is not a structurally stable situation, and we want to describe what hap pens when J1. is perturbed from 0. A simple perturbation calculation shows that the saddle points are perturbed to ( \u00b1 Jl., \u00b1 1) + O(p2). Along the segment of they-axis from ( -1, 1), the flow now has a nonzero horizontal component x = Jl., and we conclude that the trajectory which joined the two saddle points for J1. = 0 is perturbed into two saddle separatrices neither of which crosses the y-axis. The phase portraits for the flow are illustrated in Figure 6.1.1. EXERCISE 6.1.1. Verify the results of the perturbation calculations outlined above using the Melnikov method. (Since the unperturbed problem is not Hamiltonian, you will have to do Exercise 4.5.1 first.) There is a qualitative difference between the pictures for J1. < 0 and J1. > 0. When J1. < 0, the separatrix of the upper equilibrium p1 lies to the left of the separatrix of p2 and trajectories can go from x = + oo to x = - oo as t increases. When J1. > 0, the separatrix of p 1 is to the right of the separatrix 6.1. Saddle Connections 291 (a) (b) (c) Figure 6.1.1. The flows of equation (6.1.1). (a) J1 < 0; (b) J1 = 0; (c) J1 > 0. of p and trajectories can go from x = - oo to x = + oo as t increases. The limiting behavior of some of the orbits has clearly changed. The crossing of saddle separatrices may be associated with other changes in the qualitative features of a flow. The simplest situation occurs with planar flows, where the existence of saddle loops is associated with the appearance and disappearance of periodic orbits. Consider the following example: x = y, y = X - x 2 + JlY\u00b7 When J1 = 0, the system is divergence-free and has the first integral yz xz x3 H(x, y) = 2 - 2 + 3\u00b7 (6.1.2) (6.1.3) The origin is a saddle point, two of whose separatrices coincide and form a loop y. The interior of y is filled by a family of closed orbits. See Figure 6.1.2. y (a} (b) (c} Figure 6.1.2. The phase portraits for equation (6.1.2). (a) J1 < 0; (b) J1 = 0; (c) J1 > 0. EXERCISE 6.1.2. Verify the phase portraits above for 11 # 0. (Hint: Look at the divergence: use Melnikov's method.) This is not a structurally stable situation, since the most degenerate periodic orbits one expects to find in a one-parameter family are isolated saddle-nodes. Nonetheless, the example does illustrate that saddle loops are associated with periodic orbits. The degeneracy of equation (6.1.2) (divergence zero) implies that the saddle point contained in the separatrix loop has trace zero",
            " Assume (d/dJ1)(U(J1) - S(Jl)) #- 0 at J1 = Jlo. If, in addition, (3) when J1 = Jlo, tr[Df(p0 )] < 0 (resp. > 0), then there is a family r of stable (resp. unstable) periodic orbits in (x, Jl) space for the systems x = f(x, J1), whose closure contains Yo x {J10 }. The periods of these periodic orbits are unbounded as J1 -+ Jlo. There is an e close to 0 (e may be negative) such that if J1 lies in the interval between Jlo and Jlo + e, then x = f(x, J1) has exactly one periodic orbit in the family r. See Figure 6.1.3. PROOF. The proof of this theorem is formulated in terms of the return map P\" for the cross section M. We only consider the stable case, since the un stable one is proved similarly. Since M is transversal to the vector f(x 0 , Jlo) at q = M 11 Yo, by restricting attention to a small enough neighborhood of (q, J1 0 ), we may assume that 6.1. Saddle Connections 293 fL > P.o q { b) {c) (d) Figure 6.1.3. A saddle connection bifurcation (positive trace case shown). (a) M and the curves ll(fl), s(fl); (b) I'< flo: (c) fl =flo: (d) I'> Po\u00b7 f(x, f.l) is always transversal to M there. The loop Yo = Yo u {p0 } has a corner at p 0 with tangents pointing along stable and unstable eigenvectors ofp0 . Some of the orbits near y0 can escape from its neighborhood as t-+ \u00b1 oo, as Figure 6.1.3(c) shows. To eliminate such orbits, we define the return map P I'D only on that portion of M which lies inside Yo. Orbits starting near y0 on this side flow past p0 and remain close to y0 (cf. Figure 6.1.3). When f1 = flo, we argue that, as trajectories on the inside of y0 flow past Po, they are strongly attracted to Yo. We introduce coordinates (x, y) at p0 so that the local stable and unstable manifolds are the coordinate axes. Assume that the eigenvalues of Df(p0 ) are -a and {3, with a > f3 > 0. Choose b such that 1 > b > /3/a. Then, if(x,y) is sufficiently small, we have ldyjdxl = I y(f3 + \u00b7 \u00b7 \u00b7)/x(- a + \u00b7 \u00b7\u00b7)I < b I yjx 1. This means that the trajectories of our flow are less steep than b I yjx I near the origin. Consequently, Gronwall estimates (cf. Lemma 4.1.2) imply that, when 8 > 0 is sufficiently small, the solution with initial conditions (8, y0 ) reaches the horizontal line y = 8 at a point (xl, 8) with lxll < I Yo l11b(8)l-lb. Since b < 1, lxli/IYo I-+ o+ as Yo-+ o+' as was to be proved. See Figure 6.1.4. It follows from this argument that the derivative of Pl'o approaches zero as x -+ q in M. The return maps P ~' therefore all have slopes less than one in small neighborhoods of W 5(pl') n M. Observe also that the graph of pi'O approaches the diagonal in the plane as one approaches q = Yo n M, because Yo is a homoclinic orbit. Hypothesis (2) now implies that, as Jl varies, the endpoint of the graph of P ~' moves across the diagonal with nonzero 294 6. Global Bifurcations y (x ,E) y\u2022E ---(E ,y 0 ) X X \u2022 E Figure 6.1.4. The flow near a contracting saddle point. speed. (Note that the map P~' is only defined for points on M \"inside\" W 5(pl') n M, cf. Figure 6.1.5.) We conclude that the graphs of the functions P ~' look qualitatively like those of Figure 6.1.5, up to reflection in the }1-axis. This diagram contains the remainder of the proof of the theorem. In particu lar, since the slopes of the P l'o are smaller than one, each vector field has at most one periodic orbit near l'o and those periodic orbits which do occur are stable. Moreover, for J1 to one side of Jlo, periodic orbits necessarily occur. D In the next chapter we shall encounter loops formed from several saddle separatrices. Theorem 6.1.1 can be generalized to deal with this situation, (a l (b) ( d) P ,p.>p.o p. PJ.Lo ( c ) Figure 6.1.5. The Poincare map P\" and the associated vector fields. The domain of P\" in A1 x {Jl) is shown as a heavy line. (a) Jl < J1 0 ; (b) 11 = Jlo; (c) 11 > }10 : (d) the map. and the stability of the periodic orbits which occur is then determined by the quantity log n ~ ' where - i.; < 0 < p, are the eigenvalues of the ith ( n }c) ;~ t P; saddle in the loop; cf. Reyn [1979]. EXERCISE 6.1.4. Carry out the generalization of Theorem 6.1.1 referred to above. ExERCISE 6.1.5. Show that, when I + ~\u00b7 < fJ - L the following system has a loop (a homoclinic cycle) containing three saddle points: ",
            "12) If we let n -> oo, then '\"may be calculated by taking the average slope of the oscillating function arctan u(rnl\u00b7 Now arctan u(r) changes by n in the time r\" taken for u(r) to go from -oo to +oo, or for (anr +c) to go from -n/2 to n/2. Thus r\" = lja. We conclude that the average slope of arctan u(r) is n/(1/a) =an, so that, for large n (and hence large r\") (6.2.12) yields r\" = n(2/(1 + w + a)). Using this in (6.2.11) we obtain 1+w-a p(y) = 1 + w + (;' (6.2.13) where a was given in (6.2.8). A graph of the rotation number appears in Figure 6.2.1. Note that, while it is continuous at y = (1 - w)/2, it is non differentiable with limit p'(y)-> oo, as y-> (I - w)/2 from below. Thus, after 1 : 1 phase locking is lost when y passes through (1 - w)/2, decreasing, the rotation number passes rapidly through infinitely many rational and irratio nal values and approaches w as y -> 0. The properties embodied in Propositions 6.2.1 ~6.2.4 summarize the topological properties of homeomorphisms of the circle. In a sense, the rigid rotations provide models for the asymptotic behavior of any trajectory",
            " The itinerary specified in the present lemma has the block of this type of maximum length n + 1 for a periodic sequence of period 11. 0 Corollary 6.3.8. Ifn > 1 is odd, there is a periodic orbit of period n + 2 which is smaller than all periodic orbits of period n. Using Lemma 6.3.6, we can construct periodic orbits of any even period which are smaller than all periodic orbits of odd period. These orbits have the property that every even indexed term in their itineraries is I 1\u2022 We observe that the graph of/ 2 for a mapfwhose kneading invariant is of this form looks like Figure 6.3.1. There is a subinterval J of [0, I] around c which is mapped into itself. The itinerary for f 2 of a point in J will be subject to the same considerations as those which we have applied to f above, but with the role of the symbols I 0 and I 1 reversed (since the map is \"upside down\"). Thus sequences a with a; = I 1 fori even and a; = I 0 fori = I (mod 4) are smaller than sequences b with b; = I 1 fori even and b; = I 1 for some i = 1 (mod 4). This leads to: Lemma 6.3.9. If k, l are odd and m > n, then there are periodic sequences of period k \u00b7 r which are smaller than all periodic sequences of period f",
            " We abstract from the Lorenz system a family of one-dimensional map pings which correspond to the return map of the strong stable foliation for the parameter range which is approximately 10 < p < 30 (we keep CJ = 10 and {J = i fixed throughout). At the beginning of this parameter range, the flow is still simple, with a non wandering set consisting solely of the three equilibria. The nonzero equilibria q\u00b1 are stable, but one pair of eigenvalues is complex at each of them. The flow is illustrated in Figure 6.4.1(a) and the correspond- 6.4. The Lorenz Bifurcations 313 Q 0 (a) (b) Figure 6.4.1. The Lorenz system for p ~ 10, (J = 10, f3 = ~.(a) The flow: (b) the map f\". ing return map JP of the strong stable foliation in Figure 6.4.l(b). As p in creases, a bifurcation occurs in which the unstable manifold of p becomes a pair of homoclinic trajectories. From numerical computations this occurs at p = Pr ~ 13.296. See Figure 6.4.2. Recall that the slope of the map JP becomes infinite as one approaches its point of discontinuity, due to the fact that the unstable eigenvalue of p is larger than the magnitude of one of the stable eigenvalues. This fact leads to the existence of a hyperbolic invariant set topologically equivalent to the suspension of a horseshoe, immediately following the homoclinic bifurcation illustrated in Figure 6.4.2. In terms of the return map JP, the invariant set is created in the following way. The homoclinic bifurcation is followed by flows for which each branch of the unstable manifold of p crosses to the opposite side of the stable manifold of p as it descends for the first time: Figure 6.4.3. This forces the graph of JP to intersect the diagonal in a pair of fixed points r-, r +. These fixed points off correspond to unstable periodic orbits of the flow generated in much the same way that periodic orbits are generated by the saddle loop bifurcations in the plane described in Section 6.1. (a) (b) Figure 6.4.2. The Lorenz system for p = p, ~ 13.926. (a) The flow: (b) the map .f~. 314 6. Global Bifurcations q (a) (b) Figure 6.4.3. The Lorenz system for p > p,. (a) The flow; (b) the map fp\u00b7 Now we focus our attention on the graph offP in the interval [r-, r+]. An expanded picture appears in Figure 6.4.4. The slope off is large in the interval [r-, r+]; consequently, each branch of the graph off passes vertically across the entire square which has opposite vertices on the diagonal above r- and r+. Denoting by d the point of discontinuity forfP,fP has the property that the intervals [r-, d) and (d, r+] are each mapped onto [r-, r+] with derivative larger than 1. Using [r-, d) and (d, r+] as a Markov partition of [r-, r+], we identify a hyperbolic invariant set A whose symbolic dynamics are a one sided (full) shift on two symbols. A similar construction for the return map F of the cross section L produces a horseshoe as an invariant set of F. In Figure 6.4.5 we show two strips Vi in the cross section L and their images H; under f Note that F has a shift on two symbols with transition matrix (6.4.1) EXERCISE 6.4.1. Convince yourself that the above statement is correct. Use the methods of Section 5.2 (cf. Section 5.7). Figure 6.4.4. The map JP, expanded in [r-, r+]. Figure 6.4.5. A shift for the Lorenz map F. EXERCISE 6.4.2. Construct a Markov partition with four elements and show that the invariant set corresponding to the two-shift found above can be described as a subshift on four symbols with transition matrix (6.4.2) Hence conclude that the F 2\" has 4\" fixed points (F2 has a full shift on four symbols). (Hint: Cf. the construction due to Levi described at the end of Section 5.3, or see Kaplan and Yorke [1979b].) From (6.4.1) we can conclude that the map F\" has 2\" fixed points",
            "\" However, we note that the measure of the Cantor set A is zero, and almost all orbits starting in [r-, r+] eventually leave this interval and approach q- or q+. The bifurcation which makes the invariant set A of the preturbulent Lorenz flow an attractor is subtle. Asp increases, the fixed points r- and r+ of fP move toward q- and q +, while the values fp(d) move toward q- and q + more slowly. One reaches a parameter value p = Pa at whichfP.(d-) = r+ andfp.(d+) = r-. Numerical investigations suggest Pa ~ 24.06 (Kaplan and Yorke [1979b]). For this parameter value the graph off is illustrated in Figure 6.4.6. The interval (r-, r +) is now Mapped into itself by fp. and the points of this interval can no longer approach the stable fixed points q- and q+. The invariant set A of the flow has now become an attractor (although its domain of attraction is not a neighborhood of A because points near the periodic 316 6. Global Bifurcations Figure 6.4.6. Another bifurcation for f\": !\\becomes an attractor. orbits corresponding tor\u00b1 can tend to q\u00b1). The topology of A has changed from the suspension of a Cantor set to an object which contains two-dimen sional surfaces, as in Section 5.7. We have here the birth of the (geometric) Lorenz attractor occurring at a parameter value for which there are hetero clinic trajectories from the equilibrium p to the periodic orbits corresponding tor\u00b1. For values of p following the heteroclinic bifurcation which we have just described, we obtain geometric Lorenz attractors of the type described in Section 5",
            " and pair of complex eigenvalues w, w which have negative real parts (the case of A. negative and Re(w) positive is dealt with similarly). The stable manifold theorem allows us to introduce coordinates so that the local unstable manifold is contained in the z-axis and the local stable manifold is contained in the (x, y) plane. We assume further that the trajectory y in wu(O) which points upward near 0 is a homoclinic orbit which enters the (x, y) coordinate plane and spirals toward the origin as t-> oo; see Figure 6.5.1. We shall study a return map for orbits near yin this section and prove the following theorem: Theorem 6.5.1 (Silnikov [1965]). If JRe wJ <A., then the flow cPr can be perturbed to c/J; such that c/J; has a homoclinic orbit y' near y and the return map of y' for c/J; has a countable set of horseshoes. The proof of this theorem requires a careful analysis of the flow of tra jectories passing near the origin. To simplify the analysis we make an initial perturbation of cPr which makes its vector field linear in a neighborhood U of the origin. We assume throughout the remainder of the proof that our Figure 6.5.1. A homoclinic orbit to a spiral saddle. 320 6. Global Bifurcations original vector field has this property. In this case, the solution of the system of equations -{3 w = rJ. + i{J, (6.5.1) 0 which governs the flow near the origin, is given by ( x) (e'1{(cos {Jt)x(O) - (sin {Jt)y(O))) y (t) = ea1((sin {Jt)x(O) + (cos {Jt)y(O)) . z e-'1z(O) (6.5.2) We define two surfaces 1:0 and 1: 1 by 1:0 = {(x,y,z)lx2 + y 2 = r6and0 < z < zd, 1: 1 = {(x, y, z)lx 2 + y 2 < r6 and z = z1 > 0}. (6.5.3) We assume that 1:0 and 1: 1 are in the neighborhood U where the flow is linear. Trajectories flow from 1:0 to 1: 1 according to (6.5.2). We want to compute the mapping t/1: 1:0 -> 1: 1 which associates to each point a E 1:0 , the first intersection with 1: 1 of the trajectory starting at a. See Figure 6.5.2. The formula for t/1 is given by solving z 1 = e\"'z(O) fort to obtain the time of flight t = A. - 1 ln(zt/z(O)), and substituting the result into (6.5.2). We obtain (( Z )a;.< (z )a;.< \u00a2 1(x, y, z) = --j- [(cos y)x- (sin y)y], --j- [(sin y)x +(cos y)y], z1), (6.5.4) Figure 6.5.2. The sections ~0 and ~ 1. where y = {3),- 1 ln(z dz). Setting x = r 0 cos (), y = r 0 sin (), we may then express t/1: 1:0 --+ 1:1 as a two-dimensional diffeomorphism whose domain has coordinates() = tan - 1(y/x) and z, and whose range has coordinates x, y: ( ( z )a!). (z )a!). ~ t/J((}, z) = r 0 ; cos(() + y), r 0 --;- sin(() + y)} (6.5.5) ~ (t/11((), z), t/12((), z)). We note that t/1 maps a vertical segment() = const. of 1:0 to a logarithmic spiral which encircles the z-axis and lies in 1:1 ",
            " 2a > -X), consistent with the fact that the vector field has divergence 2a + )\" at the saddle point. However, since - 1 < ex/ A. < 0, even when t/1 contracts areas, vertical segments { () = const.; z E (0, z0 )} in 1:0 are mapped into logarithmic spirals of radius r0(zJiz)a1\\ and thus their lengths are stretched by an amount which becomes unbounded as z --+ 0. EXERCISE 6.5.1. Verify that equations (6.5.6) and (6.5.7) are correct. Denote now by p the intersection of W\"(O) with 1:0 and by q the point (0, 0, z 1) = W\"(O) n 1: 1 (see Figure 6.5.2). The flow from q top along W\"(O) is nonsingular, so there is a diffeomorphism </J from a neighborhood of q in 1: 1 to a neighborhood of p in the surface L0 = {(x, y, z)lx2 + y 2 = r~, I z I < z0 } which sends a point to the first intersection of its trajectory with L0 . The return map of 1:0 near p is given by <P o t/1 for those points r with </J(t/l(r)) E 1:0 . See Figure 6.5.3. Changing coordinates by a rotation around 322 6. Global Bifurcations Figure 6.5.3. The return map rjJ. the z-axis, we may assume that plies on the x-axis (8 = 0). Pick a small domain V in :E0 defined by V = {(r, 8, z)lr = r0 , 181 < b, 0 < z < e}, (6.5.8) where sis chosen such that l/J(V) is contained in the domain of\u00a2 and b will be specified later (Figure 6.5.3). The image of \u00a2 a l/J( V) is illustrated in Figure 6.5.4. Each vertical segment of V is mapped to a spiral around q in :E 1 , and \u00a2 maps this spiral diffeomorphically into f 0 with \u00a2(q) = p. If b is chosen sufficiently large, relative toe, then each spiral in\u00a2 o l/J( V) cuts through V ver tically many times until one reaches a portion of the spiral which does not cut through the top of V. We want to locate subsets of V in which \u00a2a l/J has a horseshoe. Note that (6.5.5) implies that if z varies along a vertical segment J c V with z E (z', z\"), Figure 6.5.4. V and rjJ u 1/J(V). 6.5. Homoclinic Orbits in Three-Dimensional Flows: Silnikov's Example 323 v \" w -z -z 0 Figure 6.5.5. \u00a2 c ljJ lw has a horseshoe: W n \u00a2 '1/J(W) shown shaded. where (/3/A.)(log(zdz')- log{z 1/z\")) = 2n: or z\"/z' = exp(2n:A.//3), then t/J{J) makes one full turn of a logarithmic spiral. The distance of ljJ(J) from q is of the order of (ztfzY1\\ zEJ. The ratio {ztfz)*/z--+ was z--+ 0. Fix b > 0 small in the definition of V and pick (z', z\") with the properties (i) z\"/z' = exp(2n:A.//3), (ii) z', z\" are sufficiently small that (zdzY1;. < b for all z E {z', z\"). {6.5.9) (iii) if 181 < b, then the images \u00a2 0 1/J(ro, e, z') and \u00a2 0 1/J(ro, e, z\") do not lie in ~o\u00b7 Define w = {(ro, e, z)E VlzE(z', z\")} and observe that (6.5.9) implies that the image \u00a2 o 1/J(W) looks like a horseshoe mapping; see Figure 6.5.5. To demonstrate that W n \u00a2 o 1/J(W) contains a horseshoe, we need to show that D(\u00a2 c t/J) satisfies the sectorial conditions Hl and H3 of Theorem 5.2.4. Satisfaction of the first is immediate. Moreover, since\u00a2 is a diffeomorphism on ~ 1 , from (6.5.6) we have D(\u00a2 o t/J)(r0 , 8, z) = r (21 )\u2022/;.A[c~sy 0 Z Silly -sin y] cosy -sine cos e - IX COS {} + {J sin {} A.z -a sin e - p cos {} A.z where A= D\u00a2(t/J(r0 , e, z)). We can rewrite (6.5.10) in the form where z-(\u2022!.l.+ lisc[z OJ 0 1 . [ cosy B = r0 z'l1;",
            "(b 21 c12 + b22 c22 ) remain in disjoint cones. Moreover, the eigenvectors and eigenvalues of (6.5.10) are close to those of singular matrix (6.5.12) for, being distinct, they vary smoothly with the matrix coefficients. If (b 21 c 12 + b22 c 22) is not bounded away from 0 for points of V n cpa 1/J(V) as z--> 0, then we must perturb the flow \u00a2, to accomplish this. A perturbation which has the effect of rotating trajectories around y so that the perturbed return map is the composition (on the left) with a rigid rotation does the trick; sec Figure 6.5.6. The sectorial structure for (6.5.11) is now obtained from the limiting values of the eigenvectors of this product as z', z\" --> 0. (The limit values do exist, because ()--> 0 and y (mod n) approaches the value which determines the line in L 1 which Dcp(q) maps to the horizontal line in the tangent space to Lo at p.) Any small sectors around these limiting values satisfy (H3) when z' and z\" are sufficiently small. Choosing a sequence of rectangles W in V whose heights decrease geometrically, we obtain a sequence of horseshoes for our perturbed flow, which still has a homoclinic orbit for the equilibrium at the origin. D Figure 6.5.6. A small perturbation of \u00a2,. Corollary 6.5.2 (Silnikov [1965]). Let X be a C vector field on IR 3 which has an equilibrium p such that: (i) the eigenvalues of p are I)( \u00b1 ip, A. with II)( I < I A. I and P i= 0; (ii) there is a homoclinic orbit for p. Then there is a perturbation Y of X such that Y has invariant sets containing transversal homoclinic orbits. ExERCISE 6.5.2. Analyze the bifurcation behavior associated with a homoclinic trajectory to an equilibrium with eigenvalues ~ \u00b1 i/3, A. with 0 <A",
            " Assume that, when f.l > 0, W 5(0) n W\"(O) = {0}, and that when f.l = 0, there is a point Po at which ws(O) n W\"(O) have a quadratic tangency for f 0 . By this we mean that the curvatures of W 5(0) and W\"(O) are different. When f.l < 0 is small, w\u2022(O) and W\"(O) should have two points of transversal intersection near p0 \u2022 We assume further that when f.l = 0, the segments of w\u2022(O) and W\"(O) from 0 to Po bound a region which has a convex angle at 0 and contains points of W\"(O) in its interior. See Figure 6.6.1. Clearly many other cases of tangency can occur (cf. Gavrilov and Silnikov [1973]). The first result we describe, due to Gavrilov and Silnikov, shows that there are sequences of saddle-node bifurcations accumulating at f.l = 0 from both above and below. We treat the situation in a fashion similar to that employed in describing Smale's [1963, 1967] theorem on the existence of horseshoes. Here we shall describe invariant sets that change with f.l, their periodic points appearing, disappearing, or changing their stability in the process",
            " The bifurcations of these periodic orbits will necessarily be saddle-nodes or flips, because the area contraction off\" near 0 dominates any expansion off\" elsewhere for the sets we consider, and we obtain one-dimensional center manifolds associated with the passage of simple eigenvalues of DJ: through + 1 or -1. To begin the construction of the invariant sets, we use the stable manifold theorem to pick coordinates in which the local stable manifold of 0 is a segment of the x-axis and the local unstable manifold of 0 is a segment of the y-axis. This 0 ,... >o ,...=o 1-L<O Figure 6.6.1. A homoclinic bifurcation for a planar diffeomorphism. 6.6. Homoclinic Bifurcations of Periodic Orbits 327 can be done for all J1 simultaneously because the local stable and unstable manifolds of 0 vary continuously with )1. Let us suppose then, that W\"(O) and W'(O) are \"flat\" in some neighborhood V of the origin. First consider the system when J1 = 0. Let Po = (0, y0 ) in our coordinate neighborhood V be a point of tangency between ws(O) and W\"(O). Let U c V be a small rectangular neighborhood of Po. We want to follow the iterates of U until they intersect U again, and then examine the hyper bolicity of this intersection. Recall that we have assumed that the stable and unstable manifolds intersect in the manner depicted in Figure 6.6.1. There is clearly an integer k such that .r(p0 ) lies on the local stable manifold of 0. Moreover, the curve W\"(O) intersects the x-axis tangentially at f~(p0), and we have assumed that it can be represented near this point as the graph of a function with positive second derivative. See Figure 6.6.2. We next follow further iterates of p0 and W\"(O) from .f~(p0 ). To simplify our estimates and focus upon the essential features of this iteration, we shall examine a particular example and leave the generalization of the arguments as an exercise. In particular, we assume that .fo is linear in its coordinate neighborhood about 0, so that fo(x, y) = Df0(x, y) = (px, J..y) (6.6.1) for all (x, y) in the neighborhood. We assume further thatf~ is a quadratic mapping at Po of the form f~(x, Y - Yo) = (Xo - f3(y - Y0 ), yx + b(y - y0 ) 2 ), (6.6.2) in our specified neighborhood U of p0 . Here Po = (0, y0 ), ft(p 0 ) = (x0 , 0), and [3, y, and b are positive constants (b/3- 2 is the curvature of W\"(O) at Figure 6.6.2. The neighborhoods V U, and r(U). 328 6. Global Bifurcations f~(p0) in our coordinate system). This particular nonlinear map carries vertical lines x = c in U into parabolas y = yc + (6/f3 2 )(x - x0 ) 2 near f\\Po) E Ws(O). For all n ~ O,f0+k is a quadratic mapping providedf~+i(x, y) is in our coordinate neighborhood V for i ::::; n: explicitly, we have (6.6.3) We want to show that, if n is large, then there is a rectangle with Po on its boundary for which n+k has a horseshoe. Pick B > 0, p < v <I",
            " We will show that~~+ n has horseshoes in sn for n large. First observe that the abscissas of points inf'Q+k(S\") are all smaller than p\"(x 0 + f3e) and this is smaller than v\" when n is large. Next observe that the ordinate of JZ+k(x, y) = .A.\"(yx + 6(y - y0 ) 2 ) is approximately Yo when IY- Yo!~ (y 0 .A.-\"j6)112 since .A.\"yx < .A.\"yv\"---> 0 as n---> x. Thus the image f'O+k(S\") intersects S\" in two vertical strips whose inverse images are approxi mately horizontal strips near values of y which satisfy IY Yo I= (y0 i -\"/6)1!2, cf. Figure 6.6.3. The derivative of f\"+k is Vis D{n+k [ 0 - {3p\" J . 0 = }'A\" 26.A.\"(y - Yo) . (6.6.4) When IY- Yo!= {y0 .A.-\"/6) 1 / 2 and n is large, Df'O+k is approximated by the singular map r--vn~ I I Yo+E -----H.,H,.,}-il YrrE ----- ~Hff4-' Figure 6.6.3. Quadratic tangencies imply horseshoes. (6.6.5) which has eigenvectors (1,- yA.\"12j2jYo\"J) and (0, 1). While the vertical component of(l, - yA.\"12 j2jYo\"J) is large, it is of a smaller order of magnitude than A.\"12 p-\", which is the magnitude of the slope of any vector which was originally near vertical. One checks easily that there is a constant c and a sector at each point of f-<n+kl(S,) n S, bounded by vectors of slope \u00b1cp-n A +n/ 2 which is mapped into itself by Df0n+k (cf. the analysis of Section 5",
            " We continue the discussion in terms of the quadratic example which we introduced above, but we incorporate it in a one-parameter family of mapsfw Working in a fixed neighborhood of the origin, we assume thatf\" is the linear map defined by f\"(x, y) = (px, .icy) with p < 1 < Jc < p- 1 as before, for all J.1., and assume that there is an integer k > 0 and a point p0 = (0, y0 ) near whichf; is given by (6.6.6) I:+k(x, y) = (p\"(x 0 - {I(y- y 0 )), i.\"(J1 +/'X+ 6(y- y0 ) 2 ). (6.6.7) Variation of J.1. then causes the bifurcation sequence of Figure 6.6.1. When J.1. > 0, points to the right of the y-axis near p0 have a minimum vertical coordinate 11\u00b7 Therefore, an additional n iterates carries all of these points above p0 ifn > log(y0 /11)/log A.. This contrasts with the situation we described when 11 = 0. Hence, as 11 increases from 0, many of the horseshoes which we located for 11 = 0 disappear. One can in fact solve our model equations explicitly for saddle-node bifurcations of periodic orbits of period (n + k) and even for the subsequent flip bifurcations which occur as 11 decreases towards 0 (cf",
            " Show that the sinks created in these bifurcations sub sequently undergo flip bifurcations at a second sequence fl~-k of values also accumula ting on p = 0 from above. Qualitatively, the picture of what happens when 11 > 0 is similar to the picture one has for the Henon mapping or for an appropriate iterate of the strongly nonlinear van der Pol and Dulling return maps. The parabolic sections of W\"(O) rise at the exponential rate ..1.\" starting at (x 0 , 11). Thus, increasing 11 pulls the images off\"+k(S.) up through s., destroying an entire horseshoe i\\\"+k of{\"+k(S.) in the process, cf. Figure 6.6.4. All of the issues concerned with the presence of strange attractors discussed in Section 5.6 arise in the analysis of perturbations of a diffeomorphism with a homoclinic tangency. We also note that the derivative off~+k has deter minant which approaches 0 exponentially with n, so that the bifurcations become better approximated by those of one-dimensional mappings as 11 approaches 0 from above (but see the comments at the end of Section 6.7). To ~ee what happens when 11 approaches 0 from below, note that 11 < 0 implies that ./~ has a transversal homoclinic point near f:(p0 ). Therefore, there is an iteratef~ off\" which has a horseshoe contained in a small neigh borhood of the segment of ws(O) from 0 to f~(p0 ). In particular, there are Figure 6.6.4. Disappearance of the horseshoe !\\ k + n for I~+\". 6. 7. Wild Hyperbolic Sets 331 orbits off~ whose symbol sequences for this horseshoe are periodic with blocks of length m + n of the form 10 ... 0 10 ... 0 for arbitrary m, n, where -~ --.__.-m n 1 and 0 are symbols corresponding to a Markov partition, as in Sections 5.1-5.2. We shall argue that there is no such periodic orbit forf~, and hence that saddle-node bifurcations of periodic orbits have occurred between 0 and Jl = ~~~ < 0. Because{,, is linear in the coordinate neighborhood V, a point (x, y) which starts nearf~(p0 ) and remains at a level below Yo for exactly r iterates must satisfy A_-r+ 1y0 s y < A",
            " Moreover, such diffeomorphisms are residual in open sets of the space of C2 diffeomorphisms which are near diffeomorphisms with a homoclinic tangency and can thus be expected to occur in typical families (such as the one considered in the last section). Our first step is to show that certain types of tangency are persistent. Let A be a zero-dimensional hyperbolic invariant set in the plane. The stable and unstable manifolds, w\u2022(A) and W\"(A), are each locally the product of a Cantor set with an interval (think of the horseshoe example of Section 5.1). We are interested in conditions which guarantee that there will be a point of tangency between two of the segments in these sets. See Figure 6.7.1. Note that this implies the existence of a heteroclinic orbit, containing points outside A, and connecting two orbits {f\"(x)}, {f\"(y)} (not necessarily periodic) of A, but not necessarily a homoclinic orbit. If we regard W\"(A) as a Cantor set of horizontal lines, then the question is whether some curve in w\u2022(A) has a point with a horizontal tangency which is contained in W\"(A). Naively, it would appear that if this is the case, then a slight vertical shift of w\u2022(A) would separate the Cantor set at which w\u2022(A) has a horizontal tangent from W\"(A), as happens when A is a point or a periodic orbit, as in the last section. However, for general hyperbolic sets, Newhouse observed that this is not always possible, for reasons which we now explain in a setting divorced from the dynamics. Let r 1 and r 2 be two Cantor sets contained in the unit interval. We ask for conditions on r 1 and r 2 which imply that they intersect. One such condition is that r 1 and r 2 be Cantor sets with overlapping support and Figure 6.7.1. Tangency of stable and unstable manifolds of a hyperbolic set. positive Lebesgue measure (see Section 5.4) and that the sum of their measures be greater than 1. Then {l(r I (\\ r 2) = {l(r I) + {l(r 2) - {l(r I u r 2) > 0 and r I (\\ r 2 # 0. However, the Cantor sets which arise in hyperbolic sets have Lebesgue measure zero, so that this condition is not appropriate here. For example, in the piecewise linear horseshoe, the Cantor sets are ones defined by a \"middle a\" construction in which one inductively removes the open segment which is the middle IX proportion of a closed interval",
            ") Each Ui is a subinterval of a bridge Bi of Ci which divides Bi into two bridges B~ (left) and Bj (right) of Ci+ 1 . Denoting the length of an interval J by I(J), we define The thickness t{r) is . {l(B~) l(Bj)} t({Cj}) = ~~~ l(U)'l(U) . r(r) = sup{t({C;})! {C;} is defining sequence for 1}. (6.7.1) (6.7.2) For example, if r is the Cantor set defined by the middle a-proportion construction on I, then for any defining sequence {C;} which removes at step i a set Ui which is as long as possible, we have l(B~) l(B~) (1 - IX) 1 - IX l(U) = l(Ji) = - 2- l(Bi)/rxl(B) = ~\u00b7 (6.7.3) cf. Figure 6.7.2. Thus r(r) = (1 - a)j2a. Proposition 6.7.1 (Newhouse [1970]). If r I and r 2 are two Cantor sets in IR SUCh that t(r 1) \u00b7 t(r 2) > 1, r 1 is not COntained in a gap of r 2 and r 2 is not COntained in a gap of r 1, then r 1 !\\ r 2 # 0. 12allBj) Bj[ t------::----::1)--------f: B~ U\u00b7 l I 1-a ilBjl 2 ] B~ I a\u00b7llBj l Figure 6.7.2. Thickness of a Cantor set. PROOF. Choose defining sequences {C;} from r1 and {DJ for r2 so that r({C;}) \u00b7 r({D;}) > 1. If C0 and D 0 were disjoint, then r 1 is contained in an unbounded gap of r 2 and vice versa. Thus C0 n D0 1= 0. We show in ductively that C; n D; 1= 0. Since these sets are compact and C; n D; ::::> C;+ 1 n D;+ 1, the finite intersection property then implies that r 1 n r 2 i= 0. Suppose now that C; n D; 1= 0. Let B1 and B2 be bridges of C; and D; such that B1 n B2 I= 0. Let B 1 - U; = B 1 n C;+ 1 and B2 - v; = B2 n D;+ 1 (U; or V; may be empty). We assert that (B 1 - U;) n (B 2 - V;) 1= 0. There are two cases to consider: the case in which B1 c B 2 or vice versa and the case in which B 1 - (B 1 n B2 ) and B2 - (B 1 n B 2 ) are both nonempty. See Figure 6. 7.3. If B 1 c B 2 and (B 1 - U;) n (B 2 - V;) = 0, then B 1 c V;. One of the gaps W of C; bordering B1 (say the one on the left) satisfies I(B 1)/I(W);;::: r({C;}), and the left component B21 of B2 - V; satisfies l(B21)/ I(V;);;::: r({DJ). Therefore, I < (I(B 1)/I(V;)) \u00b7 (l(B 21)jl(W)) < l(B 21)/l(W) or l(W) < l(B 21 ). This implies that (B 2 - V;) n (C;- B 1) 1= 0 so that D;+ 1 n C;+ 1 I= 0. This completes the case B1 c B2\u2022 If B1 - (B 1 n B2 ) and B2 - (B 1 n B2 ) are both nonempty and B1 contains a point to the left of B 2 , then the right end of B1 lies in B 2 and the left end of B2 lies in B 1",
            " Newhouse [1979] shows that r\"(y,y,A) is independent of y and y and may therefore be denoted by r\"(A). Moreover, he proves that r\"(A) is positive and varies continuously with C2 perturbations of the diffeomorphism defining A. Similar definitions and results hold for r 8(A). Consequently, if a diffeomorphism! of IR 2 has a hyperbolic invariant w 81 ... ~ .. \u00b7\u00b7\u00b7\u00b7\u00b7E---+--{-----:3 U\u00b7 s1r B1 E----3 ...... ! ........ E l ~ ............. ~.i.. ............ {---i E B 2L l\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7~.l ....... f----1 sz (a l (b) Figure 6.7.3. The thickness proposition. (a) B 1 c V, c B 2 ; (b) 8 1 and B2 overlap. set A with r 5(A)r\"(A) > 1 and if ws(A) has a point of tangential intersection with W\"(A), then there is an 1: > 0 such that all C 2 , e perturbations off have hyperbolic invariant sets near A, which have tangential intersections. This observation is the basis for the early work of Newhouse in his thesis [1970, 1974]. Such sets A are called wild hyperbolic sets. The second observation made by Newhouse is that a diffeomorphism f which has a homoclinic tangency to a saddle point p can be perturbed to one which has a hyperbolic invariant set A with T5(A)r\"(A) > 1 and having a tangency between ws(A) and W\"(A). The illustration of a homoclinic tangency which we consider here is the following: Figure 6.7.4, which is the \"last\" tangency before a \"full\" horseshoe containing the point p is created. Here f is a diffeomorphism with a saddle p having eigenvalues p, A with p < I <A< p- 1, as in the last section. We observe that, since there is a point q of transversal intersection between W\"(p) and W5(p), there is a hyper bolic invariant set A, near the orbit of q which is described by Smale's theorem [1963]. Moreover, this invariant set has an unstable thickness r\"(A 1) which is approximately constant asfis perturbed. By perturbing f near its homoclinic tangency, we want to create a new hyperbolic invariant set A2 with a large stable thickness T5(A 2 ), so that r\"(A 1) \u00b7 r'(A 2) > 1. To do this, we consider the image of a small rectangle R with base on W 5(p) and centered at the point t of homoclinic tangency. For large n,f\"(R) will lie close to W\"(p) and extend far along W\"(p) to come close tot, Figure 6.7.5. With increasing n, we want to study f\"(R\"), where R\" c R is a rectangle consisting of points whose images lie close to W\"(p) n R. The rectangle R\" extends horizontally across R and has a vertical height (thickness) propor tional to A-n. The width of[\"(R 11 ) in the direction normal to W\"(p), and its distance from W\"(p), is proportional top\". Thus the width ofj\"(R\") relative to the height of R\" tends to zero. Newhouse [1979] performs careful estimates which show that, for a quadratic tangency, one can select a number n and a rectangle Rn c R such Figure 6.7.4. Homoclinic tangencies lead to wild hyperbolic sets. 336 6. Global Bifurcations w\"( Pl pori of t\"(R l R 0 D,- n l ~ l-:\"77>777.~iMI<TTn777'\"\"'-'6~rrn>777:nl p Figure 6.7.5. Creating a set with large stable thickness. that j\"(R\" n f\"(Rn)) = H~ u H?, is a pair of horizontal strips, the sum of whose heights (normal to ws(p )) is almost that of R\". Thus f\" has an invariant set A2 c R\" of large stable thickness. To show that A2 is hyperbolic, sector estimates of the type discussed in Section 5.2 must be carried out, and here these are very delicate, since the \"vertical\" strips R\" n f\"(R\") = V,/ u V,2 have boundaries which are almost tangent to ws(p) and hence to the hori zontal boundaries of R\". See Figure 6.7.6. (Cf. Robinson [1982] for another derivation of this result, and for additional information.) Here we give an alternative construction of an invariant set with large stable thickness, based on the fact that, for large n, f\" is close to a one dimensional map. If we rescale the vertical coordinate near t by). -n, then the mappings f\"(Rn) approach a limiting map h which has rank 1 and has a graph like that shown in Figure 6.7.7. The map h can be regarded as one which has infinitely strong contraction along its level sets and is hyperbolic if there is an expanding direction at each point which yields the usual hyperbolic estimates. The map h is not hyperbolic in this sense, but there are small perturbations (which raise or lower the graph) which make it hyperbolic if h satisfies an appropriate hypothesis (specifically, if h has a negative Schwarzian derivative). The stable thickness of the limit sets for these perturbations of h can be made as large Figure 6.7.7. The singular map h. as one wants, as we show in the lemmas in the Appendix to this section. Hence, taking n sufficiently large, we can find a perturbation off so thatf\"(Rn) has a hyperbolic set A2 c Rn, of large stable thickness. We can also arrange that W 5(A 2 ) has a point of tangential intersection with W\"(A 1). The construction of A2 for a perturbation offwith the following proper ties is a major step towards finding diffeomorphisms with an infinite number of sinks: (1) T5(Az) \u00b7 -r\"(A 1) > 1",
            " (2) W5(A 2 ) n W\"(A 1) and W\"(A 2) n W'(A 1) both have points of transversal intersection which are not in A 1 u A2 . (3) W 5(A 2 ) and W\"(A 2 ) have a point of tangency. We have already demonstrated property (1) (recall that -r\"(A 1) varies continuously with perturbations of f). Property (2) is a consequence of the fact that the curves in W\"(A 2 ) and Ws(A 2 ) lie close to W\"(p) and W 5(p), respectively, near t. Since p E A 1 , and A2 lies on the same side of W 5 (p) as A1 , it follows that we obtain the desired intersections (Figure 6. 7.8). The next step in the construction is a generalization of the Smale-Birkhoff theorem [1963, 1967], cf. Section 5.3. Using the transverse intersections (2), we find a hyperbolic invariant set A3 ::J A1 u A2 which satisfies T 5 (A 3 ) \u2022 -r\"(A3 ) > l. Thus, further perturbations of f will have hyperbolic invariant sets near A3 which have persistent homoclinic tangencies. Referring to Figure 6.7.8, we can envisage the creation of tangencies between ws(A2 ) and W\"(A 2 ) by a perturbation which \"pulls up\" the image f\"(R). In this way we obtain a wild hyperbolic set. In the previous section, we proved that if fo has a hyperbolic fixed point p with eigenvalues p < 1 < A. < p- 1 and a point p0 of tangential intersection between W 5(p) and W\"(p), then there are perturbations ofj0 with attracting periodic orbits, which lie close to the orbit of p0 . Combining this construction iteratively with the construction of wild hyperbolic sets described above, one can produce diffeomorphisms with a countable infinity of attracting periodic orbits. 338 6. Global Bifurcations Partof fn(R) Figure 6.7.8. The invariant sets A, and A2 and the intersections of their manifolds. The argument can be summarized as follows: Starting withf0 , one perturbs to a nearby f 1 with a wild hyperbolic set. Newhouse [1980] shows thatf1 can be perturbed tof2 with a tangency between the stable and unstable manifolds of a single periodic orbit. His argument uses the density of periodic orbits in A3 to find one which contains two points near those whose stable and unstable manifolds intersect tangentially; he then perturbsf1 tof2 so that the stable and unstable manifolds of the periodic orbit for f 2 intersect tangentially",
            " For .u > 0, the nonwandering set A,.. of h,.. is hyperbolic and topo logically equivalent to a one-sided shift on two symbols (Guckenheimer [1979]). We shall study the thickness of the A~ by introducing an auxiliary, discontinuous map gP for each h~< so that g~< still has A~< as an invariant set. To define these maps g~, we need a bit more notation. Dropping the subscript J.l., we denote by q the fixed point of h in (0, 1) and by p the other point in I 6.7. Wild Hyperbolic Sets 341 components of g Figure 6.7.9. The map h. The two components of h- 1(1) n [p, q] are shown as heavy Jines. with h(p) = q. Write 1 = K 1 u L u K 2 where K 1 and K 2 are the components of h-1 [0, 1] and L = h- 1(1, oo). For those points in h- 1(1) n [p, q], we define g(x) = h\"(x) where n is chosen to be the smallest positive integer with h\"(x) E [p, q]. The map g is called the induced map of h. It has a countable set of discontinuities at points x with h\"(x) = p and hk(x) < p for 1 < k < n. We now assert that the distortion of g is uniformly bounded",
            " Moreover, if (f\")\"(p) \"# 0, then the orbit of p is stable from one side and unstable from the other. The map f can then be embedded in a one-parameter family JP., with fo = f, which has a saddle node bifurcation at ll = 0 along the orbit of p. Now vary ll to obtain a mapping g = /\"', which has no periodic orbit close to the orbit of p. The idea of Pomeau and Manneville [1980] is that the orbits of g will spend large amounts of time approximately following the periodic trajectory of p for f. The length of these episodes of almost periodic behavior can be related to 344 / / Figure 6.8.1. Near a saddle-node. 6. Global Bifurcations I f..l.t j. Pomeau and Manneville call these episodes of almost periodic behavior intermittent because they represent regular behavior which is present for varying periods of time, separated by (possibly) chaotic portions of an orbit. To study the scaling behavior in more detail, we consider the normal form for a saddle-node bifurcation in a discrete map: fix) = f..1. + x - x 2 \u2022 We are then interested in studying the dynamics off~' near 0 for f..1. < 0 with small magnitude. See Figure 6.8.1. An orbit which begins at x > 0 will be forced to spend many iterates near x = 0 before it\" escapes\" to the region where x < 0 and f(x) - x is no longer small. We wish to establish that the number of iterates spent near x = 0 is asymptotically proportional to I f..!. I- 112 as f..1. -+ 0. This can be done in two different ways for this problem, and we outline both. The first method involves replacing the discrete equation fix) = f..l. + x - x 2 with the continuous version of this problem, the differential equation (6",
            "8) Now perturbing away from this critical/ with a perturbation of the form 11 + g(x) and noting that g'(O) = 1, we obtain f.l + g()l + g(x)) ~ f.l(l + g'(g(x))) + g2(x) ~ 1(4)1 + g(2x)), (6.8.9) where g(x) is small. Once more we conclude that the number of iterates required to pass by zero is of order (- Jl) - 112 \u2022 Returning to the problem of intermittency for a one-dimensional mapping f~: I --+ I near a saddle-node bifurcation occurring at J1 = 0, we have seen that the length of time required to traverse the \"bottleneck\" region of Figure 6.8.1 scales as I 111- 112 . Since the mapping is not 1-1, it is possible for a trajectory to land directly in the middle of the bottleneck region without making its way in from the entrance. When this happens, the length of time spent in the bottleneck will be smaller. The result of this effect is a substantial variation in the length of time a trajectory takes to pass through the bottle neck on successive visits. This variation can be modeled with assumptions on the distribution of points as they land in the bottleneck, but the invariant measures of one-dimensional mappings can be very complicated and may not be adequately approximated by a simple model",
            " Throughout this section I = [0, 1] c R A map f: I --+ I with a single critical point c which lies between chaotic and nonchaotic maps has a particular kneading sequence which reflects the property thatf'(c) andt+ 2\"(c) lie on the same side of c, unless i = 2k for any k E 7L, in which case they lie on opposite sides of c. If the mapping has negative Schwarzian derivative, then the non wandering set ofjconsists of one unstable periodic orbit of period 2k for each k together with a Cantor set A depicted in Figure 6.8.2, with the numbers i representingf;(c). The Cantor set A is contained in the union of the 2\" intervals Lt(c), _t+ 2\"(c)], 1 :::;; i :::;; 2\". The intersection of these sets over all n 2 0 is A At each step of the construction, the intervals [F(c), r+ 2\"(c)], 1 :::;; i:::;; 2\" are permuted among themselves and there is no substantial spreading of trajectories which start close to one another near A. The kneading sequence I I I I I IH 2 10 14 6 8 c 1612 4 3 11 15 7 5 13 9 1 Figure 6.8.2. Eight subintervals in the construction of the Cantor set A; the endpoints are the first 16 iterates: {f'(c)}f_;: 1 . QL-----~---------L----_J 0 p' I p Figure 6.8.3. The critical map f and f 2 . a off has the remarkable property that if one defines hi = a2 i, then the sequence b is the \"complement\" of a, obtained from a by changing each symbol. (The sequence is a Morse sequence.) Further insight can be gained by examining Figure 6.8.3, which shows the critical mapping f and its second iterate F. If p and p' i= p satisfy f(p') = f(p) = p, then the observations about the kneading sequence off imply that f 2 1\u00a3p',pJ is topologically equivalent to !1 1. Thus it makes sense to inquire whether f 2 and fare related by a linear rescaling. One of Feigenbaum's fundamental observations is that there is a unique even, real analytic mapping g: [R1....,. IR1 and real number IX ~ -2.5 for which g(O) = 1, g\"(O) < 0, and 1Xg2(1X- 1x) = g(x)",
            " The mapping g can be approximately determined numer ically by solving for g as a polynomial of high degree with unknown co efficients. The mapping g above is a fixed point of the renormalized doubling operator ff defined by the relationship (6.8.10) on even functionsfwithf(O) = 1 and IX= (f2(0))- 1 = 1/!(1). Feigenbaum studied the operator ff numerically and concluded that g was an isolated fixed point and that the linearization ~ff(g) of ff at g in the space of even functions h with h(O) = 1 had a single unstable eigenvalue b ~ 4.67. This analysis leads to the following picture in function space: Figure 6.8.4. There is a surface ~ (of codimension one) consisting of functions with the same kneading sequence as g. A neighborhood of g in ~ lies in the stable manifold of g for the doubling operator ff. Approximately parallel to~ are surfaces~\" representing mappings for which the critical point is periodic with period 2\". The doubling operator ff maps ~.+ 1 to ~ \u2022. The distances from Figure 6.8.4. The structure near the universal map g in function space. 1:. to L approach zero like !5-\u2022: d(:E., 1:)/d(:E.+1 , 1:) -4 !5 as n -4 oo. For a one parameter family f\" passing transversely through 1: close enough to g, we can apply a renormalized doubling operator !Y for families which adjusts the parameter J.1.: (6.8.11) The operator !Yon families will have a stable fixed point which represents the universal behavior for the limit of a sequence of period doubling bifurca tions in a family of mappings with a nondegenerate critical point",
            "n - J.l.n-1 where J.l.. is the parameter value at which the orbit of period 2\" undergoes a flip bifurcation, giving birth to an orbit of period 2\" + 1. EXERCISE 6.8.3. Find numerically a sequence of period doubling bifurcations in the forced Duffing equation x + xx - fix + x 3 = y cos wt, both for fi = I and fi = 0. Compute the number \u00a35 in this example. (Hint: See Feigenbaum [1980].) represent band mergings: iff E B., there is a neighborhood of c for which f 2\" has a graph like that depicted in Figure 6.8.5, in which an invariant sub interval J c I is mapped so thatf2\"(J) covers J exactly twice. In the function space, the surface B. is characterized as the set of mappings whose topological entropy is(l/2\") log 2. The doubling operator maps Bn+ 1 to B., so the surfaces I Figure 6.8.5. J;\", 11 E B. Bn also accumulate on I: at the rate <5-n, but from \"above\" in the convention of Figure 6.8.4. In subsequent work, Feigenbaum [1979] noted that there is a character istic structure of the power spectrum associated with the period doubling sequences. (See also Nauenberg and Rudnick [1981].) Both the band mergings and the spectral properties can be determined from experimental data. The doubling operator fT can also be allowed to act on dissipative multidimensional mappings without changing its fixed point g or the fact that its linearization has a single unstable eigenvalue. A rigorous analysis of the doubling operators fT and "
        ],
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    },
    {
        "image_filename": "designv11_11_0002321_cdc.1998.761966-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002321_cdc.1998.761966-Figure1-1.png",
        "caption": "Figure 1: Planar Vertical 'IUe-OfF and Landing Aircraft System.",
        "texts": [
            " In section 2 we present the model of the aircraft and proceed to obtain the dynamical feedback controller which regulates a transfer of the nonminimum phase outputs between two given constant equilibrium points. Section 3 presents the simulation results and Section 4 is devoted to present some conclusions and suggestions for further research. 2 A Planar Vertical Takeoff and Landing Aircraft Stabilization Example 2.1 Description of the System In Hauser et al [2] (see also [lo]), the following model is proposed for the simplified description of the dynamics of a planar vertical takeoff and landing (PVTOL) aircraft (see Figure 1 ) f = -ulsin8+m2cos8 2 = ~ l c o s e + E ~ 2 s i n e - g e = u2 (1) where x and z are the horizontal and vertical coordinates of the center of gravity of the aircraft, respectively measured along an orthonormal set of fixed horizontal and vertical coordinates. The angle 8 is the air- craft\u2019s longitudinal axis angular rotation as measured with respect to the fixed horizontal coordinate axis. The controls u1 and u2 represent normalized quantities related to the vertical thrust and the angular rolling torque applied around the longitudinal axis of the aircraft respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003628_elan.200603535-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003628_elan.200603535-Figure1-1.png",
        "caption": "Fig. 1. Schematic structure of the conductometric immuno-biosensor with a chemoresistive layer separated from a region where enzymatic reaction occurs.",
        "texts": [
            " Both the digit width and interdigital distance were 10 mM, and their length was about 1 mm. Therefore, the sensitive part of each electrode was about 1 mm2. The internal generator of a Stanford Research System SR 830 lock-in amplifier (Sunnyvale, CA, USA) was employed to generate a sinusoidal wave with a frequency of 100 kHz and a peak-to-peak amplitude of 10 mV around a fixed potential of 0 V to each pair of electrodes, forming a miniaturized conductance cell. The schematic diagram of the experimental system was shown in Figure 1. The interdigitated microelectrodes were deposited onto ceramic substrate according to the literature [31]: (i) Electroanalysis 18, 2006, No. 15, 1505 \u2013 1510 www.electroanalysis.wiley-vch.de \u00a9 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim vacuum deposition of 0.1 mM chromium adhesive layers onto ceramic substrates; (ii) vacuum deposition of 1 mM gold on the top of the chromium layers. Prior to the bottomup layer formation process, the interdigitated microelectrodes were cleaned by immersing them in piranha solution for 5 min"
        ],
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    },
    {
        "image_filename": "designv11_11_0003037_j.ijnonlinmec.2005.07.004-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003037_j.ijnonlinmec.2005.07.004-Figure1-1.png",
        "caption": "Fig. 1. Mechanical model of a gear-pair system on deformable bearings.",
        "texts": [
            " First, some typical results are presented, obtained by applying the parametric dentification methodology for selected combinations of the system parameters. Apart from investigating problems related to the classical identification issues associated with the presence of measurement noise and model error, special emphasis is placed to cases where the system response is irregular or there coexist multiple motions. Finally, the highlights of the work are summarized in the last section. The model of the example mechanical system employed in the present study is shown in Fig. 1. This model is a special case of the model examined in previous studies [15] and is presented briefly next. It consists of a spur gear-pair with masses mn, mass moments of inertia In and base radii Rn (n = 1, 2), while both gears are supported on bearings with rolling elements. The corresponding equations of motion are first set up in the following form: I1\u03081 + R1fg( 1, 2, u, u\u0307) = M1(t, 1, \u03071), (1) I2\u03082 \u2212 R2fg( 1, 2, u, u\u0307) = \u2212M2(t, 2, \u03072), (2) m1u\u03081 + f1(u1, u\u03071) + fg( 1, 2, u, u\u0307) = Fb1, (3) m2u\u03082 + f2(u2, u\u03072) \u2212 fg( 1, 2, u, u\u0307) = Fb2"
        ],
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    {
        "image_filename": "designv11_11_0001343_1.2832457-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001343_1.2832457-Figure7-1.png",
        "caption": "Fig. 7 The normal and tangential projections of the contact surfacearea and the total interference volume at a contact region",
        "texts": [
            " The negative sign indicates a tangential contact area for a resisting contact region. The integral /J - - - dxdy = e' at i = I,] is the time-rate of interference volume at a given contact region. Equation (28) can be written for resisting and assisting con tact regions in terms of normal and tangential contact areas and the interference volume as, \u2014ha'\u201e + sa'i = e' -hai - sal = t' (29) (30) The normal and tangential contact areas and the interference volume for a typical contact region are shown in Fig. 7. As Eqs. (26) and (27) relate the interface forces and relative velocity components to deformation of the asperities, similar expressions can be developed to relate the true contact area projections and relative velocities to the rate of change of the interference volume with respect to time. Such a relationship is obtained by a summation of (29) and (30) over / andy: -hA\u201e + sA,= 'S (31) where the total normal contact area \u2022 = i j = i and total tangential contact area (=1 j = i and ,=1 y=i is the time rate of total interference volume for the entire inter face"
        ],
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    },
    {
        "image_filename": "designv11_11_0002621_1.2096535-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002621_1.2096535-Figure4-1.png",
        "caption": "Fig. 4. Cyclic voltammograms of polyaniline/cellulose films in electrolytes of (a) pH = - 0 . 2 , (b) pH = 1.0, ( c ) = pH = 2.0, and (d) pH = 3.0.",
        "texts": [
            "50V vs . SCE) with no loss of electroactivity (ca . 3500 scans, 12h at a scan rate of 100 mV/s). However, upon scanning to higher potentials (up to 1.0V vs . SCE), the polymer is oxidized to the imine form (pernigraniline, structure III, Fig. 2), which reacts with water to give qui- nones. This sequence is verified in Fig. 3 as the electroactivity of peaks c-c' and a-a' decrease and as peak b-b' increases. Further corroboration that polyaniline imparts electroactivity to the composites is given in Fig. 4. Composite film was immersed in 0.1 mol dm -3 NH4OH for 30s, thereby converting the emeraldine acid form to the base form (Fig. 6). The composite film was then placed in solutions of various pH (-0.2, 1, 2, and 3) and allowed to equilibrate for 12h prior to cyclic voltammetry. The cyclic voltammetrie response of each film was then recorded, and as shown in Fig. 4, the second redox process shifts about 118 mV/pH (114 mV/pH with a correlation coefficient of 0.9847 over the ) unless CC License in place (see abstract).\u00a0 ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 130.237.29.138Downloaded on 2015-03-06 to IP range pH = -0.2 to 3) indicative of a two proton per electron process as predicted in Fig. 2. Composite spectroscopy.--The UV-vis absorption spectra of freshly made pani/dinitrocellulose and pure dinitrocellulose films are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002090_j.scriptamat.2004.08.003-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002090_j.scriptamat.2004.08.003-Figure7-1.png",
        "caption": "Fig. 7. Polar plots of the Poisson s ratio for the monoclinic cesium dihydrogen phosphate corresponding to the cases of Fig. 6, respectively. Grey areas denote auxetic domains.",
        "texts": [
            "0, s25 = 91.2, s35 = 373.0, s46 = 3.8, units in (TPa) 1. The angles a, h range from 0 to p. and m in the plane orthogonal to the material symmetry plane, the expression of the Poisson s ratio is m1m \u00bc s12cos2h \u00fe s13sin 2h s11 : \u00f08\u00de In the second case, with n directed along x2 and m in the plane of elastic mirror symmetry, the Poisson s ratio is given by m2m \u00bc s12cos2h s25 sin h cos h \u00fe s23sin 2h s22 : \u00f09\u00de The Poisson s ratio functions corresponding to these two cases are shown in the polar plots of Fig. 7. The first case corresponds to values of mnm always positive, whereas in the second case negative values exist in the range Dh = 1.36 rad, from h1 = 0.69 to h = 2.05 rad. In this case, the minimum value of the Poisson s ratio is mmin = 1.49. For the monoclinic system, a case with an extreme negative value of the Poisson s ratio is found for lanthanum niobate. For this crystal, the Poisson s ratio behavior is shown in Fig. 8 when n lies in the plane x1x2 and m in the plane orthogonal to n. It is clear from the figure that a range of values for the angle h exists corresponding to an auxetic behavior for any a"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000534_s1474-6670(17)47309-5-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000534_s1474-6670(17)47309-5-Figure2-1.png",
        "caption": "Fig. 2. The velocity relationships between adjacent bodies when the rear body is a passive trailer. The front body may be either a passive trailer or a steerable car .",
        "texts": [
            " the standard n trailer system (m = 1). 2. the fire truck (m = 2, n2 = nl = 1) . The kinematic model of the system is found by examining the relationships between the velocities of the bodies , as defined by the rigid connections between them. If the linear velocity of the last body is v~m' then the derivatives of x and y are the projections of this velocity, y x (1) (2) Now , let vf represent the the linear velocity of the axle with angle B{. Consider first the case of a pas sive trailer; refer to Figure 2. The linear velocities of body i-I has two perpendicular components: one in the direction of the linear velocity of the ith body, J = cos((J{ 1 - (J{)J 1 , s , 1-) and the other in the direction of the angular ve locity of the ith body, Li iJi = sin((}i 1 - (}i)J 1. (3) S , 1 ' ,- When the rear body is an active car instead of a passive trailer (see Figure 3), the relationship between the two linear velocities has the form \u00b7+1 \u00b7+1 . . . . t?,.. . cos((}~ . -4l)=t?,.. . cos((}~ . -4l), J J '] and the angular velocity vector ~ "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000141_s0043-1648(97)00190-7-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000141_s0043-1648(97)00190-7-Figure7-1.png",
        "caption": "Fig. 7. Torque components acting on the sliding sho\u00a2~,.",
        "texts": [
            " However true hydrodynamic lubrication is not obtained during the acceleration phase as can be concluded from the friction coefticient remaining considerably larger than in steady-state conditions ( see Fig. 6a--d ). Also the measured electric contact resistance indicated that metal-metal contact continues to exist during acceleration. No hydrodynamic lubrication arises because the sliding shoes do not tilt last enough in the right sense and magnitude for suflicient hydrodynamic pressure generation. Fig. 7 I': Van De Velde et aL / Wear 216 \u00a219~St 138-149 145 shows the torque components acting on the sliding shoes. The situation shown corresponds to motion of the shoe to the left. The total torque ( t, ) on the shoes around the centre of rotation O in the sense favourable for hydrodynamic pressure generation (taken as the positive sense ) equals: t,=m,-.~.a +/h-- F.b ( 7 ) with m, = mass of sliding shoe ( = 68 g) , a = eccentricity of the inertia resistance ( = 3.5 ram), b=--eccentricity of the friction force ( -- 9",
            " The maximum acceleration (absolute value) which is obtained during the stick-slip tests equals 5 m/s-\" ( this maximum value is measured for lubricant m22). The inertia component m, ..i:. a therefore is negligible compared to the friction component F. b and is not further considered. The torque th by hydrodynamic pressure generation is thought to be caused by the wedges formed by the small chamfers which exist at the edges of the shoes. These chamfers. of which an amplification with typical dimensions ( the proportions are not drawn correctly ) is shown in Fig. 7, were produced during the polishing of the shoes. Fig. 8 shows the measured prolile of a polished shoe near an edge with .~ale 2.5 I , tm /cm vertically and 500 ixm/cm horizontally. Similar profiles were obtained at the edges of the shoes alter the friction tests. It is nearly impossible to calculate h, exactly because the pressure generation strongly depends on the minimum film thickness in the contact zone, which has no clear meaning for boundary lubrication. Moreover, side leakage can not be neglected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003184_2005-01-1651-Figure16-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003184_2005-01-1651-Figure16-1.png",
        "caption": "Figure 16. Wear pattern in small end bush",
        "texts": [
            " With this characterization, we can estimate the global wear rate of the small end bush and the location of the wear assuming the wear rate in elastic, elastoplastic and plastic contact are be Ke, Kep and Kp, the expression of the wear intensity for a point of the bush, called w( ) becomes: d,PrK ,PrK,PrKR 4 1w pp epepee0r 4 0 (19) with ,Pre = elastic contact pressure ,Prep = elastoplastic contact pressure ,Prp = plastic contact pressure With previous numerical data, we calculate the wear intensity and obtain the wear intensity curve given on Figure 17. Figure 16 shows that the wear pattern is asymmetric which give us information to compare with results from the field. Figure 18 displayed a worn small end bush showing that the wear pattern also asymmetric is quite uniform across the width of the bearing. For this case, where the pin is very stiff with respect to the load, the pin bending effect does not appear in this damage. It is interesting to stress the fact that the wear across the bush is highly related to the contact forces but nearly not sensitive at all to the pin speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000441_s0143-8166(00)00094-4-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000441_s0143-8166(00)00094-4-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram showing the energy deposition pro\"le (Gaussian) of the continuous wave CO 2 laser beam and con\"guration (semi-circular) of the laser irradiated zone on the yz plane, respectively. G denotes a partially melted graphite nodule with an annular melted zone of maximum width y . and located directly under the center of the laser beam. d z is the case depth along depth z.",
        "texts": [
            " The model and solution are based on an earlier approach reported by Ashby and Easterling [10]. Accordingly, the heat balance equation for heating/cooling a metallic sample following laser irradiation with a continuous wave CO 2 laser with a Gaussian energy deposition pro\"le is given by +2\u00b9! 1 a L\u00b9 Lt # q r j \"0, (1) where T is the temperature, a is the thermal di!usivity, q r is the amount of heat energy injected in the samples per unit volume per unit time, k is the thermal conductivity of the sample and t is the time. Fig. 1 schematically shows the laser beam pro\"le and location of a spherical graphite nodule G at a given vertical depth z from the surface. Here, y . is the maximum width of the annular melt zone around the nodule. During LSH, the sample stage moves along the x direction (perpendicular to the yz plane) with a linear speed v and allows an average laser-matter irradiation time (\"2r/v where, r is the beam radius) over a circular region on the surface. The other necessary assumptions to solve Eq. (1) are: 1",
            " It may be noted that the peak temperature here does not exceed the eutectic temperature. Fig. 7 presents similar thermal pro\"les generated for P\"900W and v\"60mm/s. It may be noted that the peak temperature exceeds the eutectic temperature until about depth z\"150 lm. Furthermore, partial melting of graphite nodule would occur even at greater depth depending on the local thermal history and carbon di!usion pro\"le around the graphite nodules. Fig. 8 presents the variation of matrix carbon concentration as a function of distance from the graphite}nodules interface (along y in Fig. 1) located at di!erent levels of depth z from the top surface. It is evident that the matrix carbon content is maximum at the top surface and decreases signi\"cantly as z increases at comparable distances from the graphite}matrix interface. It may be pointed out that the graphite nodules are considered 100% carbon and the matrix carbon content decreases from 2wt% (the maximum carbon level assumed at the graphite}matrix interface) to the average carbon level of the matrix (\"0.72wt% minimum [15]). Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001700_1.1636193-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001700_1.1636193-Figure6-1.png",
        "caption": "Fig. 6 Nominal bank shot angle",
        "texts": [
            " Nevertheless, such a procedure would have the individual shooter take a sufficient number of shots from selected points on the court during which the shots are photographed and the errors are determined, after which the coefficients are determined through a curve-fitting procedure. 1Equation ~27! is obtained by first showing that the y component of velocity just after the collision with the backboard is given by v253/5v sin b12/5Rv1 , in which v denotes the y component of velocity of the ball just before the collision with the backboard, and v1 denotes the angular velocity about the z axis just before the collision ~see Fig. 6!. This equation is found by summing forces in the y direction, by summing moments about the z axis, and by letting the velocity of the contact point of the ball with the backboard be zero at the end of the collision. Equation ~27! then assumes that v150. 536 \u00d5 Vol. 125, DECEMBER 2003 rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 01/29/201 First consider several cases in which the ball is thrown from the side (r0513.75 ft, u0567.5 deg). A direct swish is shown in Fig. 7 and a bank shot is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000158_s002211209700760x-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000158_s002211209700760x-Figure5-1.png",
        "caption": "Figure 5. Schematic the flow past an axisymmetric body showing (a) the notation and the downwash produced by the baroclinic, non-buoyancy effect, and (b) how vorticity is generated upstream of the obstacle by the baroclinic torque produced by the unperturbed density field and how the vorticity is then distorted and amplified as it is advected around the body.",
        "texts": [
            " For the specific case of a cylinder (Batchelor 1967, p. 543) \u03c8s = \u2212Ur ( 1\u2212 a2 r2 ) sin \u03b8 + Ua\u03b5 8 ( \u2212a 2 r2 cos 2\u03b8 \u2212 2 r2 a2 sin2 \u03b8 ) . 4.2. Three-dimensional analysis for axisymmetric bodies A significant difference between two- and three-dimensional flows is that the vorticity, which is first generated by a baroclinic torque, is then stretched and rotated by the (\u03c92 \u00b7 \u2207)v1, (\u03c92 \u00b7 \u2207)v2 terms in (2.14). In particular, when U \u00b7 \u2207\u03c10 = 0, these terms generate a streamwise component of vorticity (see figure 5). The trailing vorticity may be calculated from the linearized vorticity equation (2.16): \u03c92(x \u2032) \u00b7 s\u0302 = v1 2\u03c1B d\u03c10 dy sin \u03b1 \u222b s \u2212\u221e U2 v4 1 \u2202v2 1 \u2202n (\u22122\u03c81/U)1/2 R ds+ O ( U\u03b52/a ) . (4.7) The streamwise component of vorticity is (see Appendix B) \u03c92(x \u2032) \u00b7 s\u0302 = \u2212 U 2\u03c1B d\u03c10 dy sin \u03b1 (\u22122\u03c81/U)1/2 R ( \u2202Xd \u2202n \u2212 2v1,R v1 ) . (4.8) As to be expected from Yih\u2019s (1959) result, this is identical to Lighthill\u2019s (1953, equation 52) expression for the vorticity distribution downstream of a body in a sheared flow",
            " On the wake streamline (U \u00b7 x\u2032 \u2192 \u2212\u221e), the secondary flow, vr2, satisfying (2.18) and (4.9) is (see Auton 1987, equation 6.6) vr2,y(R, \u03b1) (Ud\u03c10/dy)/2\u03c1B = \u2212sin 2\u03b1 R2 \u222b R 0 XdRdR \u2212 1 2 (1\u2212 sin 2\u03b1)Xd (4.10) vr2,z(R, \u03b1) (Ud\u03c10/dy)/2\u03c1B = \u2212cos 2\u03b1 R2 \u222b R 0 XdRdR + 1 2 cos 2\u03b1Xd, (4.11) where R = (y2 + x2)1/2. The flow far from the centreline R/a 1 is (Lighthill 1956, corrigendum) vr2(x \u2032) = U \u03c1B d\u03c10 dy sin \u03b1 CMV 8\u03c0 \u2207 ( 1 R ( 1\u2212 x\u2032 r )) . (4.12) Equations (4.10), (4.11) and (4.12) are required to estimate the force on the body (Auton 1987). Figure 5 shows that the trailing vorticity gives a downthrust to the flow resulting in a lift force which drives the body towards the denser fluid. It also explains how the vorticity is generated by the finite baroclinic torque and is then amplified to a singular extent by the flow around the bluff body. 5. Flow when the body moves parallel to the density gradient, U \u00d7 \u2207\u03c10 = 0 5.1. Two-dimensional analysis In a two-dimensional flow, where there is no vortex stretching (\u03c9 \u00b7 \u2207)v = 0, the vorticity equation (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002848_0020-7462(84)90034-9-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002848_0020-7462(84)90034-9-Figure6-1.png",
        "caption": "Fig. 6. Deflection profiles ['or consecutive stages of loading.",
        "texts": [
            " Quite clearly, for the totally wrinkled membrane, there is only one solution for a particuhir wtlue of F. In Fig. 5 the deformation parameters the arid (/)1 are plotted for different values of the dimensionless load parameter F. Note that the maximum value of the parameter, and therelore the maximum value of the concentrated force P, is reached when ~/~o = 70.9 \u00b0 and 0 ~ = 94.3\u00b0. I f the wrinkled region is to be extended i.e. if ~/) ~ is to be increased, the value of F, and therefore I', must be redticed. Figure 6 shows the deflected shape of the membrane for successive stages of loading. The lnaximum value of the nondimensional force if, ..... = 1.521 corresponds very closely to half 0.968~R~lq<> Ihc \"'pressure l\\~rce'\" at the equatorial section: i.e. 1] ..... - 5 The relation between the dimensionless load P = P,'qoR~' = Tt/-2, and the dimensionless vertical apex displacement, ] = l / R e is shown in Fig. 7. For a given value of the load three states of equilibrium can exist, as indicated by points A, B and (\" on the load deflection diagram"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003800_ip-smt:20050073-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003800_ip-smt:20050073-Figure3-1.png",
        "caption": "Fig. 3 Possible angular displacement, d, of a single-turn search coil (not to scale)",
        "texts": [
            " The loci of the B vectors will not be circular, but elliptical, which inevitably has an impact on the value of the measured Prot value [6]. There are two methods to detect the localised flux density: (i) using a of search coil and (ii) using needle probes. The first method is used in most rotational research projects [5]. In these types of measurement the typical width of a search coil is around 20mm. There can be an angular displacement of the sensor which depends on the diameter of the holes drilled in the sample under test and the wire used for the search coil, as is depicted in Fig. 3. It is possible to locate these holes precisely with an accuracy of better than 0.01mm. The holes need to be as small as possible to minimise their influence on the magnetising process, but for diameters below 0.3mm there are practical difficulties in their fabrication using drills. If the wire is 0.1mm in diameter [1] then the angular misalignment for one coil in the worst-case situation could theoretically be as high as 0.5731. Thus, in the worst-case situation the relative angular displacement between the coils in the X and Y directions could reach 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001223_10402009508983385-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001223_10402009508983385-Figure1-1.png",
        "caption": "Fig. 1-Piston ring geometry.",
        "texts": [
            " Elastic Deformation The elastic displacement of the piston ring and cylinder wall due to hydrodynamic pressure within the lubricant film can be found from the elastic equation, Eq. [28]: 2 U ( X ) = -z jp ( ~ ) h ( x - u2d( + constant [12] Lubricant Film Thickness With the assumption of perfectly smooth surfaces, the lubricant film thickness h for a piston ring with a symmetric parabolic face subject to local elastic deformation can be expressed in terms of minimum film thickness h,( t ) , x and elastic deformation v ( x ) as: 6 where y = 7, w is the width of the ring and 6 is the (w/2) crown height of the ring shown in Fig. 1. Piston Ring Velocity The piston ring velocity is assumed to be the same as the piston velocity. I t can be developed from the engine crank mechanism shown in Fig. 2: 2 m where: o = - 60 Boundary Conditions Instead of applying pressure boundary conditions, 0 boundary conditions, written in terms of pressure acting on both leading and trailing edges, can be used for the compressible lubricant model. By substituting PI- and PT into Eq. [7], the 0 boundary conditions can be written as: and where XI- and x-,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003990_j.ijsolstr.2006.09.025-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003990_j.ijsolstr.2006.09.025-Figure1-1.png",
        "caption": "Fig. 1. (a) Schematic of a rolling wheel with a \u2018\u2018flat\u2019\u2019, and (b) contact geometries: (i) case I (emerging flat); (ii) case II (buried flat).",
        "texts": [
            "he contact problem of a wheel having a small flat, pressed onto an elastically similar half-plane, is considered. The contact law and pressure distribution is found, for all angular positions of the wheel, i.e. for all orientations of the flat under quasi-static conditions, and the evolving distributions tracked out, as the wheel rotates. 2006 Elsevier Ltd. All rights reserved. Keywords: Contact problem; Wheel with flat; Pressure distribution; Logarithmic singularity The problem to be studied is shown schematically in Fig. 1(a). A load-bearing wheel, for example a rail-vehicle wheel, is assumed to have been \u2018locked\u2019 during severe braking, so that sliding action over the rail has effectively machined a distinct \u2018flat\u2019 on its periphery. The braking action on the wheel has then been removed or reduced, so that it is in rolling freely, but the presence of the discontinuity in surface profile will have a very damaging effect on the rail as the wheel subsequently revolves. The object of this paper is to provide a description of the effect of the modified wheel geometry including, in particular, the contact pressure spikes adjacent to the discontinuity in profile,1 by studying, in detail, the contact problem with the flat positioned at arbitrary orientations",
            " A preliminary investigation of the problem, for the particular case when the flat is parallel with the free surface of the half-plane, has already been carried out (Sackfield et al., 2006). Experience in solving that symmetrical, and therefore rather simpler geometry, has permitted us to develop the more general solution, described here. 2 Clearly, because there will always be a logarithmic singularity in the contact pressure at the discontinuity, local strains there will be large, and beyond the scope of linear theory. In the real problem (Fig. 1(a)) the geometry might properly be specified in terms of the wheel radius, R, the included angle of the flat, w, and a coordinate specifying the angular position of the wheel, h, but, in the formulation, it is preferable to use an alternative set of quantities in which the dependent and independent variables are effectively exchanged. Two separate geometries will need to be considered; first (case I), when the flat is just entering or leaving the contact, Fig. 1(b)(i), and hence breaks the free surface; and second (case II), when the flat is completely submerged, and therefore bordered by regions in which a parabola, approximating the circular arc, defines the outer profile, Fig. 1(b)(ii). In each case the contact is assumed to extend from a + d to a + d, and the straight line segment representing the flat is assumed to be at an angle / to the x axis. The integral equation connecting the gradient of the relative surface profile, dv/dx, to the contact pressure distribution, p(x), is (Johnson, 1985; Hills et al., 1993) 1 A ov ox \u00bc 1 p Z a\u00fed a\u00fed p\u00f0n\u00de n x dt; \u00f01\u00de where, assuming the contacting bodies are elastically similar, A \u00bc j\u00fe 1 2l ; \u00f02\u00de where l is the modulus of rigidity, and j = 3 4m, m being Poisson\u2019s ratio"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002847_b:tril.0000044500.75134.70-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002847_b:tril.0000044500.75134.70-Figure4-1.png",
        "caption": "Figure 4. The lubrication film measurement apparatus.",
        "texts": [
            " Furthermore, it can be seen from figure 3(c) that the reconstruction of a local profile from two-beam interference theory produces an erroneous wavy surface, while according to the relation of the intensity versus gap thickness from the full optical analysis in figure 2, a realistic surface profile is acquired. In figure 3(c), when measuring the gap size between points A and B, using the cosine relationship, 34 nm is overestimated. It should be pointed out that for measuring film thickness at the micrometer level, the errors from the two-beam interferometry can be ignored. However, when local tiny thickness variations in film or ultra thin film thickness is evaluated from interference intensities, the full optical analysis should be used. A ball-on-disc optical EHL apparatus, as illustrated in figure 4, has been constructed for the implementation of the MBI scheme. A high-precision steel ball of 25.4 mm diameter is loaded against the Cr-coated side of a glass disc by a spring unit. The load can be continuously adjusted through a screwthread mounting. The glass disc and the steel ball are driven by synchronous pulleys and belts separately. Quasi-monochromatic light is obtained by a narrow band interference filter, and then collimated and reflected from the beam splitter inside the microscope. Lastly, the beam is normally projected on the EHL contact region"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002767_978-3-642-71015-5-Figure5.8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002767_978-3-642-71015-5-Figure5.8-1.png",
        "caption": "Fig. 5.8. Dielectric slab moving in rectangular waveconduit",
        "texts": [
            "11], whose feasibility (as opposed to conventional magnetic devices) derives from the interaction mechanism between a dielectric rotor and a rotating field. The present section is concerned with some of the problems involved in the last-mentioned type of wave-layer interaction, i.e. with analysis of a system which models - to a certain extent - a linear \"electric\" machine as opposed to its \"magnetic\" counterpart considered in Sect. 2.2. 5.2 Wave Propagation Inside Moving Nonmagnetic Media 245 The configuration to be investigated is shown in Fig. 5.8. A pair of extremely thin, highly-conducting plane sheets (which confine the electromagnetic field) are fixed at elevations y = \u00b1 hI in a right-handed Cartesian frame of reference x, y, z, in which the running time t is continu ously recorded. An uncharged, nonconducting and nonmagnetic dielectric slab of uniform thickness 2h2 glides within this waveconduit along the ( + x)-axis at a constant velocity v; the region above and below the slab is filled with an idealized medium (hereafter referred to as \"air\") with the electrical properties of vacuum"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003606_detc2005-85337-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003606_detc2005-85337-Figure9-1.png",
        "caption": "Fig. 9 Mobility analysis of 2-(RRR)NRa-RA(RRR)BRA PKC: (a) The original kinematic chain and (b) The kinematic chain with an equivalent serial kinematic chain added.",
        "texts": [
            " Following the procedure for the full-cycle mobility inspection, we have Step 1 Since \u2206 = 2 6= 0, go to the next step. Step 2 For this PKC, there are no inactive joints. Step 3 It can be found that the PKC has full-cycle equivalent serial kinematic chain. The full-cycle equivalent serial kinematic chain is a PPPR serial kinematic chain in which the axis of the R joint is parallel to the axes of the RA joints [Fig. 8(b)]. Thus, the PKC has full-cycle mobility. Example 4 Consider the 2-RARARARa-R\u03b1R1R1R1R\u03b1 PKC shown in Fig. 9(a) [12]. In this PKC, the axes of all the RA joints are parallel, the axes of the Ra joints are coaxial, the axes of the R\u03b1 are parallel to the axes of the Ra joints, while the axes of the R1 joints within a same leg are parallel. The mobility analysis of this PKC can be performed as follows. Instantaneous mobility analysis Copyright  2005 by ASME ms of Use: http://www.asme.org/about-asme/terms-of-use Dow The wrench system of each RARARARa leg is a 1-\u03b60-1\u03b6\u221e-system, whose base can be represented by a \u03b6\u221e whose axis is perpendicular to the axes of all the R joints and a \u03b60 whose axis intersects the axes of the Ra joint and is parallel to the axes of the RA joints",
            " (4), (7) and (8), we obtain C = 6\u2212 3 = 3 and F = C + 3\u2211 i=1 Ri = 3. The number of overconstraints of this 3-legged PKC is \u2206 = 3\u2211 i=1 ci \u2212 c = 2 + 2 + 1\u2212 3 = 2. Following the procedure for the full-cycle mobility inspection, we have Step 1 Since \u2206 = 2 6= 0, go to the next step. Step 2 For this PKC, there are no inactive joints. Step 3 It can be found that the PKC has a full-cycle equivalent serial kinematic chain. The full-cycle equivalent serial kinematic chain is a PPR serial kinematic chain [Fig. 9(b)]in which the axis of the R joint is coaxial with the axes of the Ra joints located on the moving platform and the directions of the P joints 8 nloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/07/2016 T are all perpendicular to the axes of the RA joints. Thus, the PKC has full-cycle mobility. Example 5 Consider the 4-legged 2-R\u030cR\u030cR\u030cR\u0302R\u0302-2RARARAR\u0308R\u0308 PKC shown in Fig. 10(a). In this PKC, the axes of all the R\u030c joints pass though a common point, the axes of all the R\u0302 joints pass though a second common point, the axes of all the R\u0308 pass through a third common point, the axes of all the RA joints are parallel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000967_icsyse.1990.203156-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000967_icsyse.1990.203156-Figure1-1.png",
        "caption": "Figure 1: Geometric interpretation of the vectors defining the relative Jacobian",
        "texts": [
            " During the calculation of (l), the transformation between the ith joint coordinate frame and the coordinate frame of the second robot\u2019s end effector, denoted by Ui, can be obtained from 300 CH2872-0/90/0000-0300 0 $1.00 1990 IEEE The columns of the relative Jacobian, which are composed of relative linear and angular velocity vectors due to the ith joint are closely related to the third and fourth columns of the above U matrices. In particular, it is easy to show that the relative linear velocity, U;, is given by the cross product of the third and fourth column of U; and that the relative angular velocity, U;, is given by the third column of U; (see Figure 1). The relative Jacobian, denoted J R , is therefore given by (3) where the upper 3 X 3 rotation R h l t h a from ( I ) , is required in order to express the relative velocity with respect to the first hand's coordinate frame. The composite Jacobian, denoted J c , represents the set of secondary constraints which consist of obstacle avoidance, joint limit avoidance, and absolute position and orientation requirements. The obstacle avoidance criteria is represented by an obstacle avoidance Jacobian which relates the joint rates to the absolute linear velocity of those links that contain proximity sensors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002315_robot.1993.291875-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002315_robot.1993.291875-Figure2-1.png",
        "caption": "Figure 2: The constraint wrench, A.",
        "texts": [
            " Let the wrench A be given (in axis coordinates) by A = [mf , fr]' where f i s the end-effector force and m, is the moment about the point 0. We can write Di in the form: Di = [ BT Ai Bi C 1 where AT = A, and CT = Ci. Substituting in ( lo) , we get expressions for the' ith angular and linear velocity: Aqi U , = Aimo - A;(ri x f) + Bjf (11) Aqi p i = B T m o - BT(r i x f) + Cif (12) Let h be the pitch and L the intensity of the wrench, A, while U is a unit vector along the wrench axis as shown in Figure 2. p is the position vector of a point on the axis such that p . U = 0. In other words, f = L u (13) m o = h L u + p x L u (14) Let the angular and linear components of SEA^ be denoted by Ad and Ax respectively. Then Equation (1) can be written as: n n Aqiui = A4, (Ti x ~i + pi) Aqi = AX i = l i = l where ui is the angular velocity of link i relative to link i-I, and pj is the velocity of a reference point Pi on link i. In the Cartesian coordinate system with the origin at 0 as shown, the same joint twist can be represented by a six dimensional vector Si,, given by: si, = [ u T , ( p , + ri x u"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001436_j.wear.2003.10.004-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001436_j.wear.2003.10.004-Figure3-1.png",
        "caption": "Fig. 3. Development of sharpness for abrasive particles.",
        "texts": [
            " Abrasive systems governed by multiple random interactions between the particle and the wearing surface require a statistical treatment of particle shape. Assuming that all orientations are equally likely to participate in abrasion, then it is possible to identify an asperity possessing average shape that is representative of the entire particle sample. In theory, if a particle is considered as a closed set in Euclidean 3-space, then its average shape is obtained by systematically averaging the groove functions over the domain of all possible orientations, as illustrated in Fig. 3. Each vector (\u03b8, \u03c6, \u03c8) yields its own groove function. If there are N particles in the sample (each particle indexed by n), then the average groove function can be determined by the mean-value theorem as follows: \u00b5\u039b(\u2126) = 1 4\u03c03N N\u2211 n=1 [\u222b\u222b\u222b \u039b(\u2126, \u03b8, \u03c6,\u03c8, n) d\u03b8 d\u03c6 d\u03c8 ] (1) where \u0393 is the domain of integration, i.e. \u03b8 = [0, 2\u03c0), \u03c6 = [0, 2\u03c0) and \u03c8 = [0, \u03c0). The functional form of \u039b is not known and must be numerically determined by measurements on the particles. In practice, the technique has been implemented by analysing particle projections"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001194_027836499501400503-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001194_027836499501400503-Figure3-1.png",
        "caption": "Fig. 3. We consider- a two-fingered grip of a smooth contour (usually closed) r(s), placing the fingers at s = S 1, S2. respectively. The line joining the two fingers makes angles cr ~ , cx2 with the normals at s = s 1, ~s~, respectively.",
        "texts": [
            " In either case, the fingers make a frictional contact with the curve, with coefficient of friction 1-t > 0. A general analysis will be developed for thin fingers, from which parallel jaws emerge as a special case. Fingers are placed on r(s) at s = sJ, 82. The vector joining the fingers is denoted R(sl, S2) = (r(s j ) - r(s2)). 2.3. Force Closure Following Nguyen (1988) and Faverjon and Ponce (1991), the force-closure of a two-fingered grasp is determined by the test of Figure 2, which can be expressed in the notation of Figure 3. Fingers are positioned at r(.5)) and, provided s, ~ S2, r(s2) and friction angles a], a2 are defined as shown, the angles between the inward normals to the curve at S = sl, s2 and the line joining the fingers: where R = R/IRI, and similarly for a2. Given a coefficient of friction M, the test is passed whenever each finger lies within the &dquo;friction cone&dquo; of the other-that is, when with This covers both cases of compressive grasp when cos a1 > 0 and cos a2 > 0, and of expansive grasp when cos a < 0 and cos c~2 < 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001358_s0094-114x(03)00090-9-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001358_s0094-114x(03)00090-9-Figure10-1.png",
        "caption": "Fig. 10. Assembly modes of the triad with one internal and one external prismatic joint.",
        "texts": [
            " 6) is applied in the third numerical example. The input data of the triad are given in the left part of the Table 3. By solving the sixth order polynomial equation, four real roots and two complex roots are obtained (Table 3). For each real value of the displacement s, the coordinates of the internal revolute joints B (see Table 3) and E are calculated. Finally, the displacement s1 is determined. The corresponding four assembly modes of the triad with one internal and one external prismatic joint are shown in Fig. 10. Finally, the method presented in Section 5 is used for the position analysis of the one-degree-offreedom planar mechanism with eight links including a triad with three external prismatic joints. The mechanism with decoupled structure (see up part of Fig. 11) consists of the frame 0, the input link 1, an Assur group of class 2 (dyad with links 2 and 3) with three revolute joints (F , G and D) and an Assur group of class 3 (triad with links 4, 5, 6 and 7) with three internal revolute joints and three external prismatic joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003507_jsen.2006.881421-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003507_jsen.2006.881421-Figure6-1.png",
        "caption": "Fig. 6. Illustration of initial sensor candidate locations (cm).",
        "texts": [
            " The NSNR is defined as NSNR(i) = 20 log ( di j dn j ) (13) where di j and dn j are the nodal displacements at the jth sensor location as a result of the ith defect-induced vibration and noise-induced vibration, respectively. A complete transient analysis was performed, and eight nodal solutions corresponding to the eight defect positions were obtained. Each of the eight solutions contains the nodal displacements of all the nodes as a result of transient force excitation. A total of 68 nodes on the bearing housing were selected as the initial candidate sensor locations. As marked by the dotted lines in Fig. 6, the 68 candidate nodes were distributed along the periphery of the housing plate and around the bearing, with 5\u201310-mm separation apart between adjacent nodes. Such initial nodal locations and separations were chosen in consideration of the geometrical dimension of available miniaturized accelerometers for experimental test. For each of the 68 candidate locations, the nodal displacement along both the X- and Y -directions was simulated to identify the exact orientation when uniaxial accelerometers are to be placed, as these accelerometers measure vibration along one direction only"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002077_20020721-6-es-1901.01249-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002077_20020721-6-es-1901.01249-Figure2-1.png",
        "caption": "Fig. 2 \u2013 Simplified launcher representation",
        "texts": [
            " - control the destabilizing bending modes: the aim is to attenuate these modes under a gain limit (XdB) except for the first one which can be controlled in phase with a sufficient delay margin (at least one sample period sT ). Time specifications: - limit the angle of attack i in case of wind (a typical wind profile will be given on figure 7). - limit the angle of deflection \u03b2 and its velocity \u03b2 - the consumption C must be limited to maxC where: ( ) ( )\u2211 = \u2212+= end init T Tk kkC \u03b2\u03b2 1 Robustness - all these objectives have to be robust against uncertainties (which affect rigid and bending modes) A simplified launcher scheme is given in figure 2 where the angle of attack between the launcher axis and the relative speed RV is noted i, the attitude \u03c8 , the angle of deflection \u03b2 (control input) and the wind velocity W (disturbance). The sensors allow to measure the attitude and its velocity whereas the actuators allow to control the angle of deflection for the thrusters. The challenge of such a control issue is to minimize the angle of attack i since it cannot be measured. The closed-loop structure is given in figure 3. The control design is performed along the guidance trajectory with several operating points: for each of them, a linear controller is performed according to the multiobjective algorithm presented in (Clement & Duc, 2000a) which uses Youla parameterization and LMI optimization"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003543_6.2006-6685-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003543_6.2006-6685-Figure1-1.png",
        "caption": "Figure 1. Coordinate system and error definition",
        "texts": [
            " The cost function of the general Model Predictive Control (MPC) is, J = \u03c6(X(N)) + N\u22121\u2211 i=0 Li(X(i), u(i)) (4) This function is composed of the costs on N steps into the future from the current step. To simplify the notation, the current time is set to zero, here. \u03c6(\u00b7) denotes the cost on the final state and Li(\u00b7) represents the cost on the state and input from 0 to N \u2212 1 steps. Suppose that the desired trajectory of the UAV is a line denoted by aLxdesired + bLydesired + cL = 0. (5) Let \u03b4 denote the deviation of the UAV position from the desired line in Figure 1. Then \u03b4 can be calculated by: \u03b4 = |aLx + bLy + cL|\u221a a2 L + b2 L . (6) The cost function J is composed of the sum of the squares of the predicted \u03b4, heading angle errors, and control inputs for the next N time steps. J = S\u03b4 (aLx(N) + bLy(N) + cL)2 (a2 L + b2 L) + S\u03c8(\u03c8(N)\u2212 \u03c8d)2 + N\u22121\u2211 i=0 {Q\u03b4 (aLx(i) + bLy(i) + cL)2 (a2 L + b2 L) + Q\u03c8(\u03c8(i)\u2212 \u03c8d)2 + u(i)T Ru(i)} (7) where \u03c8d represents the angle between the x axis and the desired direction of the line. The second term of the right hand side of (7) forces the UAV to follow the line in a desired direction \u03c8d, not \u2212\u03c8d, with the weights defined by S\u03c8 and Q\u03c8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003794_ac0606150-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003794_ac0606150-Figure1-1.png",
        "caption": "Figure 1. Schematic diagram of visible ATR spectrum measurement system with SOWG. 1, Xe arc lamp; 2, convex lens; 3, optical fiber; 4, slide glass; 5, flow cell; 6, coupling prism; 7, guiding layer (fused silica sheet, 50 \u00b5m thick, nD ) 1.459); 8, poly(tetrafluoroethyleneco-hexafluoropropylene film (25 \u00b5m thick, nD ) 1.338); 9, sample inlet; 10, sample outlet; 11, sample injector; 12, HPLC pump; 13, multichannel CCD detector; 14, personal computer; \u03b8i, incident angle of source light.",
        "texts": [
            " (3-Methacryloxypropyl)trimethoxysilane used for chemically anchoring the sensing membrane fabricated onto a waveguide glass was purchased from Shin-etsu Chemicals (Tokyo, Japan). These reagents were of commercially available highest purity and used as received. Nitric acid, hydrochloric acid, and inorganic salts were of reagent grade from Wako Pure Chemicals (Osaka, Japan). Deionized water was prepared with a Millipore Milli-Q system (Milford, MA). Apparatus. A schematic illustration of a visible ATR spectrum measurement system is shown in Figure 1. The system used was basically similar to that in our previous paper.15 An economical (17) Edmiston, P. L.; Lee, J. E.; Wood, L. L.; Saavedra, S. S. J. Phys. Chem. 1996, 100, 775-784. (18) Puyol, M.; Miltsov, S.; Salinas, I.; Alonso, J. Anal. Chem. 2002, 74, 570- 576. (19) Hazneci, C.; Ertekin, K.; Yenigul, B.; Cetinkaya, E. Dyes Pigm. 2004, 62, 35-41. (20) Hisamoto, H.; Tsubuku, M.; Enomoto, T.; Watanabe, K.; Kawaguchi, H.; Koike, Y.; Suzuki, K. Anal. Chem. 1996, 68, 3871-3878. (21) Hisamoto H"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000069_j100038a044-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000069_j100038a044-Figure1-1.png",
        "caption": "Figure 1. Cyclic voltammograms of Fc (0.001 M) solubilized in Triton X-100 micelles (0.05 M) at pH 7.0 and 25 \"C (a) in the absence and (b) in the presence of GO (0.945 x M) and D-glucose (0.1 M). Scan rate is 2 mV s-' and EtOH is 5%.",
        "texts": [],
        "surrounding_texts": [
            "14072 J. Phys. Chem. 1995,99, 14072-14077\nMechanism of a \u201cJumping Off\u2019 Ferricenium in Glucose Oxidase-D-Glucose-Ferrocene Micellar Electrochemical Systems\nAlexander D. Ryabov,*,t,* Anton Amon>$ Raisa K. Gorbatova,\u2019 Ekaterina S. Ryabova? and Boris B. Gnedenko\u201d Division of Chemistry, G. V. Plekhanov Russian Economic Academy, Stremyanny per. 28, 113054, Moscow, Russia, Department of Chemistry, M. V. Lomonosov Moscow State University, 000958, Moscow, Russia, and Chemobyl Test Center Ltd., Rimsky-Korsakov St. 10, 127577, Moscow, Russia\nReceived: April 4, 1995; In Final Form: June 10, 1 9 9 9\nIncorporation of ferrocene (Fc), decamethylferrocene (DMFc), and n-dodecylferrocene (DDFc) into inner cavities of anionic, cationic, and nonionic micelles in aqueous solution tunes their observed redox potentials E112. The cyclic voltammetry study showed that anionic micelles of sodium dodecylsulfate (SDS) decrease while cationic and nonionic micelles of cetyltrimethylammonium bromide (CTAB) and Triton X- 100, in contrast, increase E112 of Fc. The effect of positively and negatively charged micelles on El12 in the case of DMFc was basically the same. Thus, solubilized ferrocene, but not its decamethyl and dodecyl analogs, couples electrochemically with glucose oxidase and provides a significant catalytic current in the presence of D-glucose. The rate constants for the oxidation of the reduced enzyme by the ferricenium ion are independent of the nature of the surfactant and, in the presence of 5% EtOH, fall in the range (4.3-5.7) x lo5 M-\u2019 s-I. Based on this observation, a mechanism of the \u201cjumping off\u2019 ferricenium is presented and discussed. It is believed that Fc+ is captured by the enzyme in the rate-limiting step after its fast reversible dissociation from the micelle. The absence of such a coupling for n-dodecylferrocene in the Triton X-100 and CTAB micelles suggests that the \u201cjump off\u2019 is likely hampered by the hydrophobic side chain of this ferrocene derivative.\nIntroduction Micellar systems are customary in electrochemistry192 and bi~chemistry.~-~ The interfacial field, which might be termed as micellar bioelectrochemistry, is a much less developed area,6v7 and this report is an attempt to fill this gap with some knowledge possibly useful for creating novel bioelectrochemical assemblies, designing water-insoluble electron-transfer mediators, and understanding mechanisms of bioelectrocatalysis in such rather complicated supramolecular systems. Here, we will describe properties of and provide some mechanistic insights into the well-known bioelectrochemical system glucose oxidase-Dglucose-ferrocene,8-10 the only difference of which compared to all previous reports is that intact ferrocene and its alkylated derivatives shown in Chart 1 are solubilized by neutral, negatively, and positively charged micelles of nonionic (Triton X-loo), anionic (SDS), and cationic (CTAB)\u201d surfactants in aqueous solutions. Our current interests are associated with various aspects of organometallic biochemistry.10*12 In this context, the present study had several objectives. It has been shown two decades ago that ferrocene solubilized by the nonionic surfactant, Tween 20, is an excellent mediator-titrant for cytochrome c and cytochrome c oxidase>a*c Therefore, micellar ferrocene systems, as well as other related assemblies incorporating poorly watersoluble electron transfer mediators, could be advantageous for coupling with glucose oxidase. A principal idea of the second objective is summarized in Scheme 1. Micelles of ionic surfactants are charged. The same is true for biomolecules and oxidoreductases in particular. It could thus be possible to tune the capability of one and the same mediator to couple with an\nG. V. Plekhanov Russian Economic Academy. * Moscow State University. 9 IAESTE exchange student from the BOKU Universitat, Wien, Austria. II Chernobyl Test Center Ltd. @ Abstract published in Advance ACS Abstracts, August 15, 1995.\n0022-3654/95/2099- 14072$09.00/0\nCHART 1\nFc DMFc 1 -n-Bu-1 \u2019-(C0OH)Fc DDFc\nSCHEME 1\n0- Fc** \u201d\u0302o\noxidase by varying the micelle charge, since the charge of the water-soluble mediator is known to be crucial in determining the rate of the electron abstraction from reduced GO.13 It should also be noted that the values of pH around the isoelectric points (PI) of redox enzymes, likewise other proteins, are usually weakly acidic, neutral, or weakly basic. For example, the PI of GO equals 4.0.14 The net charge of GO can thus be adjusted by a simple pH change in the region of PI. If a redox mediator is comicellized with an ionic surfactant, the electrostatic effects could determine the rate of its interaction with the enzyme. We will, however, show that, because of a peculiar mechanism, the reactivity of solubilized ferrocene is insensitive to the micelle charge.\n0 1995 American Chemical Society",
            "Glucose Oxidase-D-Glucose-Ferrocene Systems\nExperimental Section\nApparatus and Reagents. Electrochemical voltammetric measurements were made in a three-electrode cell with a pyrographite working electrode. Potentials are vs SCE throughout. Other details are described in our recent pub1i~ation.l~ Glucose oxidase @-D-glucose: oxygen oxidoreductase, EC 1.1.3.4) from Aspergillus niger was purchased from Serva and standardized as described elsewhereI6 using the extinction coefficient of 1.31 x lo4 M-' cm-' at 450 nm for the catalytically active FAD. Thus, the obtained concentration of the active enzyme was used for calculating the rate constants k3. Ferrocene and decamethylferrocene were obtained from Reakhim and Aldrich, respectively. 1-n-Butyl-1'-hydroxycarbonylferrocene and n-dodecylferrocene were kindly provided by Dr. M. D. Reshetova. SDS, CTAB, and Triton X-100 were Serva, Chemapol, and Aldrich reagents, respectively. Inorganic salts, mineral acids, and other chemicals were Reakhim reagents which in some cases were additionally purified according to standard procedure^.'^ Micellar solutions of ferrocenes in the presence of alcohols were prepared as follows. Ferrocene was first dissolved in EtOH, and this solution was then added to buffered (0.01 M phosphate for SDS and 0.1 M phosphate for CTAB and Triton X-100, pH 7.0) micellar solutions of SDS, CTAB, or Triton X-100. The concentration of Fc in the final mixture was 0.001 M, and the content of EtOH was 5%. DDFc was initially dissolved in MeOH. Its final concentration in Triton X-100 micellar solutions was 3.3 x M at [MeOH] = 5% (by volume). DMFc was f is t dissolved in n - M H . Its final concentration in aqueous micellar solutions was 0.0001 M at [ n - M H ] = 10% (by volume). The SDS solutions of Fc were stable at 25 OC at least for 24 h, and no precipitate of ferrocenes was observed in the case of CTAB and Triton X-100 micelles. Alcohol-free micellar CTAB and Triton X-100 solutions of ferrocene were prepared by stirring overnight a weighted amount of Fc in the surfactant (0.05 M) buffered solution (0.1 M phosphate). SDS does not form stable solutions without EtOH even at a lower phosphate concentration.\nJ. Phys. Chem., Vol. 99, No. 38, 1995 14073\nResults\nElectrochemical Behavior of Fc in Micellar Systems. We share the views of Brajter-Toth that shifts in Eln due to partitioining can be useful for regulating reactivity.I8 Therefore, the electrochemical behavior of ferrocenes in micelles of different charge in the presence of 5% EtOH has been studied keeping in mind that changes in Ell2 may affect the interaction with GO. The representative data obtained in this work are in Figures l a and 2. The former shows the voltammetric trace of Fc incorporated into micelles of Triton X-100. Figure 2 indicates that the half-wave potential Eln, defined as a midpoint between the anodic and cathodic maxima, (1/2)(Epa + EF), is a function of both the nature and the concentrations of Triton X-100, SDS, and CTAB in solution. The effect of surfactants on the behavior of redox-active species has been studied by several groups of researcher^.'^-^^ Our data are in general agreement with the results of other workers, although the experimental conditions were not always identical. In particular, we used pyrolytic graphite as an electrode exposed to water with its basal plane. The graphite seems to be very advantageous for electrochemical studies in micellar systems, since in this case \"the surfactant assembly is thought to be more micellelike and di~ordered\".~~ In accord with this, the current characteristics were not affected by the adsorption of surfactants on electrode surface. Only in the SDS case the anodic Fc maximum was sometimes followed by a smaller peak, probably of adsorptive origin. The plots of the limiting current i, against\nthe square root of the scan rate (v ) are linear for all surfactants studied in the range 2-50 mV s-l, indicative of the absence of adsorption at the hydrophobic surface of the working electrode. This is also in accord with the report of Kamau et al., who showed that the CTAB micelles protect Fc from adsorption on pt electrode^.^^\nThe peak separation (Epa - Epc) is only slightly dependent on surfactant concentration and the scan rate. In particular, it is 40 and 58 mV at [SDS] = 0.1 M at scan rates 2 and 40 mV s-', respectively. In the case of CTAB, the corresponding values are 52 and 67 mV. A tentative rationale for the peak separation being lower than 59 mV at low scan rates is that a micelle with incorporated ferrocenes might sometimes behave as a two-electron mediator under the conditions used. An attractive feature of these systems, which was discussed by other workers in more detai1,'9-25,27,28 is the dependence of the observed redox potentials E I ~ of comicellized Fc on the nature and concentration of surfactant (Figure 2). The variation of El12 depends on the detergent charge. Anionic SDS reduces while cationic CTAB and nonionic Triton X-100 increase the observed redox potential. The values of E1n level off at high surfactant concentrations (Figure 2). To get a formalized feeling of the limiting values of E1/2,-, the data obtained mostly in the presence of spherical micelles31 were fitted to eq 1.\nE112,o + acE112.-\nEl/, = 1 + a c",
            "14074 J. Phys. Chem., Vol. 99, No. 38, 1995\nRyabov et al.\nHere, E1/2,0 is the redox potential in the absence of surfactant, c stands for the surfactant concentration, and a is a parameter. The best fit values for E112,0, E,/,,-, and a are summarized in Table 1. The largest difference in E112,- is caused by SDS and Triton X-100 micelles and is as high as 189 mV. The effect observed is comparable to that in the case of methylviologen solubilized in 70 mM SDS and CTAB, which was 40 and 170 mV for the first and the second reduction, re~pectively.~~\nThe results reported both here and in the literature reveal that the redox potentials are always increased in the presence of CTAB, while the effect of SDS is variable. As seen in Figure 2, SDS micelles decrease the potential of Fc. The same is observed for methyl~iologen,~~ while for the O~(3+/2+) '~ and related Co(3+/2+) complexes there is an increase in E112 as in the case of CTAB micelle^.^^^^^ A qualitative rationale for variation in E112 for Fc might readily be proposed, at least in the case of SDS and CTAB micelles. The oxidation is easier when a redox probe is incorporated into the anionic assembly, which has a stronger affinity to the anode compared to the cationic aggregate. Altematively, stabilization of the oxidized product in the Stem layer of the negatively charged SDS micelle can also contribute to the reduction of the redox potential.\nA quantitative rationalization of dependencies such as in Figure 2 is not an easy task. Attempts have previously been made,'9-24,28 but a complete analysis, with limited assumptions, is still rather complicated. The most generally accepted, key equation which is commonly used for rationalization of the effect of surfactants or microemulsions on observed redox potentials is given by eq 2.'9921328\nE,,, = + (RTl2nF) ln(DR/Do) + (RTInF) ln[Ko(KR + l)/KR(Ko + l)] (2)\nHere, KR and KO are the partition coefficients between aqueous and micellar phases of the reduced and oxidized species, respectively, and DR and DO are the diffusion coefficients of the reduced and oxidized species, respectively. It is a common assumption in the ferrocene case, which is based on substantial aqueous solubility of Fc+, that KO > 1. Equation 2 simplifies to28\nE, , = + (RT/2nF) ln(DR/Do) + (RT/nF) h[(KR + l)/KR] (3)\nIn principle, eq 3 accounts well for the increase in E112 by increasing the amount of surfactant,2s since & becomes bigger at higher surfactant concentrations while DO remains constant. The situation is less obvious in the case of SDS (Figure 2). It appears that a positively charged ferricenium ion has an enhanced affinity toward negatively charged SDS micelles, and hence, the relative values of DRIDo and &/KO are different.\nBehavior of DMFc and DDFc in Micellar Systems. Decamethylferrocene is oxidized by 570 mV more cathodically than Fc in CHZC~,.~, Its self-exchange +IO rate constant in MeCN is also higher,33 viz. 3.8 x lo7 vs 5.3 x lo6 M-' s-l for F c . ~ ~ DMFc is more hydrophobic and thus deserves a comparative electrochemical and bioelectrochemical study in micellar solutions. The electrochemistry of DMFc was inves-\ntigated under similar conditions, but in the presence of n-PrOH which was used for solubilization. The final concentration of DMFc in solution was 1 x M at a total content of 10% n-PrOH by volume. In fact, this system is reminiscent of a microemulsion rather than a true micellar solution. A typical voltammogram of DMFc under such conditions is shown in Figure 3a. The effect of positively and negatively charged micelles on E112 was basically the same as that for Fc. SDS and CTAB micelles decreased and increased the values of El/,, and the limiting values were ca. -160 f 15 and -60 f 10 mV, respectively. The main dissimilarity was a higher peak separation, ca. 70 mV, which decreased with increasing [SDS]. Such an electrochemical behavior of DMFc contrasts to that in nonaqueous media were it is truly re~ers ib le .~ , ,~~\nDodecylferrocene was chosen for electrochemical studies in micellar systems on the following grounds. Obviously, its long hydrocarbon chain is an anchor that precludes KO > 1. In other words, DDFc will probably be bound to micelles in the oxidized form as well. It could still be a substrate of GO, since monosubstituted ferrocenes do usually couple electrochemically with the enzyme.8 DDFc is reasonably soluble in the Triton X-100 micelles. Its electrochemistry can be rationalized as reversible under these conditions. In particular, the peak separation was 55-60 mV with E112 at 294 mV. The peak current was a linear function of YI/, in the range 2-50 mV s-,. There was no true reversibility in CTAB micelles at [DDFc] = 5 x M. Cyclic voltammograms of such solutions showed that E1/2 is close to 345 mV. The reduction peak was broader compared to the oxidation one. Correspondingly, the cathodic peak current was about 30% lower.\nBioelectrochemistry in Micellar Systems. As seen in Figure lb, the ferrocene current in micellar solutions does strongly increase in the presence of GO and D-glucose. The \"bioelectrochemical\" voltammogram of Fc in Triton X-100 micelles matches such water-soluble ferrocene derivatives.8-'0 Similar voltammograms were observed in the presence of CTAB and SDS micelles. However, the catalytic current was not observed when micellar solutions of DMFc or DDFc were tested in the presence of GO and D-glucose (Figure 3). DMFc and DDFc are inappropriate for electrochemical coupling with GO. There was also no catalytic current in a micelle-free system when the solubility of DMFc was increased by the addition of a larger amount of the alcohol (30%) into the aqueous buffered solution.\nThus, there is an interaction between two supramolecular associates, viz. GO and a Fc-containing micelle. And is it"
        ]
    },
    {
        "image_filename": "designv11_11_0000080_1.2834409-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000080_1.2834409-Figure1-1.png",
        "caption": "Fig. 1 Schematic of inside pressurized beliows type mechanical seal",
        "texts": [
            " Then, existing dy namic analyses (extended, to account for partial contact) could be used to check the stability and tracking at various times during the transient, using the previously computed coning as input. In the present work, the model is applied to a particular seal, under particular operating conditions, and subjected to a particular transient, to illustrate its use and to display some of the types of seal behavior one can expect during transient operations. However, the model is intended to be applicable to a wide variety of seals, operating conditions, and transients. Analysis Figure 1 contains a schematic of an inside pressurized bel lows type mechanical seal, commonly used in the aerospace industry. It is assumed that the seal is axisymmetric, perfectly aligned, stable, and experiences only axial translation. Considering the equation of axial motion of the stator assem bly, order of magnitude estimates for practical operating tran sients indicate that the inertial term (the product of the mass and acceleration) is at least six orders of magnitude smaller than the individual forces acting on the stator",
            " When little or no contact occurs, solutions are faster than when significant contact occurs. The speed of the analysis is not significantly affected by the inclusion of the squeeze film term. Typical CPU times for the liquid analysis vary between thirty and sixty seconds per time step. The gas analysis requires times varying between forty-five and ninety seconds per time step. Results The analysis, described above, has been applied to the inside pressurized bellows seal, schematically shown in Fig. 1, op erating with gas. This seal is used on an executive turbojet engine. The rotor is 440c steel; the stator is carbon graphite; and the retainer is a metal alloy with an elastic modulus of 148 GPa, Poisson's ratio of 0.12, thermal conductivity of 10.7 W/ m-K, and thermal expansion coefficient of 4.6 X 10\"^ K ' . The sealed fluid is treated as air at 180\u00b0C. A typical steady-state operating condition consists of a shaft speed of 3.351 X 10' rad/s (32,000 rpm), a sealed pressure of 6 X 10^ Pa, and an ambient pressure of 10^ Pa",
            " Figure 11 also shows that the leakage rate decreases rapidly during the first 2.5 seconds of the deceleration (when the seal is noncontacting), and then much more slowly (when the seal is contacting). Again, parallel observations can be made for the acceleration portion of the transient. While coned seal face profiles can be expected early in the life of a seal, the wear of contacting seal faces results in parallel faces late in life (Lebeck, 1980). Simulations of the inside pressurized seal of Fig. 1 with parallel faces are discussed be low. Journal of Tribology APRIL 1998, Vol. 120 / 195 Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Fig. 11 Leal<age rate history, outside pressurized seal Time (s) Under steady-state conditions the film thickness is 0.37 mi crons and the contact pressure distribution is uniform, as seen in Fig. 12. The film pressure distribution is almost linear, with film pressures substantially higher than contact pressures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000235_1.601679-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000235_1.601679-Figure1-1.png",
        "caption": "Fig. 1 Domain D discretized into finite elements; a simplified mesh is shown for clarity.",
        "texts": [
            " This reduction replaces continuous PDE, whose solution space is generally infinite dimensional, with a finite set of algebraic equations whose solution space is finite dimensional. In general, the reduction of continuous PDE into a set of discrete algebraic equations is performed by identifying a finite number of discrete points within the domain of interest. These points are called nodes and it is at these locations that approximations to the true solution are computed. For instance, consider the FE method in which the domain of interest is fully discretized into finite elements ~Fig. 1!. In the case of structural problems and a displacement formulation, the deformation field on each element is written in terms of known interpolating functions and unknown nodal displacements. By considering element e in the domain D of Fig. 1, coordinates (x ,y) and displacements (u ,v) within the element can be written, using 2-D isoparametric elements, as x5( i51 NN Nixi , y5( i51 NN Niy i , ~1! and u5( i51 NN Niui , v5( i51 NN Niv i , ~2! where NN is the number of nodes in the element; (xi ,yi) and (ui ,v i) are the nodal coordinates and unknown nodal displacements, respectively; and Ni represents the interpolating or shape functions, which for a linear approximation can be written as Ni5 1 4 ~11jj i!~11hh i!, ~3! oaded From: http://opticalengineering"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003321_00207170500036225-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003321_00207170500036225-Figure1-1.png",
        "caption": "Figure 1. Harmonic drive gear components (a) and assembly (b) (Harmonic Drive AG 1995).",
        "texts": [
            " The proposed control development is based on recent results on the integral manifold approach and guarantees asymptotic stability. We present simulation and experimental results to further demonstrate the effectiveness of our approach for practical application. Our results thus establish a solid basis for high-speed, high-precision control design for harmonic drive systems. Harmonic drives are special flexible gear transmission systems developed during the mid-1950s (Musser 1955, 1960) and modified thereafter. The modified version is composed of components identified in figure 1(a) (Harmonic Drive AG 1995). The wave generator is a rigid steel core having an elliptical shape with very small eccentricity. It is surrounded by a flexible race ball bearing. The flexible spline (or flexspline) is a thin-walled hollow cup made up of alloy steel. External gear teeth are machined at the open end of this cup while the closed end is connected to the output shaft. The circular spline is a rigid internal gear having two teeth more than those on the flexspline. Upon assembly, the wave generator fits into the open end of the flexspline cup and gives it an elliptical shape at that end. The circular spline teeth then mesh with the flexspline teeth at the major axis of the ellipse defined by the wave generator. A fully assembled harmonic drive is shown in figure 1(b). In the most common speed reduction configuration, the wave generator serves as the input port, the flexspline acts as the output port and the circular spline is held immobile. Details of harmonic drive operation can be found in Harmonic Drive AG (1995) and Gandhi (2001). Typical construction of harmonic drives with meshing at two diametrically opposite ends gives them many useful properties. These include compact design with less weight, higher gear reduction with almost zero backlash, and higher torque-to-weight ratio"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002204_s1474-6670(17)31748-2-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002204_s1474-6670(17)31748-2-Figure8-1.png",
        "caption": "Fig. 8 Simulation and evaluation period for optimization",
        "texts": [
            " To reduce the future tracking error for the optimal course, we optimize the following receding horizon cost function J (Allgower and Zheng, 2000). N J= LIYJr)-Y,(r)1 (23) r =M where, f a(r) denotes the optimal deviation of the minimum-time solution and Y, (r) is the simulated one of the controlled ship. First, the MMG model based simulation is carried out assuming the rudder compensation ~8 as an appropriate setting for the future time period [t, N] and the value of J is calculated as the \"error area\" for receding horizon [M, N] as shown in Fig. 8. Next, to optimize the cost function, the simulation and evaluation are repeated based on the linear search as shown in Fig. 9. 4. PRELIMINARY EVALUATIONS BY COMPUTER SIMULA TlONS Before implementing the proposed minimum-time maneuvering system, computer simulations of both basic and proposed scheme are perfonned for non linear dynamical model of the Shioji Maru . Figure 10 and 11 show the simulation results for mInImum-time deviation problem with wind disturbances by using basic (NN only) and proposed (NN+model predictive compensator) control system respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001933_6.2003-5729-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001933_6.2003-5729-Figure7-1.png",
        "caption": "Fig. 7 Obstacle avoidance",
        "texts": [
            " \u2022 Arrival Arrival is seek with zero velocity at the target point. Thus arrival command will slow down the boid when it is inside a specified radius. Figure 6 shows the arrival behavior. For an ordinary aircraft a slow down to zero speed will result in stall, so it may only be used for vehicles with hover capabilities. \u2022 Obstacle Avoidance Obstacle avoidance looks ahead for obstacles that are in the way and steers before the boid reaches the obstacle. Any obstacles that intersect the search cylinder in the forward direction is considered. Figure 7 shows the obstacle avoidance behavior. \u2022 Wander Wandering is doing a random walk steering. Reynolds has proposed to add a random steering amount to the surface of a steering sphere in front of the the boid. Wander behavior can be useful for searching something. \u2022 Path Following Path following is developed to move the boids through a predetermined path. This was developed to simulate people walking down a corridor. Path following behavior will predict the future position based on current velocity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000516_20.952635-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000516_20.952635-Figure5-1.png",
        "caption": "Fig. 5. Equipotential lines of the analysis model before the voltage is turned off.",
        "texts": [
            " The second-order differential equation (6) combined with Houbolt algorithm result in an equation, which needs to be solved to find the displacement. The step-by-step procedure is given below [10]. 1) From the known initial conditions and , find using (7). (7) 2) Select a suitable time step 3) Determine using (8). (8) 4) Find and using the central difference equation (9). (9) 5) Compute , starting with the and using (10). (10) The initial value of node displacement is zero. The rotor has a residual unbalance mass of 10 (g mm) and the rotation speed is 2000 (rpm). Fig. 5 shows the equipotential lines of the analysis model just before the phase is turned off. In order to simply the magnetic field analysis, a half model with about 4532 triangle elements is used. Fig. 6 shows the instantaneous global radial magnetic for one phase excitation when the air gap is uniform without the eccentricity. This radial force as a faction of time is obtained by the electromagnetic FEM using time stepping. This rapidly change of the radial force can excite the rotor and stator so that the vibration become severe"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003192_icnsc.2005.1461232-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003192_icnsc.2005.1461232-Figure2-1.png",
        "caption": "Fig. 2. Adding a control node to the graph.",
        "texts": [
            "1: Let A be a set of agents with bk = 1, b, = 0,Vi # k , and u k ( t ) = kp(csp - Ek) where ESP is a constant setpoint and k , > 0 is a constant gain. Then the consensus strategy of (4) achieves global asymptotic consensus for A, with if and only if node k is a spanning node for the communication graph G . PrOOf Necessity: It is easily shown by counterexample that consensus is not achieved if node k is not a spanning node. Suficiency: Assume node k is a spanning node. The control law uk(t) = k p ( ( \" P - bTE) is equivalent to adding a new node to the graph, as shown in Fig. 2. This node can be interpreted as a node with no incoming links that communicates only with node k. Also, if node k is a spanning node, then so is the added new node. Further, we note that iSp = 0. Thus we can write the new graph, or, equivalentIy, the \"closed-loop system\" as . = Ccl( t; ) Now, it is easily seen that that bbT is zero except for the kk entry, which is IC,. Thus, we can argue that every row in Ccl sums to zero, its diagonal elements are non-negative, its offdiagonal elements are positive, and it has a spanning tree. Thus, the properties PI mentioned above are satisfied. But, because the new node has no incoming links, by Lemma 2.2 we know all go to the same value, which in this case Figure 3 illustrates this result for the the communication topology shown in Fig. 2, with all non-zero gains k , = 1, for kp = 1, and starting from an arbitrary set of initial conditions. The setpoint ESP is zero until t = 15, at which point it is changed to E S P = 5. It can be seen that initially the agents negotiate to a consensus value of zero, but after application of the forcing input the states all converge to must be E\",. & = 5. IV. MULTIPLE, CONSTRAINED CONSENSUS VARIABLES In many applications it is the case that a single coordination variable cannot capture the information required for the team objective to be achieved"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002266_ijmee.31.2.5-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002266_ijmee.31.2.5-Figure2-1.png",
        "caption": "Fig. 2 A schematic for derivation of eqn (10).",
        "texts": [
            " Otherwise, as will be shown later, incorrect results will be obtained. The physical curvature of a beam differs from the mathematical curvature in that a certain x coordinate on a physical curve corresponds to the same material point, as opposed to the mathematical curvature case [17]. The physical curvature can also be obtained from eqn (2). A different notation will be used for elastic displacements. Elastic displacements of any point on the median line of a beam in the x and y directions are denoted as u and v, respectively. Consider Fig. 2, which shows the final (or instantaneous, in a dynamic case) positions of two points which were infinitesimally close to each other before deformation. It is obvious that the following relationships exist: (7) and tan q = + d d d d v x u x 1 k = + \u00ca \u00cb \u02c6 \u00af \u00c8 \u00ce\u00cd \u02d8 \u02da\u0307 d d d d 2 y x y x 2 2 3 2 1 d d d d d d 2 q t y x y x = + \u00ca \u00cb \u02c6 \u00af 2 2 1 International Journal of Mechanical Engineering Education 31/2 at HEC Montreal on July 10, 2015ijj.sagepub.comDownloaded from International Journal of Mechanical Engineering Education 31/2 (8) Note that dr approaches ds at the limit"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000951_papcon.1993.255813-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000951_papcon.1993.255813-Figure12-1.png",
        "caption": "Figure 12 Excessive Thrust on a Spherical Ro l l e r Bearing",
        "texts": [],
        "surrounding_texts": [
            "NEW TECHNOLOGIES\nOne o f the newer l u b r i c a t i o n schemes i s the O i l - A i r method. The O i l - A i r l u b r i c a t i o n method was developed f o r high speed spindles where temperature r i s e was t o be kept t o a minimum. I t i s used i n place o f grease, je t , and o i l m is t and requires the Least amount o f lubr ican t 111. O i l - A i r l u b r i c a t i o n consists o f supplying 0.01- 0.06 m l . o f o i l per f i x e d t ime unit by compressed a i r t o the bearing. I t i s growing i n p o p u l a r i t y because i t i s more s t a b l e and requires less o i l than t h e o i l - m i s t method. O i l - A i r l u b r i c a t i o n has a maximum speed L i m i t which i s considerably higher than grease. Above t h i s l i m i t , j e t l u b r i c a t i o n i s used t o minimize temperature r i s e and c a r r y heat generated away from the bearing. Jet l u b r i c a t i o n requires about 3 - 4 L i t e r s h i n U t e o f lubr ican t per bearing.\nFor those pushing the s t a t e o f the a r t , Ceramic b a l l s may be the answer t o boost ing speed and lowering losses. Ceramic b a l l s weigh approximately 60% less than s tee l balLs, and therefore, t h e c e n t r i f u g a l fo rce i s s i g n i f i c a n t l y reduced. The reduced fo rce a l t e r s the bearing loss charac ter is t i cs and r e s u l t s i n lower losses and temperature r i s e . I n addi t ion, ceramic bearing par ts a re cor ros ion res is tan t , have a higher temperature range, higher hardness (78 Rockwell C ) , and higher s t i f f n e s s . With respect t o operat ing l i m i t s , Figure 7 [ I ] dep ic ts the present s ta tus f o r h igh speed spindle bearings.\nREFERENCE LIBRARY\nOne o f the best methods t o a s s i s t i n the analysis of bearing f a i l u r e s i s t o develop a reference l i b r a r y of p ic tu res o f known causes of bearing fa i lu res . The fo l low ing i s a sample o f some o f the more t y p i c a l types o f f a i l u r e s .\nFatigue Fa i lu res\n1. I n c i p i e n t 2. Advance 3 . Extreme\nMisalignment\n1. Load Paths 2. Out-of-Round 3 . Skewed Paths 4 . Edge Loading 5 . Smearing\nDefect ive Fits/Seats\n1. Loss o f In te rna l Clearance 2. Loose F i t s 3 . Skidding 4 . Creep 5. F r e t t i n g Corrosion\nContamination\n1. Chips i n Race Way 2. Damaged/Faulty Seals 3 . Abrasion\nMechanical\n1. Mounting 2. Parasi te Thrust 3 . False B r i n e l l i n g 4 . True B r i n e l l i n g 5 . F l u t i n g from Rotat ional V ib ra t ion\nExcessive Temperature\nImproper Lubr ica t ion\nOverspeeding\nShaft Currents\n1. P i t t i n g 2. F lu t ing 3. Welding\nThe fo l low ing sect ion provides the reader w i th p ic tu res showing some of the more comnon bear ing f a i lures l i s t e d above.\nDe fec t i ve F i t s / S e a t s\n43",
            "Fatique Mechanical\nEa r l y Stages o f Spa l l i ng Caused by Excessive Preload",
            "Contamination Temperature\nSmear Marks on Ro l l e r Caused by Debris\nFigure 18\nDamaged Caused by Water In t rus ion\nFigure 19\nThe Bibl iography contains references tha t w i i L provide the reader addi t ional p ic tures o f f a i l u r e s .\n45"
        ]
    },
    {
        "image_filename": "designv11_11_0002668_05698190500414300-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002668_05698190500414300-Figure5-1.png",
        "caption": "Fig. 5\u2014(a) Forces and moments acting on a ball and coordinate systems, (b) traction force and sliding velocity acting on the area dXdY of the elliptical contact surface at point B \u2032.",
        "texts": [
            " The ball sliding velocity at pointB\u2032, relative to the inner raceway velocity, is given as ViB\u2032 \u2212 VbB\u2032 = D 2 [ (\u03c9\u2212\u03c9c) ( cos \u03b1i \u2212 dm D ) +\u03c9b cos(\u03b1i \u2212\u03b2) ] j\u0302 [40] Let us define Vs \u2261 | VbB\u2032 \u2212 ViB\u2032 | To obtain the distributions of the sliding velocity formed in the contact area between a ball and the inner raceway, the component of the ball\u2019s spinning velocity relative to the inner raceway in the direction of the rB\u2032 vector is needed. It is stated as \u03c9si = ( \u03c9b \u2212 \u03c9i ) \u00b7 rB\u2032 | rB\u2032 | = (\u03c9c \u2212 \u03c9) sin \u03b1i + \u03c9b sin(\u03b2 \u2212 \u03b1i ) [41] Define a new coordinate system (X, Y, Z) such that the origin point is positioned at the center of the contact ellipse. The major axis of this ellipse is the X-axis, and the minor axis is the Y-axis in Fig. 5(a). As shown in Fig. 5(b), the ball sliding velocity relative to inner raceway is composed of two components. One component is the sliding velocity resulting from the ball spinning relative to the inner raceway; it is given the value of rs\u03c9si, where rs is the length of the rs vector that links the center of a small element dXdY and the center of the contact ellipse. Another component is the sliding velocity Vs , resulting from linear translation in the Y direction. The velocity component in the X direction is vX = \u2212\u03c9sirs sin \u03bb [42a] and the velocity component in the Y direction is vY = \u03c9si rs cos \u03bb + Vs [42b] Then the sliding velocity at the center of the small element, dXdY, is us = \u221a v2 X + v2 Y [43] Different lubricant film thicknesses are formed in the contact area between a ball and the inner raceway because of different sliding velocities",
            " [44] is given as (Kannel and Walowit (12)) \u03c4 = \u00b50use\u03b1\u2217 p tan\u22121( \u221a 2 ) h \u221a 2 [50] where the parameter is given as = us \u221a \u00b50\u03b3 \u2217e\u03b1\u2217 p 8Ka and Ka denotes the lubricant thermal conductivity and h represents the film thickness. The hydrodynamic pressure p in Eq. [44] or Eq. [50] is theoretically solved by the point-contact elastohydrodynamic lubrication (EHL) arising in the thin liquid film between a ball and its inner raceway. However, the simplification using the Hertzian contact pressure to replace the point-contact hydrodynamic pressure is necessary in order to alleviate very complicated numerical analyses for EHL. The Hertzian contact pressure formed in the projection area of the contact ellipse [Fig. 5(b)] with the length of a as the semimajor axis and the length of b as the semiminor axis is written as p = \u03c3max \u221a 1 \u2212 ( X a )2 \u2212 ( Y b )2 [51] where \u03c3max denotes the maximum Hertzian stress, \u03c3max = 3Qi 2\u03c0ab . The film thickness between the ball and the inner raceway varies with the position in the contact. In the present analysis, the minimum film thickness is adopted to replace the local film thickness h shown in Eq. [50]. Therefore, the average flash temperature obtained in this study is theoretically the highest of all contact temperatures in the contact area",
            " In the present study, the average of the maximum us max and the minimum us min(= 0) is taken as the value of us . Therefore, us = 1 2 (us max + us min) = 1 2 us max [56] then V = 1 2 us = 1 4 us max The dimensionless materials parameter, G, is defined as G \u2261 \u03b1\u2217 E\u2032 The elliptical parameter, k, is defined as k \u2261 ( RY RX ) 2 \u03c0 [57] The variables exhibited in the preceding four dimensionless parameters are RX, effective radius in the X direction, 1 RX = 1 D/2 \u2212 1 ri and RY, effective radius in the Y direction, 1 RY = 1 D/2 + 1 di/2 As Fig. 5(a) shows, the component of the traction force in the X direction, which is created between a ball and the inner raceway, is given as FX = \u222b a \u2212a \u222b b \u221a 1\u2212(X/a)2 \u2212b \u221a 1\u2212(X/a)2 \u03c4 sin \u03c6dYdX = 0 [58a] because the Xcomponent velocity of the contact area is symmetrical with respect to the Y axis. The component of the traction force in the Y direction is FY = \u222b a \u2212a \u222b b \u221a 1\u2212(X/a)2 \u2212b \u221a 1\u2212(X/a)2 \u03c4 cos \u03c6dYdX = ab \u222b 2\u03c0 0 \u222b 1 0 \u03c4 cos \u03c6\u03c1d\u03c1d\u03bb [58b] where \u03c1 = \u221a( X a )2 + ( Y b )2 X = a\u03c1 cos \u03bb, and Y = a\u03c1 sin \u03bb are satisfied",
            " The thermal effect seems insignificant to the ball\u2019s spinning velocity unless the cage\u2019s angular velocity is elevated to be sufficiently high. The effect of controlling the outer raceway temperature To on the ball\u2019s spinning angular velocity is investigated at three different values; the results are shown in Fig. 7(d). It shows the behavior that the ball\u2019s spinning velocity is elevated by raising the outer raceway temperature, especially at the bearing position angles near \u03c8 = 0\u25e6. The linear slip velocity Vs is defined to be the sliding velocity of a ball at point B\u2032 in Fig. 5(b), relative to the inner raceway. This velocity is moving parallel to the minor axis of the elliptical contact area. This slip velocity is held constant at a contact area but is varied with the bearing position angle. Pure rolling happens between the outer raceway and a ball if the ball bearing is assumed to be operating under the outer raceway control. However, under D ow nl oa de d by [ Fl or id a St at e U ni ve rs ity ] at 0 7: 21 0 7 O ct ob er 2 01 4 Fig. 7\u2014The ball\u2019s spinning angular velocity vs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001172_60.556361-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001172_60.556361-Figure1-1.png",
        "caption": "Fig. 1. Cross-sectional view of two phase iiiduction machine with shifted b-phase winding.",
        "texts": [
            " The multiple d a n c e f ime model is also used to a n a l p the effects of operating point ancl machine pamneters on the W e r function It will be show that the -er function contains a mnan t peak which becomes incxasingly accentuated as rotor speed in-. It is also shown that the resonant peak may be attenuated either by increasing the rotor inertia or by inmasing the rotor mistance. 11. MACHINE VARIABLE MODEL A machine variable model of a Wephase induction machine with non-orthogonal stator windings is set forth in this section. In this development it is asslnmed that the machine is sinusoidally excited, that the stator w\"gs are sinusoidally distributd, and that A mss-seciional diagmn of a 2-pole machine appears in Fig. 1. Therein, the stator and rotor whdings are designated as-as', bsbs', a r d , and br-br'. In the case of a -e-phase machine, the a-phase represents the main w\"g and the bphase the auxhry winding. As can be seen, the bphase stator \\nnding is shifted h m the quadrature psition by &,m &pes. The positive direction for the shift angle is opposite the direction of rotation. Mechanical rotor position and speed are denoted and corm, nqxdvely. The electrical b-phase stator shift + b , the electrical rotor position 0,, and the electrical rotor sperxl O r , are PE times the cOrreSpOnding mechanical quantities, where P denotes the number of magnetic poles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003251_j.memsci.2005.11.045-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003251_j.memsci.2005.11.045-Figure1-1.png",
        "caption": "Fig. 1. Three-compartment electrodialysis cell scheme.",
        "texts": [
            " All chemicals were reagent grade and were used as received. The zinc complex solutions were prepared mixing zinc oxide, sodium hydroxide and a minimal quantity of deionized water under stirring, until the dissolution of zinc oxide was observed [23]. After the dissolution, the volume was completed with deionized water. The same procedure was adopted to prepare solutions with cyanide. Sodium was analysed by flame photometry meanwhile cyanide and zinc were determined by titration [24,25]. The experiments were carried out in duplicate. Fig. 1 shows a scheme of the three-compartment cell used at the experiments. The electrodialysis experiments were conducted using mechanical stirring in all compartments. To the compartments C1 and C3 a sodium hydroxide solution 0.1 M was added. The work solution was placed in compartment C2. Table 1 presents the different work solutions. The sodium concentration in compartments C1 and C3 (0.1 M NaOH) was different from compartment C2 (2.2 M NaOH or 1 M NaCN). This difference was used in order to make the sodium transport through the anion-exchange membrane difficult"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002118_10402000308982642-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002118_10402000308982642-Figure1-1.png",
        "caption": "Fig. 1-Schernatlc of lip seal.",
        "texts": [
            " KEY WORDS Rotary Seals; Lip Seals; Elastohydrodynamic Lubrication; Surface Finish; Surface Roughness INTRODUCTION The rotary lip seal is the most widely used type of dynamic seal; large numbers of these seals are manufactured each year for use in the automotive, industrial and appliance industries, as well as in many other applications. Although much progress has been achieved in recent years in understanding the fundamental physics of lip seal behavior, there are still a number of significant aspects of the lip seal behavior that are not understood. The effect of shaft surface finish on lip seal behavior is one of those aspects. A schematic diagram of a lip seal is shown in Fig. 1. It has been known since the 1950's that a thin lubricating film of fluid exists between the rotating shaft and the lip surface (Jagger, (5)). This film prevents damage to the lip from excessive heat generation, and mechanical stresses at the lip-shaft interface. It is also known that the load support, necessary for maintaining the film, and the sealing mechanism, necessary for preventing leakage through the film, are produced by the microasperities on the lip Scheduled for Presentation at the 58th Annual Meeting in New York City April 28-May 1,2003 Final manuscript approved December 20,2002 Review led by Tom Lai surface in the sealing zone, between the lip and the shaft (Salant, (20))"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003686_j.ijmachtools.2005.10.017-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003686_j.ijmachtools.2005.10.017-Figure1-1.png",
        "caption": "Fig. 1. Model of micro-drilling machines.",
        "texts": [
            " Relationships between the bend deformation amplitude of the drills and the clamped length of the drills, stiffness and damping of the bearings, the spindle speed, the eccentricity, and axial drilling force are determined by analyzing the model. From this relationship, stresses on the weakest section are studied using the measured drilling axial force and torque. ARTICLE IN PRESS P. Yongchen et al. / International Journal of Machine Tools & Manufacture 46 (2006) 1892\u201319001894 The structure of a micro-drilling machine can be simplified as shown in Fig. 1. In Fig. 1, spindle A is supported by two identical isotropic bearings in radial direction; spindle A and drill clamp C\u2013D is connected by shaft B; micro-drill E\u2013F is fixed in the clamp D. Drill part with the screw slots is taken as uniform shaft F by equivalent of the bending stiffness. Structure dimensions and parameters of the model are shown in Table 1. The drilling process is considered in three cases [4] for analyzing: (a) a drill does not contact the workpiece; (b) a drill just contacts the workpiece; (c) a drill tip penetrates the workpiece. Firstly, spindle system in Fig. 1 is divided into the number of elements given in Table 1. Then, from the Lagrange equation and the rotor dynamics, the dynamic model of the elements is established using the Timoshenko beam element. Finally, the dynamic model of the drilling system is developed using the element model, the bearing model, and the corresponding boundary conditions. Since the stiffness of micro-drills is small and there is eccentricity in the drilling system, the micro-drill and spindle bend when the axial drilling force acts",
            " Stiffness and damping coefficients of the model are kx, cx in x-direction and ky,cy in y-direction, respectively. Assume that displacement and velocity of the bearing ARTICLE IN PRESS P. Yongchen et al. / International Journal of Machine Tools & Manufacture 46 (2006) 1892\u201319001896 center are xc; yc and _xc; _yc in x- and y-directions. The bearing force produces virtual work as dWb \u00bc dWb c \u00fe dWb k, (12) where dWb c \u00bc dqe u T cxfNbg TfNbg _q e u h \u00fe dqe v T cyfNbg TfNbg _q e v i , dWb k \u00bc dqe u T kxfNbg TfNbg qe u h \u00fe dqe v T kyfNbg TfNbg qe v i . \u00f013\u00de fNbg is value of fNg at s \u00bc b. From structure in Fig. 1, dynamic model of the drilling system is obtained using the finite element methods [8] and the above equations as \u00bdM f \u20acqug \u00fe O\u00bdC f _qvg \u00fe \u00bdK P Kp fqug \u00bc O2\u00f0 fF sing sin\u00f0Ot\u00de \u00fe fF cosg cos\u00f0Ot\u00de\u00de, \u00bdM f \u20acqvg O\u00bdC f _qug \u00fe \u00bdK P Kp fqvg \u00bc O2\u00f0fF sing cos\u00f0Ot\u00de \u00fe fF cosg sin\u00f0Ot\u00de\u00de. \u00f014\u00de The model includes effects of the rotational inertia, the gyroscopic moment, the centrifugal force, the axial drilling force, and the bearings on the bending deformation of the drilling system during machining. The correctness of Eq",
            " But, influence of the eccentricity on the dynamic stress is not obvious, and stress curves for different eccentricities are in superposition. This is because compared with the stresses produced by the axial drilling force and drilling torque, the stress caused by the bending is small and the proportion of drawing Fig. 5 is limited. The maximum dynamic stress occurs on segment F. This is because the diameter of segment F is the minimum in the drill system. Since there is the stress concentration at interface between segments E and F with the screw slots and diameter of segment F is small, as shown in Fig. 1, the interface is one of the critical sections for micro-drill strength. Now, the effects of several factors, such as the clamped length of micro-drills, the bearing stiffness and damping, the spindle speed, and the axial drilling force on the stress on the interface are analyzed as follows. Assume that span between the two bearings is L1 and length from drill tip to the bearing positioned down is L2, as shown in Fig. 1. The length that a micro-drill is fixed in the drill clamp is called as the clamed length. And, the length L2 depends on the clamped length mainly. Therefore, adjusting the clamped length of micro-drills changes length L2. Effect of changing length L2 on stress on the interface is analyzed using Eq. (21) when length L1 is constant, as shown in Fig. 6. The figure shows that there is a critical value for cantilever ratio L1/L2 of the drilling system. When L1/L2 is beyond the critical value, decreasing length L2 increases the stress rapidly (length L1 is structural parameter of a drilling machine, it is constant), that is the small-clamped length of micro-drills increases the stress"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002062_1.1825703-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002062_1.1825703-Figure3-1.png",
        "caption": "FIGURE 3 \u2014 Cross-sectional view of a multi-pixel test cell.",
        "texts": [
            " Secondly, the optical performance of the double-layer system will not depend on the thickness of the intermediate water layer as long as this is sufficiently thick to avoid mixing of the top and bottom oil layer to occur. This is highly advantageous when the electrowetting principle is used in flexible displays, since one of the most important difficulties in that case is the cell-gap thickness variations upon flexing of the display. A side view of a single-layer monochrome multi-pixel test cell is depicted in Fig. 3. As a substrate, we use aluminum-coated glass. The Al is patterned to obtain the required pixel structure. A submicron-thick amorphous fluoropolymer layer is deposited on the Al by dip-coating. The strong hydrophobic nature of this layer ensures the spreading of the oil film in the field-off state. The physical pixel structure is realized by photolithographic walls, whereas an outer PET seal contains the water. The water, forming a continuous phase throughout the test cell, acts as a common electrode",
            " After the dc voltage has been applied for 10 msec, the array shows a steady state, exhibiting a white area of about 60% [Fig. 7(b)]. Within 10 msec after the voltage is removed, the array returns to its original state, as shown by the final photograph [Fig. 7(c)]. In addition to the video-speed response, Fig. 7 shows that the pixel-to-pixel homogeneity with the current fabrication is quite good. As for any display principle, addressing will be an important aspect in the development of a final product. Several aspects of the addressing of electrowetting displays are worth mentioning here. As can be seen from Fig. 3, presumably activematrix addressing will be required. Currently, the voltages required for a high brightness optical state are about \u201315 to 296 Feenstra et al. / A video-speed reflective display based on electrowetting \u201320 V. Such a TFT backplane would add a significant cost to the final display, since these voltages are non-standard, i.e., higher than the ones typically used for LCDs. Moving to lower voltages, we need to reduce the thickness of the oil film and/or the insulator. For single cells, we have already operated pixels with a 3-V battery"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001618_robot.1998.680751-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001618_robot.1998.680751-Figure3-1.png",
        "caption": "Fig. 3: Definition of system variables for Gyrover.",
        "texts": [
            ", m } ( 6 ) d t a q j a g j s = where L = T - P is the Lagrangian function, Tis the total kinetic energy of the system, P is the total potential energy of the system, and each h, is a Lagrangian multiplier which accounts for the system constraints. To represent the Gyrover wheel, we require six coordinates, three for position (X, Y , Z ) and three for orientation (a , p, y) . The Euler angles (a , D, y ) represent the precession, lean and spin angles of the wheel, respectively, and are illustrated in Figure 3. 2.2 Coordinate transformation For the discussion below, let the inertial frame { X , Y , Z } be attached to the ground x-y plane, which represents a perfectly flat surface upon which the Gyrover wheel rolls (see Figure 4). Let the body coordinate frame { x B , yB , z B > be attached to the mass center of the wheel, where z B represents axis of rotation for the wheel. The composite rotation matrix which transforms the wheel from state 1 to state 2 in Figure 4 is given by R, , ure 3. If we assume perfect rolling without slip, vc = 0 and (13) reduces to, V A = W B X r A t C (14) vA = - R(y + &cp)m + RPn vA = X i + Y j + Z k , (17) X = R ( y c a + &cact i - fisasp) Y = R(Vsa + &cpsa + pcasp) Z = Rpcp (20) v A = {-&spI + &rz t (y + &cp)n} x {-RI} (15) (16) Transforming (16) to the inertial frame, we get the following expression for v A : where, (18) (19) Equations (18) through (20) represent the three velocity constraint equations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003747_j.bios.2006.04.005-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003747_j.bios.2006.04.005-Figure3-1.png",
        "caption": "Fig. 3. Structure of glycosylated porphyrin.",
        "texts": [],
        "surrounding_texts": [
            "4 d Bio\nu r p s a c a t a s o t a o t M d a a a m t a s o r A T i v\n2\n2\nf r t b P T 2\n2\nt s b B u a w a p 7 ( C ( ( ( ( ( t T\n2\n1 a s U p u 7\n2.2. Apparatus\nFluorescence measurements were carried out on a HITACHI F4500 fluorescence spectrophotometer (Japan). A peristatic\n24 F.-C. Gong et al. / Biosensors an\nsing platinum(II)-coproporphyrin label coupling with timeesolved fluorescence and evaluation of the phosphorescent alladium(II)-coproporphyrin labels in separation-free hybridiation assays, respectively (O\u2019Shea and Berney, 2005; Burke et l., 2003). The success of the aforementioned indicates the appliation potential of the supermolecular recognition of porphyrin nd metalloporphyrin in chemical and biological analysis. To he best of our knowledge, no efforts have been made on the pplication of the drug optical sensor incorporated with glycoylated metalloporphyrin in optode membrane for the detection f benzimidazole analogous species. Inspired by the success of he above outlined molecular recognition research, the present uthors tried to develop a drug sensor for LEV assay with a flurometric finish. In the present work, we make the first attempt o design and use a Mg(II) coordinating glycosylated porphyrin\ngT(o-glu)PPCl-based fluorescence sensor for selective LEV etection that does not require any specific preparation of the nalyte. The LEV sensor has been fabricated by including an ctive material MgT(o-glu)PPCl in chitosan matrice, which acts s a optode membrane for the optical fiber sensor. The response echanism of the sensor was investigated and the results showed hat its fluorescence quenching response was caused by the interction of LEV with MgT(o-glu)PPCl. Owing to the unique tructure of MgT(o-glu)PPCl, the MgT(o-glu)PPCl-modified ptode membrane showed excellent selectivity toward LEV with espect to a number of interferents and exhibited stable response. n improved selectivity for LEV detection has been realized. he prepared sensor is applied for the determination of LEV n pharmaceutical preparations and the results agreed with the alues obtained by the pharmacopoeia method.\n. Experimental\n.1. Materials and Reagents\nLevamisole (Fig. 1), albendazole and chitosan were obtained rom Shanghai Chemicals (Shanghai, China) and used as eceived from the supplier. Doubly distilled water was used hroughout all experiments. Before use, dichloromethane and enzaldehyde were subjected to simple distillation from K2CO3.\nyrrole was distilled under atmospheric pressure with CaH2. PPH2 was synthesized by Adler\u2019s method (Zhang et al., 001).\nF n b\nelectronics 22 (2006) 423\u2013428\n.1.1. Synthesis of T(o-glu)PPH2\nThe synthesis of T(o-glu)PPH2 was performed according o a known procedure. An appropriate amount (9 g) of freshly ynthesized ortho-(2,3,4,6-tetraacetyl- -D-glycosylphenyl)enzaldehyde, 1.4 g of freshly distilled pyrrole and 1 ml of F3\u00b7Et2O were dissolved in 1.6 L of CH2Cl2 and stirred nder nitrogen atmosphere at room temperature for 24 h. After ddition of 3.4 g of dichlorodicyanobenzoquinone, the mixture as refluxed for a further 2 h, then 20 g of silica was added nd the solvent evaporated. The residue retained on silica was urified by column chromatography (silica CH2Cl2/acetone :1). After removing of the solvent, 1.03 g of T(o-glu) PPH2 yield, 20.5%) was obtained. Anal. calc. for C100H102N4O40: , 60.1; H, 5.1; N, 2.8. Found: C, 59.8; H, 5.0; N, 3.1. UV\u2013vis CH2Cl2): max: 418, 516, 544.5, 587.5, 654 nm. HNMR CDCl3)(ppm): 8.84 (4H, pyrrole); 8.67 (4H, pyrrole); 7.86 4H, benzene); 7.78 (4H, benzene); 7.70 (4H, benzene); 7.51 4H, benzene); 4.79(4H, glucose); 4.68 (4H, glucose); 4.62 4H, glucose); 4.14 (12H, glucose); 3.68 (4H, glucose); \u22121.20 o 0.25, 0.5\u20131.3, 1.51\u20132.19 (48H, CH3CO\u2013), \u22122.81 (2H, NH). he structure of glycosylated porphyrin is shown in Fig. 2.\n.1.2. Synthesis of MgT(o-glu)PPCl An appropriate amount of DMF (35 ml) solution containing 40 mg of T(o-glu)PPH2 was stirred under refluxing with the ddition of 0.7 g of MgCl2\u00b7H2O for 6 h. TLC (silica gel, CH2Cl2) howed the complete disappearance of the starting material and V\u2013vis spectroscopy showed the absence of a non-metallized orphyrin ring. After evaporation of the solvent in vacuum, colmn chromatography gave 170 mg of MnT(o-glu)PPCl (yield 9%). UV\u2013vis (CH3OH): \u03bbmax: 403, 425, 514, 575, 651 nm.\nig. 2. Configuration of fluorescence device: 1. doubly optical fiber: 2. fixing ut for optical fiber: 3. flow-through cell: 4. optode membrane: 5. fixing nut for lade: 6. vessel.",
            "F.-C. Gong et al. / Biosensors and Bioelectronics 22 (2006) 423\u2013428 425\np t t e\n2 m\nw t A w f w w\n2\nF w c d t s o t S b w c\n2\ni a\n2\ni 1 e a f\n3\n3\nw m L s b o i w o L t b g f\nm\nump was used to generate flowing stream (Jiangsu Elecrochemical Instruments, Jiangsu, China). A model CSS501 hermostat (Chongqing Instruments, Chongqing China) was mployed to control the incubating temperature.\n.3. Preparation of MgT(o-glu)PPCl modified optode embrane\nA mixture was prepared by adding a 2 ml acetone solution ith 0.5% MgT(o-glu)PPCl into a 50 ml of 2% acetic acid soluion containing 2% (w/v) chitosan and mixing them thoroughly. n appropriate amount of 100 m resulting mixture solution as doped on the cleaned glass blade and left to dry at 60 \u25e6C or about 2 h. A MgT(o-glu)PPCl modified optode membrane as obtained and could be used after washing with distilled ater.\n.4. Measurement procedure\nThe optical chemical sensor configuration is illustrated in ig. 3. The measurement procedure is as follows: The first step as to fix the optode membrane onto the flow-through reaction\nell in the path of flowing stream integrating into a fluorometric evice. A BR buffer solution was pumped through the flowhrough reaction cell. After the background fluorescence was tabilized, the fluorescence of the MgT(o-glu)PPCl modified ptode membrane in BR buffer solution was recorded at excitaion and emission wavelengths of 425 and 646 nm, respectively. econd, a LEV-containing solution was added to the same BR uffer solution. The fluorescence signal of optode membrane as recorded again. The increase of fluorescence intensity was alculated.\n.5. Renewal of the sensor surface\nThe optode membrane could be renewed by simply washing n turn with a BR buffer solution (pH 9.0) and distilled water for bout 15 min.\nt I s p\n2), 4 \u00d7 10\u22126 (3), 6 \u00d7 10\u22126 (4), 8 \u00d7 10\u22126 (5) and 10 \u00d7 10\u22126 (6) M L\u22121. The oncentration of MgT(o-glu)PPCl in the chitosan film was 2%.\n.6. Sample preparation\nAn amount of 10 pharmaceutical tablets of LEV were ground nto powder. The resulting powder was then extracted with 00 ml of acetone solution containing 0.1% HCl. After being xtracted, the extract filtered was added into a calibrated flask nd then diluted with a BR buffer solution of pH 7.5 to 1000 ml or determination.\n. Results and discussion\n.1. Optode membrane response and principle of operation\nThe optode membrane was essentially weakly fluorescent here exposed to plain BR buffer solutions of pH 7.5. When the embrane was in contact with the aqueous buffer containing EV, an increase in fluorescence intensity was observed. Fig. 4 hows the fluorescence emission spectra of the optode memrane with the addition of LEV solution. As expected from the riginal design, interaction of the MgT(o-glu)PPCl with LEV ncrease the fluorescence intensity of the membrane at 646 nm, hich correspond to the T(o-glu)PPH2 emission. The degree f fluorescence enhancement is proportional to the amount of EV in analytical samples. The fluorescence enhancement of he MgT(o-glu)PPCl-based optode membrane by LEV could e attributed to the ligation interaction of LEV with MgT(olu)PPCl and weakening the inhibiting of the electron tansfer or metalloporphyrin.\nThe fluorescence enhancement of the metalloporphyrinodified optode membrane by LEV is based on the complexaion with the central metal moiety (Mg2+) of metalloporphyrin. f the complex equilibrium between LEV in the aqueous sample olution (aq) and metalloporphyrin in the chitosan membrane hase (org) will form an m\u2013n complex, the over equilibrium can",
            "4 d Bioelectronics 22 (2006) 423\u2013428\nr\nm\nw p c e a\nK\nw f t\ni d t\n\u03b1\nw a fl s p d [\nT t i i t i r\n3 o\nt c fl p e T p g w T g r\nt w a fl s t m o v i g M f\n3 m\ns e i f a T i d i a d\nthought to follow the reaction scheme as shown in Fig. 5. As far as the substitution in the benzene rings is concerned, the glucopyranosyl group bound at the benzene rings of MgT(oglu)PPCl formed a three-dimensional cage which might act as\n26 F.-C. Gong et al. / Biosensors an\nepresented as:\nA(aq) + nB(org) K\u2212\u2192AmBn(org) (1)\nhere A represents levamisole and B represents the metalloorphyrin. If the difference between the activities and conentrations is neglected for simplification, the corresponding quilibrium constant, K, can be expressed by the law of mass ction,\n= kb \u00d7 \u03b2 = [AmBn](org)\n[A]m(aq)[B]n(org) (2)\nhere kb and are the distribution coefficient and complex ormation constant; and [AmBn], [A], and [B] are the concenrations of the respective species.\nFor the description of the performance of this optically sensng membrane, it is useful to introduce the degree of reaction, , efined as the ratio between the free metalloporphyrin concenration [B], to the total concentration of metalloporphyrin, CB,\ncan be expressed as:\n= [B] CB = F\u03b1 \u2212 F F\u03b1 \u2212 F0 (3)\nhere F is the fluorescence intensity of sensing membrane ctually determined at a defined LEV concentration, F0 is the uorescence intensity of the optode membrane in the plain buffer olution, and F\u03b1 is the fluorescence intensity when the metalloorphyrin is completely complexed by LEV. \u03b1 is shown to be ependent on the concentration of LEV in the aqueous sample A], as follows:\n\u03b1n\n1 \u2212 \u03b1 = 1\nnKCn\u22121 B [A]m\n(4)\nhe relationship between [A] and \u03b1, as expressed by Eq. (4), is he basis of the quantitative determination of LEV concentration n aqueous solution by using this optode membrane. The expermental data were fitted to Eq. (4) by changing the ratio of m o n and adjusting the over equilibrium constant K. The results ndicated that the complex ratio and K were 1:1 and 1.8 \u00d7 104, espectively.\n.2. Selection of active materials for recognition element in ptode membrane\nThe optical properties of porphyrin compounds are related o its molecular skeleton. T(o-glu)PPH2 is a highly fluoresent compound. When it is coordinating with a metal ion, uorescence quenching by metal is, of course, a well-known henomenon (Takeuchi et al., 2001). So metalloporphyrins are ssentially weakly fluorescent species compared to porphyrins. he characteristic performance of the optode membrane incororated with different porphyrin compounds including MgT(olu)PPCl, ZnT(o-glu)PPCl, FeT(o-glu)PPCl and T(o-glu)PPH2\nere investigated by fluorometric finish. The results are shown in able 1. It can be observed that the membrane based on MgT(olu)PPCl, ZnT(o-glu)PPCl and FeT(o-glu)PPCl exhibited better esponse characteristic than that of based on T(o-glu)PPH2. It is\nhought that the interaction of LEV with porphyrin compounds as via the coordination with metal center of metalloporphyrin nd weakened the inhibiting of electron transfer increasing the uorescence of metalloporphyrin. T(o-glu)PPH2 does not posess central metal capable of coordinating with LEV. Therefore, he poor fluorescence response characteristics of T(o-glu)PPH2 odified optode membrane are expected as compared to those f MgT(o-glu)PPCl, ZnT(o-glu)PPCl and FeT(o-glu)PPCl. In iew of the significant selectivity of the MgT(o-glu) PPCl modfied membrane compared with ZnT(o-glu)PPCl and FeT(olu)PPCl-modified membrane as described in the next section, gT(o-glu)PPCl was used as the LEV sensitive carrier in all urther studies.\n.3. Selectivity of the MgT(o-glu)PPCl-modified optode embrane\nSix possible interfering substrates were used to evaluate the electivity of the LEV sensor. The fluorescence recorded for ach interfering substrate at a concentration of 5 \u00d7 10\u22126 M L\u22121 n the presence of 5 \u00d7 10\u22126 M L\u22121 LEV was used as an indicator or the sensor selectivity in comparison with the LEV readings lone. The results of the interference investigation are listed in able 2. From the data in Table 2, one can observe that nitroimdazole, dimetridazol, antibilin, imidazole, and o-aminophenol o not cause any interference (\u22643% change) under the expermental conditions. The most obvious interfering species is lbendazole, it seems that albendazole can compete the coorinated sites, and thus, interferes in the determination of LEV.\nThe interaction mode of LEV with MgT(o-glu)PPCl is"
        ]
    },
    {
        "image_filename": "designv11_11_0001068_bf01573694-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001068_bf01573694-Figure2-1.png",
        "caption": "Fig. 2. MMF and density of conductors of 0-th elementary winding",
        "texts": [
            " If the winding produces the MMF described by (1 a or 1 b), then it is equivalent to a number of hypothetical sinusoidal windings connected in series, corresponding to separate harmonics of the Fourier series. Let us consider this by the example of winding \"b\". Its elementary sinusoidal winding for harmonic 0 has the pole pitch ~z/]0] and the conductor density (see 1 b): g b ~ L 1 dObe 2wbkb (Q) ib dx o r s i n o ( x - x b ) f o r f f = l , 2 .... oo (7) 1 gbo. = j - O Wb Mej~ x~ for 0 ~ ~ (8) Figure 2 shows the MMF 0bo (1 b) and the conductor density (7) of the pth elementary winding. The elementary \"sinusoidal coil\" with discretized portion of turns gbe d x is marked there. Thus, we can regard the hypothetical sinusoidal winding for the 0th harmonic as consisting of 0 elementary sinusoidal coils connected in series, each of the pitch rc/[O[. The number of these windings depends upon the number of terms taken into account in the Fourier series (1 b). Such a procedure establishes the entire hypothetical winding equivalent to the given one"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000469_(sici)1521-4109(199809)10:11<752::aid-elan752>3.0.co;2-t-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000469_(sici)1521-4109(199809)10:11<752::aid-elan752>3.0.co;2-t-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the integrated needle-type sensor for lactate and glucose monitoring.",
        "texts": [
            " This layer of polymer has three functions: increasing the stability of the platinum black particles; enhancing the selectivity of the electrode so that the response cannot be affected by most electroactive interferents existed in physiological samples; serving as the substrate for the further enzyme immobilization. Using the needle external surface as the working surface can miniaturize the sensor size, provide a large sensing area to ensure sufficient sensitivity, and increase the rigidity of the whole sensor body. Another working electrode (lactate sensor) was made from platinum wire which was fixed in the needle hollow body. Figure 1 presents the cross section schematic of the integrated sensor tip. Glucose oxidase is immobilized on the needle surface, and lactate oxidase is immobilized on the surface bulb tip to give two separate working electrodes. The bulb was fixed and insulated by epoxy throughout the inside of the needle. Two open type silver/silver chloride (Ag/AgCl) reference electrode are make of chlorinated silver wire twisted around the needle. Silver wires are insulated by shrinking tubes to avoid contact. GOD and LOD working electrodes are separated in space by 5 mm epoxy insulation (see Fig. 1). A stainless steel needle (18 gauge) was cut at both ends to remove the plastic cap and the pointed end, and the ends were smoothed using files and fine sand paper. The needle was soaked in carbon tetrachloride for 5 days followed by washing in stirred distilled water. Before electrodeposition the needle was treated in 10 % HCl solution cathodically and anodically at the current density of 5 mA/ cm2 [19] for 1 min respectively. The electrodepostion of platinum black was performed at 1 mA/ cm2 current for 80 s, and was followed by electropolymerization of from 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001072_robot.1990.126043-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001072_robot.1990.126043-Figure2-1.png",
        "caption": "Figure 2 An example illustrating a set of routes that can be generated by using t-vectors.",
        "texts": [
            " As an example, Figure 3 shows a path divided into a number of segments. A robot traveling along the path has speed 1 segmenthxond. A time resolution of 1 second is used to detect the interference with moving obstacles at each segment. The detected collision is then registered on the constraint map shown to the right of the graph. In [15,19], path planning using traversability vectors is presented for a point robot amidst static polygonal obstacles. As a result, a set of routes are generated for the robot to bypass obstacles as shown in Figure 2. These routes are efficient in distance and the shortest one can be de-ned easily. 3. Resolution of time Constraints Assume a moving obstacle is represented by A(Q)& - &) e 0 at t = to, and has trajectories d(t) for translation, and a(t) for rotation. For t > to. the moving obstacle will have model coefficients A(t) = [A(to)R-l (a(to))lR(a(t)), .and d t ) = the rotation matrix. For a given set of routes, the occupancy of these routes by moving obstacles can be determined. We first decompose each route into a number of segments according to a time resolution z"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001366_pime_proc_1992_206_183_02-Figure14-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001366_pime_proc_1992_206_183_02-Figure14-1.png",
        "caption": "Fig. 14 Schematic drawing of apparatus for simultaneous film thickness and friction force measurements (38)",
        "texts": [
            " With this apparatus a film thickness measurement by the electrical resistivity technique is also made (37). Another experimental work is that of Bassani et al. (38). A versatile test rig for the simultaneous measurement of some of the fundamental quantities of lubricated contacts is used to measure the friction force (with a force transducer) and the film thickness (by the interferometric method) of two motor cams. The surface roughness of the engine cam makes interpretation of the Part D: Journal of Automobile Engineering interferometric fringes difficult. The apparatus is shown in Fig. 14. Studies on the friction in complete valve trains, considering guides, camshaft bearings, springs, etc., are also made. However, if different geometries of the cam and follower are possible with often very different film thicknesses and friction forces, more kinds of complete valve trains are possible, as reported, for example, in reference (39). Some calculated drive torques of one camshaft for three different engines are shown in Fig. 15. The torques of these multi-cylinder engines are obtained by summing up each cam\u2019s torque shifting firing interval"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001892_robot.1998.680743-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001892_robot.1998.680743-Figure3-1.png",
        "caption": "Figure 3: Notation of different paths (xP = original desired path, xd = sensed desired path, x, = actual path, x, = actual edge, x, = nominal edge, Ax, = sensor value, Axd = modification of the desired path due to a difference between the nominal and the actual edge)",
        "texts": [
            " Thus at timestep k the path modification module calculates the modified diesired path as qd(k+i ) = i n ~ - k i n [ k i n [ q ~ ( k + i ) ] + A ~ d ( k + i , k ) ] (2) or qd(k + i) = i n~k in [x , (k + i) + A ~ d ( k -I- i, k ) ] (3) from the original desired path qp or xp and the cartesian difference Axd(k + i, k ) between the programmed and the sensed desired path at timestep k+i, measured at timestep k . kin[.] and inw-kin[.] denote the forward and inverse kinematic transformation, respectively. The path modifications Axd are calculated from the actual position Z, (which is transformed from qa) , the sensor values Axs, and the nominal edge positions x, (see figure 3). This approach allows the control of (curved) paths which do not coincide with an edge. The positions x are expressed in the Cartesian sensor coordinate system which is chosen such that the robot moves along for instance the y-direction. So the y-direction is not senijor controlled. However deviations due to the robot dynamics are compensated in all components. Hence, In this notation indices x, y or z as second indices represent the corresponding components of the vector. At timestep IC the sensor values Axs(IC + i , k ) are taken which look at the positions xP(k + i) by measurements from the current position x,(k)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002698_tmag.2005.844348-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002698_tmag.2005.844348-Figure4-1.png",
        "caption": "Fig. 4. Portion of laminated core at a T-joint of a transformer ( =",
        "texts": [
            " 2), for which fluxes and MMFs are expressed as unknown nonlocal quantities depending on the whole system behavior. The complementary parts of the system are the lumped element regions including the necessary MMF sources and lumped reluctances with pre-defined values. Computed MMF-flux ratios are given in Fig. 3, which points out the correct convergence of both formulations when increasing the number of degrees of freedom. A second problem concerns a T-joint of a transformer with a particular layout of laminations (Fig. 4). Such a layout, with 1000; = 10 Sm , lamination thickness 0.35 mm, overlap length of two successive laminations 12 mm, airgap 0.1 mm, stacking factor 0.95; dimensions of airgap, thickness and insulator are amplified for clearness). Two symmetry planes corresponding to each lamination mid-plane limit the studied domain to 2 half-lamination portions, of which the exterior skins are drawn. The peripheral boundary is a flux wall , interrupted by three flux gates (not drawn). the resulting distribution of magnetic flux and eddy current densities, could not be modeled for the whole 3-D system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003715_026-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003715_026-Figure1-1.png",
        "caption": "Figure 1. Dynamic model of a gear pair.",
        "texts": [
            " All these methods are not validated for stiff differential equations. Gear method is presented for solving nonlinear dynamics differential equations in this paper. Compared with other numerical methods, Gear method can not only obtain higher calculation precision and efficiency, but also can change step size automatically. GEAR method is validated especially for stiff differential equations and is a general method of numerical calculation [2,3]. The dynamic model of a gear pair with backlash supported by rigid mounts as shown in figure 1. Given viscous damping coefficient ce driving gear base radius Rp, driven gear base radius Rg the equation of the torsional model of the gear pair can be given by )())(()( 2 2 tTeRRtkR td ed td d R td d RcR td d I pggppep g g p pep p p (1) )())(()( 2 2 tTeRRtkR td ed td d R td d RcR td d I gggppeg g g g peg g g (2) where Ip, Ig are the polar mass moment of inertia of driving and driven gears respectively(kg m2), p , g are torsional displacement of driving and driven gears, )(tTp , )(tTg are the torque of driving and driven gears (N m), e is static transmission error of the gear pair(m), )(tke is time variant meshing stiffness of the gear pair (N/m) which can be given by harmonic form )cos()( 5 1 je j jme tjAktk "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002365_robot.1994.350994-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002365_robot.1994.350994-Figure2-1.png",
        "caption": "Figure 2: The relative position of the camera and the 2-DOF Planar Arm",
        "texts": [
            " A second approach to the the simultaneous optimization of observability and manipulability is to formulate a cost functional that allows us to independently consider observability and manipulability. We can modify the cost function given in (13) to include manipulability, i 9 (J:)~J=; 5 1, cost(r, qc) = - Jpv(wv(r, qc)) + kr(wr(r))ldt (23) where k, and k, are constants that allow us to weight the relative importance of observability and manipulability. The advantage to this formulation is that it allows us to decouple the tasks of robot trajectory planning and camera trajectory planning. 6 2-DOF Planar Arm We consider a two-link planar arm (Fig. 2), where the task space can be described by P ( X , Y ) , a point on the robot's end-effector and the joint space is described by (el,&). The camera position is described by the spherical coordinates (&e,+) while the orientation of the camera is fixed such that its optical axis is maintained parallel to the 2 axis. Now, for visual servo control of the ZDOF planar robot, two image parameters would be sufficient, as described earlier. We consider the image of the point P, given by (U, U) to be the feature to be tracked and used for visual control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001958_2001-01-1060-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001958_2001-01-1060-Figure2-1.png",
        "caption": "Figure 2. The fifteen degrees of freedom nonlinear",
        "texts": [
            " vehicle model VEHICLE MODELING FOR EVALUATION OF THE CONTROLLER \u2013 The vehicle lateral motion is generated by the nonlinear tire forces, which are created by the variation of the normal forces caused by both the longitudinal and lateral weight transfer. Therefore, the precise modeling of the multi-degrees of freedom vehicle model is indispensable to the research on the vehicle stability control system. In order to evaluate the proposed controller, we use 15 degrees of freedom nonlinear vehicle model based on ADI(Applied Dynamics International) model[9], which is shown in figure2. Brake systems are simply modeled as the torque actuator that both the driver and the vehicle stability control system directly handle the brake torque with simple dynamics. Even through this model has lower degrees of freedom than the multi-body dynamics model[8], it can sufficiently express the vehicle motions that are considered by the vehicle stability control system. The vehicle model is verified by comparing its simulation results with the experimental results of a middle size passenger-car"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002297_robot.1998.680701-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002297_robot.1998.680701-Figure2-1.png",
        "caption": "Fig. 2 Motlcl of tlie yvitciri",
        "texts": [
            "[l] and Montaria[lS] formiilatcd t,hc kineiriatirs of riiwrii~)iilatioii of olijtcts iiiiclcr rolliqg col i - tiicth wit l i t Iir fiiig(>i.t i l l . Li ('1 ; i I . [ I 11 p ro i )o~c t l i i iiiotion plaiiiiiiig irictliotl wit,li iioiilioloiioiriic coiist,r:iiiit. Howard et, a1.[15] anc l Mackawa et a1.[16] studied the stiffness effect for the oliject motion with rolling. Cole et a1.[2] and Paljug et, al.[3] proposed a control scheme for the object motion. Within our knowledge, this is the first challenge for enveloping mnltiple object,s based on rolling contacts. 3 Modeling Fig.2 shows the hand system enveloping m objects and n fingers, where finger j contacts with object i . and additionally object i has a. common contact point with oI)jcct I . En. Z=Jj, ( i = 1 , . . . , m ) and C F l k (,j = 1. . . . _ I ) . . k = 1. ' . . , c j ) denote tlie coordiriat,e systciris fixed at, t,hc 1)ase. at tlie ceiitcr of gravity of the ol),ject i arid a t the finger link inclucling the kt,li contact of finger j. rcspcct,ivelv. Let p,, and RB, be the positioii vector arid the rot,ation miltriX Of C R ~ , and p ~ j k allti R F J k bC those Of C F ~ ~ , wit11 respect to C H "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002028_978-1-4613-9030-5_37-Figure37.3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002028_978-1-4613-9030-5_37-Figure37.3-1.png",
        "caption": "Figure 37.3: The McMahonimal, a running robot. The length of the body is 33 cm.",
        "texts": [
            " Furthermore, it shows how reflexes (most importantly the stretch reflex) act to increase muscle stiffness and main tain that stiffness at a level nearly independent of the force at moderate and high force levels. The board bouncing experiments showed that although the leg spring stiffness is nearly independent of the force, it depends on the knee angle because the mechanical advantage of the ground reaction force acting about the knee changes with knee angle. 37.2. Leg Springs and Robots 37.2.1 The McMahonimal In 1976, an undergraduate, Michael Jacker, wanted a design project. I suggested he build a machine that would run. The final product is shown in Figure 37.3. It had four legs, each of which had an elbow or ankle with a spring acting to keep it extended. The rotary motions of the hips and shoulders were coupled using large gears so that moving the rear legs backward caused the front legs to move forward and vice versa. A microswitch was positioned to close when the ankle joints dorsiflexed past a certain angle; this caused a solenoid to open, sending pressurized nitrogen to an air cylinder that pulled a tendon, thereby plantar-flexing the ankles and extending the hips"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003088_tmag.2005.844840-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003088_tmag.2005.844840-Figure1-1.png",
        "caption": "Fig. 1. Tested linear motor with open magnetic system.",
        "texts": [
            " They are employed in high-speed transport (magnetic levitation), electric hammers, pumps for electrochemists, and many other electromechanical systems. Tubular linear reluctance motors (TLRMs) belong to the group of cyclic actuators with reversal (oscillating) movement of their movable parts (called runners or rotors) [2]. In the hitherto existing construction of the motors, the packages of iron roads or solid magnetic cylinders (made from composites) are mainly used for the runner completing [2], [3]. Taking into account the small losses in the steel\u2013silicon thin sheets, we have proposed to make use of them for the runner construction (Fig. 1) [14]. This way, we keep the eddy currents in such runners to a minimum. In this case, it is interesting to investigate the nonlinearity and lamination impact on the magnetic field distribution [12], [13]. We investigated motors with closed and open magnetic circuits as well. There are sundry types of stators with magnetically closed circuits for TLRM construction [3]. For example, the construction based on the U-shaped stack silicon sheets is used. However, in the first place, most of the stators in TLRMs are with axial symmetry structure [8]",
            " The influence of the stack benching on the integral parameters of the magnetic field and static characteristic has been comparatively examined in this work. The magnetic flux density components for the actual physical model of the motor have been measured and compared with the values obtained from the calculations. The physical model (with long stroke) considered in this work can be used in an electric hammer. In this motor, the axial magnetic field is excited first. An axonometric view of the physical model construction, with the tubular solenoid-type stator, is presented in Fig. 1. It is Digital Object Identifier 10.1109/TMAG.2005.844840 the motor with so-called open magnetic circuit [8], [9]. Owing to cutting the stator piece away, the stepped stack of sheets, creating the runner core, is visible in the figure. Moreover, the return spring located in the body of the motor is shown. The stator coils are fixed between two springs (Fig. 1). The coil system constitutes the stator\u2019s winding of 16 cm length. External and internal diameters of the coils are cm and cm, respectively. The stack of the silicon sheets of the rotor\u2019s moving core (runner) is formed and placed in the runner tube with internal diameter of cm. Thus, the gap with air permeability between the winding wires and the ferromagnetic core is mm. The weight of the runner is 1.05 kg. Because such motors are used at low speed, the eddy-current effects in the moving core can be neglected [4]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002189_mech-34368-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002189_mech-34368-Figure4-1.png",
        "caption": "Fig. 4 The Y-axis should be the X-axis, the X-axis should be Y-axis and in the opposite direction as shown.",
        "texts": [
            " Standard test plane and standard test path are used as two important steps in reducing the amount of testing work involved in testing and comparing the performance of different industrial robots from different manufactures. Both standard test plane and standard test path are defined based on the concept of working space center point. A wrong working space center point will waste the tremendous amount of testing work, and should be avoided. Most of the errors in the standard, unfortunately, are related to working space center point. Working space center point plays a very important role in this standard. 2.1 Center Point Location in Working Space On page 11 of the standard, in figure 4, the position of the working space center point is positioned incorrectly. Along the same x-axis shown, Cw should be located at the midpoint of the x-axis line and not off centered. . 1b) After corrected 1a) Original figure 4 Fig. 1 Cw should be located at the midpoint of that X-axis li 2 2 Copyright \u00a9 2002 by ASME tp://proceedings.asmedigitalcollection.asme.org/ on 04/11/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: ht 2.2 Coordinate Associated with Center Point Definition On page 11 of the standard, in figure 4, X1Y1 coordinate is needed. 2.3 Standard Test Plane and Its Reference Plane On pages 21and 22 of the standard, figures 12 and 13 are both mislabeled. They are not standard test plane and exception test plane, but the standard reference plane and exception reference plane respectively. The standard test plane is the plane that parallel to the standard reference plane and passes through the work place center point. 3 3 Copyright \u00a9 2002 by ASME tp://proceedings.asmedigitalcollection.asme.org/ on 04/11/2018 Terms of Use: http://www",
            " 4 4 Copyright \u00a9 2002 by ASME p://proceedings.asmedigitalcollection.asme.org/ on 04/11/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: htt 2.5 Location of Standard Test Plane and Coordinate System On page 23, Figure 15 has the same errors as figure 14 mentioned above. 5 5 Copyright \u00a9 2002 by ASME p://proceedings.asmedigitalcollection.asme.org/ on 04/11/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: ht Table 1. List of Errors page No. Before Revised After Revised 11 In Fig. 4, the position of the working space center point is positioned incorrectly. Along the same x-axis See Fig.1 See Fig. 2. 11 X1Y1 coordinate is needed. See Fig. 3 See Fig. 4. 22 In Figure 14, the Y-axis should be X. The X-axis should be Yaxis in the opposite direction. See Fig. 9 See Fig. 10 23 Figure 15 has the same errors as Figure 14. See Fig. 11 See Figure 12. 25 In item 4. STP Cycle Test, Deviation From STP, Section is \"8.4.2.8\". There is no section with that number. It should be \"8.4.2.7\". 26 Section 7.3 second line is \"(Table 2)\". Table 2 should be \"(Figure 17)\" On page 10 of the standard, the explanation of the working space center point conflicts with the definition of how to find it, given on page 24 of the standard"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003770_00423110500143728-Figure24-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003770_00423110500143728-Figure24-1.png",
        "caption": "Figure 24. Geometrical contact conditions.",
        "texts": [
            " For harmonic excitation at the point of contact to the wheel, the partial differential equations for the rails are reduced to dynamic stiffnesses. Contact conditions. Vehicle motion and track displacement are coupled by the contact between the wheels and the rails. For the point of contact the conditions for the contact geometry, the relative speeds and the contact forces can be calculated. D ow nl oa de d by [ U O V U ni ve rs ity o f O vi ed o] a t 0 1: 03 0 7 N ov em be r 20 14 Railway vehicles, track and subgrade 509 Figure 23. Vehicle\u2013track model. (1) As depicted in figure 24 wheel and rail touch each other tangentially at one contact point. This leads to the following vector equations: nWC \u00d7 nRC = 0, (13) rWC \u2212 rRC = [0, 0, 0] eC. (14) The normal vectors of the wheel and the rail surface have to point into the same direction. The position vectors have to be equivalent. From these conditions one gets for the contact point the contact coordinates xC and the angular orientations of the contact coordinate systems eC = D C e0 of wheel and rail. (2) At the contact point hold the relative velocities, the creep \u03bdx and \u03bdx , \u03bdx = vWCx \u2212 vRCx v0 , (15) \u03bdy = vWCy \u2212 vRCy v0 , (16) and the spin creep \u03c6: \u03c6 := \u03c9WC z \u2212 \u03c9RC z v0 with \u03c9 = D\u0307 C D\u22121 C (17) D ow nl oa de d by [ U O V U ni ve rs ity o f O vi ed o] a t 0 1: 03 0 7 N ov em be r 20 14 510 K"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000629_s0921-4526(99)00692-4-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000629_s0921-4526(99)00692-4-Figure1-1.png",
        "caption": "Fig. 1. Scheme of the lamination model.",
        "texts": [
            " These problems can be sometimes reduced to a one-dimensional analysis, considering the prevalent transversal dimensions of the lamination with respect to its thickness. In other cases (e.g. teeth and bridges in electrical motor cores), even if the #ux is unidirectional, the edge e!ects are not negligible and a more general 2D approach, accounting for the eddy current closure paths, is developed. In 1D formulation, the time periodic unidirectional #ux U(t) #ows in the z-direction and the electromagnetic \"eld quantities only depend on the x-coordinate along the lamination thickness, having neglected the edge effects (Fig. 1). Thus, the domain under study is reduced to a 2d long segment along the x-axis, being 2d the lamination thickness. Under periodic time evolution, the governing equation, for the nth harmonic at the kth FP iteration, is l FP R2A 1 (n) k Rx2 \"junpA 1 (n) k ! RR 1 (n) k~1 Rx , (8) where u is the fundamental angular frequency, p the electrical conductivity; phasors A 1 (n) k and R 1 (n) k~1 represent the magnetic vector potential (A\"(0, A(x, t), 0)) and the residual term, respectively. Problem (8) is completed by Dirichlet boundary conditions imposing the #ux U through the lamination: A 1 (n)D x/~d \"!1 2 U 1 (n), A 1 (n)D x/d \"1 2 U 1 (n). (9) In 2D problems, the domain X is the cross section of the lamination in xy plane (Fig. 1). Introducing an electric vector potential T (J\"curlT ), normalized as T\"(0, 0, \u00b9(x, y)), the resulting equation at the kth FP iteration is curlcurl T 1 (n) k #jnuk FP p AT 1 (n) k ! 1 SPX \u00b9 1 (n) k dsB \"!jnupA U 1 (n) S #R 1 (n) k~1 ! 1 SPX R 1 (n) k~1 dsB, (10) where phasor U 1 (n) represents the nth harmonic component of the supply #ux. Homogeneous Dirichlet boundary conditions impose that current density J is tangential to the boundary of X. 4.2. Two-dimensional yux excitations The analysis of 2D electromagnetic \"eld problems with magnetic #ux #owing in the xy-plane is conveniently handled introducing the magnetic vector potential A, normalised as A\"(0, 0, A(x, y, t))"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001256_3.10686-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001256_3.10686-Figure1-1.png",
        "caption": "Fig. 1 Space crane as an adaptive structure.",
        "texts": [
            " Space cranes used in space construction can be adaptive structures.10 An adaptive structure can change its geometry without creating internal stresses. It is, in general, a statically determinate structure, in particular, a statically determinate truss. The response computation of statically determinate trusses is reviewed in the next section where an algorithm with 0(n2) computational complexity and 0(n) storage demand is referred to for the required \u00abth-order matrix inversion. A space crane using the adaptive structure concept is shown in Fig. 1. It is clear from the figure that the crane is essentially a statically determinate truss with some length-control mechanisms installed in some of the members. The end-effector of the crane traces the desired trajectory of the payload upon the activation of the length-control mechanisms to induce appropriate elongations/shortenings in appropriate bars. Because of the adaptive nature of the truss, no stress in the truss members develops when the payload is coasting along its trajectory. The knowledge of the payload's trajectory enables one to compute the corresponding elongations/shortenings of the controlled bars"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002506_ac00288a024-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002506_ac00288a024-Figure1-1.png",
        "caption": "Figure 1. (a) \u201cDouble-injection\u201d enzyme electrode, allowing easy, fast change of both sample and filling solution: (1) microelectrode; (2) opening for Internal filling solution; (3) electrode chamber; (4) sample chamber; (5) empty space; (6) droplet (film of internal filling solution); (7) O-ring; (8) sample change; (9) membranes; (10) sample (1 mL); (1 1) magnetic stirring spin bar (2 X 7 mm). (b) Modified jacket for regular ammonla electrode.",
        "texts": [],
        "surrounding_texts": [
            "Apparatus. All the pH measurements have been made with a Corning pH-meter, Model 110, coupled to an Omniscribe recorder through a dc offset module (Schlumberger). The electrodes used were an ammonia sensitive electrode set, Type 015833055 (Radelkis, sold in the U.S. by Universal Sensors, P.O. Box 736, New Orleans, LA 70148), MI-410 micro-combination pH probes (Microelectrodes, Inc.), and a Corning pH-combination electrode. The hydrophobic membranes studied for their permeability were polypropylene (Celgard), \u201cRubber Teflon COz\u201d (Radelkis), silicone rubber (Radelkis), and \u201cpOz\u201d (Corning). Their commercial names and the pore sizes (when specified by the manufacturer) are given in Table 111. Some of the membranes were laminated upon supporting layers, such as polypropylene unwoven or screen of different porosity. This porosity of the support is not specified by the manufacturer but, since the main purpose of this part of the experiment is purely practical, this specific knowledge is not required. There is one important difference between our work and those described by Arnold et al. (11): the laminated support on the membrane used by them was facing the external (sample) solution, whereas our supporting layer was placed between the hydrophobic membrane and the electrode glass surface. Their approach is quite proper for ammonia assay, but since we were concerned with both the ammonia and urea producing ammonia assays, where an extra membrane (e.g., intestine) is added, it was more appropriate to have the support reversed to reduce the escape of ammonia. The Radelkis \u201cFil-NH3-1\u201d or 0.15 M NH4Cl saturated with AgCl were used as the electrode internal filing solutions. The internal filling solution for the \u201cDouble Injection Electrode\u201d was M ammonium chloride. Initially, lo9 M HC1 is injected into the electrode which is transformed into loF3 M NH4Cl by the diffusing ammonia. Flgure 2. Comparison of typical response curves for ammonia assays and base line recovery with (1) \u201cDouble Injection Electrode\u201d and (2) regular (Radelkis) electrode: Celgard 2400 (pobpropylene) membrane: ammonia concentration 3 X lo-* M; base line recovery in buffer (0.2 M Tris pH 8.5) with Radelkis electrode (bottom curve) or with Double Injection Electrode (after injection of fresh filling solution into the electrode (top curve); B, base Ilne; BR, base line recovery; S, response to \u201c3. Figure l a shows the principle of the new design of an enzyme electrode, which allows a fast change of both the filling and the sample solutions. Both the electrode jacket and the cell are made of Plexiglas, lined inside with Teflon to reduce carry-over. Both solutions are changed by injections with syringes. After the upper electrode compartment was filled with filling solution, the solution was blown out of the lower electrode compartment with air. Only minute amounts (several microliters) of the solution remained in the compartment after such a treatment, and this is mainly in the form of a film covering the tiny 1.2 mm 0.d. tip of the electrode, extending 1.5 mm up to its reference junction. The electrode tip is the only wettable part inside the electrode compartment. The volume of the sample chamber was about 1 mL, small enough to avoid unnecessary dilution of the evolving gas, which would result in slow attainment of equilibrium, and still large enough to produce a high concentration in the filling solution. The principle of changing the internal filling solution was also applied in an alternative design shown in Figure lb. A regular pH electrode was mounted into a modified jacket, allowing a change of the internal filling solution after every assay. Reagents. Chymotrypsin, urease, bovine serum albumin, and glutaraldehyde were obtained from Sigma Chemical Co., St. Louis, MO. The other chemicals used were reagent grade. Procedure. With both the standard (Radelkis) and injection type electrodes, the immobilization procedure used was as follows: The electrode jacket was covered first with the hydrophobic membrane and then with the pig intestine membrane. \u201cPlastic Rubber\u201d (Duro) was used as sealant and the membranes were kept in place and stretched with an O-ring. A drop of chymotrypsin solution (0.5 mg in 0.5 mL of H,O) was put upon the intestine. After 10 min the intestine was rinsed with water and wiped with tissue paper. Twenty microliters of a 0.2 M Tris buffer (pH 8.5) solution containing 15 mg of bovine serum albumin and 5 mg of urease was applied upon the intestine and was left for 5 min to d a w the solution to penetrate (partially) into the intestine. Then 1 ML of a 6.25% aqueous solution of glutaraldehyde was added and the mixture was stirred and spread uniformly with a piece of nylon string, until the polymer formed. The electrode was allowed to dry at room temperature for 3 h and then was placed in an open jar containing water at about +5 OC. The membrane was kept about 1 in. above the water, in order to prevent drying, which usually results in peeling of the enzyme gel off of the support."
        ]
    },
    {
        "image_filename": "designv11_11_0000235_1.601679-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000235_1.601679-Figure2-1.png",
        "caption": "Fig. 2 Optical setup for recording and processing of EOHs: BS, beamsplitter; PS1, reference beam phase shifter; PS2, object beam phase shifter; S1 and S2, reference and illumination beamshutters; MO, microscope objective; FO, fiber optic cable; SI, speckle interferometer; IL, object imaging lens; CCD, imaging device; IP, image processing computer; BE, illumination beamexpander; OB, object under investigation; and SH, piezoelectric transducer (PZT) shaker for object excitation.",
        "texts": [
            "2 Experimental Investigations: EOH EOH has been successfully applied to different fields of nondestructive testing of mechanical components subjected to static and dynamic loading conditions.4,5,8,9 Being noninvasive and providing qualitative and quantitative fullfield information are some of the main advantages of EOH over other experimental techniques. In addition, it requires much less mechanical stability than that required in conventional holographic interferometry, which makes it very suitable for on-site investigations. EOH is based on a combined use of speckle interferometry, phase stepping, and image acquisition and processing techniques. Figure 2 depicts a typical experimental setup for generation of interferograms using the EOH technique. In this system, the laser output is divided into two separate beams by means of a beamsplitter ~BS!. One of the beams is directed toward a beamexpander ~BE! to illuminate the object ~OB! uniformly. This beam, modulated by interaction with an object is transmitted by the object imaging lens ~IL! to the object input of the speckle interferometer ~SI!. The other beam is directed toward a microscope objective ~MO"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003351_pvp2005-71333-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003351_pvp2005-71333-Figure12-1.png",
        "caption": "Fig. 12 The mechanism of the nut rotaion",
        "texts": [
            " In the same section it was also pointed out that, for case ii and case iii, alternating stress is observed but quite small relative to the other frictional stresses which prevent nut rotation. In case ii, the nut rotation resistance is the frictional stress due to the bolt pretension. In case iii, the resistance is mainly the frictional stress due to the nut lateral displacement and additional friction occurs due to the increase of the bolt tension at the nut lateral displacement. In this case the frictional stress which causes the nut rotation is not large enough. If we examine the phenomena, as indicated in Fig 12, the bolt threads plunge into nut thread when it is displaced laterally. At this time, the stress that is normal to the thread surface occurs. As the threads are inclined to the bolt axis, this stress has the components both of the stress along to the bolt axis and the stress perpendicular to the bolt axis. The stress along to the bolt axis increases the bolt tension and the nloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/29/2016 perpendicular stress generates the torque to the nut"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000824_la980440s-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000824_la980440s-Figure1-1.png",
        "caption": "Figure 1. Scheme of the device that converts surface tension force to the ac voltage.",
        "texts": [
            "33 Additionally, we will try to explain possible reasons that may cause nonzero values of the second term (\u2202q/\u2202\u03b5e) in eq 5. As will be shown, the nonzero values of this derivative should be a rule rather than exception for solid surfaces if experimental conditions are close to purely elastic. Further in the text of the paper we shall use shorter notations of these quantities: \u03b3E for (\u2202\u03b3/\u2202E)\u03b5e, \u03b3q for (\u2202\u03b3/ \u2202q)\u03b5e, and q\u03b5 for (\u2202q/\u2202\u03b5e)E,P,T,n. The device that converts the surface tension force to ac voltage is shown in Figure 1. It consists of a piezoelectric plate holder, a bipolar piezoelectric plate, and a working electrode with its holder. The bipolar piezoelectric plate (BPP) was made from two identical lead zirconate titanate plates (Gzhel, Russia) covered with silver foil which served as the electrodes. The plates were glued together (with epoxy) in a +-/+- configuration. The outer electrodes of BPP were shorted with each other and connected to ground. One of the upper corners of the BPP was inserted into the gap of its holder and glued with epoxy, the inner electrode was connected through a screw in the holder to the input of a narrow-band amplifier U2-9 (Russia)",
            " The conversion of the surface tension at the electrode surface (meniscus contact) into a voltage of the piezoelectric plate takes place in the following manner. The elastic surface tension force is a function of the potential of the working electrode; thus, an alternating potential applied to the working electrode induces an oscillatory variation of the surface tension force. The surface tension force leads to mechanical deformations of the electrode which in turn lead to minute deformations of the BPP. The amplitude of the mechanical deformations is very small and usually cannot be detected by BPP. However, the whole mechanical system shown in Figure 1 exhibits several (usually three to five) mechanical resonances in the frequency range 0.5- 20 kHz. At these frequencies, the mechanical system is in resonance with an applied periodic force and the amplitude of oscillation of BPP becomes very large compared to nonresonance oscillations. The output amplitude and phase of BPP are proportional to the amplitude and the phase of the surface tension force. In practice, we have performed measurements at the resonances where the BPP output signal was not less than 10 (33) Clavilier, J",
            "06 \u00d7 1010 N/m2 34), A is the cross-sectional area of the plate (A ) 0.005 \u00d7 0.00025 ) 1.25 \u00d7 10-6 m2 ), and F is the force normal to the cross-sectional plane of the plate (F ) 0.1 \u00d7 0.005 ) 5 \u00d7 10-4 N). The sideways contraction may be ignored in an approximate calculation. Substituting these values into the equation, one find an approximate value of the strain \u2206\u03b5 ) 5 \u00d7 10-9. This value is far below the elastic limit of real metals. This means that the conditions \u2126 ) const, \u03b5 tot f 0, and \u03b5tot ) \u03b5e are fulfilled in an estance experiment. As seen from Figure 1, the mechanical system, which converts surface tension force to electrical signal, is quite complex. To obtain absolute values of \u03b3q or \u03b3E an additional calibration of the sensitivity of the device has to be carried out. Gokhshtein9,10 proposed several ex situ calibration methods, which were used by other investigators.23 He also emphasized that properties of the electrochemical system themselves could be used to find calibration coefficients KE and Kq for quantities \u03b3E and \u03b3q: where UE and Uq are correspondingly the E- or q-modulated response of the BPP"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001532_s0022-460x(03)00283-9-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001532_s0022-460x(03)00283-9-Figure2-1.png",
        "caption": "Fig. 2. Working diagram of the flexible supported Stewart platform. 1\u20138: suspension cables; 9\u201312: pretension stabilized cables.",
        "texts": [
            " Firstly, the Gough\u2013Stewart platform for active vibration reduction is briefly introduced and the system is described as a standard control system. Then, the rigid multi-body modelling of the system is carried out in terms of the Newton\u2013Euler equations. Finally, a PD control law is proposed and the control effects are simulated under the generated wind excitations. Conclusions regarding the feasibility of the Gough\u2013Stewart platform for active vibration reduction are tentatively drawn. The model of the radio telescope is shown in Fig. 1. As shown in Fig. 2, the flexible supporting structure (including 8 suspension load cables and 4 pretension stabilized cables) supports the base platform (including the cable car in the Fig. 1) of the Gough\u2013Stewart platform. The two platforms are connected by six extensible legs with spherical joints at the stabilized platform end and universal joints at the base platform end. The payloads are installed on the stabilized platform. The objective is to alleviate the vibration of the stabilized platform by adjusting the six actuators when the base platform is disturbed by winds or other unknown excitations",
            ", strokes for the six actuators so that the displacement xb \u00bc #rb %rb of the stabilized platform from its ideal position %rb is under the given root-meansquare specification ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E\u00bdxbi\u00f0t\u00dexbi\u00f0t\u00de p pdi; \u00f01\u00de where i \u00bc 1; 2;y; 6 indicate the six components of xb: In Fig. 3, the top operator \u2018\u2018 V \u2019\u2019 gives observed state, and \u2018\u2018 \u2019\u2019 gives predicated valuable or ideal position. In this section, the dynamic modelling of the multi-body system of the plant is carried out in terms of the Newton\u2013Euler equations with Lagrange multipliers. The multi-body dynamics model of the Gough\u2013Stewart platform mechanism shown in Fig. 2 includes 14 rigid bodies. Two of which represent the base and stabilized platforms, and every leg is composed of two rigid bodies. Fig. 4 illustrates the base platform, stabilized platform and the ith leg of the Gough\u2013Stewart platform. In the following equations, the subscript \u2018\u2018a\u2019\u2019 denotes the base platform, \u2018\u2018b\u2019\u2019 denotes the stabilized platform, \u2018\u2018Ui\u2019\u2019 denotes the upper part of the ith leg and \u2018\u2018Li\u2019\u2019 denotes the low part of the ith leg (i \u00bc 1; 2;y; 6). Let X 0 kY 0 kZ0 k be the corresponding local reference frame, let rk denote the position vector of center of mass of body k; and pk be the Euler parameter orientation co-ordinates of the kth rigid body with reference to the global reference frame XYZ: Let s0ai and s0bi; respectively, denote the position vector of point Pai in the frame X 0 aY 0 aZ0 a; and that of point Pbi in X 0 bY 0 bZ0 b: To further simplify the notation, define r \u00bc rTa ; r T b ; r T U1; r T L1;y; rTU6; r T L6 ; p \u00bc pT a ; p T b ; p T U1; p T L1;y; pT U6; p T L6 ; G \u00bc diag \u00f0Ga;Gb;GU1;GL1;y;GU6;GL6\u00de; J0 \u00bc diag\u00f0J0a;J 0 b; J 0 U1;J 0 L1;y;J0U6;J 0 L6\u00de; FA \u00bc FAT a ;FAT b ;FAT U1;F AT L1 ;y;FAT U6;F AT L6 ; n0A \u00bc n0AT a ; n0AT b ; n0AT U1 ; n 0AT L1 ;y; n0AT U6 ; n 0AT L6 : \u00f02\u00de where mk is the mass of the kth body",
            " The control law of the ith leg can be written in the following form: ui\u00f0k \u00fe 1\u00de \u00bc \u00f0Kp\u00dei\u00f0%li\u00f0k \u00fe 1\u00de li\u00f0k\u00de\u00de%ii\u00f0k \u00fe 1\u00de; i \u00bc 1; 2;y; 6; \u00f023\u00de where \u00f0Kp\u00dei and \u00f0Kv\u00dei are, respectively, the position and velocity gains. In this section, simulation results for the plant are computed via the model described in the previous sections. The dimensions of the plant are shown in Fig. 7. The system includes: base platform, the stabilized platform and the six actuators. The base platform is supported by 12 springs, including 8 suspension springs and 4 stabilized springs (see Fig. 2). The parameters of the Gough\u2013Stewart platform are given in Appendix B. The Adaptive Adams methods with Runge\u2013Kutta Starters [13] and the generalized co-ordinate partitioning approach [12] are used to solve Eq. (3). The algorithms are implemented with the object-oriented C++ language. In the simulations, the assumed values of position and velocity gains of the Control Law (23) are (arrived at by trail and error), respectively, \u00f0Kp\u00dei \u00bc 20; 0000 and \u00f0Kv\u00dei \u00bc 24; 500 for i \u00bc 1; 2;y; 6: The spring coefficient of the springs is 20,000N/m and the damping ratio x \u00bc 0:05: The selection of the parameters of the springs is to insure that the main frequency of the plant is about 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001625_robot.1994.351105-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001625_robot.1994.351105-Figure5-1.png",
        "caption": "Fig. 5: Initial and final configurations",
        "texts": [],
        "surrounding_texts": [
            "features and B\u2019s ones in contact. For an example, the type-A contact is a contact state where a A\u2019s face and a B\u2019s vertex is in contact. From the assumption that A and B are convex polyhedra, the topology can be determined only by the topology of A and B\u2019s boundary faces independent of the geometry of C-surfaces. In the following, we show the algorithm to construct the topology and that to determine a topological path on this adjacency graph.\n3.1 Constructing the topology\nFigure 2 shows the algorithm to construct the topology of C-Obstacle boundary faces, where a C5face is defined by a boundary face of the CObstacle with five dimension corresponding to a point contact between A and B, a C4 f ace by that with 4- dimension to an edge contact, and a C3face by that with %dimension to a face contact. The function\nl.for every face f of A for every vertex v of B C5f aces-A <- Create-C5f ace(f v) 2.for every face f of B for every vertex v of A C5f aces-B <- Create-C5f ace(f v) 3.for every edge el of A for every edge e2 of B C5faces-C <- Create-CSface(e1 el) 4.for every face f of A\n4-1. C4faces-A <- Create-C4face(f e2) 4-2. Make-Arc(C4face-A(f e2) C5face-A(f Pvert(e2))) Make-Arc(C4face-A(f e2) CSface-A(f Nvert(e2))) 4-3. for every edge el of f\n5.for every face f of B\n5-1. C4faces-B <- Create-Clface(e1 f) 5-2. Make-Arc(C4face-B(el f) CSface-B(Pvert(e1) f)) Make-Arc(C4face-B(el f) C5face-B(Nvert(el) f)) 5-3. for every edge e2 of f\n6.for every face fl of A\n6-1. C3faces <- Create-CBface(f1 f2) 6-2. Make_Arc(C3face(fl f2) C4face-A(fl e2)) 6-3. Make-Arc(C3face(fl f2) C4face-B(el f2)) 7.Return C-Obstacle(C5faces-A,B.C, Clfaces-A,B C3faces)\nfor every edge e2 of B\nMalre-Arc(C4face-A(f e2) Clface-C(e1 e2))\nfor every edge el of A\nMake_Arc(C4face-B(el f) C5face-C(el e2))\nfor every face f2 of B\nfor every edge e2 of f2\nfor every edge el of fl\nFig. 2: Algorithm Constructing C-Obstacle Topology\nCreate-Cface generates a node of the graph which stores the combination of A\u2019s feature and B\u2019s feature. The nodes for C5faces are generated in step 1-3, those for C4 f aces in step 4-1, and those for C3 f aces\nin step 6-1 respectively. A C4face-Type-A corresponding to the contact between a face f and en edge e2 is adjacent to the C5face-Type-A to that between a face f and a vertex Pvert(e2) (Nvert(e2)), where Pvert(e2) d Nvert(e2) are two end points of e2 respectively. The C4face-Type-A is also adjacent to the C5face-Type-C corresponding to the contact between every edge of the face f and the edge e2. The corresponding arcs of the graph are made in step 4-2 and 4-3, and illustrated in Fig.3. We can make the arcs between C4face-type-\nB and C5face-type-B in the same way. This process is shown in step 5-2 and 5-3.\nA C3face between faces f 1 and f 2 is adjacent to the C4face between the face f l and every edge e2 of the face f 2 and that between every edge e l of f 1 and the face f 2. The corresponding arcs are made in step 6-2 and 6-3, and illustrated in Fig.3. Note that a C5face is adjacent to a C3face if two vertices become contact with a face simultaneously. We omit such arcs because the corresponding motion is very difficult to realize by an actual robot. We also exclude the C4face corresponding to the contact between a vertex and an edge for the same reason. However, they must be required if we want to determine the boundaries of Cfaces completely, which is out of our current interests.\nFrom the assumption that A and B are convex, we have no Cfaces with the dimension less than three. So we can obtain the whole topology between Cfaces by the algorithm.\n3.2 Complexity of the algorithm\nLet us analyze the asymptotic time complexity of the algorithm described above. Assume that T A , the number of the faces of A is equal to T B for simplicity. Let the number be T . Then the maximum number of the edges is 3r - 6 and that of the vertices 2r - 4[10]. Therefore, we can compute step 1-3, 4-1, 5-1 and 6- 1 in 0 ( r 2 ) . We can also execute step 4-2, 4-3, 5-2 and 5-3 in 0 ( r 2 ) if we search C5face-A(f Pvert(e2))) etc. by the hashing. Step 6-2 and 6-3 are a little bit complicated. Let the number of the edges on the i-th",
            "face of A be vi, and that of the j-th face of B w,. Note that one edge is on two faces, we can have the relation,\nc r r r\n+. r\n5 2(3r - 6) + C 2 ( 3 r - 6) i= l j=1\n= 12r2 - 2 4 ~ . (16)\nSo these steps can be computed in O(r2) . Consequently, the asymptotic time complexity of the algorithm is O(r2) . It is optimal because the number of Cfaces is also O ( r 2 ) .\n3.3 Determining a topological path\nWhen the adjacency graph is obtained, we can have various way to determine the topological path from the initial Cface to the final one. The best way depends on what kind of path we want to find. In this paper, we use the breadth first search. It implies that we find a path with the minimum length. An example of the path is shown in Fig.4.\n4 Roadmap on C-Obstacle boundary\nIn this section, we describe how to plan a motion on a C-Obstacle boundary face. Our approach can be classified into the roadmap methods[ll]. If we can solve six equations each of which is such equation as (ll), (13) or (15), we can obtain the roadmap. The number of variables in Equation ( l l ) , (13) or (15) is seven, and it can be reduced to six in each cube Ci if each equation is divided by e! and use O j s instead of ejs (See Sec.2). However, the complexity of the algorithm to solve such equations is very bad, so we must avoid to solve them naively. In our algorithm,\nthe roadmap can be determined by solving three equations symbolically only in rotational variables, and by substituting the solution to the other three equations with the translational and rotational ones.\n4.1 Geometry of the roadmap\nWe can give the algebraic equations to determine the roadmap for every combination of two adjacent C-Obstacle boundary faces. For an example, we have the algebraic equations corresponding to the transition from C5face-Type-A to C4face-Type-A. The number of the combinations is twelve. Since it is impossible to describe all of them due to the limit of the space, we present the part of them along the following example. At each transition from one contact state to another, we have many possible motions. We chose the following motions considering the robustness for such errors which may occur in the red world.\nLet us consider the example whose initial configuration is shown in Fig.S(a) and final one in (b). The\ninitial configuration is on C5face-Type-B and the final one on C5face-Type-C. First, the topological path is determined by the algorithm presented in Sec.3. The obtained path is (C5face-Type-B, C4face-TypeB, C5face-Type-C, C4face-Type-B, C5face-Type-C), which is illustrated in Fig.4.\nThe first motion makes the diagonal line VA~VA, parallel to the face F B ~ while keeping the positions of V A ~ and VA, (See Fig.6). The motion is specified by\nQVA, Qt + X = Vil ,\nQ(VA, - VA,)Q~ = Vi, - Vi 1 '\n(17)\n(18) where Vil and Vi, are the position of V A ~ and VA, respectively where A is at the initial configuration. Equation (17) keeps the position of VA, and Eq.(18) the orientation of the edge VA,VA~. We can have\nx = vi, - QVA,Q+, (19)",
            "from Eq.(17). Therefore, the total equations can be solved by substituting the solution of Eq.(18) to Eq.(19). That is, we can have the desired curve in the configuration space by solving the quadratic equations with three variables because the number of variables in Eq.(18) can be reduced to three in each cube Ci. The end point of the curve is determined by\n(20) 1 Z~~(&(VA' - V A ~ ) @ N B ~ ) = 0,\nwhich is the condition that VA,VA' is parallel to the face FB, whose normal vector is represented by NB, . We computed the solution for the example, but it is too long to be written down here. So it is illustrated in Fig.7. The equations are algebraic but nonlinear,\nso several solutions can be found in general. We used the applicability conditions presented in Sec.2 to select the proper solution.\nNext we move the edge V A ~ V A ~ to be in contact with the face F B ~ while keeping the position of V A ~ . This motion can be given by Eqs.(l7), (20) and\n1 - t r ( N ~ , (Viz - Vil )Q(VA~ - V i )Qt) = 0, 2i (21)\nwhich determines the axis of rotation. The motion terminates when\nThese equations can also be solved in three variables, and the planned motion is shown in Fig.8. If we con-\nsider the edge contact as the conjunction of two point contacts, the obtained algebraic equations may include\n1 1 - ~ ~ ( - - B , Q Q ~ 2 + N B ~ ( Q V A ~ Q ~ + Q Q ~ X ) ) = 0, (23) - t r ( -dB1~Qt 2 + N B ~ ( Q V A ~ Q ~ + QQ+W = 0, (24)\ninstead of Eqs.(l7) and (22), which consider the edge contact as the conjunction of one point contact and the orientation of the edge being parallel to the face. Then we must solve the equations with six variables, which should be much more difficult than our equations. Though Eqs.(23) and (24) have the linear forms in X as pointed out in [6], but they can not be solved only in variables z,y,z. Because the coefficients of these variables come from the same N B ~ , so Eqs.(23) and (24) are linearly dependent with respect to z, y, z .\nThough the edge can be in contact with the face by a single motion from the initial configuration, instead of the above motions. But we use two motions because the first motion makes the polyhedron be a robuster configuration. and the second motion can be used for the transition which is intermediate in the topological path as well as initial.\nNow the edge V A ~ V A ~ is in contact with the face Fsl, and must be moved to the edge VB~VB~ in the next according to the planned topological path. This sliding motion can be specified by Eqs.(20), (22) and\n1 2 -Q(VA~ + V A ~ ) Q ~ + X\nwhere Viz is the current position of VA~. The midpoint of the edge V A ~ V A ~ is at the initial position if t = 0, and at the midpoint of the edge VB, Vg2 if t = 1. Besides, the final orientation of the edge VA,VA~ can be determined by"
        ]
    },
    {
        "image_filename": "designv11_11_0000177_(sici)1097-4628(19990705)73:1<121::aid-app14>3.0.co;2-9-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000177_(sici)1097-4628(19990705)73:1<121::aid-app14>3.0.co;2-9-Figure3-1.png",
        "caption": "Figure 3 Effect of [PDS] on Rh. [ANI]A/[OT]B 5 0.30 mol L21, [HCl] 5 1.00 mol L21, temperature 5 45\u00b0C, weight of PET 5 0.20 g.",
        "texts": [
            " In the present case, the added fiber for grafting and the formed homopolymer may cause the autoacceleration effect due to the surface effect. Using the previously described facts, the rate of PANI or POT formation was monitored for different [PDS] and [ANI] or [OT]. To arrive at the kinetic equation as applicable to the present case, it is worthwhile to analyze the dependence of Rp(ANI) on [ANI], [PDS], and the amount of PET fiber. It can be seen that Rp(PANI) versus [ANI] (Fig. 4, plot A) is found to be linear, with a definite intercept and Rp versus [PDS] (Fig. 3, plot A) is a straight line and with negligible intercept. Using the above facts, Rp~ANI! 5 k1[ANI][PDS] 1 k2[ANI][TAS] 1 k3 Table III Effect of [PDS] on Graft Parameters [PDS] (mol L21) Rh 3 107 (mol L21 s21) Rg 3 107 (mol L21 s21) % Grafting % Efficiency a b a b a b a b 0.005 20.21 15.55 3.81 14.93 1.60 7.20 0.41 0.63 0.010 39.01 24.15 6.82 23.12 2.85 11.65 0.55 0.97 0.015 68.01 60.55 9.22 26.12 3.85 12.60 0.74 1.58 0.020 89.12 108.66 12.36 28.61 5.15 13.80 1.10 1.73 0.025 76.71 136.14 18.33 32",
            " where k1, k2, and k3 are rate constants for the formation of PANI on bare, due to surface effect by homopolymers, backbone fiber and due to the grafted surface, respectively. [TAS] 5 total available surface (includes homopolymer and backbone on weight basis). If homopolymerization of ANI alone is the only possibility (without grafting onto PET), the rate constant k1 would have been the simple rate constant of the formation of PANI. The rate constants as applicable to the ANI case are evaluated from the slope and intercept of the plots Rp(PANI) versus [PDS] (Fig. 3, plot A) and Rp(PANI) versus [ANI] (Fig. 4, plot A). It was found that the k1 value for the present case is different from the one obtained by Tzou and Gregory23 for the simple PANI formation (rate constant 5 0.0008 min21). For the present case, PANI k1 was found to be 0.96 min21, which is far higher than the simple homopolymerization rate constant and augumenting the autoacceleration effect on homopolymerization by TAS and grafting. From the fact that Rp versus [PDS] (Fig. 3, plot A) passes through the origin, it can be inferred that the surface factor rate constant k2{k2(TAS)} and k3 are low and obviously suggesting lower rate of grafting in comparison with homopolymerization. This is in accordance with the dependence of amount of fiber taken on Rg (Table IV) and suggests that grafting contributes through the third factor in eq. (1). Also Rp(PANI) versus [ANI] has a definite intercept that gives the value of k3 as 1.62 3 1024 mol L21 s21. This k3 can now be taken as a contribution to the surface changes due to chemical grafting. A similar procedure gives k1 and k3 values for the POT case as 0.15 min21 and 1.37 3 1024 mol L21 s21, respectively. Two linear regions for Rp(POT) versus [PDS] (Figure 3, plot B) were found. Although the lower region gives k1 value lesser than PANI case, in the upper region the slope of the plot gives a higher k1 value. This fact is in accordance with the trend of Rg toward changes in [PDS]. It may be inferred that, at lower [PDS], the POT grafting efficiency is more than PANI. However, in the higher [PDS], the reverse grafting efficiency was noticed. Such a surface effect was noticed for fabric, PANI, alumina by Tzou and Gregory,23 but the changes in the surface factor could be correlated meaningfully"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001060_s0167-8922(00)80165-0-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001060_s0167-8922(00)80165-0-Figure1-1.png",
        "caption": "Figure 1. The fluorescence test rig",
        "texts": [
            " Experiments are made on static and sliding contact of smooth surfaces as well as on sliding in the mixed lubrication regime with rough surfaces. A fluorescent substance absorbs radiation at a certain wavelength band, and re-radiates some of the absorbed energy at a longer wavelength. These wavelengths depend on electrochemical structure of the substance, and in many cases the optimum absorption wavelength is in the ultraviolet region. A fluorescence microscope is designed to illuminate a target thereby causing fluorescence and at the same time to allow only fluorescent light to be viewed by an observer. Figure 1 schematically shows the test rig used, in which a disk is driven by a motor and makes sliding contact with a stationary ball under a fluorescence microscope. The microscope is equipped with a high pressure mercury lamp, a filter unit and a monochrome CCD camera. The filter unit consists of an exciter filter, a dichroic mirror and a barrier filter. Spectrum properties of the filters are chosen such that the exciter filter transmits light which is strongly absorbed by a fluorescent substance, while dichroic mirror and the barrier filter transmit only light of longer wavelength"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003256_j.jsv.2004.06.029-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003256_j.jsv.2004.06.029-Figure1-1.png",
        "caption": "Fig. 1. Ball bearing: (a) with linear spring characteristics, and (b) with weak nonlinearity spring characteristics [2].",
        "texts": [
            " In this work, a fuzzy model is proposed for the vibration analysis of nonlinear rotor-bearing systems. In rotating machines, nonlinear spring characteristics appear due to various causes as stated earlier. When the restoring force is expressed as a function of the deflection, the nonlinearity is often classified into two types; it is called weak nonlinearity when the deviation from a linear relationship is small, and is called strong nonlinearity when it deviates appreciably from a linear relationship. Fig. 1 shows two cases of spring characteristics that are obtained when the lower end of an elastic shaft is supported by two different types of bearings. The upper end is supported by a double-row self-aligning ball bearing in both the cases. Fig. 1(a) denotes a case where the lower end is supported by a double-row self-aligning ball bearing. As the inner surface of the outer ring forms part of a sphere, the inner ring can turn freely and the supporting condition will be a simple support. In this case, the spring characteristic of the shaft will be linear. Fig. 1(b) indicates the case where the lower end is supported by a single-row deep-groove ball bearing. Because the balls roll in the grooves carved in both the inner and outer rings, the inner ring cannot incline relative to the outer ring and therefore the supporting condition will be a fixed support. However, due to the small clearances present among the inner ring, balls, and the outer ring, the inner ring can incline slightly and the supporting condition becomes a simple support within this clearance. In bearing engineering, the terms radial clearance and axial clearance are commonly used to express the accuracy of bearings. But as it is most convenient to express the clearance by an angle in the treatment of restoring force, the term angular clearance is used in vibration engineering. This angular clearance exists in every direction and can be expressed by a cone as shown in Fig. 1(b). The supporting condition is a simple support when the centerline of the shaft is located in this cone and becomes a fixed support when it is out of the cone. Thus, the restoring force will have the nonlinear characteristics of a piecewise linear type, as shown in Fig. 1(b). In a practical setup, the transition from a simple support to a fixed support occurs gradually because clearances around each ball disappear one by one as the inclination of the shaft increases. Therefore, the practical transition is comparatively smooth and the spring characteristics can be approximated by a power series of low order. Hence, the setup shown in Fig. 1 is generally assumed to have a weak nonlinearity. Some machine elements cause strong nonlinearity in the system. For example, since ball or roller bearings have little damping effect, aircraft gas turbine engines generally adopt squeeze film damper bearings for some of their bearings. A simplified model of such a bearing is shown in Fig. 2. Damper oil is supplied between the bearing holder A and the casing B. Holder A is supported by a weak spring S and is kept at the center of the casing B. When the shaft vibrates, element A moves relative to element B, and therefore the oil dampens the vibration",
            " The mass unbalance forces are given by f eu \u00bc meO2 cos \u00f0Ot \u00fe j0\u00de; f ev \u00bc meO2 sin \u00f0Ot \u00fe j0\u00de; (12) when the mass m is situated at a distance e from the geometric center of the shaft. The restoring forces in the x and y directions can be expressed, in a general form, as [2] f u \u00bc c1u2 \u00fe c2uv \u00fe c3v2 \u00fe c4u3 \u00fe c5u2v \u00fe c6uv2 \u00fe c7v3; f v \u00bc d1u2 \u00fe d2uv \u00fe d3v2 \u00fe d4u3 \u00fe d5u2v \u00fe d6uv2 \u00fe d7v3; \u00f013\u00de where ci and di, i=1,2,y,7, are constants. In this work, bearings with weak nonlinearity spring characteristics, as shown in Fig. 1, are considered. In this case the bearing restoring forces are usually modeled by the third power of the displacement, so that the bearing forces can be expressed, including linear damping characteristics, as [10,11] f bu \u00bc K1u \u00fe K3u3 \u00fe C _u; f bv \u00bc K1v \u00fe K3v3 \u00fe C _v; (14) where K1 and K3 are the linear and nonlinear stiffness coefficients and C is the linear damping coefficient. These and other coefficients of the rotor are shown in Fig. 5 and the numerical values of the bearing parameters used in the simulations are listed in Tables 1 and 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000963_cp:19971080-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000963_cp:19971080-Figure1-1.png",
        "caption": "Fig. 1: Representation of skewed rotor bar",
        "texts": [
            " Representation of Skew Axial variations in the geometry of a skewed induction motor could be included in a full 3-D finite-element model. However such an approach is still too computationally expensive to produce results in a reasonable time. An alternative method of modelling skew must therefore be found. Williamson, Flack and Volschenk have demonstrated that the finite-element model described above can be extended to represent skew in machines [6]. In this extended model the skewed bar of Fig l a is represented by a number of straight rotor bar segments each offset from each other as shown in Fig 1 b. As the number of segments included in the model increases the accuracy with which the model represents a skewed bar increases. Using this approach the skewed motor can be represented by a number of 2-D slices each at a different position along the axis of the skewed motor. Two-dimensional finite-element analysis can be used to calculate the flux-distribution in each slice. The calculation in each slice is independent of that in other slices, therefore if M slices are used in the model and there are N nodes in each slice then M N-node solutions are required"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000179_1.2893956-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000179_1.2893956-Figure6-1.png",
        "caption": "Fig. 6 Coordinate transformation of the location angle",
        "texts": [
            " S,\u201e = (5, \u2022 e\u201e)e\u201e, Sj\u201e = (Sj- e\u201e)e\u201e (4) where, e\u201e is a unit normal vector of the contact point defined as e\u201e = sin /3e^ + sin a cos Piy + cos a cos pe, (5) Using Eqs. (3), (4) and (5) we can get the normal displace ment vectors as follows. Sinis) = ((Xi + rtd^) sin (3 + {yi + sd,j) sin a cos /? + (Zi \u2014 rid; \u2014 sByi) cos a cos /?)e\u201e Journal of Vibration and Acoustics APRIL 1999, Vol. 121 / 143 Downloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use y which is given in Fig. 6. Then the general stiffness matrix [Kc] of the gear pair can be written as [Ka] = [R(y)V [K'a]lR(y)] (11) where [R(y)]isa general transformation matrix for the rotation 7- Considering static transmission errors in the gear meshes, such as pitch errors or axial apex wobbles, which are the result of above errors, the contact points will vary as a function of rotating angle. So the reaction force of the mesh can be rewritten as follows (Kishor and Gupta, 1989). [ ^ G ] ( { q ] ( P c } ) = [to (12) where {q} is the displacement vector of the two gears' nodes and { PG } is the vector of transmission error"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002327_s11044-004-2516-1-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002327_s11044-004-2516-1-Figure1-1.png",
        "caption": "Figure 1. Torsion beam mesh with shell and rigid elements.",
        "texts": [
            " The modal reduction was operated starting from a linear finite element (FE) model of the torsion beam. Several wheel travel and static load analyses were performed, varying the stiffness of chassis connection bushings. The results of multibody simulations were compared with those obtained from a non-linear FE model in order to evaluate the possible limits of the multibody model, where the elastic deformation of the torsion beam is based on a linear modal superposition approach. First of all, the mesh of the torsion beam was created (Figure 1). The same mesh was used to build both a non-linear FE (ABAQUS) and a linear FE model (NASTRAN). The structure was modelled by means of shell elements and rigid elements in the points where the beam is attached to the chassis and other suspension parts. The attachment points (shown in Figure 1) are: \u2022 chassis bushing attachments: points 1, 2; \u2022 springs lower attachments: points 3, 4; \u2022 shock absorbers lower attachments: points 5, 6; \u2022 wheel bearing centres: points 7, 8. The non-linear FE model includes the other suspension elements, such as: springs, bumpstops, chassis attachment bushings, wheel bearings and shock absorbers elastic forces. It also includes the static subcases to run the elastokinematic analyses. These subcases consist of the commands which assign vertical displacements or applied loads to the wheel centres",
            " The number, q, of significant eigenmodes is chosen in the q-set. A certain number of internal nodes (collected in the c-set) can be chosen as measurement points and points for graphical representations. 2. A modal analysis for the reduced virtually unconstrained system is performed in order to get the eigenvectors [\u03a6m] and the corresponding eigenvalues \u03c9m, which should be close to those of the original system. For the torsion beam, the b-set of master nodes includes the attachment points from 1 to 8 (Figure 1) where forces and constraints have to be applied within the multibody model. The c-set contains some internal nodes for the graphical representation of deformations. The number of dynamic DOFs in the q-set was put equal to 16 (= 6 rigid body modes + 10 eigenmodes up to \u2248500 Hz) in order to consider a frequency range up to max = 250 Hz for future dynamic analysis. In Table 2 the eigenvalues of the reduced unconstrained system (excluding rigid body modes) are shown together with those of the original system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000966_20.717601-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000966_20.717601-Figure2-1.png",
        "caption": "Fig. 2. S&ematics of the benchmark problem-Twin-disk rotor.",
        "texts": [
            " This fact leads to the numerical results of table I (section B) and to the conclusion that the analytical solution with respect to r and to z reported below V O J O 2 02 .C (-l>'+j j'sin(e-e,)ln[ri - r , cos(e-ep)+rII] d e (8) 01 Po J o Be =-- 2 0 2 01 Br = ~ 4x iJ=1 4n (-i)'+j j'cos(e-ep)zn[rz -rpcos(e-eP)+r,,]de (9) Po Jo z,j=l Bz = ~ 4x where: must be preferred in other to save computational time. This aspect is important especially in inverse and optimization problems. Iv. A BENCHMARK PROBLEM ( 5 ) In this section an experimental validation of the expressions reported in this paper made by means of the benchmark problem shown in fig. 2 is presented. This benchmark problem deals with the evaluation of the induced field created by a twin-dwk rotor. The magnetic induction was calculated and measured along the two lines a-b and c-d, shown in the same fig. 2. The measurements were made by means of an Hall probe and a digital millivoltmeter. In table I1 are reported the m a n parameters of this benchmark configuration. In the figures 3, 4 and 5 are reported the values of the inagnetic induction calculated and measured The experimental data confirm the numerical results Differences may be explained by the fact that the calculations neglect the effects of the current paths in the linking connections among the disk sectors (shown in black in Fig. 2). (6) (7) 2604 TABLEII MAIN PARAMETERS OF THE BENCHMARK CONFIGURATION - T W I N DISK ROTOR inner radius rl 300 mm outer radius r2 1300 mm &sk thcknes Az 25 mm 120 mm space between the d~&s s current I 10 A (DC) poult a (quotes ul mm) poult b (quotes In mm) poult c (quotes U1 mm) p o d e (quotesmmm) polnt f (quotes In mm) r, = 800,6, = -n/8 rad, z, = -50 rb = 800, &, = -d8 rad, q, = 50 rc = 400, BC = - d 8 rad, zc = 0 re = 800, Be = -7c/4 rad, ze = 0 rf= 800,Bf= 0 rad, q= 0 poult d (quotes ul mm) rd=1200,ed=-n/8rad,Zd=O V"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001548_spire.2000.878181-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001548_spire.2000.878181-Figure1-1.png",
        "caption": "Figure 1. A membrane structure.",
        "texts": [
            ". Introduction P systems are a class of distributed parallel computing models inspired from the way the alive cells process chemical compounds, energy, and information. In short, in the regions delimited by a membrane structure (see Figure 1 for an illustration of what this means), are placed multisets of objects, which evolve according to evolution rules associated with the regions; the objects can also be communicated from a region to another one, according to certain target indications, while the membranes can be dissolved (and then the objects of the dissolved membrane remain free in the region directly outside it) and divided (then the contents of the divided membrane is copied in each of the resulting membranes); the rules are applied in the maximally parallel manner (in each time unit, all objects which can evolve should evolve); a computation consists of transitions among system configurations, while a complete computation is a halting one; the result of a complete computation is either the number of objects present in the halting configuration in a specified output membrane, or it is read outside the system, as the sequence of objects leaving the system during the computation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001224_1.2801113-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001224_1.2801113-Figure2-1.png",
        "caption": "Fig. 2 Experimental configuration",
        "texts": [
            ", computed Cartesian po sition and orientation, actual and reference joint position) and/ or overwrite them according to the results of PC-executed con trol algorithms at the frequency of 1000 Hz. The ATI (Assur ance Technology Inc.) 6-axes wrist force/torque sensor is fitted to the arm end-effector and linked to the PC through a parallel link (force data transmission takes 0.4 ms). In the experiments, all the motors have been braked but the one moving the fifth joint, in order to obtain a single-axis robot arm, while the tip of the tool, ensuring a point contact, has been made contacting a very massive marble table, directly leaned to the wall. Figure 2 shows the experimental configuration from the top: a fixed Cartesian frame is chosen such that the axes x and y are, respectively, normal and parallel to the interaction surface and lie in an horizontal plane, while axis z (not shown in figure) is aUgned with the axis of motion of the fifth (revolute) joint; / = 20 cm is the distance of the point of contact from the fifth joint axis and 0 is the angle between the y axis and the normal to the z axis, intersecting the point of contact (0 = e = 45deg, inFig. 2). Under these experimental conditions it is possible to establish a clear and direct matching of the physical setup with the simple linear models widely used in the literature to analyze force control dynamic stability. In fact, neglecting link flexibility with respect to transmission (joint) compliance (which is a reason able hypothesis when dealing with industrial robots) the con strained robot can be modelled by the (lumped-parameter) 2- mass model depicted in Fig. 3, where r \u201e is the torque delivered by the fifth joint motor, 9^ and 6i - p9 are respectively the motor and link coordinate referred to the motor shaft (p = 50 is the gear ratio), J\u201e is the rotor inertia and 7; is the moment of inertia of the fifth link, referred to the motor shaft, D\u201e, ac counts for the passive viscous damping acting on the motor coordinate (only linear damping is here considered), Ki and /), are, respectively, the transmission chain stiffness and damping, Tj = K^d, + Dfi, is the reaction torque, being K^ and D, the contact stiffness and damping, all referred to the motor shaft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000659_s0043-1648(02)00033-9-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000659_s0043-1648(02)00033-9-Figure5-1.png",
        "caption": "Fig. 5. Attachments for inducing additional tangential force between two rollers.",
        "texts": [
            " 4 shows the sizes of each artificial indentation compared with the sizes of contact ellipses calculated without the indentation taken into account. As will be discussed later, tests were performed under three load conditions with the Rockwell indentations and under a single load condition with the Vickers (L) and (S) indentations. In all cases, it should be noted that the indentation size is much smaller than the contact ellipse size. As another characteristic of this study, testing with additional tangential force between rollers was conducted only when the large roller was operated as the follower. Fig. 5 shows the attachments for applying additional tangential force between rollers, which consisted of a half-copper disk with a dead weight and permanent magnets. The half-copper disk and dead weights were attached to the end of the follower shaft as shown in Fig. 2. In this manner, a non-contacting tangential force is applied during half of each rotation, specifically when the outer periphery of the half-copper disk passes thorough the aperture of the permanent magnets. The dead weight was attached to the half-copper disk for balance so as to keep the rotation stable",
            " In this table, the rotational speeds of the small rollers are displayed. As indicated in Fig. 1, the radius ratio of the large and small rollers is 4:1, i.e. the rotational speeds of the large rollers are one fourth that of the small rollers. Lubricant was supplied to both rollers by pads. Due to the fact that the slip ratio could not be measured successfully at the actual conditions, Table 2 shows additional tangential force as simply mentioned \u201cwith\u201d or \u201cwithout\u201d using the attachments as shown in Fig. 5. Table 3 shows the test results where the small roller was operated as the driver and the large roller as the follower. In these tests, the rotational speed of the small roller was 4000 rpm, and the Rockwell indentations were on the large roller. The data shown reflects the variation resultant from the changes in the number of indentations, contact load, and additional tangential force. Table 4 shows the test results in which the small roller was operated as the follower and the large roller as the driver"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000052_978-3-642-58552-4_41-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000052_978-3-642-58552-4_41-Figure9-1.png",
        "caption": "Fig. 9. Derivatization reaction of primary amino acids with o-phthaldialdehyde in the presence of a nucleophile (2-mercaptoethanol) and under alkaline conditions yields highly fluorescent isoin doles which gradually degrade to non-fluorescent derivatives.",
        "texts": [
            " Several fluorogenic reagents are available, among which o-phthaldialdehydel2-mercap to ethanol (OPAIMCE) based reagent is the most common for analysis of physiological amino acids. In the alkaline medium (borate buffer, pH 9.5), the primary amino acids and some related amines react rapidly already at room temperature with OPA in the presence of nucleophile (MCE) to form various substituted isoindoles. These com pounds, when excited at 340 nm, emit fluorescence light at 450 nm. However, the fluo rescence isoindoles are rather unstable and subsequently degrade to non-fluorescent derivatives (Kehr 1993), as depicted in the reaction scheme in Fig. 9. Precolumn deriva tization with OPA/MCE allows easy automation and a use of reversed-phase columns for gradient separations (Lindroth and Mopper 1979). Several instrumental systems were described for rapid separation of amino acid neurotransmitters aspartate (Asp) and glutamate (Glu) (Kehr 1998a) or y-aminobutyric acid (GABA) (Ungerstedt and Kehr porating column wash-out steps with acetonitrile (ACN) is the simplest and most cost- effective HPLC system for automated analysis of aspartate (Asp) and glutamate (Glu) based on pre-column derivatization and fluorescence detection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000618_s0020-7462(97)00052-8-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000618_s0020-7462(97)00052-8-Figure2-1.png",
        "caption": "Fig. 2. Plot of tanh(ax).",
        "texts": [
            " The control algorithm which determines the stabilizing torques for the system having a general base point motion is designed as follows: Mh\"!(kh#mog)h!K $hhQ !moG 0 sgn(hQ ) D h D!moF 0 sgn(hQ )!K 1 tanh(a 1 h) , Mt\"!(kt#mog)t!K $ttQ !mo(G 0 #F 0 ) sgn(tQ ) DtQ D!moH 0 sgn(tQ ) !K 2 tanh(a 2 t), (4) where F 0 , G 0 and H 0 are D fI$ (t) D, DgJ$ (t) D and Dh3\u00ae (t) D or greater. The terms related to K i and a i (i/1,2) are the parameters of the compensation torques with the hyperbolic function tanh(ax)\" eax!e~ax eax#e~ax . Referring to Fig. 2, as aPR, the hyperbolic function tanh(ax) tends to sgn(x). The inclusion of such compensation torques controls the region within which the control system is stabilized as discussed by Cai and Song [20] and as will be demonstrated in our simulations. To discuss the solution concept and system stability, the state-space model of the inverted pendulum is first derived. Assuming that the state space vector x\"Mx t , x 2 , x 3 , x 4 NT, where x 1 \"h and x 2 \"t, the state-space model for the system described by equations (1) and (4) is xR 1 \"x 3 , (5a) xR 2 \"x 4 , (5b) xR 3 \" 1 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002364_robot.2001.933087-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002364_robot.2001.933087-Figure3-1.png",
        "caption": "Fig. 3. The automotive waterpump selected as object 6.",
        "texts": [
            " To judge the ease of computation, worst case execution times, TE, for each method applied to a set of test objects and friction coefficients will be measured. 4.2 Testing Procedure To cover a range of complexity, the set of test objects consists of the following: 1. Equilateral triangle, 2. Scalene triangle, 3. Rectangle, 4. Irregular pentagon, 5. Irregular hexagon and 6. Automotive waterpump housing modeled by a 74 sided polygon. These objects are shown in Figures 4-6. A photograph of the waterpump housing is shown in Figure 3. Grasps were planned for the six test objects using: the minimum sensitivity method with the number of guesses ng=100 (termed MS1); the same method with ng=1000 (termed MS2); the maximum wrench ball method with ng=100 (termed WBl); the same method with ng=1000 (termed WB2); the method of Mirtich and Canny (termed hlC); and the two cases of the method of Ponce and Faverjon (termed PF1 and PF2). The two cases PFI and PF2 require further explanation. With the PF method, the optimization is performed for each triple of object edges, and then the overall maximum is selected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000179_1.2893956-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000179_1.2893956-Figure3-1.png",
        "caption": "Fig. 3 Nodal coordinate system of a finite shaft element",
        "texts": [
            " The finite element consists of two nodes, where each node has 5 degrees of freedom by way of two lateral displace ments, two bending rotation angles, and a torsional rotation angle. A lumped mass modeling is used for the analysis of axial vibrations. Then the equations of motion of a typical rotor bearing system can be written as, [M]{q] + ( [ C ] - I a [ G , ] ) { q } + [K]lq} = ( f ) (1) where the global displacement vector {q} and the force vector { f ) , based on the nodal coordinates system as shown in Fig. 3, are represented by f 1 = (2) 3.3 Gear Modeling. The gear pair is modeled by rigid disks and linearly distributed springs along the contact lines. The gear pair used for analytical modeling is shown in Fig. 4, where a and /? are transverse pressure angle and helical angle respectively. The displacement vector of the contact points can be written as a function of .j, which is a local coordinate to the axial direction. Si(s) = (Xi + rAi)e, + (y, + se,t)e, + {z, - r,9, - ,s^\u201e.)e, Sj{s) = {Xj - rjB^j)e, + {yj + s9,j)ey + {Zj + rjdj j)e\\ (3 ) Then the normal displacements of the contact points can be obtained by using of following vector calculations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003820_tmag.2005.852177-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003820_tmag.2005.852177-Figure2-1.png",
        "caption": "Fig. 2. Madelung\u2019s rule of regularity and its meaning to the anhysteretic reversal curve.",
        "texts": [
            " In principle, the Preisach model purely identified from the symmetric minor loops can satisfactorily predict symmetric hysteretic behavior; however, in order to enhance nonsymmetric modeling, a greater amount of data collected from the anhysteretic reversal curves will lead to more accurate hysteresis modeling. The anhysteretic reversal curves can be either measured or constructed from the symmetric minor loops and the initial magnetization curve. The definition of the symmetric minor loops must satisfy Madelung\u2019s rule which states the following. \u201cIn Fig. 2, if some point of the initial magnetization curve becomes a reversal point, then the reversal curve that starts from point reaches point , which is symmetric with respect to the point about the origin .\u201d This qualitative rule with other useful regularities were reported in the early twentieth century known as Madelung\u2019s rules and also restated in [7]. So the definition can be also interpreted in a slightly different way as was reported by Bertotti in [8]: \u201cIf one applies a cyclic field around the origin of variable amplitude to the demagnetized state, one obtains the set of symmetric minor loops",
            " The observation how to create the initial magnetization curve is important and useful, first, for locating the anhysteretic reversal points, which represent the starting points of the anhysteretic reversal curves, and second for composing the anhysteretic reversal curves. It is noticed that the anhysteretic reversal points are lying on the initial magnetization curve and the extension curves needed for the symmetric minor loops to reach the point are identical segments of the initial magnetization curve. The measurement of an anhysteretic reversal curve may be achieved by starting the field from the origin and then reversing it at some point, say , and continuing until reaching the saturation point (see Fig. 2). With the availability only of the symmetric minor loops, an anhysteretic reversal curve is obtained by adding a portion of the initial magnetization curve to the upper (or lower) part of a symmetric minor loop in order to reach the point . That is, one half of the symmetric minor loop, say - , will be added to the segment - , which is copied from the initial magnetization curve. Noticing that the segment - by itself represents another anhysteretic reversal curve will be used in the identification process likewise"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002299_027836402761393487-Figure15-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002299_027836402761393487-Figure15-1.png",
        "caption": "Fig. 15. Triangle by geodesic line.",
        "texts": [
            " We further planned the trajectory of contact coordinates within the CSR. The feedback controller of an object under NE is considered to be our future research topic. Letting uCO = [u1 u2]T , the differential equation of the geodesic line is given by (O\u2019Neill 1997) d2ui ds2 + 1,2\u2211 j,k Ai jk duj ds duk ds = 0, (i = 1, 2), (A1) where s denotes the parameter representing the length of a curve, and Ai jk denotes Christoffel\u2019s notation. We draw an equilateral triangle by the geodesic line on a spheroid (Figure 15). Projecting a geodesic line onto the tangent plane, we obtain a straight line (O\u2019Neill 1997). Therefore, the geodesic line including the pole on a spheroid coincides with the geographical line. To determine the shape of the equilateral triangle with an edge length of l, we use the following method: 1. Start drawing two segments of the geographical lines, with an edge length of l, from the pole. 2. Find the geodesic lines including two ends of the segments of the geographical lines. If there are more than two geodesic lines, select the one with the shortest length between two ends. 3. Change the angle between two geographical lines and find one geodesic line with a length of l between two ends. From this algorithm, we can determine the shape of the equilateral triangle. The inner angles can also be determined for a given length of edge. Then, assuming that the largest triangle is the triangle (B) whose vertices is on the red line as shown in Figure 15(b), we prove the following theorem: THEOREM 2. (Monotonicity of Inner Angle) Inner angles of an equilateral triangle on a spheroid are monotone functions with respect to the length of edge. Proof. Increase the size of the equilateral triangle until the triangle (B) is obtained. We have q2 = \u03c0/2 for the triangle (B). By using reductio ad absurdum, assume that q2 is not a monotone function. In this case, there is the same q2 for different lengths of the edge. First, consider the case where at UNIV OF WISCONSIN MADISON on July 19, 2012ijr"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001209_107754639800400503-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001209_107754639800400503-Figure2-1.png",
        "caption": "Figure 2 depicts a ball bearing system in which the global-coordinates system X Y Z has its origin at the bearing center, with the X-axis coinciding with the bearing axis. The frame ib Jb2b is a rotating-coordinates system spinning with the bearing cage angular velocity, S2~ (rad/s), where the z6-axis coincides with the bearing axis. The bearing\u2019s inner ring is lightly fitted on its shaft and is modeled as an integral part of it and therefore rotates with the velocity Qs. But for zero deadband, the bearing outer ring is fitted into its rigid and nonrotating housing (S2o = 0). The assumption of rigid housing will be relaxed in another paper to follow. It should be noted, however, that the velocities S2S, 52~, and Q,, are absolute. In our current developments, the dynamics of bearing rolling elements are neglected, which is an acceptable approximation for low and moderate bearing speeds of rotation (Harris, 1984). Without loss of generality, the bearing is treated as a two degrees of freedom system and is allowed to oscillate along, respectively, the Y- and Z-axes, where the coupling between the bearing rotating elements and the elastic rotating shaft is of forceelastic oscillations type. That is, the input to the bearing system is the shaft elastic motions, and, in return, the generated bearing forces are inputted to the shaft at the corresponding stations (nodes). Let the global response of the rotating shaft element at its bearing station",
        "texts": [
            " The proposed models that are the subject of this study are very effective tools for predicting dynamic behavior and bearing loads of rotor bearing systems under mass unbalance excitation, as affected by the radial ball bearing clearances, nonlinear stiffness, speed of rotation, and system elasticity. 2. ANALYTICAL MODEL DESCRIPTION Figure 1 shows a rigid disk of circular shape mounted through its center to an elastic shaft that in turn is mounted on two elastic radial rolling element bearings. These supporting bearings, however, are mounted into their rigid housings. The details of the bearing are shown in Figure 2. In Figure 1, the triad XYZ is a global coordinates system with its origin at the geometrical center of the shaft\u2019s left bearing, where the X-axis coincides with the shaft bearings centerline in the nonworking (zero-speed) position of the system. at EASTERN KENTUCKY UNIV on April 22, 2015jvc.sagepub.comDownloaded from 543 Figure 1. Elastic shaft-bearings configuration. The orientation of the deflected rotor element in space (see Figure 3) is monitored using Euler angles (see Figure 4). The elastic rotating shaft is discritized using a Co four-node isoparametric Timoshenko beam element (see Figure 5) with four degrees of freedom assigned to each node-namely, two translational motions plus two total rotations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003698_s00453-005-1202-x-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003698_s00453-005-1202-x-Figure7-1.png",
        "caption": "Fig. 7. (a) Notations of normals of edges and concave vertices. (b) Vertex p is in the simplex S(e) of edge e.",
        "texts": [
            " However, this would cost even more than O(mn) time. Therefore we develop a specialized algorithm based on the lemma below. First, we introduce some notations used in this section. Let e\u2032 and e\u2032\u2032 be the edges incident to p. Let n\u2032p be the inward normal to e\u2032, and let n\u2032\u2032p be the inward normal to e\u2032\u2032. Let Cone(n\u2032p, n\u2032\u2032p) be {\u03bb\u2032n\u2032p + \u03bb\u2032\u2032n\u2032\u2032p|\u03bb\u2032, \u03bb\u2032\u2032 > 0}, that is, the set of all positive linear combinations of n\u2032p and n\u2032\u2032p. In the same way, let Cone\u2212(n\u2032p, n\u2032\u2032p) be the set of all positive linear combinations of \u2212n\u2032p and \u2212n\u2032\u2032p (see Figure 7(a)). For each edge e, let ne be the inward normal to e, and let the open simplex S(e) be s\u0302(e) \u2229 H(e) (see Figure 7(b).) LEMMA 3.4. Placing two point contacts at a concave vertex p and on an edge e immobilizes a polygon if and only if: (i) ne \u2208 Cone\u2212(n\u2032p, n\u2032\u2032p), and (ii) p \u2208 S(e). PROOF. Let e\u2032 and e\u2032\u2032 be the adjacent edges to p, shrunk onto the vertex p, so that s\u0302(e\u2032) is the line orthogonal to e\u2032 through p, and s\u0302(e\u2032\u2032) is the line orthogonal to e\u2032\u2032 through p. We first show that any three edges e, e\u2032, and e\u2032\u2032 satisfying the above statement must satisfy Lemma 3.1. Since p = s\u0302(e\u2032)\u2229s\u0302(e\u2032\u2032) \u2208 S(e) \u2282 s\u0302(e), we must have s\u0302(e)\u2229s\u0302(e\u2032)\u2229s\u0302(e\u2032\u2032) = \u2205"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003408_0166-6851(87)90042-9-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003408_0166-6851(87)90042-9-Figure3-1.png",
        "caption": "Fig. 3. Reciprocal plot~ of respiration rate against [02] for whole N. brasiliensis. The 02 dependence of whole N. brasiliensis was determined. Conditions used were as described in Fig. 1; no exogenous substrate or CCCP was added. Error bars indicate standard error of the means calculated from data obtained in five experiments.",
        "texts": [
            "03 nM 02 s -1 and 143 -+ 9 nM 02 s-1 (mg protein) -1 respectively. 0 2 affinities o f whole N. brasiliensis in the presence or absence o f inhibitor. 02 dependence of respiration over the range 5-210 ~M 0 2 was determined for whole N. brasiliensis suspended in 100 mM potassium phosphate buffer p H 7.2 sup- plemented with antibiotics. Double reciprocal plots were used to calculate the apparent K m values for 0 2 of whole N. brasiliensis utilising endogenous substrate. For five batches of untreated N. brasiliensis (Fig. 3), respiration was diminished at 0 2 concentrations >60 -+ 7.4 p,M and at air saturation was only 33% of its maximal rate. nM 02 s -1 (worm) -1. In the presence of inhibitors, 02 dependence (not shown) followed a similar pat tern to that observed in Fig. 3; the results from the double reciprocal plots are shown in Table I. The SHAMsensitive port ion of respiration proceeding in the presence of antimycin A, was least sensitive to inhibition at high 0 2 concentrations, decreased respiration occurring at 0 2 concentrations >125 -+ 11.0 t*M and at air saturation; this portion of respiration was still 62% of its maximum value. Respiration in the presence of S H A M showed highest affinity for oxygen, giving an apparent K m of 7 -+ 0.5 p,M 02. At air saturation this main respiratory chain mediated activity was only 46% of its maximum value. from whole worms and isolated mitochondria to be made. Activity in the presence or absence of inhibitor followed a similar pattern to that observed in whole N. brasiliensis (Fig. 3); results obtained from double reciprocal plots are shown in Table I. From these observations it can be seen that the variations in Km values found in whole N. brasiliensis are not seen in isolated mitochondria, the highest affinity for 02 was that of mitochondria in the absence of inhibition (3.5 -+ 0.2 I~M 02). Comparison of the threshold values for 02 did, however, show a similar trend to those observed for whole N. brasiliensis, with antimycin A inhibited respiration, giving the highest value (100 -+ 11"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001700_1.1636193-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001700_1.1636193-Figure2-1.png",
        "caption": "Fig. 2 Dimensions of backboard, hoop and court",
        "texts": [
            " mg1fB1fH5maC , (1a) rB/C\u00c3fB1rH/C\u00c3fH5Ia (1b) where m is the mass of the basketball, g52gk, is the gravity vector, aC is the acceleration vector of the mass center C of the ball, I is the mass moment of inertia of the ball assuming that it is a thin spherical shell, a is the angular acceleration vector of the ball, rB/C5rB2rC and rH/C5rH2rC in which rB , rH , and rC denote the position vectors of the contact point B on the backboard, the contact point H on the hoop and the mass center C of the ball, respectively, and where fB is the contact force vector exerted on the ball by the backboard and fH is the contact force vector exerted on the ball by the hoop. The dimensions of the backboard, hoop, and court are shown in Fig. 2. Notice in this formulation that the aerodynamic effects are neglected because of their smallness and because they would not be exploited by the shooter. Contact With the Backboard. The contact force between the basketball and the backboard is fB5NB1FB ~Figs. 1 and 3!, where NB is the normal component and FB is the friction component. The normal component and the friction component of the contact force between the ball and the backboard are given by ~see Appendix 1!: NB5NBi, NB5kuB1cu\u0307B (2) FB52mNBS vB vB D , (3) where k is the stiffness of the ball, c is the damping of the ball, uB5R2a2x"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000201_0025570x.1995.11996356-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000201_0025570x.1995.11996356-Figure6-1.png",
        "caption": "FIGURE 6.f",
        "texts": [],
        "surrounding_texts": [
            "As already mentioned in section 3, finding the common tangents of two parabolas is, in general, analytically a cubic problem. Since ( 07* ) makes it possible to fold the common tangents of two parabolas, it is to be expected to be possible to fmd cube roots utilizing (07*), which is of course, not possible by Euclidean methods. In this section, we shall become acquainted with a simple method of folding the cube root of the quotient of the len~s of any two given line segments.\nA method of folding ';/2 is given in [8]. The more general method we shall use here is based on parabolas with a common vertex and perpendicular axes. That such parabolas intersect in points whose coordinates solve simple cubic equations was already known to Descartes, and that such parabolas have something to do with fmding cube roots was even known in antiquity (see [ 4], p. 12, or [1], pp. 342-344). Since folding does not allow us to work with points of intersection, but rather with common tangents, we must deal with the dual problem, which works just as well, as we will see.\nWe consider the parabolas with the equations\np1 : y2 = 2ax and p2 : x 2 = 2by.\nSince these parabolas intersect in two points with real coordinates, they have only one real common tangent. We assume this tangent (which cannot be parallel to either axis) to be\nt: y=cx+d.\nWe assume further that P1(x 1, y 1) is the point at which t is tangent to p 1. Then, t also has the equation\na ax1 y=-\u00b7x+-. Y1 Y1\nTherefore\na and d= axl c=-\nY1 Y1\na and d -yl = c xl = c\na2 d --=2a\u00b7-c2 c\n-a= 2cd.\nWe further assume that P2(x2 , y2 ) is the point in which t is tangent to p2 . Then, t also has the equation\nTherefore\nx2 c = b and d = -y2\n- x 2 = be and y 2 = - d -b2c2 = -2bd bc2 -d=-T",
            "We therefore see that\nbc2\na = 2cd and d = - 2\nWe see that the slope of the common tangent is the (negative) cube root of the quotient of the parameters of the parabolas.",
            "368 MATHEMATICS MAGAZINE\nA slight generalization of the method presented in the preceding section allows us to solve general cubic equations. We can see this in the following manner.\nWe consider the parabolas with the equations\np1:(y-n)2=2a(x-m) and p2:x2=2by.\nAs before, we assume that the equation describing a common tangent of p 1 and p2 (which need not be unique in this case), is\nt: y=cx+d.\nAgain, such a common tangent cannot be parallel to either axis. We assume, as before, that PI(xi, !h) is the point in which t is tangent to PI\u00b7 Then, t is also represented by the equation\n( y - n )( y I - n) = a( x - m) + a( xI - m) a axi -2am\n-y= --\u00b7x+n + --''---- YI-n YI-n\nTherefore\nand\na c=--\nYI -n\na +nc =yi=-c-\nand d ax 1 - 2am = n + ___.:'---\nYI-n\nand d-n xi =-c-+2m,\n= a2 = 2a( d- n + m) c2 c\n=a=2c(d-n+cm).\nAs in the preceding section, assuming P2(x 2 , y2) to be the point in which t is tangent to p2 , we fmd that t is also represented by the equation\nx2 y=1i\u00b7x-y2,\nwhich again leads to\nSubstituting for d, we obtain\na=2c(-b~ 2 -n+cm)\n- bc3 - 2mc2 + 2nc +a = 0\n3 2m 2n a -c - T\u00b7c2 +T\u00b7c+ \"[j =0.\nThe slope of the common tangent is therefore a solution c of the cubic equation\n3 2m 2 2n a c -T\u00b7c +T\u00b7c+b=O."
        ]
    },
    {
        "image_filename": "designv11_11_0002642_1.2165234-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002642_1.2165234-Figure2-1.png",
        "caption": "Fig. 2 The model consists of auxiliary spring in series with the Kelvin model",
        "texts": [
            " Note that neither the Maxwell nor Kelvin model represents the behavior of most viscoelastic materials, including the glass balls used in Newton\u2019s cradle device illustrated in Fig. 1. For example the Maxwell model 13 predicts that the stress asymptotically approaches zero when the strain is kept constant. On the other hand, the Kelvin model does not describe a permanent strain after unloading. In this study, a second spring is placed in series with the Kelvin model used in Ref. 8 , to develop a model of linear viscoelastic material equivalent to a Maxwell model with a spring in series. The schematic of the three-parameter model used in this study is shown in Fig. 2. The success of theoretical approach such as that discussed in Ref. 8 is limited for nonlinear problems because of difficulties of analysis. However, a numerical approach has become popular because collision processes can be studied under realistic situations, where the action of loads suddenly applied to a body such as a Table 1 Material properties Material Properties Symbol Value Glass Elastic modulus E 6.3 1010 Pa Density 2390 kg/m3 Poisson\u2019s ratio 0.244 Chemical compositions SiO2 66.0% Nd2O 16",
            "asmedigitalcollection.asme.org/ on 01/27/20 core remains locked between the plastic regions where the highest effective stress, eff, is located. The present model may offer an accurate numerical solution for the inelastic impacts, which will be discussed in the following. Inelastic Collisions. Here, a three-parameter model, namely two springs with one dashpot, was used in order to generalize the numerical approach described in the preceding section. The schematic of the three-parameter model is shown in Fig. 2. One of the central problems in devising descriptions of viscoelastic materials is the question of how to describe the manifestation of both elastic and viscous effects. Mase 20 suggested that in developing the three-dimensional theory for viscoelasticity, distortional and volumetric effects must be treated independently. To this end, the stress tensor may be resolved into deviatoric and spherical parts, given as ij = Sij + 1 3 ij kk 13 where Sij = 0 t s t\u2212 t deij /dt dt , and the relaxation function used in the model is given by s t =G + G0\u2212G e\u2212t/ "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001321_s0013-7944(03)00050-x-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001321_s0013-7944(03)00050-x-Figure1-1.png",
        "caption": "Fig. 1. Critical cross section.",
        "texts": [
            " We will limit ourselves to the first problem, i.e., prediction of the service live of the gearing during designing. Geometric particularities are taken into account by means of the shape factor and the tooth stress intensity factor [3] and the real loading by means of mathematics modelling of actual gearing. In our model we propose a new parameter by which we describe the fracture mechanics conditions in the tooth root where the defects, causing destruction, occur statistically most frequently as shown Fig. 1 [3]. We must emphasise that this factor does not apply in general, but only for gears and for calculation of conditions in the tooth root, i.e., for calculation of their service life. We named that factor the tooth stress intensity factor Z. The value of the factor Z related to propagation of the plastic zone, deformation and orientation of grain in case of short cracks and stress intensity factors in case of long cracks. There are three forms of the factors Z for three different area of crack length according to Fig",
            " By means of the least square method from equation: da dN \u00bc z1\u00f0DZ\u00dez2 \u00f034\u00de For each pair of data thus obtain with the some stress level we determined the corresponding value of coefficient of the material for short cracks: z1 \u00bc 120; 571; 742 and z2 \u00bc 3069 The value of the tooth stress intensity factor Z is related to propagation of the plastic zone, deformation and orientation of grain in case of short cracks and stress intensity factors in case of long cracks. When we want to approximate the tooth stress intensity factor for general use for crack initiation, propagation of micro and macro crack, the stress intensity factor for gear tooth becomes a more complex form according to Eq. (14) and Fig. 1, where the shape factor [3] is Y \u00f0a=S\u00de \u00bc cosu c L sinu Ym\u00f0a=S\u00de S 6L sinuYt\u00f0a=S\u00de \u00f035\u00de where Ym\u00f0a=S\u00de is the bending part and Yt\u00f0a=S\u00de is the known shape factor for the compact tension specimen. For practice is more convenient polynomial form according to Y a S \u00bc 2:2486135 3:7173537 a S \u00fe 33:95 a S 2 137:536 a S 3 \u00fe 210:91 a S 4 \u00f036\u00de By the replica method we followed up the propagation of short fatigue cracks in the observed direction, i.e., along the tooth width. The test was performed so that the loadings, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002378_robot.1998.680881-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002378_robot.1998.680881-Figure3-1.png",
        "caption": "Figure 3. Considered variables.",
        "texts": [
            " So, we propose in this paper a global approach of the problem which searches a feasible motion from one point to another and considers the velocity and joint constraints of the system, without decoupling the mobile manipulator into two sub-systems. 3. Motion generation The initial position of the vehicle and the initial configuration of the arm are supposed to be known. The problem is to join the initial position to the final position by computing some successive configurations acceptable for the system. The initial position of the vehicle in the world reference frame F can be represented by the displacement 'DVcinit) between the world reference frame F and the initial vehicle reference frame Mv. As shown in figure 3, the non-holonomic motion between two successive vehicle reference frames Mv,,, and Mv(,+~,) can be represented by the displacement YDV(tl. As we will see in the following, this displacement \"DV(,) can be written as a function of S (the inverse of the breaking radius R) and v (the velocity of the vehicle), using homogeneous matrices or dual quaternions. XV,\",I = At any time t, the position of the end-effector in the vehicle reference frame Mv,,, can be represented (figure 3) by the displacement \"De(,, between Mv,,, and Me,,,. This displacement can be written as a function of the arm joint parameters 0,, e, ..., 0, at time t. So, at any time t+dt, the position of depends on the previous position of the vehicle Mv(,, and the current joint values of the arm 0=[0,(t+dt), e,(t+dt), ..., O,(t+dt)lT. x\",\",l = Om 'p\",\",, = Odeg %l\",t = Odeg in the world reference frame F =Om Therefore, after n displacements, the position of the end-effector in the world reference frame is given by the displacement FDe(,n, which is the composition of FDv(init), VDv(l,l for i=l",
            " In this section, we express the displacement FDv(,,,l,, with dual quaternion: ( 1 2 f 0 I 0 0 For a circular motion of the vehicle (using equation 3), displacement YDV(ll) can be written thanks to the dual quaternion of equation (8). For a rectilinear motion of the vehicle (using equation 4), displacement YDV(tl) can be written thanks to the dual quaternion of equation (9). ( 0 1 i ~ , dQvi ,. = 1 sin(+] I 1 '-'dQvi = vi.dt (9) 2 0 0 0 ( 0 , .os(+) (8) Ri.sin( +) 0 l : l dual quaternion product G C3 Z = [ (z:,,) represents the displacement FD, from frame F to frame Mz. This product can be written: with: So, at any time t, the displacement \"De (figure 3 and 5 ) can be represented with the dual quaternion v Q e = v Q b \u20ac 3 b Q e , where \"Q,, is the dual quaternion representing the displacement between Mv and the arm base referential Mb and b Q e is the dual quaternion representing the PUMA direct kinematics. Therefore, the total displacement represented in figure 4 and 5 is FD-, represented by the dual quaternion : Qe=FQy(init) [ ii-' dQvi)@' Qectn) (1 1) This dual quaternion represents the feasible displacement within n iterations for the global system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003828_tmag.2005.844561-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003828_tmag.2005.844561-Figure3-1.png",
        "caption": "Fig. 3. Brushless DC motor mesh.",
        "texts": [
            " To use high order interpolation only on the interface , modified elements appears close to it (Fig. 2). Hierarchic interpolation is also convenient to generate the interpolation functions for this type of element: it is only necessary to add one degree of freedom on the edge on the interface without changes in the original first order functions. The local contributions for matrices and with second order hierarchic interpolation on are (11) with and (12) where . For cubic interpolation on , the hierarchic functions are and . For this machine, the mesh shown in Fig. 3 is used. This motor has an airgap of 0.7 mm in which the upper side is iron and the lower side the magnet. To compare the methods, the same mesh is used for both cases, with 39 edges on both sides of the interface. The rotor displacement step is set in a way that five steps are necessary to overpass one element on . Fig. 4 shows better results with the MEM than MB, for first order interpolation on . As shown in Fig. 4, the experimental and simulation results are in very good agreement. Only with a zoom can we see the oscillations due to the movement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002735_acc.2003.1244101-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002735_acc.2003.1244101-Figure1-1.png",
        "caption": "Figure 1: Bi-steerable car model showing the flat output (point H ) with respect to the reference frame of the robot placed at point F .",
        "texts": [
            " We then compute in section 5 a dynamic feedback allowing for the exact linearization of the general BiS-car and thus leading to a linear closed-loop control law. In section 6 we present simulation and experimental results on trajectory tracking using our bisteerable platform. We close the paper with some concluding remarks and guidelines on future work in section 7. 2 Flatness in bi-steerable cars We define a BiS-car as a vehicle capable to deflect the rear wheels in function of the front steering angle (cpr,,, = f(cpjront))7 see Figure 1. For (nonholomic) modeling purposes, an imaginary wheel is placed at both points F and R so that the associated velocity vectors are collinear to the orientation of the respective wheel. Assuming that cp E ] - 4, $[, then for a robot reference frame placed at point F , the 2-input driftless control system of a BiS-car is: \u2018Indeed, a few research laboratories are equipped with these kind of robot; e.g. the car\" prototype of IEF (\u201cInstitut d\u2019Electronique Fondamentale\u201d of Paris-Sud University.)and the Cycab robot at INRIA in France and NTU in Singapore",
            " G(,)L) we denote the unitary vector in the direction (.) (resp. the direction (.) + 2) and by (.)(P) the total derivative of (.) of order p . Finally, we will write := (U(\u2019 ) , . . . , U ( \u201d ) ) , to denote a set of derivatives of U up to order v. Now if we let A(cp) = cos2(cp)f\u2019(cp) - cos2(f(cp)) B(cp) = Wcp) sin(cp)f\u2019(cp) - cos(f(cp)) sin(f(cp)), then the flat output are the coordinates of a point H in the world\u2019s Cartesian frame PH := ( z H , yH) = (yl,yz), computed as a function of the state as follows (see Figure 1) [ 141: (2) -4 p;I = p;. + P(\u2019p)Gie + Q(\u2019p)G@ where P ( p ) and Q(\u2019p) are coordinate functions relative to the robot\u2019s reference frame: P(cp) = M(cp) cos(P(cp)) - Ncp) sin(P(cp)) (3) Q(cp) = M(cp) sin(P(cp)) + N c p ) cos(P(cp)) Conversely, x can be found from y and a finite number of its derivatives. More precisely, if one knows the flat output\u2019s velocity along the path it describes and the curvature of the path det (y(\u2019), Y(2)) K . = ([yi\u201d] + [Yi\u201d] 2, 3\u20192 then one can obtain the state of the robot as follows: \u2018p = IC-\u2019 ( K ) I 9 = Y -+P(\u2019p) (7) FF = P H - P(\u2019p)G,5\u2019 - Q(v)u\u2019/j\u2019I where These expressions are formal relations between x and y together with its derivatives up to order 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001057_cdc.2002.1184684-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001057_cdc.2002.1184684-Figure2-1.png",
        "caption": "Figure 2: Solar forces on control plate",
        "texts": [
            " The radiation torques are derived from two identical, highly reflective, lightweight control surfaces PI and P2 which can undergo rotations 61 and 62, respectively, from the y b axis as described in 161. The equation of motion describing the pitch dynamics of the satellite is given by 161 d2X /de2 = Mg + M. (1) where A l , denotes the gravity gradient torque, and M, is the torque generated by the solar controllers. The gravity gradient and the radiation torques are given by M, = -3KsinXcosX (2) Ma = C[COSC~ICOSC~~COS~I - C O S ~ ~ ~ C O S C ~ / C O S ~ ~ ] 1239 where t k ( k = 1,2) is the angle of incidence on the ith solar control plate shown in F i g 2 The radiation force is shown in Fig.2; and the incidence angle is given by = 00-5sin(e + p + x + 6,) (3) U($+) = . 1 - sin24sin2i p(4) = -tan-'(tanf$cos(i)) Since the solar aspect angle 4 varies from 0 to 2a radians in a year, U and p are extremely slow variables. The solar parameter C is given by c = Z ~ P A E / ( C P I , ) (4) Let a be the orientation of the satellite with respect to the inertially fixed axis Y, then one has a = X + e ( 5 ) where the orbital angle is 8 = a t , and R is the orbital rate. Substituting X = a - 8, in Mg and M, gives A{,(@, 8) = wodda, 8) K ( a , & P ( 9 ) , 4 6 ) ) = ~ d i ( a ~ 4 0 ( 4 ) ~ 4 9 ) ) (6) where WO = K , wl = C , and do = -i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001138_095440503772680578-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001138_095440503772680578-Figure1-1.png",
        "caption": "Fig. 1 Solid freeform fabrication process [1]",
        "texts": [
            " The following terms are often used interchangeably when referring to rapid prototyping technology: solid freeform fabrication, desktop manufacturing, layered manufacturing and tool-less manufacturing. Solid freeform fabrication (SFF) is one of the fastest growing automated manufacturing technologies that have signi\u00aecantly impacted the length of time between initial concept and actual part fabrication. However, to fully realize the potential cost and timesavings associated with rapid prototyping, the capacity to go from computer aided design (CAD) models directly to metal components and tooling is crucial (as shown in Fig. 1) [1]. Initially, rapid prototyping was viewed as a tool for the rapid development of three-dimensional models. The savings in terms of time and money mostly occurred during the developmental phase of a product. The driving force was the potential reduction in time to a \u00aenal design and prototype of the part due to the relative ease of doing the physical model iterations during the design stage. The prototype parts were simply threedimensional models that were used to verify the feasibility of the design"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000543_jsvi.1996.0465-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000543_jsvi.1996.0465-Figure2-1.png",
        "caption": "Figure 2. Sketch of the element.",
        "texts": [
            " (9) No mention has been made up to now of whether a disc or an array of blades is being considered: the previous expressions are independent of this distinction and will thus be employed not only for the present study of a disc element but also for the future development of an array of blades. With account taken of the time dependence of angles q and a in equations (3) and (6), the absolute velocity {V}XYZ = {P XYZ}, can be obtained as the time derivative of equation (7). The explicit expression for {P XYZ} is not reported here for simplicity. To define the shape functions approximating u(r, q, z, t), v(r, q, z, t), w(r, q, z, t) in their dependence on the location r, q, z of point P, the disc has been subdivided into annular elements of the type shown in Figure 2. The thickness h(r) is assumed to be a linear function of the distance between the inner and the outer radii ri and ro . A non-dimensional radial co-ordinate x vanishing at the inner radius and taking unit value at the outer one is defined. They are expressed in terms of the radial increment Dr= ro \u2212 ri and the thickness variation Dh= h(ro )\u2212 h(ri ) as x=(r\u2212 ri )/Dr, h= h1 + xDh. (10) The displacement field u(x, q, z, t), v(x, q, z, t), w(x, q, z, t) within the element can then be expanded as a trigonometrical series in the angular co-ordinate q: u(x, q, z=0, t)= u0 \u2212 r 82 0 2 + s n i=1 [uic cos iq+ uis sin iq] v(x, q, z=0, t)= r80 + s n i=1 [vic cos iq\u2212 vis sin iq] w(x, q, z=0, t)=w0 + s n i=1 [wic cos iq+wis sin iq] (11) The harmonic terms contribute differently to the dynamic behaviour",
            " In the above formulation the displacement field within the elements is such that the midplane of the disc deviates from the original plane configuration. Since the beam elements modeling the shaft are based on the assumption that their sections remain plane during deformation, to insure the compatibility of the displacement field at the disc-shaft interface, a disc element cannot be linked directly with beam elments. A suitable transition element has been developed for that purpose. This element is provided with two nodes, of the same type of node 0 and node 2 of the disc element (see Figure 2). The node at the center is connected directly with the shaft elements and coincides with the central node of all disc elements used to model a disc at a given axial location. The second node coincides with the internal node of the subsequent disc element. Node 0 has two complex degrees-of-freedom for flexural behaviour and one real degree-of-freedom for torsional and axial behaviour. Node 1 has four complex degrees-of-freedom for flexural behaviour, one real degree-of-freedom for the torsional behaviour and two real axial degrees-of-freedom"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.17-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.17-1.png",
        "caption": "Figure 3.17. The calculation was performed using the finite element method and, although the material used for the calculation was only transversely isotropic, with the axis of symmetry coinciding with the z axis, the results are close to the ones obtainable for isotropic materials.",
        "texts": [
            " Apart from these considerations, a closer look at the actual stress distribution in quasi-isotropic rotors will show that the strength of the material is not at all independent from the stacking sequence. Much research has been devoted to the determination of an 'optimum' ply orientation and stacking order, and is still taking place. The major drawback of quasi-isotropic discs, particularly in the case of variable thickness, is the low shear and axial strength. Axial strength of a glass-fibre-epoxy laminate can be as low as 1/20 of the maximum in-plane strength; a two-dimensional stress analysis such as that whose results are given in Figure 3.17 will therefore be needed. Also interlaminar stresses can be very dangerous, particularly near the outer edge of the layers. The value of constant B for constant-stress disc must be carefully chosen, remembering that by increasing B, the in-plane stress aD decreases but axial and interlaminar stresses increase. Quasi-isotropic rotors can be built with any type of composite material and plywood. Building these by hand with vacuum bag autoclave curing is possible. However, if a large number of discs is required then automated processes, such as matched metal die compression moulding techniques, are preferred for material properties and for economy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002204_s1474-6670(17)31748-2-FigureI-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002204_s1474-6670(17)31748-2-FigureI-1.png",
        "caption": "Fig. I Ship's coordinate in horizontal plane",
        "texts": [],
        "surrounding_texts": [
            "2.1 Formulation The minimum time maneuvering problem is formulated to control a ship from a certain condition to another one in a minimum time. This kind of problem is considered as a two-point boundary value problem, in which an initial point as the one condition of the ship (for example, the starting point) and a terminal point as another condition of the ship (for example, the stopping point). Such control problem might be solved using the theory of calculus of variations. However, since ship's motion has high non-linearity, it is impossible to find an analytical solution. Thus it is inevitable to adopt some numerical methods for solving the problem. In this paper, the sequential conjugate gradient-restoration (SCGR) method developed by Miele et af. (1992) was used. 298 The mInimum time maneuvering problem is formulated as follows: A performance index of this problem is defined by a functional 1= J~f(x,uc,r,t)dt= J~rdt=r (1) where I is a scalar value, x is the state vector, Uc is the control vector, t is the actual final time value and r is the normalized time value. And the solution of the problem is minimized the performance index with constrains as follows: 1) The differential constraints, O~t~l (2) where <I> denotes a non-linear hydro dynamic model for representing ship's motions, and 2) The boundary conditions: i) The initial ship's state, [m(x)]o = 0 (3) ii) The final state of the ship, specified by the function [\\{I(x, rH = 0 (4) where the function \\f is a q-dimensional vector (O~q ~ n). 3) The non-differential constraints: S(x,uc,r,t)=O,O~T~1 (5) may be added, by which it is possible to set the maximum limits of rudder angle, propeller blade angle, and power of the bow and stem thrusters, to be applied. 2.2 Ship's motion model Shioji Maru is equipped with a bow and stem thrusters, besides a rudder and a controllable pitch propeller (epp). Her principal dimensions are shown at Table I and the coordinate system is shown in Figure 1. speed v, yaw rate r, rudder angle 0 for X-Y coordinate and CPP angle Bp The control values are order rudder angle 0' , order CPP angle e;, notch of bow thruster bt' , notch of stem thruster s( . CAMS 2004 Referencing to this, the sophisticated mathematical model (called MMG model) is written by X=ucos'l'-vsin'l' (6) m( iI - vr) = X H + X P + X R (7) Y = u sin 'I' + vcos 'I' (8) ~iI-V~=XH+XP+XR m y=usin'l'+vcos'l' (8) m(v+ur)=YH+Yr+YR +YTh (9) lfi=r (10) Ii = N H + N T + N R + NTh (11) 8 = (0'-0) (12) (IO'-OITRuD +a) e = (e'p--8p-ep7;p) ep (13) p 7;p (le' p -e p - e p7;p ITen + a) 7;p where m and I are the mass and the turning moment inertia. T RUD ' Tcpp and a are time constants. The subscripts H , P, Rand Th denote the highly non-linear hydrodynamic force induced by the hull, propeller, rudder and thruster. For detail of the hydrodynamic force, see (Ohtsu et al., 1996). 2.3 Minimum-time parallel deviation maneuvering problem and the non-linearity o/its solutions In this paper, the minimum-time parallel deviation maneuvering problem and its solutions are considered as a simple example of the feasible study realised by CAMS 2004 proposed control system. Figure 2 shows the initial course line and terminal one of the minimum-time parallel deviation problem. Where .e is the distance between two parallel course lines. In this case, the boundary conditions for the two-point boundary value problem and the non differential constraint are as follows. I) The initial ship's state [x(O) y(O) u(O) v(O) reO) V'(O) 8(O)Y =given (14) 2) The final state of the ship [y(1) 1(1) r(1) 1!f(1) o(1)y =[Yf VI rf lJII oJ =0(15) 3) The non-differential constraints 8' (t) - sigmoido Dumy(t) = 0 , 0 ~ t ~ 1 (16) where, o~. is the dummy variable for the order ~my rudder angle calculated by SCGR method without constraint. The 'sigmoid' means a kind of saturating function which guarantees the range of o\u00b7 (t) in permissible value. Under these conditions, the minimum-time control solutions can be obtained using the SCGR method. The first examples are minimum-time deviation problems with different deviations. In this case, the ship must deviate lOOm and 200m away from the initial approach line in a minimum maneuvering time, using the rudder. The ship's initial cruising speed is 12 knots, and the side ways speed must disappear and the head must be redirected on the original course after ending the deviation. Figure 3 and 4 show the optimal paths and the corresponding time histories of the rudder angles in each case. It should be noted that the time histories of the heading angles have almost the same patterns, whereas those of the rudder angles are different in each case. This means that the ship's minimum-time maneuvering system should have the real-time ability to calculate the optimal solutions. 3. MINIMUM-TIME MANEUVERING SYSTEM WITH NEURAL NETWORK AND NONLINEAR MODEL PREDICTIVE COMPENSATOR 3.1 Optimal solution generator using neural network In the proposed system, the real-time solution for a new maneuvering condition will be generated by 299 interpolating the pre-computed solutions for typical conditions using neural network (NN). Figure 5 shows the three-layered neural network used in this research (Okazaki et al.,1997) . The inputs Xi for the neural network are the ship's state values, which include the ship's position from the terminal course line y, its heading If! , and its speed v. The output of the neural network 0 = 8 corresponds to the rudder angle Don for minimum-time maneuvering solution. In Fig.5 Wij' Vi are synaptic weights between input and hidden layer, hidden and output layer respectively. The outputs of the hidden units are, And the output of the network are defined by 0= f(s) = f('IAv j + ho) (17) (18) where, xo ' ho are the off sets for the inputs, and i ,j denote the numbers of units in input and hidden layer respectively. The non-linear function fO in the unit is a sigmoid function of the form : (19) As a learning algorithm for this network, the following back propagation method is adopted. (20) .1v; (n) = 11.e.f(s).(l- f(s\u00bb.h; + ~.VI (n -1) (21) llwij = 11 \u00b7 e.f(s).(I- f( s\u00bb .vj ).f(u j ).(1- feu ).X; (22) +llwij (n-l) where L1 denotes the update quantity of each variables at iteration n . 11 and a are the learning rate and the momentum term. During the network training, the time series of ship state values are fed to the input layers and the network synaptic weights w v . are updated to reduce the error between the lJ' Jk network output signal and the minimum-time maneuvering solutions D OPT (optimal control values). After sufficient training, the neural network could make appropriate time series of control values (rudder angle D ) for arbitrary minimum-time maneuvering within certain range of course deviation. Furthermore, the calculation time to interpolate these solutions is less than one second. In this case, the structure of the neural network (number of hidden 300 units j = 4) is determined heuristically and verified by using AIC ( Akaike's Information Criterion) and MDL (Minimum Description Length Principle). 3.2 Compensation of tracking error by using nonlinear model predictive compensator By using off-line trained neural networks, the optimal solutions for practical conditions can be computed as \"closed loop configuration\" in real-time and a ship's minimum-time maneuvering may be implemented by the basic structure as shown in Fig.6. with nonlinear model predictive compensator However, from practical point of view, some disturbances (for example, wind and tidal current etc.) should be taken into account. For this problem, we recommend to introduce the nonlinear model based compensator into the control system as shown in Fig. 6 (Mizuno et al., 2003), because we have already construct the sophisticated non-linear dynamical model ( MMG model) of the ship and can use it. In the proposed system, \"nonlinear model based compensator\" is composed of the MMG model based ship 's dynamic simulator and the search mechanism for optimal rudder compensation /\";.D to reduce the tracking error based on the receding horizon cost function J as described later. Although the MMG model is very complicated, the computational time is very short compared with the time which is required for solving the optimal solution by SCGR method with the same model. For example, the computational time for simulating the future 150 [sec] ship's behaviour is less than 1 [msec] using the computer with the Pentium III CPU at IGHz clock. This means that we can simulate about 100 times with different conditions during the sampling period 1 [sec] in experiment. To simulate the future behaviour of the ship, we can use the neural network based optimal solution generator \"NN\" for generate the future control values to the ship as shown in Fig. 7, because the generation CAMS 2004 of the solution (rudder order) is perfonned in closed loop configuration mentioned before. To reduce the future tracking error for the optimal course, we optimize the following receding horizon cost function J (Allgower and Zheng, 2000). N J= LIYJr)-Y,(r)1 (23) r =M where, f a(r) denotes the optimal deviation of the minimum-time solution and Y, (r) is the simulated one of the controlled ship. First, the MMG model based simulation is carried out assuming the rudder compensation ~8 as an appropriate setting for the future time period [t, N] and the value of J is calculated as the \"error area\" for receding horizon [M, N] as shown in Fig. 8. Next, to optimize the cost function, the simulation and evaluation are repeated based on the linear search as shown in Fig. 9. 4. PRELIMINARY EVALUATIONS BY COMPUTER SIMULA TlONS Before implementing the proposed minimum-time maneuvering system, computer simulations of both basic and proposed scheme are perfonned for non linear dynamical model of the Shioji Maru . Figure 10 and 11 show the simulation results for mInImum-time deviation problem with wind disturbances by using basic (NN only) and proposed (NN+model predictive compensator) control system respectively. The ship must deviate 150 m away from the initial course line. In these cases, the winds blow from the stem (180[ deg]) at relative wind velocities of 12 m/sec . The neural network \"NN\" in both the basic and proposed maneuvering system has been off-line trained using the four minimum time CAMS 2004 solutions with f = lOOm and 200m for the ship speed u = 5.0m / s and6.6m / s under the constraint of 18 1 :;; 5 [deg] . For the proposed method, the optimal value of the rudder compensation !l8 is searched in the range of \u00b1 7.0 [deg] with the resolution of 0.1 [deg]. Moreover, for the safe of ship's maneuvering, the maximum rudder order is restricted as 18 +881:;; 1O.0[deg]\u00b7 Moreover, the same MMG model is used to simulate the ship's bahaviour and is used in model predictive compensator. In these figures, the dashed lines show the minimum time solution for wind free case and the solid lines are with wind disturbance. From these results, it should be noted that the error between the ship's dynamics and the actual one does not exist, whereas the path obtained using only NN is rather different from the optimal one. Thus, it is generally concluded that the control system should have a feedback compensator, in order to avoid the influence of disturbances . 5. ACTUAL SEA TEST system, the actual deviation using the Shioji Maru of Tokyo University of Marine Science and Technology (Fig. 12). 5.2 Real Time Control System signals are available to provide accurate positions of ship. Figure 15 shows the typical experimental result using proposed scheme under wind disturbance. t: \" 'f' .It! \" n. .. _ 0 ) ./ Pa>ition Y[m] ~I:~ ...... , , .. , ~ (J \\ 'S: J\"; 2Q 4/1... .\u2022 .00 .. 1:1:1 -IQ Timo [0] Tim .. [ .. ] Fig. 15 The typical experimental result using proposed scheme (l50m deviation, 8rn1s wind from the bow side) In these cases, the settings for the controller are same as the simulation. From these results, it can be concluded that the proposed mlmmum-time maneuvering system with NN+nonlinear model predictive compensator is feasible in actual sea conditions. 302"
        ]
    },
    {
        "image_filename": "designv11_11_0002444_s0080-8784(04)80016-4-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002444_s0080-8784(04)80016-4-Figure3-1.png",
        "caption": "FIG. 3. Diagram of a single compartment, glass electrochemical cell (Granger et al., 2001). The following are labeled in the figure: (a) metal plate current collector, (b) the diamond thin-film electrode, (c) the o-ring gasket, which defines the area of the electrode exposed to the solution, (d) inlet for the nitrogen purge gas, (e) the counter electrode, and (f) the reference electrode.",
        "texts": [
            " The resulting structural defects could lead to localized and premature breakdown of the film during the imposition of harsh electrochemical conditions of pH, temperature, and current density. Third, diamond films deposited on non-diamond substrates can possess significant internal stress, both intrinsic and thermal (Michler, Mermoux, yon Kaenel, Haouni, Lucazeau and Blank, 1999). The role that stress exerts, either macroscopically or microscopically, on the electrochemical response is not understood at present. One possible manifestation of localized stress could be less morphological and microstructural stability during exposure to harsh electrochemical conditions. Figure 3 shows the design of a typical electrochemical cell used for measurements with diamond (Granger et al., 2001). The three-neck, singlecompartment cell is constructed of glass with about a 10 ml internal volume. The diamond working electrode is pressed against a Viton TM o-ring and clamped to the bottom of the glass cell. Ohmic contact is made using either a bead of Ga/In alloy or Ag paste on the backside of the scratched and cleaned substrate. The substrate is then placed in contact with either a Cu or an A1 plate current collector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000499_3516.891047-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000499_3516.891047-Figure8-1.png",
        "caption": "Fig. 8. Vector representation of signal fluctuation compensation. (a) Two strain gauges. (b) Three strain gauges.",
        "texts": [
            " The answer is found by inspection of the conditions to obtain a nontrivial solution of the system of equations (9). Size of the system of equations (9) is . Therefore, we can formulate the following relation to obtain a nontrivial solution: (10) That is, the minimum number of strain gauges needed to compensate the signal fluctuation is (11) For example, to compensate one, namely, the basic frequency component , a minimum of three strain gauges is needed. To compensate two frequency components , a minimum of five strain gauges is needed, and so forth. Vectors in Fig. 8 graphically represent an example of basic frequency component compensation. In Fig. 8(a), it is shown that by two strain gauges it is possible to minimize the signal fluctuation, but impossible to perfectly compensate the basic frequency component of the signal fluctuation. On the contrary, by three strain gauges in Fig. 8(b), the basic frequency component can always be perfectly compensated. A recently obtained experimental result with the proposed signal fluctuation compensation method is presented here. A Harmonic Drive with fixed flexpline, torque capacity of 100 N m, and gear reduction ratio of 51 was used. Three strain gauges were cemented on the diaphragm part of a flexpline with angle distance 60 . In this experiment, only compensation of the basic frequency component was investigated, therefore, only three strain gauges were cemented"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002001_1.1649662-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002001_1.1649662-Figure7-1.png",
        "caption": "FIGURE 7. Rocker-bogie Wheel Mechanism, Initial Design. FIGURE 8. Final Design, with Four Wheels.",
        "texts": [
            " Minimization of torque favored shallower cuts, narrower buckets, narrower rover widths and more buckets. As the minimization of torque also minimizes the reaction forces, those characteristics are favored for a low-gravity application. The final design of the bucket wheel is indicated in Table 1b. The chassis modeled in the original simulation was also changed somewhat because it was concluded that the support for the boom was insufficient and produced stresses in the chassis. In the original concept, a modified rocker-bogie wheel system was utilized (Figure 7), in which the three wheels on each side are linked and the mechanism pivots around a single point on the body of the rover. Adding the boom to the front of the chassis acts as a cantilevered mass to this configuration and creates large stresses at the pivot point of the wheel assembly on the rover body. To alleviate this problem, a fourth, fixed wheel was added to each side (Figure 8). This final excavator design has been built in order to test its soil excavation capabilities (Figure 9). An entire vehicle was developed, with some deletions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001735_s0020-7683(01)00198-6-Figure13-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001735_s0020-7683(01)00198-6-Figure13-1.png",
        "caption": "Fig. 13. Reflected flat rounded punch.",
        "texts": [
            " z\u00f0x\u00de \u00bc Aaxa; \u00f0A:10\u00de p0\u00f0s\u00de \u00bc aP \u00f0a\u00de aa sa 1; \u00f0A:11\u00de P \u00f0a\u00de \u00bc 2 ffiffiffi p p C \u00f0a \u00fe 1\u00de=2\u00f0 \u00de AC a=2\u00f0 \u00de z\u00f0a\u00de; \u00f0A:12\u00de p\u00f0a; x\u00de \u00bc P \u00f0a\u00de a pa ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 x2 a2 r F 1; 2 a 2 ; 3 2 ; 1 x2 a2 ; 06 x6 a: \u00f0A:13\u00de /p\u00f0a;w\u00de \u00bc iP \u00f0a\u00de 2pw F a 2 ; 1 2 ; a \u00fe 2 2 ; a2 w2 : \u00f0A:14\u00de o/p\u00f0a;w\u00de ow \u00bc iP\u00f0a\u00de 2pw2 F a 2 ; 3 2 ; a \u00fe 2 2 ; a2 w2 : \u00f0A:15\u00de The Muskhelishvili potential for a symmetric wedge with a sharp edge (a \u00bc 1 in Fig. 12) has the form (J\u20acager 1995) /p\u00f0a;w\u00de \u00bc iP \u00f0a\u00de 2pa arcsin a w ; o/p\u00f0a;w\u00de ow \u00bc iP \u00f0a\u00de 2pw ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi w2 a2 p : \u00f0A:16\u00de A.4. Mirrored flat punch with rounding and singularity The solution for a flat punch in contact on s < x < a follows fromEqs. (3)\u2013(5) after substitution of (Fig. 13) xnew \u00bc x\u00fe snew; anew \u00bc a\u00fe snew: \u00f0A:17\u00de Insertion of Eq. (A.17) in Eq. (4) and omission of the index new gives the displacement outside of the contact area uz2\u00f0a; x\u00de \u00bc uz2\u00f0a; a\u00de A p p02\u00f0s\u00de ln 2x s aj j a s \u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f02x s a\u00de2 \u00f0a s\u00de2 1 s ! ; x6 s or xP a: \u00f0A:18\u00de The flat punch solutions can be superposed analogously to Section 2. The gap z2 must be the integral of the displacement increments before the point x makes contact z2\u00f0a; x\u00de \u00bc A p Z a s\u00bcx p02\u00f0s\u00de ln a\u00fe s 2x a s \u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0a\u00fe s 2x\u00de2 \u00f0a s\u00de2 1 s "
        ],
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    },
    {
        "image_filename": "designv11_11_0000173_s0925-4005(97)80245-6-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000173_s0925-4005(97)80245-6-Figure2-1.png",
        "caption": "Fig. 2. Cyclic voltammograms of Fc+/nafion film in 2.0 mM Fc + at scan rate of (a): (1) 1, (2) 5, (3) 10, and (4) 40 mV s-1, respectively.",
        "texts": [
            " In contrast, the Fc + is slightly water soluble, and it is litter easily released from the film into bulk solution than ferrocene. Fc + could be stored in nation at a higher concentration according to its distribution coefficient for cation between the nation and solution. It was found that the film thickness would influence the incorporation process of Fc +. For a thin film, Fc + can diffuse more quickly into the film than that for a thicker film, meanwhile, the vol tammograms changed more slowly with the increase of sweep numbers, moreover, only less amounts of Fc + could be incorporated into the film. Fig. 2 showed the dependence of cyclic voltammograms on the scan rate on a nafion/Fc + electrode when Fc + was incorporated in nation in a 200 m M Fc + phosphate buffer solution. With the increasing scan rate, the cathodic peak potential shifted toward a more negative direction, and the anodic peak potential would shift in a more positive value. Meanwhile, for the scan rate shown, the peak current correlated linearly with the square root of the scan rate. This resemblance to a semi-infinite diffusion process was consistent with the slow charge transport in nation [19]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000878_jsvi.1995.0088-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000878_jsvi.1995.0088-Figure4-1.png",
        "caption": "Figure 4. The free body diagram of station j(a) and field j(b) of a coupled torsional and flexural vibrating system.",
        "texts": [
            " , n+1, (42) in which one of the initial state variables, u L 1 , has been found previously and the substitution of the actual value of m\u0304t and the sought values of u L 1 and f into equations (1) and (25) will determine the correct value of m 't ; based on the latter, the station transfer matrix [T S ]j given by equation (27) is defined. 4. TRANSFER MATRIX METHOD FOR COUPLED VIBRATION ANALYSIS For a shafting system, if the locus of the mass centers does not coincide with that of the shear centers, coupled torsional and flexural vibration will occur [4]. In Figure 4 is indicated the free body diagram of station j and field j of a damped discrete system of n+1 stations and n fields. The nomenclature is defined as follows: W is the deflection along the beam, C is the slope of the deflected beam, M is the bending moment induced by deflection, Q is the shearing force, u is the twisting angle, M T is the twisting moment, m is the lumped mass, e is the eccentricity and x is the co-ordinate of the station. Among these symbols, W, C, M, Q, u and M T represent the \u2018\u2018amplitudes\u2019\u2019 of responses. The subscripts j and j+1 refer to the station numbers. Following procedures similar to those presented in the previous section and referring to Figure 4(b) and the book by Meirovitch [4], one obtains the relationship between the state variables at left and right ends of field j as K L K LW W G G G G C CG G G G G G G GM M G G G G Q =[SF ]j Q , (43) G G G G G G G Gu u G G G G M T j+1 M T jk l k l where K L1 Dxj (Dxj )2/2EIj \u2212(Dxj )3/6EIj 0 0 G G 0 1 Dxj /EIj \u2212(Dxj )2/2EIj 0 0G G G G0 0 1 \u2212Dxj 0 0 G G[SF ]j = 0 0 0 1 0 0 . (44) G G G G0 0 0 0 1 \u22121/(kj +ivci ) G G 0 0 0 0 0 1k l Similarly, from Figure 4(a) and reference [4], one has K L K LW R W L G G G G C CG G G G G G G GM M G G G G Q =[S S ]j Q , (45) G G G G G G G Gu u G G G G M T j M T jk l k l where K L1 0 0 0 0 0 G G 0 1 0 0 0 0G G G G0 0 1 0 0 0 G G[S S ]j = \u2212v2mj 0 0 1 \u2212v2ejmj 0 . (46) G G G G0 0 0 0 1 0 G G v2ejmj 0 0 0 v2(e2 j mj + Ij )\u2212 ivc0 1k l Equations (44) and (46) provide the required field and station transfer matrices for torsion-and-flexure-coupled free vibration analysis. It is noted that Meirovitch [4] derived only the field and station transfer matrices of a torsion-and-flexure-coupled vibration system without damping and without excitation torques; the solution technique was not mentioned at all",
            " (54c, d) Upon setting u L 1 =1\u00b70 and using the relations (50), (54a) and (54b), equation (53) becomes W(r) 0 K L K L C(r) S CG G G G G G G GM(r) 0 G G G G G G G GQ(r) = t 1 j= p\u22121 [S (r)]j S Q , p=2, 3, . . . , n+1. (55) G G G G G G G Gu (r) 1 G G G G M (r) T L p 0k l k l The initial state variables and the ones obtained from equation (55) by letting p=2, 3, . . . , n+1, respectively, constitute the rth mode shape. The elementary transfer matrices for free vibrations and those for forced vibrations are different in their station transfer matrices only. Referring to Figure 4(a) and equation (46), one has the transfer matrix of station j for forced coupled vibration as K L1 0 0 0 0 0 G G 0 1 0 0 0 0G G G G0 0 1 0 0 0 G G[SS ]j = \u2212v2mj 0 0 1 \u2212v2ejmj 0 (56) G G G G0 0 0 0 1 0 G G v2ejmj 0 0 0 v2(e2 j mj + Ij )\u2212 ivc0 +m 't 1k l or [SS ]j =[S S ]j +[S S ]j , (57) where [S S ]j is given by equation (46) and K L0 0 0 0 0 0 G G 0 0 0 0 0 0G G G G0 0 0 0 0 0 G G[S S ]j = 0 0 0 0 0 0 . (58) G G G G0 0 0 0 0 0 G G 0 0 0 0 m 't 0k l As when obtaining equation (48), when equations (44) and (57) are substituted into the expressions [S]j =[SF ]j [SS ]j , j=1, 2, "
        ],
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    },
    {
        "image_filename": "designv11_11_0003779_s11044-006-9028-0-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003779_s11044-006-9028-0-Figure6-1.png",
        "caption": "Fig. 6 X-mechanism in its reference configuration",
        "texts": [
            " The remaining two kinematic constraints are obtained from Equation (28). These constraints are independent and the mechanism has the DOF 1. The configuration in Figure 5 is singular, and the constraints (28) are redundant (only in the singular configuration) in Springer accordance with the mechanism\u2019s kinematics. An advantage when using the involutive closure basis is that the matrix C4 is well conditioned and its decomposition is numerically stable. 4.4 X-mechanism Also for the X mechanism in Figure 6, the constraint algebra is not obvious. Assume for simplicity the side lengths a = b = \u221a 2. Evaluating D\u03b1 for all four joints shows that always d = dim clos D\u03b1 = 3. It can be shown analytically that clos D3 is equivalent to so (3). Using J3 as cut-joint, the Jacobian in Equation (20) is L3 = \u239b\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239d 0 cos q1 \u22121 sin q3 sin q2 cos q3 0 cos q3 \u2212 sin q1 sin q3 0 sin q3 sin q1 cos q3 0 0 \u2212c1 1 0 0 0 \u239e\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u23a0 . Assembling C\u03b1 , and with P\u03b1 as above, the SVD yields U\u0304 = 1\u221a 2 ( \u22121 0 0 0 0 0 \u22121 \u22121 0 0 ) and U\u0304 P3 L3 = 1\u221a 2 ( 0 \u2212 cos q1 1 \u2212 sin q4 \u2212 sin q1 cos q4 0 ) , which gives two independent constraints for the three generalized velocities (q\u0307a) = (q\u03071, q\u03072, q\u03074). Hence, the mechanism DOF is 1. Again, the reference configuration in Figure 6 is a singular configuration, but very likely chosen as initial configuration for the X-mechanism. There are only two independent constraints in this configuration, and a simple rank determination is not admissible for the elimination of redundant constraints. Springer 4.5 6R mechanism A counter example, where the proposed procedure is unable to remove redundant constraints, is the 6R mechanism in Figure 7 constructed from two planar 3R chains, where the respective planes of motion are orthogonal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003739_j.wear.2005.11.001-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003739_j.wear.2005.11.001-Figure1-1.png",
        "caption": "Fig. 1. Loading configuration and crack orientation.",
        "texts": [
            "26 racture toughness (MPa m1/2) 6\u20137 ardness (Vickers indentation) (kg/mm2) 1520\u20131650 (at 10 kg) emains in the on mode for more than 1 s the drive motor will cut ut and the timer will stop. An increase in the general bearing ibration level is indicative of spalling fatigue failure of a bearng component. When an increase is sensed by the transducer, he test machine is shut down automatically to prevent the proression of the damage and loss of failure initiation data. All of he present tests were conducted at a shaft speed of 5000 rpm. Fig. 1 shows the loading geometry of the test machine and the eometric attitude of a crack on the contact track. The contact oad is given by the formula: = L 3 cos \u03d5 (1) here P is contact load, L denotes applied load (shaft load), \u03d5 epresents the contact angle (\u03d5 = 35.3\u25e6). The maximum contact ressure and contact radius are calculated using the following xpressions [12]: 0 = ( 6PE\u22172 \u03c03R\u22172 )1/3 (2) = ( 3PR\u2217 4E\u2217 )1/3 (3) E\u2217 = ( 1 \u2212 \u03bd2 1 E1 + 1 \u2212 \u03bd2 2 E2 )\u22121 (4) R\u2217 = ( 1 R1 + 1 R2 )\u22121 (5) where p0 is maximum contact pressure, P is contact load, a denotes contact radius, E1, \u03bd1 is the Young\u2019s modulus and Poisson\u2019s ratio of the ceramic ball, E2, \u03bd2 is the Young\u2019s modulus and Poisson\u2019s ratio of the steel ball, R1 is the radius of the ceramic ball, and R2 is the radius of the steel ball"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003856_iciea.2006.257366-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003856_iciea.2006.257366-Figure1-1.png",
        "caption": "Fig. 1. The schematic diagram of the TRMS",
        "texts": [
            " In this paper the performance of the PID controller is verified by using the simulation and the field test. The conventional PID seems to be inadequate for this complex problem resulting to a poor performance under the disturbance. The performance of the controller can be improved by adjusting gains, but this has its limits. We discuss the design of a fuzzy logic controller for this TRMS system. The fuzzy controllers with the multi section gain provide better performance, especially operating under the large disturbance. The TRMS, shown in Fig. 1, is a laboratory set-up designed for control experiments [1]. In certain aspects it behaves like a helicopter. The TRMS consists of a beam pivoted on its base in such a way that it can rotate freely both in the horizontal and vertical planes responding to yaw and pitch moments, respectively. At such end of the beam there are two rotors driven by DC motors. The main rotor produces a lifting force allowing the beam to rise vertically (pitch angle), while the tail rotor is used to control the beam turn the left or right (yaw)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001366_pime_proc_1992_206_183_02-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001366_pime_proc_1992_206_183_02-Figure11-1.png",
        "caption": "Fig. 11 Representation of film thickness variation around a cam during a cycle in a cam and follower contact (EHL theory-cam speed 3000 r/min) [reprinted with permission from reference (34)]",
        "texts": [
            " (33) using an apparatus with load cells @ IMechE 1992 that allow the measurement of the three components of the contact force to be taken. A traction coefficient ratio between the traction and the normal forces at the contact, ranging from 0.10-0.14 is found, indicating an operation in the mixed or boundary lubrication regime. Theoretical and experimental studies on the cam and faced follower are made by Dowson and his group. In a more theoretical work also considering the elastohydrodynamic lubrication (34), the film thicknesses around the cam (Fig. 11) and the friction torque (Fig. 12) are calculated together with other quantities. A parametric study to assess the influence of some variables is also made. For example, by increasing the viscosity of the lubricant the film thickness increases but the effect upon the power loss is marginal because a limiting value of the friction coefficient applies over Proc lnstn Mech Engrs Vol 206 at CORNELL UNIV on July 30, 2015pid.sagepub.comDownloaded from 230 E CIULLI Cam angle deg Fig. 12 Calculated friction torque for an automotive cam and follower contact [reprinted with permission from reference (34)] most of the cycle; film thickness and power loss increase by increasing the cam rotational speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002483_05698198508981652-FigureI-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002483_05698198508981652-FigureI-1.png",
        "caption": "Fig. I-Apparatus used tor measuring the balllpocket friction",
        "texts": [],
        "surrounding_texts": [
            "Measurement of Cage and Pocket Friction in a Ball Bearing for Use in a Simulation Program@\nC. R. GENTLE and M. PASDARI Trent Polytechnic\nNottingham NGI 4BU, United Kingdom\nI;(!III I I I C ~ L S I L ~ ~ ~ I C I L ~ S /I(LUC euer been mnde of the drug forces arising itself to be successful in predicting the sliding speeds, ball it1 (1 bcrll Oeco-iicg due Lo uiscow fi-ic~ioiz of Lhe balk rotaling in Lhe attitude angles, etc. for the deep-groove and angular contact c(tge P O C ~ C I S crtlrl l t~c crge rolalivg inside the raceway. his paper bearings investigated experimentally by h n e s s and Chapre/)orts ittecrs~trci~tcn~s of boltt 111ese so~czes of friclion on simulations man (10) for axial loads. The expressions used in it for cage of jlrsl otie bearitig, b~rl ltte dr~Lri crrc coinpared ruilh general mzn- drag and balllpocket friction were a mixture \"a priori\" assumptions and indirect experimentation, derived as follylicr~l esl,rcssio~w. for/)redicti~zg lIic friction, and agreew~ent is good. , IOM'S. Fincrlly, Il~c (lola for rlre balllpockel fi-iction are compared against Assume cage drag is due to turbulence caused by making (I /h~oreticol ~tlodel b(w.ed O I L simnple uisco~~s sizear and are stzozun the cage and ball assembly as a whole rotate in a viscous lo be in (!.~celletiI ~br).eet?zetzL. medium. It could, therefore, be represented as a torque by\nINTRODUCTION\nWhen clesigning new ball bearings, or even planning novel applications For existing bearings, i t is essential to predict their performance as accurately as possible using a computer simul:~tion program which fully analyzes the dynamic 1)ch:tvior. Vario~ls analyses have been developed over the years with increasing sophistication and the more recent ones ( I ) , (2), (3), (4) have included detailed modelling of the role playecl by the lubricant in the bearing, thereby auempting to obviate the need for the \"race control\" assutnptions of earlier theories ( 5 ) , (6). However, while expressions for the l~tbricatnt's film-forming ability, its traction ch~u.acteristics, and its high-pressure elasticity have all been firmly based on experimental data for these programs, there has been little direct evidence for the nature of the various drag forces assumed in the analyses although some work by Nypan (7), (8) ancl Mabie (9) is now available. The I I L N ~ O S ~ of the work described here was to generate experimental clata on the lubricant drag torque opposing the rotation of each ball insicle its cage pocket, and the torque opposing rotatiot~ of the cage and ball assembly as a whole ittsicle the bearing. These data wo~tlcl then be substituted in the analysis program developed by Gentle and Boness (2), (3) ancl Gentle and Pasclari (4). This program had proved\nPresented as an American Soclety of Lubrlcatlon Engineers paper et the ASLEIASME Lubrication Conference in\nSan Diego, Callfornla, October 22-24, 1984 Final manuscript approved May 31, 1984\n536\n7c;tge drag = K C T D ~ ( D ~ ) * L 1 1 where K, = a constant of proportionality for the cage, with\na value discussed later D = pitch circle diameter (m) (L = cross-sectional area of the ball and cage assem-\nbly perpendicular to the direction of rolling\n(m2) R = angular velocity of cage rotation (rpm)\nq = viscosity of lubricant inside the bearing (Pa.s)\nThe value of K, was taken as a constant for a particular bearing and was based indirectly on experiment because it could be estimated by performing a force balance calculation on the test bearing in (10) from the measured porver loss at low speed. The idea behind using low speed was to ensure fully flooded lubrication.\nAssume balllpocket friction is due to viscous shear of the lubricant inside each pocket of the cage between the pocket edge and the ball surface. The expression was based on a simple application of Newton's Law of Viscosity, hence the total drag force for the full set of balls was given by\nwhere K p = a constant O F proportionality, with a value discussed later\nNB = number of balls r = radius of the balls (m) o = ball angular velocity of rotation (rpm) p = dynamic contact angle\nD ow\nnl oa\nde d\nby [\nN an\nya ng\nT ec\nhn ol\nog ic\nal U\nni ve\nrs ity\n] at\n1 5:\n16 2\n6 A\npr il\n20 15",
            "Measurement of Cage and Pocket Friction in a Ball Bearing for Use in a Simulation Program\nT h e value of K p tvas again based on a force balance from the measured power loss at low speed. Clearly, both these expressions are open to criticism of being simplistic, and are certainly not as well founded as the rest of the analysis program. This then was the reason for the present investigation.\nMEASUREMENT OF BALLIPOCKET FRICTION\nThe overall aim of this experiment was to duplicate, on a single ball, the situation investigated by Boness and Chapman (10) for a 25\" angular contact ball bearing of 35-mm bore, and 13.49-mm ball diameter, with an outer ring riding cage of stratified textile resin. The arrangement eventually chosen is depicted in Fig. 1. Essentially, the ball was mounted via a spark-eroded hole onto a vertical shaft supported in two precision, high-speed ball bearings and driven from below. T h e bearings were adjustable in all directions ensuring alignment and hence providing minimum friction. Furthermore, the bearings were degreased and lubricated solely with a few drops of a thin water-repellant fluid to further reduce friction. T h e ball itself was located inside a polycarbonate cup which acted as a reservoir as well as a safety shield (in the event of the ball becoming separated from the shaft). T h e speed range of the bearing tested in (10) was up to 16 000 rpm, leading to a ball speed required in this case of up to 40 000 rpm. AL these speeds, it proved essential to ensure that the ball ran true axially to <2.5 km, and that it was cemented in place, otherwise unbalanced centrifugal loads occurred which separated the ball from the shaft.\nThe high speed was achieved by driving a gear cut onto the shaft by a large gear wheel mounted on DC motor/ generator capable of reaching 3000 rpm. Care was taken in aligning this mechanism so that noise and vibration were kept to a minimum, and a Further reduction was achieved by mounting the various parts of the apparatus on rubber pads. T h e feedback loop from the generator attached to the motor ensured overall speed control of 1 : 1000, and the feedback signal itself could be used as an indicator of not just motor speed but also driving torque. This feature dictated the experimental technique adopted, which was to measure the torque output of the motor while the ball was rotated at the chosen speed in air, and then while the ball was rotating inside a single lubricated pocket cut from the correct cage. The difference would be a measure of the ball/ pocket friction. The cage mounting allowed for simple position adjustment in the direction which would be described as radial in the complete bearing. It also allowed for vernier controlled movement in the tangential direction to produce different positions of the ball inside the pocket. This feature was felt to be important as the balls can be juxtaposed to drive the cage against the cage drag forces, and, therefore, would be pushed up against the leading edge of the pocket. For the first tests, the lubricant was placed in the reservoir around the ball and cage at the start of the test, the shaft1 reservoir interface being guarded by a precision seal, once the cage position had been adjusted using a long focal length microscope. T h e lubricant chosen throughout the tests was commercially available multigrade oil.\ntorque\nIt was found that tests using this procedure could only be conducted up to ball rotational speeds of 8000 rpm due to the effects of air entrainment. Beyond this speed, a deep vortex developed above the ball. Hotvever, the results shown in Fig. 2 indicate that there is little difference between the - data points for the three positions of the cage:\n1. centrally mounted around the ball 2. lightly touching the ball at one edge 3. midway between these two positions\nAccordingly, the subsequent tests were carried out only for the centrally mounted position.\nT o overcome the problem of air entrainment at high speeds, later experiments were conducted by supplying oil to the cage via two nozzles directed at the leading and trailing edge. With a copious supply of lubricant, the annular space between the ball and the cage remained full at moderate speeds, according to direct observation through the microscope, and as far as could be determined there was no air entrainment. At high speeds, the view was obscured due to oil being flung onto the reservoir walls.\nWith this arrangement, the experiment could be per- - formed over the full speed range. Care was taken to look for any marked temperature rise using a trailing thermocouple. Even though none was found, the results were repeated for decreasing speeds to overcome the possibility of a time-dependent heating. This procedure was performed three times as a check, usingjust one ambient temperature, - - as the intention was solely to relate the friction to a given viscosity. T h e data were collected using a UV-recorder and tvere monitored simultaneously with a digital voltmeter. The results are presented in Fig. 3 and confirm the linear relationship found with the previous arrangement, but this\nD ow\nnl oa\nde d\nby [\nN an\nya ng\nT ec\nhn ol\nog ic\nal U\nni ve\nrs ity\n] at\n1 5:\n16 2\n6 A\npr il\n20 15",
            "Flg. 2-Belllpocket frlctlon\nM~dway -\n0' 2000 LOW 6000 Bm0 ( r p m l BALL SPEEDS\n6 --\nmeasurements at low speed for three ball positlons\n-I -I u m\nZ 0 u a 0 ,-\nFlg. 3--Balllpocket frlctlon measurements at hlgh speed for centrally located ball.\n6 - .\ntime up to a ball speed of approximately 25 000 rpm. Beyond this, there is presumably cavitation or air entrainment giving efrectively a lower viscosity and hence a lower slope. Nevertheless, the experiment indicates that the earlier assumption of direct proportionality between balllpocket friction and speed (Eq. [2]) is valid, but allows a better estimate of K,,, the constant of proportionality, to be made.\nLocat~on of Ball in b c k e t\n2 -. O Central\nk Edge\nMEASUREMENT OF CAGE DRAG\n-fhe technique chosen for measuring cage drag was similar to that used in measuring balllpocket friction. The ap1~;~;1tussShown i Fig. 4 is nearly identical to the apparatus in Fig. 1. Because of the requirements of greater torque but accompanying lesser speed range for the full cage test, the gear drive was not used and the drive shaft was directcouplecl LO the drive motor. The maximum cage speed with this me~hocl was 3000 rptn, equivalent to a bearing speed of ;tbout 8000 rpln depending on sliding speed, load, etc. Ini~i;illy, he cage was fitted with an extra outer cage of thin\naluminum with undersize pocket holes to prevent the balls being flung outwards, and the whole assembly was rotated inside the prefilled reservoir. It was found, however, that at low speeds up to 150 rpm the oil within the cage rotated along with it, while at higher speeds most of the oil was pushed out of the cage by centrifugal force. Clearly, neither of these situations simulated the operation of a real bearing cage, and so the apparatus was modified to take advantage of the way in which the oil lined the reservoir wall from low speeds upwards. First, the proper cage was discarded and the aluminum outer cage was fastened directly to the drive shaft on a \"spider.\" The balls were placed on the lower rim of the cage and the motor was brought up to a speed of about 250 rpm, by which time each ball had located itself firmly in a pocket, held in by the centrifugal load. Sufficient lubricant was then poured into the reservoir to reach up to\nFlg. 4--Apparatus used for measuring the cage drag torque\nD ow\nnl oa\nde d\nby [\nN an\nya ng\nT ec\nhn ol\nog ic\nal U\nni ve\nrs ity\n] at\n1 5:\n16 2\n6 A\npr il\n20 15"
        ]
    },
    {
        "image_filename": "designv11_11_0003446_1.2735339-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003446_1.2735339-Figure3-1.png",
        "caption": "Fig. 3 Anatomy of skew axis gear pair",
        "texts": [
            " Here, the kineatic geometry of motion transmission can be parameterized usng a system of spherical coordinates and a transverse surface is a phere concentric with the intersection of the two axes. Dooner nd Serieg 21 proposed a system of cylindroidal coordinates u , ,w to parameterize the kinematic geometry of motion transission between skew axes. Such coordinates were devised speifically to parameterize the kinematic geometry of motion transission between fixed skew axes in terms of: E=perpendicular istance between axes; =included angle between axes; and g instantaneous speed ratio between axes. \u201cInput\u201d and \u201coutput\u201d axes are referred to as \u201cfixed\u201d and \u201cmovng\u201d axes, respectively. Figure 3 depicts two hyperboloidal pitch surfaces in first-order ontact or tangency, two axes $ f and $m of rotation, the perpenicular distance E between the two axes $ f and $m, along with the ncluded angle between the two axes $ f and $m. These hyperoloids are produced by rotating a line or generator about a cenral axis. Rotating the common generator $gen between the fixed nd moving body about the central axis $ f produces the fixed yperboloidal pitch surface. The shape of this hyperboloidal pitch urface depends on the angle and the distance u"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003351_pvp2005-71333-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003351_pvp2005-71333-Figure3-1.png",
        "caption": "Fig. 3 Finite Element Model",
        "texts": [
            " Using the same method, it is found that normal bolt/nut system may become loose, but the market-sold eccentric bolt/nut systems[3] can prevent nut rotation that induces bolt loosening. ABAQUS (V6.4) was used for the finite element analyses. This section addresses the analytical model. The concept of the model is shown in Fig. 1, and the dimensions are indicated in Fig. 2. The size of the bolt is M8 that has the maximum dimensional tolerance of 0.014mm[4] in the radial direction. As the bolt thread slips most on the nut surface in the condition of maximum dimensional error, the analytical model employed this maximum allowable error. The analytical model is shown in Fig. 3. The finite element model has \"modified\" quadratic tetrahedral solid elements (C3D10M). This type of element is special for ABAQUS [5], and has high quality (accuracy). Although it is a quadratic solid elements, it can handle contact problems. The top portion of the bolt is defined as rigid body to maintain the circle shape during the loading, and is subjected to the radial motion. The whole nut portion is also meshed by C3D10M 1 Copyright \u00a9 #### by ASME 1 Copyright \u00a9 2005 by ASME erms of Use: http://www",
            " In this case, no inclination of the nut occurs, as it does not occur when the bolt joint fastens flat surfaces. The pretension load of each bolt is applied using the special \u201cbolt-pretension\u201d capability of the program [5] and the bolt length is \"fixed\" after tightening so that the changes of the bolt-tension can be captured. The material properties used in the analyses are as follows: Young\u2019s Modulus, E=190000MPa Poisson\u2019s Ratio, \u03bd = 0.3. The following conditions were analyzed using the model shown in Fig. 3. (1) Constraints (Boundary conditions) The following cases (a) to (c) were considered to model different nut conditions: (a) Nut is allowed to rotate about its axis that is collocated to the bolt axis. Bolt top is allowed to move only in the radial (x-) direction. This is the case of \"normal\" situation. (b) Nut is allowed to rotate about its axis that is collocated to the bolt axis. Bolt top is allowed to move only in one radial (x-) direction, and the bottom is constrained not to move in the radial directions (x- and y-directions)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000849_s0003-2670(01)01023-6-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000849_s0003-2670(01)01023-6-Figure2-1.png",
        "caption": "Fig. 2. Schematics for the flow-cell. (1) Bifurcated optical fiber; (2) mounting screw nut; (3) flow-cell body; (4) sensing membrane covered quartz glass plate; (5) detecting chamber; (6) inlet and outlet channel for sample solution.",
        "texts": [
            " High molecular weight poly(vinyl chloride) (PVC), tetrahydrofuran (THF), di-iso-octyl phthalate (DIOP), di-nonyl phthalate (DNP), and dioctyl sebacate (DOS) were purchased from Shanghai Chemicals (Shanghai, China) and used as received. TPPH2 was synthesized by Adler\u2019s method [22]. Chloro(tetraphenyl-porphinato)manganese (TPPMnCl) was prepared according to documented procedures [23,24]. The porphyrins synthesized were identified by elementary analysis, UV\u2013VIS spectroscopy and IR spectra. All fluorescence measurements were carried out on a Hitachi M-850 fluorescence spectrometer with excitation slit set at 10 nm and emission at 20 nm. A home-made poly(tetrafluoroethylene) flow-cell (shown in Fig. 2) and a bifurcated optical fiber (30+30 quartz fibers, diameter 6 mm and length 1 m) were used for the BE sensing measurements. The excitation light was carried to the cell through one arm of the bifurcated optical fiber and the emission light collected through the other. A quartz glass plate (diameter 10 mm) covered with sensing membrane was fixed on the top of the flow chamber by the mounting screw nut with the membrane contacted with the sample solution. The sample solution was driven through the flow-cell by a peristaltic pump (Guokang Instruments, Zhejiang, China) at a flow rate of 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002801_nme.1620231107-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002801_nme.1620231107-Figure5-1.png",
        "caption": "Figure 5. Cylindrical finite element: set of connectors in local axis",
        "texts": [
            " and (I 3)): The following assumptions are made for displacement rates and strain rates (see formulae (1 2) \u201c 1 .=[ 0 0 1 s s2 s3 l s 0 0 0 - 6hs d U = 0 0 0 -h/s - 2h 0 0 0 L::: 0 0 - 2h The corresponding connectors ( qp) are shown in Figure 3. The connection matrix is then 2080 P. MORELLE In the case of the cylindrical shell element, the compatibility equations (5 1)--(54) become: where the following dimensionless quantities are used: R being the radius of the cylinder. We choose dU= 0 1 :: 0 S . _ __ r 0 0 - and we define the nodal displacement in the way illustrated Figure 5. So, the connection matrix C, has exactly the same form as that of the conical element (69)-(75) For all cases, we consider the following discretization for the (A): which leads us to a reasonable number (ai = 24) of di. Taking into account the fact that (8\u201d are discretized in the following way: 1 ( S ) i = c,- + c2 + c,s + c,s2 (87) referring to the preceding discussion, it is clear that we cannot reach a true upper bound S NUMERICAL SHAKEDOWN ANALYSIS 208 1 of the limit factor with such a linear choice of (xi)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003587_bfb0035226-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003587_bfb0035226-Figure3-1.png",
        "caption": "Figure 3. (a),(b),(c) Different contact surfaces considered for computing tangential forces, (d) normal behavior of wheel-soil contact",
        "texts": [
            " There is another longitudinal component, called rolling resistance. This force, denoted by Fx, is always opposite to the travel direction and thus has a negative value. This force is due to soil compaction or to the energy dissipation in the tire carcass. 2.1. T a n g e n t i a l b e h a v i o r The interaction between a wheel and the soil is mainly governed by deformations of bodies in contact. A realistic model must take into account the material behavior laws of this bodies. It seems judicious to investigate the three following cases (fig.3): 1. a rigid wheel on soft soil, 2. a flexible wheel on rigid soil, 3. and a flexible wheel on soft soil. We thus practically cover all possibilities for a macroscopic observation of contact behavior. The case of a rigid wheel on a rigid soil is not developed because, except for railway vehicles, it is not interesting in practice. R ig id whee l on soft soil : This case, not very useful, is interesting to study in order to deduce the general case. W'e note that a pneumatic wheel with a hight inflation pressure on a relatively soft soil can be assumed to behave as a rigid wheel",
            " [8][9] who use the parameterization of contact motions and forces defined in paragraph 2. In this model, the portion of the wheel in contact with the soil is supposed to be composed of a set of bristles which are flexible in the two directions of the tangent plane. The relationships are given in appendix A. E la s t i c whee l on soft soil : This case does not have an analytical solution. We propose a solution by a simple combination of the 2 previous cases. We assume that the contact is established into 2 regions (cf. fig.3(c)) : (1) a first region where the wheel has a rigid behavior on a soft soil, (2) a second one where the wheel has an elastic behavior on a rigid soil. Tangential components are then given by the sum of components exerted at each region (cf. appendix A). The different models, developed here, are homogeneous since they use an identical parameterization. To sum up, these forces are expressed as a function of the longitudinal slip s, the side slip angle c~, the normal force F~ and then they can be written as follows: F,, = f ( s , c~, F~, ",
            " N o r m a l b e h a v i o r The normal force depends on normal wheel and soil deformations. The computation of the contact surface between an elastic wheel and a soft soil locally irregular needs a refinement of the contact by considering a finite-element mesh [10]. In order to provide a realistic and useful model, we choose to characterize the normal behavior as a rigid tread band, connecting to the wheel center by a parallel joint of a spring and a damper, and rolling on a rigid geometric profile of the soil. This is illustrated in figure 3(d). If 5 is the relative displacement between the wheel center and that of the rigid tread band, the normal force (including the case of contact breaking off) can be expressed by: /;~ = max(0,/c~5 + a ~ ) (r) where/% and a~ express the radial (or normal) stiffness and damping of the wheel. 3. Dynamic equations The development techniques of dynamic equations for wheeled or walking robots has been widely discussed. However, these equations are based on no-sliding condition. This assumption implies a mechanical topology with parallel chains, then the dynamic model is defined by a differential-algebraic system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.11-1.png",
        "caption": "Figure 3.11 Constant-stress disc with constant-thickness outer rim. Geometrical definitions",
        "texts": [
            "75) The total ballast mass mb needed in order to achieve the required stresses at the outer radius can be easily calculated as: mh = nr*hcpe-B/B (3.76) The shape factor K and the velocity factor \u00a3 can be obtained with simple calculations: K = \\-e~ Z = J2B (3.77) (3.78) These values of K and \u00a3 are plotted in Figure 3.10 as functions ofB. In practice, constant stress flywheels are constant stress discs with an outer rim which exerts the required radial stress on the disc, while also contributing to its strength. The simplest type of rim is the constant-thickness one (Figure 3.11). If the ratio a between the thickness of the rim and the outer thickness of the disc equals unity, the plane stress assumption can be used with confidence, at least if the ratio hD/hc is not too small, i.e. if the value of B is not too high. Otherwise the step at the disc-rim connection will cause a stress concentration, even if the profile is suitably blended. The simple calculations which follow are based on the plane stress assumption and need to be checked against two-dimensional numerical solutions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002525_s0022-460x(85)80146-2-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002525_s0022-460x(85)80146-2-Figure1-1.png",
        "caption": "Figure 1. (a) Co-ordinates and displacements of a thin shell of revolution; (b) co-ordinates and geometries of a thin shell finite element of revolution (region indicated on (a) enlarged for detail).",
        "texts": [
            " The natural mode shapes are presented in 3-D perspective, drawn by the plotting routines developed in this study, in addition to the conventional 2-D presentation. Figure lea) shows a typical shell of revolution such as a tire, where z is the axis of symmetry, and r (shown in Figure l(b)) and () are the radial and angular co-ordinates, respectively (a list of symbols is given in the Appendix). The displacement components U, v and ware in the directions normal to the shell surface, along the meridian, and along the circumference, respectively. A thin shell finite element of revolution capable of modeling such structure is shown in Figure 1(b). The symbol Ck is the meridional length of the kth element and x is the surface co-ordinate measured in the meridional direction from the mid-meridian. The radii RJ and R2 define the curvatures in the meridional and circumferential directions respectively. Six degrees of freedom were assumed at either end circle of the finite element: w, u, v, {3 ( = Wx - u/ R), UX and vx, where the subscript x represents the derivative with respect to the x-co-ordinate. The nodal displacement vector for the kth finite element is The subscript k of the nodal displacement vector {qd will be removed throughout the derivations of the stiffness matrices for the purpose of presentation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003606_detc2005-85337-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003606_detc2005-85337-Figure4-1.png",
        "caption": "Fig. 4 Some 2-DOF single-loop kinematic chains with a 1-\u03b6-system: (a) kinematic chain with a 1-\u03b6\u221esystem and (b)-(c) kinematic chains with a 1-\u03b60system.",
        "texts": [
            " The wrench system of this serial kinematic chain is always a 2-\u03b60-3-\u03b6\u221e-system . The mobility of the single-loop kinematic chain can be calculated as F = f \u2212 (6\u2212 c) (3) whereF denotes the mobility of the single-loop kinematic chain, f denotes the sum of the DOF of all the joints, and c represents the order of the wrench system of the twist system formed by the twists of all the joints. It is noted that c can be determined using the geometric relation between a wrench system and its associated twist system. Figure 4 shows several single-loop overconstrained kinematic chains as well as their wrench systems. There are 17 types of multi-DOF single-loop overconstrained kinematic chains that are composed of one or two of the 4 ownloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/07/2016 Ter above composition kinematic chains. These single-loop overconstrained kinematic chains as well as their corresponding c are shown in Table 1. In the type synthesis synthesis of singleloop mechanisms, the Nos"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000667_s0026-265x(02)00042-5-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000667_s0026-265x(02)00042-5-Figure8-1.png",
        "caption": "Fig. 8. Difference spectra (with respect to open circuit conditions) of an electropolymerized film of ZnTAPc on an ITO surface immersed in 0.10 M KClO at pH 10.97. For spectra labeling see Fig. 6.4",
        "texts": [
            "60), the difference spectra for CoTAPc films show the same features observed at the lower pH (5.75). The difference spectra for electropolymerized films of ZnTAPc on ITO surfaces immersed in 0.10 M KClO , pH 5.75, do not show MLCT4 bands (Fig. 7b). Only the Soret and Q bands are recorded, and this may result from a lack of charge increase on the central metal ion, and hence no reduction of the central metal ion. When the pH of the solution is raised to 10.60, significant changes are observed in the spectrum (compare Fig. 7b and Fig. 8). Between 600 and 800 nm, absorption bands are observed when the applied potential is y0.500 and y1.000 V. These two bands (appearing in the spectra identified as e and f ) are assigned to E \u00a7A transitions. Undoubt-g 1u edly, the increase in wOH x (or concomitanty decrease in wH O x) significantly affects the avail-q 3 able electronic transitions in the ZnTAPc film, and the photon absorption behavior of these films at pH 10.60 approaches that exhibited by CoTAPc films. When electropolymerized films of CoTAPc and ZnTAPc on glassy carbon surfaces are immersed in aqueous solutions of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002638_1.1645297-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002638_1.1645297-Figure6-1.png",
        "caption": "Fig. 6 Crankshaft and block finite element mesh and cylinder pressure trace for an automotive V6 engine",
        "texts": [
            " The stiffness matrix correction @B#n11 i and the damping matrix correction @P#n11 i at the i th iteration of the n11 time step, are calculated as @B#n11 i 5@T#F ]QI ]hI G n11 i @T#T, @P#n11 i 5@T#F ]QI ]hI\u0307 G n11 i @T#T (35) where the transformation matrix @T# is given by Eq. ~30!. With a simple area transformation from nodal pressure P to nodal force Q, the @]QI /]hI # and @]QI /]hI\u0307 # terms in Eq. ~35! represent the oil film stiffness and damping matrices respectively. The oil film stiffness matrix is calculated from Eqs. ~12! and ~13!. Similar expressions are used for the oil film damping matrix. Transactions of the ASME s of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F An automotive V6 engine is analyzed in this section. Figure 6 shows the finite element model of the engine block and crankshaft, including the pulley and the flywheel. The crankshaft is modeled with 21,136 solid elements and 37,713 nodes with a total of 113,139 DOF. The block is modeled with 106,766 solid elements and 78,151 nodes with a total of 234,453 DOF. The crankshaft-block system is described with respect to an orthogonal XYZ coordinate system with its origin placed on the centerline of the crankshaft journals, under the center of the first pin when the first piston is at the top dead center ~TDC",
            " Including the rigid-body rotation, the final number of DOF for the system is 240. A set of four different crankshaft-block system analysis results is presented here. They include crankshaft rigid body dynamics effects and different bearing support treatments. The crankshaftblock interaction forces acting over the bearing load-carrying area are used to compare the results in an integral sense. The analysis was conducted at the peak torque condition with 4500 RPM engine speed and a maximum cylinder gas pressure of 4.6 Mpa ~Fig. 6!. The crankshaft-block interaction forces are computed using both the detailed hydrodynamic bearing stiffness and damping characteristics and a simplified, rapid approach which replaces the oil film hydrodynamic pressure forces with a set of nodal, nonlinear springs with a force-displacement relationship, given by Eq. ~36!. Q55 4310421.5923107h11.5923109h2 for 0,h<0.005 200S 12 h20.005 c020.005D for 0.005,h,c0 0 for h>c0 (36) The spring forces given by Eq. ~36!, vary linearly with the nodal film thickness h, when 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000858_cta.4490220606-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000858_cta.4490220606-Figure8-1.png",
        "caption": "Figure 8. Reachable points in the q,-cycle and possible state trajectories",
        "texts": [
            " The initial polarization curve coincides with the horizontal axis up to the value e = u; , then it coincides The area a; of the q;-cycle is with the ascending branch of the q;-cycle. a; = 4C;u; (e, - u ; ) (18) and contributes to the area A of the overall Q-cycle as N A = C a; (19) i = l For each C; every reachable point in the (e, q i ) plane corresponds to a uniquely defined state. At any of such points the next (increasing or decreasing) behaviour of e results in the evolution of the local state along one or two well-defined trajectories. This is clearly illustrated in Figure 8, where the various kinds of reachable points are shown and the arrows indicate the possible state trajectories. As one can see, branching may occur only on the ascending (point F) or descending (point G ) branch of the cycle. The trajectories for the points A to E are fully reversible. Following Mayergoyz, the q;-hysteresis is said to have a local memory. However, the behaviour of Q as a result of the sum of N local q;-memories does not always have the characteristics of a local memory. If N < 2, the Q-hysteresis has a local memory, since for N = 1 it is the ql-'cycle' and for N = 2 the result of the sum of a single-valued function (q;-'cycle') and a hysteresis cycle with a local memory (q2-cycle)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000672_la9907984-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000672_la9907984-Figure1-1.png",
        "caption": "Figure 1. Schematic of a hemicylinder rolling on a flat plate. The hemicylinder was rolled on the flat substrate by applying an external load P to one end of the glass plate. The torque per unit length needed to roll the hemicylinder is the product of P and S.",
        "texts": [
            " Here we present a method to estimate the values of Wa and Wr independently and simultaneously. The starting point of our analysis is based on eqs 2 and 3, which relate Wa and Wr to the rolling torque and external load acting on the cylinder.17,18 Here P and \u03c4 are the external load and torque acting on unit length of the cylinder. E* is defined as 1/E* ) (1 - \u03bd1 2)/E1 + (1 - \u03bd2 2)/E2. Ei and \u03bdi, respectively, are the Young\u2019s moduli and Possion ratios of the cylinder and substrate. R is the radius of curvature of the cylinder and b is the half-width of contact deformation (Figure 1). The Method of Rolling Contact Mechanics. The basic protocol used to carry out the rolling contact experiment is shown schematically in Figures 1 and 2. The method had been discussed previously in ref 18. Briefly, an elastomeric hemicylinder, attached to a thin glass plate, is first brought into contact with a flat substrate resting on an electrobalance. The cylinder is rolled on the flat plate by tilting one end of the thin glass plate with a micromanipulator. As the cylinder rolls, the net normal force applied on the cylinder is recorded in a computer that is connected to the electrobalance",
            " When a cylinder rolls on a flat plate, new surface areas are created at the trailing (or receding) edge while free surface areas disappear at the advancing edge. The concomitant change of surface energy is provided by the external torque. An energy conservation approach yields Equation 5 was used as another check for the validity of the adhesion energies obtained from eqs 2 and 3. With a silicone (Dow Corning Sylgard 184) hemicylinder (R ) 1.52 mm) and a clean silicon wafer, we carried out several rolling experiments by applying the external force at different values of S (Figure 1), all other conditions being constant. Table 1 summarizes the values of P, S, and \u03c4 as well as those of Wa and Wr obtained from eqs 2 and 3. Note that the values of Wa and Wr cluster around 41 ( 3 and 621 ( 27 mJ/m2, respectively, which agree well with the values of Wa (45 mJ/m2) and Wr (639 mJ/m2) obtained from the standard loading-unloading experiments. It is noteworthy that the value of \u03c4 is nearly constant even though S varies from 0.11 to 0.23 cm, implying that the value of P is adjusted by the system to ensure a constant torque (\u03c4)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003070_j.mechmachtheory.2004.11.006-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003070_j.mechmachtheory.2004.11.006-Figure2-1.png",
        "caption": "Fig. 2. Nomenclature.",
        "texts": [
            " Hence the remaining three degree of freedom are redundant. For control and simulation of such systems, kinematic analyses of Dodekapod are proposed in this paper. Since the development of Stewart platform [3,4] various authors have addressed the problems related to kinematics and dynamics of parallel manipulators [5\u201313]. It has been shown in [6\u20138] that the Stewart platform of general geometry has 40 distinct solutions. Solutions of the generalized Stewart\u2013Gough platform are also obtained in [9]. Referring to Fig. 2, which shows a kinematic structure of the Dodekapod, it may be noted that all joints other than the six leg joints can be grouped to lie in four distinct planes. Fig. 2 shows the grouping of these joints in planes a, b, c and d. Passive or unactuated joints in each plane are denoted by the alphabet identifying the plane with suffixes from 1 to 6 as there are six joints in each plane. For the purpose of kinematics analyses two right-hand coordinate frames are attached. The fixed reference frame B has its origin at the center of the base platform on plane b. Its Yb-axis passes through the midpoint of line b1b6, Zb-axis is normal to the plane b and the Xb-axis of the coordinate system is determined by the right hand rule. Similarly, the movable frame C has its origin on plane c, with its Yc-axis passing through the midpoint of c1c2 and Zc-axis being normal to plane c. Leg cylinders are numbered from 1 to 6, base cylinders from 7 to 9, and the top cylinders from 10 to 12, as shown in Fig. 2. All the cylinders can be actuated whenever required. For example, leg cylinders are used to manipulate the object whereas the base and top cylinders are used only when the adjustment has to be made for an object of different shape and size. Fig. 3 shows schematic diagram of the base and top platforms in detail. The paper is organized as follows: Sections 2 and 3 provide the inverse and forward kinematics algorithms, respectively, whereas Section 4 gives the results of a numerical example. Finally, conclusions are given in Section 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003146_1-84628-214-4-Figure4.3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003146_1-84628-214-4-Figure4.3-1.png",
        "caption": "Fig. 4.3. An example swimbot with six parts.",
        "texts": [
            "2 shows a close-up view of a group of swimbots to show variation in an unevolved population. Food bits can be seen scattered around. 84 Ventrella Food bits replicate by periodically sending imaginary spores out, which appear nearby. Thus, the food bits occupying the initial disk region begin to spread, as swimbots consume them. Swimbots are made of parts, ranging in number from 2 to 10. Parts are rigidly connected from end to end and rotate off each other in pendulum fashion, using sine functions. Parts come in six colors (red, orange, yellow, green, blue, and violet). Figure 4.3 shows a swimbot that has six parts. Genes for morphology determine the length, thickness, color, and \u201cresting angle\u201d of each part. (The resting angle of a part is relative to the angle of the part to which it is attached.) Genes for motor control determine the phases and amplitudes of the sine functions, per part. Figure 4.4 shows how three unique sine waves, determined by six genes, combine to create a unique periodic swimming motion in the whole body. Frequency of sine-wave motions is constant among all the parts, but can vary among swimbots according to another gene"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000964_robot.1991.131992-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000964_robot.1991.131992-Figure3-1.png",
        "caption": "Fig. 3. Experimental set-up at the IPR robotics laboratory",
        "texts": [
            " are able to automatically carry out complex sensor-guided tasks and to react to unforeseen events within a limited range. Using this kind of low-level fault-tolerance, the robot can adapt its behaviour to the uncertainties of a real-world environment [61. 3 . The KAMRO Test Site at the IPR For demonstrating the capabilities of the KAMRO system, a test site was constructed at the IPR consisting of an experimental assembly cell. Among others, this cell includes several work tables to which the robot can drive and perform an assembly. One of the experiments undertaken so far is as follows (Fig. 3): The robot is docked at the power station maintaining its batteries. A set of parts belonging to the Cranfield assembly benchmark [2] is placed arbitrarily but nonoverlapping on a second work table. The experiment starts by giving the robot an order to assemble the benchmark parts. This assignment includes both the goal description of the assembly (see Chapter 4) and the information about the work table on which the parts can be found. First, KAMRO plans a safe path to get from the present to the target station"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002344_6.2004-4909-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002344_6.2004-4909-Figure1-1.png",
        "caption": "Fig. 1 Reference for tracking control",
        "texts": [
            " Four different robust control design techniques are used and the resulting controllers are evaluated in frequency and time domain. The results lead to conclusions and recommendations that will be used at Delft University of Technology for further development of software enabled control of unmanned helicopters. In order to provide intuitive control for an RC pilot, the following reference signals for tracking are chosen: the three velocities Vx, Vy , Vz in a rotating geodetic axis system complemented with heading turn rate \u03c8\u0307 as shown in figure 1. For the purpose of control system design, these four commanded velocities are transformed to the body reference frame using pitch angle \u03b8 and roll angle \u03c6 according to equation (1).5 ur = Vx cos \u03b8 + Vz sin \u03b8 vr = Vx sin \u03b8 sin\u03c6+ Vy cos\u03c6\u2212 Vz cos \u03b8 sin\u03c6 wr = Vx sin \u03b8 cos\u03c6\u2212 Vy sin\u03c6\u2212 Vz cos \u03b8 cos\u03c6 pr = \u03c8\u0307 sin \u03b8 qr = \u2212\u03c8\u0307 cos \u03b8 sin\u03c6 rr = \u2212\u03c8\u0307 cos \u03b8 cos\u03c6 (1) Because of helicopter aerodynamic relations, it is impossible to control u and q or v and p simultaneously. Furthermore there are four control inputs available in the system (collective pitch \u03b4coll, longitudinal cyclic \u03b4lon, lateral cyclic \u03b4lat and tail rotor control \u03b4tr) which means that at most four reference signals can be tracked"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002418_s0967-0661(02)00319-2-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002418_s0967-0661(02)00319-2-Figure3-1.png",
        "caption": "Fig. 3. Sketch of the system as seen from the xz vehicle-fixed plane.",
        "texts": [
            " Also, the rules have to guarantee that only one ai is high at a time to avoid conflict between the secondary tasks. An example of application of the approach is developed in the following case study. To demonstrate the application of the proposed redundancy resolution technique, we have considered a 9-dofs UVMS (Podder, 1998); the vehicle is modelled as a box of dimension \u00f01 0:5 0:25\u00de m and each link of the manipulator is a cylinder of length 1 m: A sketch of the system as seen from the side is reported in Fig. 3, where the relevant reference frames are also shown. In the figure, the initial configuration for all the simulation runs is shown; namely, g \u00bc \u00bd0 0 0 0 0 0 T m;deg; q \u00bc \u00bd45 90 45 T deg, corresponding to the end-effector position xE \u00bc \u00bd2:41 0 1 T m: The simulation runs presented are aimed at the common objective of moving the end effector by 1:5 m along xi and, after a steady state, by 2:8 m along xi (see Fig. 4, the points marked with the labels A, B and C will be described later); hence, the primary task variable is represented by the end-effector position and it is, xp \u00bc xE \u00bc \u00bdxE yE zE TAR3: The primary task Jacobian can be obtained either by numerical or symbolic computations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001700_1.1636193-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001700_1.1636193-Figure1-1.png",
        "caption": "Fig. 1 General free body diagram",
        "texts": [
            " Contributed by the Dynamic Systems, Measurement, and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Division Aug. 2, 2002; final revision, April 21, 2003. Associate Editor: Goldfarb. Copyright \u00a9 2 rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 01/29/201 hensive studies of the basketball shot can be performed in future works based on the shooting dynamics problem formulated in this paper. Conclusions are presented in Section V. Governing Equations. The equations that govern the motion of a basketball are ~see Fig. 1! mg1fB1fH5maC , (1a) rB/C\u00c3fB1rH/C\u00c3fH5Ia (1b) where m is the mass of the basketball, g52gk, is the gravity vector, aC is the acceleration vector of the mass center C of the ball, I is the mass moment of inertia of the ball assuming that it is a thin spherical shell, a is the angular acceleration vector of the ball, rB/C5rB2rC and rH/C5rH2rC in which rB , rH , and rC denote the position vectors of the contact point B on the backboard, the contact point H on the hoop and the mass center C of the ball, respectively, and where fB is the contact force vector exerted on the ball by the backboard and fH is the contact force vector exerted on the ball by the hoop",
            " CONDB 5 contact condition ~51 when in contact with backboard, 50 if not! CONDH 5 contact condition ~51 when in contact with hoop, 50 if not! g52gk 5 gravity vector; ft/s2 (g532.2) R, RH 5 ball radius and hoop radius; ft (R529.75/24p , RH5(915/16)/12) @NCAA 2001# m, I 52mR2/3 5 mass, mass moment of inertia; slugs, slug ft2 (m521/16/32.2) @NCAA 2001# k, c 5 stiffness, damping; 1b/ft, lb s/ft (k52000, c 51.53) m 5 kinetic coefficient of dry friction ~m51.00! a, b, h, h0 5 backboard parameters shown in Fig. 1; ft (a 51.25, b56.0, h53.5, h051.25) @1# Appendix 1: Numerical Treatment of Visco-Elasticity. The basketball is a thin, lightly-damped elastic body that undergoes small motions. As such, it\u2019s behavior can be accurately characterized by a linear, visco-elastic model in which the normal contact force acting on the ball is of the form given in Eq. ~2!. An alternative approach, which is a special case of the analysis given Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F below, assumes that the contact is instantaneous"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001762_1.483209-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001762_1.483209-Figure1-1.png",
        "caption": "Fig. 1 High Speed Bearing Chamber Test Rig: \u201e1\u2026 squeeze-film-damped roller bearing; \u201e2\u2026 rotor; \u201e3\u2026 ball bearing; \u201e4\u2026 housing; \u201e5\u2026 roller bearing support; \u201e6\u2026 flange; \u201e7\u2026 chamber cover; \u201e8\u2026 under-race lubrication; \u201e9\u201ea,b\u2026\u2026 three-fin labyrinth seals; and \u201e10\u2026 vent",
        "texts": [
            " The outline of this paper is as follows. A brief description of the experimental arrangement is presented, followed by a sample discussion of local and mean heat transfer coefficients. Next, heat transfer coefficients and operating conditions are reduced to Nusselt and Reynolds numbers, respectively, and individual dependencies are shown. Finally, the empirical correlation for nondimensional heat transfer coefficients is introduced. Bearing Chamber Rig. The test rig, shown in a co-axial sectional view in Fig. 1, is already the second modification for smaller heights of a setup that was introduced by Wittig et al. @3#. At each side of the squeezefilm-damped roller bearing ~1!, separate chambers ~III, IV! are formed. The rotor ~2! is supported by 000 by ASME Transactions of the ASME 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F use of a Radial Drive Shaft location ball bearing ~3!, which was taken from a production engine and tolerates axial loads and rotational speeds that are high enough to compensate thrusts and rotational loads occurring during rig operation. The chambers are bounded by a thick-walled housing ~4!, the roller bearing support ~5!, the rotor, a flange ~6! realizing the sealing air supply of chamber III and the support of the housing, and a cover ~7! for chamber IV. It can be readily concluded from Fig. 1 that the bearing chamber geometries of our test rig were abstracted from the very complex arrangements given by a real engine to a more or less rectangular shape. Air and oil flows are arranged in the same way as in the real engine. An under-race lubrication ~8! supplies the roller bearing with preheated oil. This system is capable of flow rates of V\u0307F ,t <400 l/h. Typical oil temperatures were set to TF5423 K. To prevent oil leakage, the chambers were sealed using three-fin labyrinth seals ~9~a,b"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000507_027836499501400207-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000507_027836499501400207-Figure8-1.png",
        "caption": "Fig. 8. Infinite friction velocity cones.",
        "texts": [
            " Slip occurs for any pusher velocity such that (1) vp has a positive component in the contact normal (vpy > 0), and (2) vp is outside the velocity cone. The first condition ensures that the slider must move in response to the push: a force is applied at the pushing contact. The second condition ensures that the slider velocity vs is not equal to the pusher velocity vp: the contact is slipping. For sticking contact to occur the fence would have to apply a force f away from the slider, which is impossible without adhesion. at The University of Iowa Libraries on June 8, 2015ijr.sagepub.comDownloaded from 178 Figure 8 shows the velocity cones for infinite It and different rod lengths 1. The pusher-slider contact will slip for pushing angles just less than 180 degrees. Figure 9 demonstrates slipping contact for l = 5. The rod endpoint velocity Vg cannot equal the pusher velocity v~, because v~, lies to the left of the velocity cone. Therefore, the contact is slipping to the right and the applied force f lies on the left edge of the friction cone. This gives rise to a rod endpoint velocity v~ on the left edge of the velocity cone"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001756_jsvi.2001.4016-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001756_jsvi.2001.4016-Figure5-1.png",
        "caption": "Figure 5. The ith element of rotor.",
        "texts": [
            " The total kinetic energy of a system is the summation of the translational and rotational kinetic energies of rigid disks, gears and rotors as \u00b9\" m V ) V # G ) . (9) If the terms of higher order are neglected, the kinetic energy can be approximated as \u00b9+ [ m (xR #yR #zR )# J ( # Q ) # J ( R # Q )!J Q ], (10) where m (i\"1, 2,2, n) is the total lumped mass of the ith element, J (i\"1, 2,2, n; j\"d, z) the diametrical and polar moments of inertia, x , y , z , , and the three translational displacements of the mass center, two tilting angles, and torsional angle of the ith lumped mass respectively. Figure 5 shows the deformation of the ith element of rotor, where S ,M , Q ,N , S , M , Q , N are the forces and moments acting on the (i!1)th and ith elements respectively. The potential energy of the system results from the lateral, torsional and axial deformations, i.e., ;\"; #; #; . (11) From the equilibrium equation of the ith element, one can obtain the transfer equation in x direction as x M S \" 1 l l 2EI !l 6EI 0 1 l EI !l 2EI 0 0 1 !l 0 0 0 1 x M S , (12) where E is the Young's modulus, I the second moment of inertia of the shaft section, l the length of the shaft section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000289_analsci.9.783-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000289_analsci.9.783-Figure1-1.png",
        "caption": "Fig. 1 Schematic representation of the flow-injection system and the measuring cell for the amperometric assay of NADH.",
        "texts": [
            "31,33 The film thickness of the poly(thionine) films prepared on electrode surfaces was measured with a stylus profiler (Dektak 3030, Veeco Instruments lnc., Sloan Technology Division, California) without stripping the films from the electrode surface. The BAS-200 electrochemical analyzer along with a DM2M-1024 Solution Delivery Pump of the dual- plunger type and an injector (SV 1-507, Sanuki Kogyo Co. Ltd.) was used in the flow-injection experiments.25,30 Schematics of the flow-injection system and the measuring cell are shown in Fig. 1. The flow cell used for electrochemical detection was of the thin-layer design (LC-17A, BAS). The Ag/AgCI (3 M NaCI) reference electrode (RE-4, BAS), the potential of which was 0.015 V above that of the Ag/AgCI (KCI saturated) electrode, was positioned opposite to the working electrode, and the auxiliary electrode was positioned directly across the thin-layer channel (the gap: ca. 50 \u00b5m) from the working electrode. The working electrode was poly(thionine)-modified GC electrodes (MF-1000, BAS) and the auxiliary electrode was stainless steel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003978_j.oceaneng.2005.10.004-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003978_j.oceaneng.2005.10.004-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the biorobotic autonomous underwater vehicle.",
        "texts": [
            " These results show that the adaptive controller accomplishes yaw angle trajectory tracking in spite of large parameter uncertainties of the nonlinear BAUV model. The organization of the paper is as follows: Section 2 describes the mathematical model of the BAUV. An adaptive dorsal fin control law for yaw plane control is obtained in Section 3. Simulation results and the conclusion are presented in Sections 4 and 5, respectively. A schematic of the BAUV model with the dorsal fins and the coordinate systems is shown in Fig. 1. Here OI X I Y I is the inertial coordinate system. The vehicle is moving in the X I 2Y I plane. X B, Y B, ZB form the coordinate axes with the center of buoyancy as the origin, that is, \u00f0xB; yB; zB\u00de \u00bc 0. xG, yG, zG are the coordinate of the center of gravity of the vehicle. The yaw and sway equations of motion for a neutrally buoyant vehicle are described by coupled nonlinear differential equations with respect to the moving coordinate frame OBX BY B. These equations describing the AUV model are (Gertler and Hagen, 1967) _c \u00bc r, Iz _r\u00fem\u00bdxG\u00f0_v\u00fe ur\u00de \u00fe yGvr \u00bc r 2 l5\u00f0N _r _r\u00feNrjrjrjrj\u00de \u00fe r 2 l4\u00f0N _v _v \u00feNurur\u00de \u00fe r 2 l3\u00f0Nuvuv\u00feNvjvjvjvj\u00de \u00feNf , m\u00f0_v\u00fe ur\u00fe xG _r yGr2 \u00bc r 2 l4\u00f0Y _r _r\u00fe Y rjrjrjrj\u00de \u00fe r 2 l3\u00f0Y _v _v \u00fe Y urur\u00de \u00fe r 2 l2\u00f0Y uvuv\u00fe Y vjvjvjvj\u00de \u00fe Ff "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001024_978-1-4757-5070-6_3-Figure3.34-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001024_978-1-4757-5070-6_3-Figure3.34-1.png",
        "caption": "FIGURE 3.34. Cyclic voltammetry at 50mV/s of RuJIlIlI reaction for Pt/poly[Ru(vbpY)~+l (5.3 X 10-9 mol cm -2) electrode in 0.1 M Et4NCI04/CH3CN. S = 39p.A cm -2. Curve B: anodic part of curve A corrected for base current; (e) data calculated from Eqn. 41 with G = - 3.4, curve C: difference between observed and calculated curves in curve B. (From Ref. 99.)",
        "texts": [
            " (99-102) Employing this concept and disregarding the film solution potential drop, the following modified charging curve is obtained: E = E(J' + RT(1 - 26)G + RTln 6 2nP nP (1 - 6) (40) where Err is the formal potential equal to the average of the cyclic voltammetry peak potentials; G is the site-site interaction parameter; n is the stoichiometric number of electrons transferred in oxidizing/reducing the polymer redox sites; and 6 is the fraction of redox sites oxidized (as in Eqn. 36). The corresponding voltammetric current density i is given by . n2p2r Tv(1 - 6)6 1 = RT[1 _ G(1 _ 6)6] (41) where r T is the amount of redox sites per unit area and v is the potentiodynamic sweep rate. In Fig. 3.34 a cyclic voltammogram 418 KARL DOBLHOFER AND MIKHAIL VOROTYNTSEV obtained with the kind of PVPy/Ru(bipy)z polymer shown in Fig. 3.1 is analyzed on the basis of Eqn. 41. A good fit is obtained with an interaction parameter G = - 3.4. (99) The combined effect of both the Donnan potential and site-site interactions is shown in Fig. 3.35.(102) Calculated values of Donnan potential and relevant concentrations in the polymer phase are presented as a function of the electrode potential. The polymer is again of the PVPy/Ru(bipyh type; i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000118_0022-0728(94)03818-n-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000118_0022-0728(94)03818-n-Figure2-1.png",
        "caption": "Fig. 2. First three vol tammetr ic cycles o f thionine SAM on S-modif ied gold. Each cycle was per formed after a rest per iod o f 30 s with",
        "texts": [
            " Bonding to the S adatom increases the electron density in the aromatic system of the attached molecule and thus the adduct will be reduced at more negative potentials than the parent molecule [12]. The reduction of both the parent and the adduct molecule is generally assumed to occur by the exchange of two electrons (1). The first electron in the reduction of the adduct enters in the antibonding molecular orbital, destabilizing the S-S bond, and the phenothiazine moiety will be detached from the sulphur surface site. Detachment is experimentally observed as a decreasing reoxidation signal. Fig. 2 shows successive cyclic voltammograms of the thionine SAM on S-modified gold in 0.05 M phosphate buffer, pH 7.9. Each cycle was performed after a rest period of 30 s at the upper potential limit ( - 110 mV) with stirring at the end of each positive-going sweep in order to limit the redeposition to that occurring during the sweep. Stirring was stopped before recording the reduction. The reduction voltammogram has a peak at - 3 8 0 mV which is 150 mV more negative than for the solution couple [13]",
            " reduction leads to the complete detachment of leucothionine (LTH). The net electrode reaction is + 2 e + H ' H , N ~ N H , S H :, (2) H2N S NH~ + S The sulphur adlayer is not affected by the detachment as (1) after repeated detachment experiments the cyclic vol tammogram becomes identical to the vol tammogram of the initial S-adlayer (curve 0), and (2) on reimmersion into the thionine solution the cyclic vol tammogram is identical to that of the initial thionine monolayer (curve 1). The presence of the reoxidation peak in the cyclic vol tammograms in Fig. 2 can be ascribed to oxidative at tachment of LTH that was detached during reduction (the reverse of reaction (2)), but remained in the solution in the vicinity of the electrode surface. This reaction scheme holds fk)r both methylene blue and thionine on sulphur-modified surfaces of gold and platinum [15]. This process is not clearly put in evidence when continuous cycling voltammetry is used [11]. concentration is 2.8 \u00d7 10 -1() mol cm 2. The average surface area for the thionine molecule would be 0",
            " The peak potential of the first reduction voltammogram is - 3 2 0 mV and the FWHM lies within 125 _+ 5 mV for all the cases studied. The corresponding reduction charge is 80.5 p.C cm 2 (Table 1). Compared with the first vol tammogram of the thionine SAM on S-modified gold, the peak potential is 6(1 mV more positive, the FWHM has close to doubled and the reduction charge gives an increase in surface concentration of thionine of 45%. There is no reoxidation peak that would correspond to the first reduction. As opposed to the case of the thionine SAM on S-modified gold (Fig. 2) a new redox couple appears at more positive potentials. The decrease in current indicates a reductive detachment, mainly during the first scan. To test this hypothesis more carefully we performed a series of experiments (Figs. 5 and 6) where after the first reduction (R1) the electrode was removed from the solution at the lower potential limit of the scan and it was re immersed at the initial potential ( + 5 0 mV) after stirring the solution. In this way we eliminate the interference of L T H molecules that were detached during the first reduction cycle (curve 1 in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002619_095440505x32247-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002619_095440505x32247-Figure1-1.png",
        "caption": "Fig. 1 Lorythmic swingweight scale [4]",
        "texts": [
            " Maltby defines swingweight as \u2018the measurement of a golf club\u2019s weight distribution about a fulcrum point which is established at a specific distance from the grip end of the club\u2019 [3]; thus swingweight is equivalent to the first mass moment of a golf club. The most B01004 # IMechE 2005 Proc. IMechE Vol. 219 Part B: J. Engineering Manufacture *Corresponding author: Sports Technology Research Group, Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire LE11 3TU, UK. email: t.harper@lboro.ac.uk at University of Birmingham on June 1, 2015pib.sagepub.comDownloaded from widely used swingweight scale in the industry is the Lorythmic scale shown in Fig. 1. The scale has a fulcrum located 14 in from the grip end of the club; when a club is placed onto the scale, a moment is generated about this fulcrum by the weight of the club. A known mass m is positioned to balance the club moment. Swingweight is calculated by multiplying m by the distance d between the fulcrum and m, providing a value of swingweight measured in inch-ounces, where two inch-ounces are equal to one swingweight. Industry convention allocates swingweight measurements with alphanumeric values ranging between A0 and G9, where A0 is one swingweight point lighter than A1 and B0 is one swingweight point heavier than A9"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002073_s0096-3003(03)00574-5-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002073_s0096-3003(03)00574-5-Figure3-1.png",
        "caption": "Fig. 3. Elliptical orbit of the shaft center.",
        "texts": [
            " The first-order continuity equation for the ith cavity is G1 oP1i ot \u00fe V0i Rsi oP1i oh \u00fe P0i Rsi oV1i oh \u00fe G2iP1i 1 \u00fe G3iP1i \u00fe G4iP1i\u00fe1 \u00bc G5i oH1 ot \u00fe V0i Rsi oH1 oh ; \u00f012\u00de where the coefficients G s are given in terms of zeroth-order variables as G1 \u00bc A0 _q0; \u00f013\u00de G2i \u00bc \u00f0C0l0Cr\u00de2P0i 1; \u00f014\u00de G3i \u00bc 2\u00f0C0l0Cr\u00de2P0i; \u00f015\u00de G4i \u00bc \u00f0C0l0Cr\u00de2P0i\u00fe1; \u00f016\u00de G5i \u00bc _q0LP0i: \u00f017\u00de Similarly, the first-order circumferential momentum equation can be ob- tained as X1i oV1i ot \u00fe V0i Rsi oV1i oh \u00fe A0 Rsi oP1i oh \u00fe X2iV1i _q0V1i 1 \u00fe X3iP1i 1 \u00fe X4iP1i \u00bc X5iH1; \u00f018\u00de where the coefficients X s are given in terms of zeroth-order variables as X1i \u00bc P0iA0 RT ; \u00f019\u00de X2i \u00bc _q0 \u00fe 1:75ss0iasL V0i 1:75sr0iarL V0i Rsiw ; \u00f020\u00de X3i \u00bc _q0 P0i 1 P 2 0i 1 P 2 0i \u00f0V0i V0i 1\u00de; \u00f021\u00de X4i \u00bc _q0 P0i P 2 0i 1 P 2 0i \u00f0V0i V0i 1\u00de \u00fe 0:75L P0i \u00f0ss0ias sr0iar\u00de; \u00f022\u00de X5i \u00bc _q0 Cr \u00f0V0i V0i 1\u00de \u00fe 0:125Dh0L \u00f0B\u00fe Cr\u00de2 \u00f0ss0ias sr0iar\u00de: \u00f023\u00de We obtain periodic solutions to the linearized first-order continuity and circumferential momentum equations resulting from the perturbation analysis developed in the previous section. The forcing terms in the linearized continuity Eq. (12) and circumferential momentum Eq. (18) consist of a seal clearance function H1\u00f0t; h\u00de and its derivatives. In order to obtain this we assume that the rotor center whirls with a constant angular velocity in a small elliptical orbit. Fig. 3 depicts the geometry associated with such an elliptical orbit, which has a major axis of length 2ea and a minor axis of length 2eb. The coordinates of the shaft center A, with respect to a fixed coordinate system \u00f0X ; Y \u00de passing by the center point O are denoted by \u00f0x; y\u00de. We can then write x \u00bc ea cosXt; y \u00bc eb sinXt; \u00f024\u00de where X is the whirling frequency. It can be shown that using complex number notation the clearance function can be written as H1\u00f0t; h\u00de \u00bc Re a b 2 ei\u00f0h\u00feXt\u00de \u00fe a\u00fe b 2 ei\u00f0h Xt\u00de ; \u00f025\u00de where i is the unit imaginary number"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003923_1217809.1217816-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003923_1217809.1217816-Figure1-1.png",
        "caption": "Figure 1. Hardware part of the FAR demonstrator, illustrating its distributed control system, where the nodes on the vehicle are connected through a TT-CAN network.",
        "texts": [
            " The system specification phase addressed overall solution approaches and structures for functionality, mechanics and electronics hardware were developed. The final phases of the project focused on module development and step-wise integration. Competition model cars were used as a basis for a mechanical redesign where the individual wheel steering, braking and driving required special attention. The car can be programmed into several modes of operation including manual driving, cruise control and with a simplified collision avoidance functionality. Figure 1 illustrates the hardware components of the demonstrator. The FAR project indicated the advantages of running this type of student project in close connection to research. The project was one of the first (if not the first) in the world to deploy a TT-CAN network inside a (model) car. The result provided a useful case study in complex systems development, for example adopted in the EAST-EAA project to evaluate modeling concepts for automotive embedded systems, [9]. The software architecture, illustrated in Figure 2, and development approach were seen as quite promising in that it combined component based and model based development with support for distributed systems through the global TT-CAN based clock and the off-line scheduling facility in the Rubus RTOS, [12]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.66-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.66-1.png",
        "caption": "Figure 3.66 Some proposed variable inertia flywheels, (a) and (b) Rigid element, (c) and (d) Flexible wires or fibres; (e) Flexible tape. (Ullman, D. G. et al. [80-72])",
        "texts": [
            " The fluid transfer to and from the rotor is critical; any variation of the momentum of the liquid, if not properly performed, leads to dissipative actions. The pumps and hydraulic motors needed for the input and output of the liquid must handle a power which is of the same order of magnitude as the output power. The use of the hydraulic system as a variable ratio transmission with a fixed inertia flywheel will probably solve the problem in a simpler, more efficient and economical way. The basic concepts for some other solutions are shown in Figure 3.66. All these solutions lead to energy densities which are inherently lower than those of conventional flywheels, especially if the rotors alone are compared. Flywheels testing 161 Only if the interface with the load allows a corresponding weight or cost saving, can variable inertia rotors be considered. It is a common opinion that this can be achieved only at the expense of the flexibility of the system by fixing a certain law J(OJ). The output torque is again a function of the angular acceleration, but this function is different from the one characterizing a fixed inertia rotor. If the inner hub, the outer casing and the load of a coiled-band variableinertia flywheel (Figure 3.66(e)) are connected, for instance, through a planetary gear, the power recirculation needed for the variation of the inertia can be obtained with very high efficiency and the system is quite simple, at least from a conceptual point of view. The equations describing the behaviour of a rotor of this type are developed in [80-72]. The time history of the acceleration of a fixed load is shown in Figure 3.67. Variable inertia flywheels, possibly in this simple version in which the behaviour is determined by fixed parameters, are possible for some applications, particularly for machines with fixed working cycle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001061_2002-01-3355-Figure13-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001061_2002-01-3355-Figure13-1.png",
        "caption": "Figure 13: Approximate estimate of engine friction in a Formula 1 engine at 18000 rpm (valve train friction estimate is uncertain due to lack of information)",
        "texts": [
            " Unfortunately, we do not have sufficient details of a Formula 1 valve trains system to enable us to calculate the total engine friction of a Formula 1 engine. However, we know that at the maximum engine speed, 18000 rpm, the valve train friction is likely to make a smaller contribution than at lower speeds. We estimated piston assembly losses of around 30 kW, and bearing friction losses of 25 kW. At 18000 rpm, we would expect valve train friction losses to be less than 10 kW (and that this would mainly be hydrodynamic friction losses in the valve train). Figure 13 summarises this very rough analysis for a Formula 1 engine at 18000 rpm. The strategy for minimizing engine friction in a Formula 1 engine is fairly simple. If the engine has a lot of boundary friction, you would use a higher viscosity lubricant, with a friction modifier, whereas if the engine has less boundary friction, you would use a lower viscosity lubricant (again with a friction modifier). By looking at engine friction results for the conventional engine, it is possible to decrease engine friction by 10 or 20% by using the correct lubricant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003160_0022-0728(85)80080-2-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003160_0022-0728(85)80080-2-Figure3-1.png",
        "caption": "Fig. 3. Cyclic voltammetry curves with a stationary plat inum electrode for N204 oxidation and N O ~ reduction in suifolane (+0 .1 tool dm -3 TEAP) at 303 K. [ N 2 0 4 ] = 5 . 7 6 \u00d7 1 0 -3 mol dm -3 (1); [NO2C104] = 7 .17\u00d710 -3 tool dm -3 (2). Scan rate: 10 m V / s .",
        "texts": [
            " The height of the wave increases as the temperature increases and the half-wave potential is shifted to lower potentials with the temperature increase: E l ~ 2 = + 1.63 V at 298 K shifts t o El~ 2 - - + 1.50 V at 324 K with 109 reference to the half wave potential of the ferrocene/ferricinium system. We have also noticed that the limiting current as a function of the rotation speed, ~0, of the platinum electrode, is unchanged in the range: 20.9-83.7 rad s -1. In addition, the peak potentials (Ep, E~) of the cyclic voltammograms corresponding to the oxidation of N204 and the reduction of NO~- are almost the same [16] (Fig. 3). These results are in accordance with a reaction sequence involving a chemical reaction preceding the electron transfer. Accordingly, the oxidation reaction of N204 can be written as: kl N204k~_ 12 NO~ (1) N204 is not an electroactive species in the experimental potential range and so the 110 II/ A 4 . 9_ J I Fig. 4. Cyclic voltammetry curves for N204 oxidation in propylene carbonate (+ 0.1 mol d m - 3 TEAP) at various scan rates. [N204] = 8.91 \u00d710 -3 mol dm -3. Scan rate: 20 (1); 50 (2); 100 m V / s (3). oxidation proceeds through NO~ radical formation. It is worth noting that the cyclic voltammogram of NO~- exhibits an anodic peak which is smaller than the cathodic one [16] (Fig. 3). The RDEV and CV results indicate that the rate constant k 1 of the monomerization reaction is small and can control the electrochemical process at high rate of rotation speed of the electrode or at high potential scan rate. (1) Cyclic voltarnmetry A general mathematical formulation for electrochemical systems such as (1) + (5) has been previously described [17]. The cyclic voltammograms exhibit a characteristic i-E pattern with current plateau (Fig. 4). At slow scan rate, the system is diffusion controlled: the anodic current i~ is proportional to 01/2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000549_bf02969521-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000549_bf02969521-Figure5-1.png",
        "caption": "Fig. 5. Schematic representation of distance of electron shuttling between FAD and the metal electrode surface. (a) Without Au particles, (b) with Au particles.",
        "texts": [
            " The electron transferring rate coefficient of in the molecule, between the molecules, between the electrode and the adjacent ion or molecule decreases exponentially with the distance increasing between electron transfer centers. In protein mole cules, the electron transferring rate would decrease 10 4 times when the distance between the acceptor and the giver increases from 0.8 nm to 1.7 nm. So it is not strange that the direct electron transfer does not occur between the GOD (1 600 Da) and the simple metal electrode. When GOD is immobilized without Au nanoparticles (see fig.5 (a)), the distance between the enzyme and metal electrode surface (dEM) is so long that the electron transportation hardly happens. With the GOD-Au sol depositing onto an electrode surface, the electron transferring rate between the enzyme and the electrode significantly increases. Fig. 5(b) shows that the distances between FAD and Au nanoparticles (d EA), between particles (dAA) and between Au nanoparticles and metal electrode (d ) are all much shorter than dAM EM. Therefore it is very probable that the electron transfer between FAD and the Pt electrode comes true through Au nanoparticles. Hydrophilic Au nanoparticles may attach to FAD, which would shorten dEA and dAM. And gold is a good electrical conductor, thus the colloidal gold particles covered with GOD can function as electron-conducting pathways between the enzyme and the electrode surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003163_robot.2003.1241578-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003163_robot.2003.1241578-Figure2-1.png",
        "caption": "Figure 2: Side vicw of a Scout.",
        "texts": [],
        "surrounding_texts": [
            "1 Introduction Tasks such as Scout motion prediction and simula-\ntion require a mathematical formulation of the effects of the motion types on the Scout's pose. The models developed in this paper describe the configuration changes a Scout undergoes over time.\nThe Scout robot (see Figure 1) is equipped with two kinds of actuators: two wheels and a winch. With these, three types of motion can he achieved. Rolling alters the Scout's location in the plane; tilting lets the robot rotate around its own main axis; and jumping opens up movement in three dimensional space. In order to better understand the effects of these three types of motion on the Scout's pose, it is necessary to investigate them in more detail. In the following sections, models for all three motion types are derived.\n2 Scout Robot Description The Scout is a cylindrical robot of 11 cm in length\nand 4cm in diameter [4]. Two wheels, one on each end, allow the robot to roll over flat terrain. A spring foot mounted to its shell is used as a counterweight when rolling or.for jumping more than 30cm into the air. The actual height achieved depends upon the strength of the spring.\nA frame of reference for the robot must be established to base the model on. The reference frame is attached to the Scout's center as shown in Figures 2 and 3. With these definitions, with respect to the robot, forward motion corresponds to a positive displacement along the y-axis, and a left turn is equivalent to a positive rotation around the z-axis. Reverse (backward) motion and a right turn are defined analogously. Likewise, a forward control command actuates the wheels clockwise around the x-axis: while a backward control command causes counterclockwise wheel motion. The Scout is said to he upside when its z-axis points away from thc ground plane; it is upside down when the z-axis points toward the ground plane. This becomes important when the camera is used, bccause the image may be flipped.\nThe Scout's fivedimensional configuration space consists of the two-dimensional position in the plane, the orientation around the robot's z-axis, the tilt augle, and the displacement from the ground.\nThe mechanical schematics of the Scout [3] define the hasic quantities as: dbody = 39.878 mm, dwheel = 50.8mm, dwhe& = 109.347mm, and L = 60.96mm.\n'\n3 Model Derivation all three actuation modi. The effects of actuation are suhsequeutiy derived for\n3.1 Winching The winch is comDrised of a mechanism that changes the length of the winch cable and a locking mechanism that fixates the foot on the body once the cable has been reeled in completely. The locking mechanism is necessary to hold the foot in place while the winch cable is unwound for the jump. When the cable is fully extended, the lock can he removed resulting in an explosive release of the foot. As the foot hits the ground, the Scout is propelled into the air.\nAltering thc length of the winch cable deforms the spring foot. For appreciating the resulting effect on the Scout's state, four cases must be considered. Other than changing the shape of the spring, winching has no effect if the foot does not touch the ground. This is because either the Scout is tilted such that the foot\n0-7803-7736-2/03/$17.00 02003 IEEE 90",
            "Hence,\nis fully in the air or the foot is contained within the space between the robot's body and the wheels. In the latter case, the tilt nngle remains unaffected. If the foot does touch the ground with either the tip or some mid-point along the spring, the Scout performs a tilting motion. Additionally, a minuscule change in position can also he observed as the Scout finds its new equi l ibhn under a changed contact point of the foot with the ground.\nUnderstanding these cases requires foremost knowledge of the deformation of the foot, given a length of I the winch cable\n(a) Release point w of the winch cable.\n3.1.2 Foot Deformation The underlying problem of the deformation the spring foot is subjected to with respect to the length of the winch cable, is that of elastic bending of a thin plate. The plate is claniped at the mounting point, while the other end experiences a load through a fixed point.\nHere, the deformation is modeled as a segment of a circle as shown in Figure 4(b). This approach neglects the complex effects of thin plate bending [2, 51, while retaining a good approximation of the geometric properties under the assumption of constant curvature under spring bending.\nThe function that maps a winch cable length to the corresponding curve of the spring circle is\nIn order to evaluate this function, the radius of spring circle must be determined.\nTo specify the foot's shape for a known winch cable length, it is sufficient to find the point t representing the foot's tip. Then, the spring circle, on which the corresponding segment of the foot lies, is uniquely identified. Three non-collinear points on the circle are given by the foot's mounting point, the position of the tip, and, using symmetry, the tip's mirror point with respect to the z-axis.\nThe coordinates of the tip lie on the winch circle with radius r,inci, around the winch point w and the spring circle with radius rSpring. Because of the tension of the bent foot, only the intersection point of the two circles with the smaller y-coordinate is reasonable. In addition, the angle y is a function of the foot's segment witb arc lenath L on the surina circle. The CorresDond-\nnchc*&\n(b) Definition of spring and winch circles.\nI . I ing constraints can be expressed through Figure 4: The foot is modeled as a circular segment.\n(2)\n(3) 2 3.1.1 Release Point of Winch Cable Twinch' = It - wl The release point w of the winch cable from the Scout's bodv is imoortant for manv subseauent calculations. TspringZ = It - C.pringlZ\n(4) L\nrapring = 7 obtain 2 7\nUsing the geometric relationships from Figure 4(a), we _ _\nT with t = (0, t,, and = tr--'.pring+rbody cSpring = (n,n, - Tbody) , . Rewriting Equation (3) t. and solving for y yields"
        ]
    },
    {
        "image_filename": "designv11_11_0002097_j.ymssp.2004.01.007-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002097_j.ymssp.2004.01.007-Figure5-1.png",
        "caption": "Fig. 5. Experimental set-up.",
        "texts": [
            " These form parallel lines (constant h) meaning that only the value of constant C changes. Therefore, constant C can be considered as an intensity factor relating the wavelet coefficients to the singularity strength. The Hoelder exponent h; is related to the singularity pattern meaning that it will change only if the cause of singularity changes [19]. The experimental rig consists of two electrical machines, a pair of spur gears, a power supply unit with the necessary speed control electronics and the data acquisition system. Referring to Fig. 5, a DC machine of 1.5 kW rotates the pinion. The load is provided by an AC asynchronous machine which is configured as a brake. The transmission ratio is 35/19=1.842 which means that an increase in rotational speed is achieved. The characteristics of the spur gear pair are given in Table 1. The vibration signal generated by the gearbox was picked up by an accelerometer bolted to the pinion body and the electrical signal was transferred to an external charge amplifier through slip rings. No form of signal averaging is used as the signal to noise ratio is considered high enough"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003206_j.mechmachtheory.2003.12.003-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003206_j.mechmachtheory.2003.12.003-Figure4-1.png",
        "caption": "Fig. 4. Stephenson six-link mechanism in the Watanabe et al. example [6] and two domains of the driving link.",
        "texts": [
            " 3(b) and (c) are five domains of motion of the driving link on the coupler curve and five relationships between the input angle and the coupler angle of the constituent four-link mechanism, respectively. That is, the number of domains of motion of the driving link is accounted to five. Besides, a more valid variable than the output angle is adopted for discriminating domains of the driving link, which corresponds one to one to the point of the coupler curve. So, two circuits to be illustrated one over another in the Chase and Mirth Fig. 1(b) can be separated automatically. Fig. 4(a) is the Stephenson-3 six-link mechanism of the Watanabe et al. example [4]. Fig. 4(b) and (c) are two domains of motion of the driving link on the coupler curve and two relationships between input and output angles, respectively. Then, the driving link oscillates within an interval of the input angle such that 2p < h6 < 4p. In the six-link mechanism of Fig. 4, the number of domains of motion is two, and numbers of circuits and branches are one and two, respectively. When the input angle h6 takes a value within the interval whose lower and upper bounds correspond to the point of marks h and the upper limit point on the h6 / curve, respectively, two roots of the sixth order polynomial of the displacement analysis belong to one domain of motion of the driving link, that is, one branch. The variable to be newly adopted is suited to the procedure for discriminating the domains of motion of the driving link in consideration of the complicated property above-mentioned",
            " (20) correspond to a same link-chain configuration. Then, newly, let h2k (k \u00bc 1 or 1\u20132) denote such real roots of Eq. (20) and let /k denote the value of / which corresponds to h2k. If there is not exist the real root of h2k which are secured for the lower limit position /l in the above-mentioned manner, let the value of k be zero. The domain of motion [1.924, 10.226, d\u00f0h6\u00de > 0] of the six-link mechanisms of Fig. 3 and two domains of motion [6.169, 15.809, d\u00f0h6\u00de > 0], [6.169, 15.809, d\u00f0h6\u00de < 0] of the six-link mechanisms of Fig. 4 are examples of such six-link mechanism that the driving link rotates greater than 2p and less than 4p. If the domain of motion \u00bd/l;/u has the point /k, the driving link oscillates within an interval of the input angle such that 2p < h6 < 4p. In such cases, we deal with the calculated interval \u00bdh6l; h6u of the input angle as two intervals \u00bdh6l; h6l \u00fe 2p and \u00bdh6l \u00fe 2p; h6u \u00fe 2p which correspond to two jointed domains \u00bd/l;/k , \u00bd/k;/u , respectively. We call such a points on the coupler curve and corresponding points on the number line of the angular displacement the extension point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002070_j.ast.2004.03.005-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002070_j.ast.2004.03.005-Figure2-1.png",
        "caption": "Fig. 2. Reaction torques at the boundary.",
        "texts": [
            " By using the position and acceleration vector components derived, the final governing equations of motion can be expressed as I1\u03c9\u03071 + (I3 \u2212 I2)\u03c92\u03c93 + 2 [ mtya3|x=l + l\u222b l0 ya3 dm ] = u1, I2\u03c9\u03072 + (I1 \u2212 I3)\u03c92\u03c93 (10) \u2212 2 [ mtla3|x=l + l\u222b l0 xa3 dm ] = u2, I3\u03c9\u03073 + (I2 \u2212 I1)\u03c92\u03c91 + 2 [ mt(la2 \u2212 ya1)|x=l + l\u222b l0 (xa2 \u2212 ya1)dm ] = u3, where the control torque input applied to the center body has been introduced as u = [u1, u2, u3]T. The above equations describe equilibrium between the applied input torque and resultant angular momentum change of the whole system. Eq. (10) can be rewritten in a vector notation as J \u02d9\u0302\u03c9 + \u03c9\u0302 \u00d7 J\u03c9\u0302 + 2\u03c4\u0302 = u. (11) Internal reaction torques are graphically illustrated in Fig. 2 to assist physical interpretation. The reaction torque has been used in constructing a stabilizing output feedback control law for a single-axis slew maneuver of a flexible spacecraft ground model [2,3]. In addition to the moment equilibrium equation, force equilibrium for a small mass element of the flexible structures can be established. Since the appendage deflection is constrained to the b2 direction only, the force equilibrium equation can be approximated as \u03c1a2 + EI \u22024y \u2202x4 = 0, l0 < x < l, (12) where the inertial acceleration (a2) is defined in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003023_001-Figure19-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003023_001-Figure19-1.png",
        "caption": "Figure 19. A cross-sectional drawing of a fibre-optical intravascular Po,, Pco2 and pH blood gas sensor (after Gehrich et a/ 1986).",
        "texts": [
            " These workers used the ratio of fluorescence intensity at 520 nm measured with 460 nm excitation, to that measured with 410 nm excitation, as a relative measure of the basic and acidic forms of the dye. This dye measured the change in pH of a bicarbonate buffer, as CO, varied. The buffer was encapsulated in a hydrophobic gas-permeable silicone matrix, to Provide mechanical and ionic isolation from the blood. The sensor worked in the Pco, range 1-13 kPa, and a diagram of the sensor, illustrating how Po2, Pco2 and pH can be measured on the same catheter, is shown in figure 19. 30 C E W Hahn 8.1.4. Performance. Few performance details are available for the optical Po, and Pco, intravascular sensors. Peterson et a/ (1984) reported that volatile and gaseous anaesthetics caused interference, the halogenated anaesthetics causing serious problems. Their sensor had a 2 min response time for 98% response, at 25 \"C, in water, with a maximum error of 0.13 kPa over the range 0-20 kPa. Gehrich et a/ (1986) do not quote a response time for their sensor in liquids and did not address the problem of interference from anaesthetic agents"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003987_j.surfcoat.2006.06.035-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003987_j.surfcoat.2006.06.035-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the experimental apparatus used in the investigation. The target is moved with respect to the laser beam by mounting it on a two-axis CNC table. The beam was focussed on the top surface of the target. The treated region is protected using argon gas.",
        "texts": [
            " This calls for an excellent knowledge of the influence of operating parameters on melt profile and an in depth understanding of its effect on structure and properties. This paper describes the experimental investigation of the effect of process parameters on melt profile, structure and micro hardness of laser treated titanium alloy Ti\u2013 6Al\u20134V. It also explores the functional relationship between the melt profile and the process parameters taken together. A schematic diagram of the experimental apparatus used in the investigation is shown in Fig. 1. A pulsed Nd\u2013YAG laser with an average power 400 W, peak power 5 kW and a beam diameter 0.3 mm at focus was employed for obtaining linear overlapping spots on 4 mm thick Ti\u20136Al\u20134V plates of 150\u00d780 mm2 size in solution treated and aged condition. Process parameters, namely pulse energy (J), pulse width (w), pulse frequency (h) and scan rate (U), varied in the ranges of 2 to 12 J, 2 to 20 ms, 5 to 30 Hz and 5 to 25 mm s\u22121 to obtain lenticular shapedmelt zone free from surface cracks. The surface of the specimen was always maintained at the focus of the beam"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001696_s004540010017-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001696_s004540010017-Figure9-1.png",
        "caption": "Fig. 9. When the e to f angle is reflex.",
        "texts": [
            " It is clear that d is contained in1e and that d divides P into two subpolygons, PL (the one in our figures lying below d, and in general Morphing Simple Polygons 7 the one lying to the left of d viewed as oriented from v to e) and PU . We define \u03be(e) > 0 to be the length of the perimeter of PL , including d itself. See Fig. 8. To prove our claim we consider the successor edge f to e as we proceed around P (and PL ) counterclockwise. Let g be the successor edge to f . We distinguish three cases, according to the angles between e, f , and g: Case A. Suppose e and f make a reflex angle, as in Fig. 9. Now we translate f parallel to itself toward the interior of P . Either f will prove to be good, or it will get stopped at another pointw, which must be a point of PL , as the whole area swept out by the parallel move of f is in PL . The shortest segment d \u2032 joining w to f partitions PL and generates another subpolygon P \u2032L , which clearly has a strictly smaller perimeter than PL . Thus the edge f has the property that \u03be(e) > \u03be( f ) \u2265 0. Case B1. Suppose e and f make a convex angle, but the angle from f to g is reflex"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000090_s0967-0661(98)00082-3-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000090_s0967-0661(98)00082-3-Figure1-1.png",
        "caption": "Fig. 1. Coordinate frames.",
        "texts": [
            " Even leaving aside those the most natural ones, which are automation and facilitation of sailors\u2019 work, precise ship track-keeping increases a ship\u2019s safety in crowded and/or constrained waters, like straits, coastal waters, and water lanes. Moreover, special operations, for instance convoy sailing, placing a cable, or delivering food and fuel to ships at sea, also need increased precision of ship control. Finally, the requirement of keeping the ship on a given trajectory can also be connected to the sailing regulations that are valid within an actual stretch of water. In ship track-keeping, a desired trajectory is usually determined as a broken line, with specified coordinates for the successive turning points (x k , y k ) (Fig. 1). Between the turning points, the set track usually has the form of a straight line with a fixed direction t ok , measured in relation to the X 0 axis. Here, X 0 \u00bd 0 is the earth-fixed clock-wise Cartesian frame. It is convenient to define two additional reference frames X 1 \u00bd 1 and X\u00bdZ, see Fig. 1, where X 1 \u00bd 1 is the clock-wise Cartesian frame related to the current segment of the trajectory, and X\u00bdZ is the moving clock-wise frame, fixed to the ship. The origin O of the last frame coincides with the center of gravity of the ship. The goal of the ship track-keeping is for the real ship\u2019s trajectory to match the given one as closely as possible. The control of the ship\u2019s movement along the pre-defined reference path is mathematically equivalent to the stabilization of the transverse deviation of the model\u2019s center of gravity from this path at a zero level. 0967-0661/98/$\u2014 See front matter ( 1998 Published by Elsevier Science Ltd. All rights reserved PII S 0 9 6 7 - 0 6 6 1 ( 9 8 ) 0 0 0 8 2 - 3 The transverse deviation is equal to y 1 within the X 1 \u00bd 1 frame. The remaining variables used in the model of the process are as follows, see Fig. 1: x, y position coordinates in X 0 \u00bd 0 frame; u, v longitudinal and transverse components of the ship\u2019s speed vector \u00bb; t heading angle in X 0 \u00bd 0 frame; r turning rate. In the design of the track controllers, a simple dynamic linear model was used: vR (t)\"a 11 ) v#a 12 ) r#b 1 ) d#w 1 rR (t)\"a 21 ) v#a 22 ) r#b 2 ) d#w 2 tR (t )\"r (1) yR 1 (t)\"u ) sin(t!t ok )#v ) cos(t!t ok )#t cy 0R cy (t)\"w 3 where a ij , b k (i, j, k\"1, 2) ship dynamics parameters; d rudder angle; w 1 , w 2 , w 3 disturbances, modeled as zero-mean Gaussian white noise processes; t cy sea current transverse component of the pre-defined trajectory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001169_0944-2006-00057-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001169_0944-2006-00057-Figure2-1.png",
        "caption": "Fig. 2. Displacement, velocity and driving force F = Fo sin \u03c9ot at resonance as function of time.",
        "texts": [
            " Detailed analysis of simple harmonic mo- Zoology 105 (2002) 2 tion driven by a periodic force requires the solution of the differential equation (9) as function of the driving frequency f. One finds that the phase angle \u03b4 changes smoothly from \u03b4 = 0 to \u03b4 = \u00b9 as the driving frequency f is increased, Fig 1a. For the most efficient power input, Fig. 1, point (2) the driving force should vary sinusoidally at the frequency f = fo and it should lag behind the displacement by \u03b4 = \u00b9/2. Then very little energy is needed to maintain the motion, and the amplitude has its largest possible value. Fig. 2 shows displacement, and velocity for a simple harmonic motion driven by a sinusoidal force at the resonance frequency fo = \u03c9o/2\u00b9. The power to drive a simple harmonic motion at its resonance is at an absolute minimum, Fig. 3. The width of the dip in the power curve depends on the damping of the motion: \u03b3 = \u03c9o/5 is assumed here. If the system has more than one resonance frequency relatively close together the power minimum is broadened. The angular frequency \u03c9 = 2\u00b9f of the driving force can be arbitrarily set"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001442_0043-1648(95)06851-1-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001442_0043-1648(95)06851-1-Figure3-1.png",
        "caption": "Fig. 3. Ring-on-block test machine.",
        "texts": [
            " 3, Experimental veritkation This section presents an experimental verification of the mathematical model for predicting abrasive wear of partially lubricated sliding contacts. The results of the theoretical analysis are in good agreement with experiment as far as the dependence of wear rate oil load and sliding velocity are concerned. Agreement between theory and experiment on various materials has not been obtained because it is very difficult to measure solid viscosity. 3.1. Apparatus, piu2terials andpr~edure The experiments were carried out on a ring.on-block machine (see Fig.3) where stationary loaded blocks ( 12.35 X 12.35 x 19 mm) of different materials were rubbed against a standard rotating ring of steel GCrI5 (049.24 mm), hardened to Rockwell C58-62 and finished to R,=0A p.m. The material of the blocks is steel 45(I-IB266), H'I20-40(HBI52) and ZQAI9-4(HB72.4), respectively. All the blocks were finished to Ra = 0.4 p.m. Ordinary machine oil 40# was used as lubricant. The lubricant dropped down from the oil tube and was provided to the contact area by entrainment of the ring"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002011_ecc.2003.7086519-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002011_ecc.2003.7086519-Figure2-1.png",
        "caption": "Figure 2: Coordinate system and free-body diagram of the four-rotor rotorcraft.",
        "texts": [
            " The only potential energy which needs to be considered is the standard gravitational potential given by 1 ) 4 (3) The Lagrangian representing6 , ' trans 9 ' rot : 1 ) * , - , 9 .* ,# - 0 ,# : ) 4 (4) The model of the full rotorcraft dynamics is obtained from the Euler-Lagrange Equations with external generalized force ;<< > ? A? , : ? A? ; where ; ; C D and D is the generalized moments. ; C is the translational force applied to the rotorcraft due to the control inputs. We ignore the small body forces because they are generally of a much smaller magnitude than the principal control inputs F and D . We then write: G; HI KKF LM (5) where (see figure 2) F N O 9 N Q 9 N ! 9 N S and N T V T W QT X . [ [ [ \\ where V T ] K is a constant and W T is the angular speed of motorX ` T X . [ [ [ \\ , then ; C d G; (6) where d is the transformation matrix representing the orientation of the rotorcraft. We use e g for h j l and m g for l n o . d HI e g e q m q m g : m ge q m g m s : m q e s m q m g m s 9 e q e s e g m se q m g e s 9 m q m s m q m g e s : e q m s e g e s LM The generalized forces on the # variables are D ( HI D wD xD y LM (7) where and where is the distance from the motors to the center of gravity and is the couple produced by motor ",
            " The control input is used to set the yaw displacement to zero. is used to control the pitch and the horizontal movement in the ; -axis. Similarly, is used to control the roll and horizontal displacement in the < -axis. In order to simplify let us propose a change of the input variables. - % (15) where ! (16) are the new inputs. Then (17) Rewriting equations (13)-(14): ; 1 2 4 5 6 (18) < 1 7 8 2 6 2 4 5 : (19) = 1 7 8 2 6 7 8 2 : (20) ? (21) 6 (22) : (23) where ; and < are the coordinates in the horizontal plane, and = is the vertical position (see figure 2). ? is the yaw angle around the = -axis, 6 is the pitch angle around the (new) < -axis, and : is the roll angle around the (new) ; -axis. The control inputs 1 , , and are the total thrust or collective input (directed out the bottom of the aircraft) and the new angular moments (yawing moment, pitching moment and rolling moment). The control of the vertical position can be obtained by using the following control input. 1 &A A (24) where = = = \" (25) , are positive constants and = \" is the desired altitude"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000579_cdc.1997.657811-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000579_cdc.1997.657811-Figure3-1.png",
        "caption": "Figure 3: Backlash-free system",
        "texts": [
            " 3 Backlash-Free Design with Flexibility In this section we design a partial-state feedback controller for the backlash-free system (2 .1 ) in the presence of unmodeled flexibility l l k , which can be a major source of tracking error at high frequencies. Disregarding flexibility, that is assuming IC = CO, may lead to a design which renders the closed-loop system unstable even when A = 0. 3.1 Stability Margin for Flexibility In the absence of backlash (A = 0) the system in Figure 1 reduces to the system in Figure 3 in which the contact force is uC = k(B, - 02) + b ,k1 /2 (8m - 82). The open-loop transfer function of system (2 .1 ) with e ~ ( t ) as its output is then M Mi Mob,k\u201d2+Mibm+Mmbi , a12 = where a14 = +, a13 = k b a b s k \u2019 \u2019 Z + k M n S b m b ~ , k MO = Ml + Mm and bo = bl + b,. This fourth order transfer function has relative degree three. If only 81 and 81 are used for feedback, we can use a control law of the form U = - K & - ~ ~ ) - K ~ ( ~ ~ + ) + U f f ( 3 . 2 ) where u f f is a feedforward term required for tracking"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002801_nme.1620231107-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002801_nme.1620231107-Figure3-1.png",
        "caption": "Figure 3. Tronconical finite element: set of connectors in local axis",
        "texts": [
            " Nevertheless, it is well known that this plastic condition is not safe in the sense that low-cycle fatigue can be achieved in the inner shell at lower load levels that those which cause alternating plasticity in terms of generalized stresses. We shall see in the examples the meaning of the \u2018sandwich\u2019 from a practical viewpoint. Discretization of the plastic fields kinematic theorem) become For a conical shell, equations (51)-(54) (expressed in terms of the mean quantities of the (63h (64) where B and s are illustrated in Figure 3. and (I 3)): The following assumptions are made for displacement rates and strain rates (see formulae (1 2) \u201c 1 .=[ 0 0 1 s s2 s3 l s 0 0 0 - 6hs d U = 0 0 0 -h/s - 2h 0 0 0 L::: 0 0 - 2h The corresponding connectors ( qp) are shown in Figure 3. The connection matrix is then 2080 P. MORELLE In the case of the cylindrical shell element, the compatibility equations (5 1)--(54) become: where the following dimensionless quantities are used: R being the radius of the cylinder. We choose dU= 0 1 :: 0 S . _ __ r 0 0 - and we define the nodal displacement in the way illustrated Figure 5. So, the connection matrix C, has exactly the same form as that of the conical element (69)-(75) For all cases, we consider the following discretization for the (A): which leads us to a reasonable number (ai = 24) of di"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000925_20.917621-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000925_20.917621-Figure5-1.png",
        "caption": "Fig. 5. Pair of glass plates and oil.",
        "texts": [
            " 4 shows lower half part of herring bone groove of Table III (eight grooves, groove depth is 4 m ). White part means high pressure and black part is low pressure. P1 stands for the negative pressure close to the gas-liquid interface (about 0.3 mm from the end), P3 for the maximum pressure in the center line of the herringbone groove, and P0 for the atmospheric pressure at the gas-liquid interface. The calculated result shows that P1 at the low pressure section is Pascal Pascal and P3 at the high pressure section is Pascal Pascal. Calculation of Surface Tension and Suction Height: Fig. 5 shows the calculated film heights of oil. Oil is raised into the clearance by surface tension, and this film height or suction height can be calculated using Formula (2): We considered of oil is raised strongly the bubble is difficult to mix. - - - - - Formula (1) - - - - Formula (2) : Film height of oil (cm) : Surface tension of oil (33 dyn/cm) : Specific gravity of oil (0.9) : Radial clearance (5, 15 m) : Depth of groove (4, 100 m) (cm) Consideration: Figs. 6 and 7 show pressure and groove angles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002427_50009-5-Figure7.34-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002427_50009-5-Figure7.34-1.png",
        "caption": "FIGURE 7.34 Example of field generation by means of non-enwrapping windings for on-line testing of a strip along the TD. The two removable arrays of parallel conductors, placed both above and beneath the strip, realize current sheets and the ensuing flux along TD is flux-closed by means of a double-C yoke (not shown in the figure) with end faces placed as close as possible to the strip edges [7.108].",
        "texts": [
            " This occurs because the eddy current fields generated in the plates restrain the AC flux component normal to the sheet plane. With non-oriented laminations, the problem arises of testing the moving strip in the TD. This cannot be done with enwrapping magnetizing solenoids. A solution can been devised, which consists in generating the transverse magnetizing field by means of current sheets, obtained by laterally removable arrays of parallel conductors placed immediately above and beneath the moving strip (see Fig. 7.34) [7.108]. The induction signal can be obtained by a couple of enwrapping coils, crossing the strip at 45 ~ and connected in such a way that the detected variations of the flux component along the rolling direction subtract and those along the TD add one to the other. Non-enwrapping secondary windings can also be devised, as discussed in detail by Beckley [7.108]. To cope with the strong demagnetizing fields ensuing from the finite width of the strip, a transversally placed flux-closure yoke should be used",
            " high permeability GO Fe-Si laminations), provided a circular or hexagonal specimen is used because one can better cope with the presence of a hard direction in trying to achieve optimum control of the 2D flux loci [7.52]. Three-phase systems have the additional advantage of requiring less exciting power to the single supply channels for the same value of the applied field. Closed samples are seldom tested under rotational fields. Examples are provided by the classical cross-shaped specimen [7.122], where induction is homogeneous in a very small central 7.3 AC MEASUREMENTS 397 region of the sample only, and Epstein strips with diagonal secondary coils (similar to Fig. 7.34), where flux loci control is very demanding because of the strong asymmetry of the sample [7.123]. Whatever the magnetizer, some form of 2D adaptive control of the modulus IJI and the angular velocity ~ of the magnetic polarization vector must be accomplished. With circular loci, both these quantities are to be kept constant. This is automatically obtained under a field vector H a of constant modulus which rotates at constant speed if the sample is circular and perfectly isotropic or it is cut as such a small disk that the demagnetizing field alone is sufficient to impose the required feedback conditions [7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000500_1.2830598-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000500_1.2830598-Figure1-1.png",
        "caption": "Fig. 1 Geometry of three-pad foil bearing",
        "texts": [
            " The predictions reveal the most important advantages of a foil bearing in terms of uni form force coefficients and increased damping values at low frequency excitations. The material presented helped the au thor to clarify his perspective on foil bearings, and allowed him to comprehend some of the relevent issues associated with foil bearing technology. Analysis Consider the turbulent and isothermal bulk-flow of a vari able properties fluid in the region between a rotating journal and a bearing surface of compliant characteristics. Figure 1 shows the geometry of a 3-pad foil-journal bearing, the co ordinate systems and variables of interest. The fluid material properties are solely defined by the local pressure and a mean flow uniform temperature. The flow model ignores thermal effects on the flow field, although turbulent energy dissipation mechanisms may bring large temperature rises in the fluid and solids bounding the flow. This oversimplification is solely jus tified in terms of simplicity. Thermohydrodynamic models for cryogenic liquid annular seals and hydrostatic bearings are given by Yang et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003634_j.matdes.2006.10.008-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003634_j.matdes.2006.10.008-Figure4-1.png",
        "caption": "Fig. 4. The result of t = 6 s.",
        "texts": [],
        "surrounding_texts": [
            "Fig. 3\u20135 are the simulated results for the temperature field at the times of the laser operating of t = 2 s, t = 6 s, and t = 11.6 s, respectively. The figures show that the maximum Unknown 400 500 600 700 800 900 1700 691 703 710 712 712 712 712 10.3 11.8 12.8 24.3 lt of t = 2 s. temperature rises with time. When t = 2 s, the maximum temperature is 1833 C. But, when t = 11.6 s, the maximum temperature has reached 1919 C. The reason for this is that the thermal conductivity of the ceramics is less than that of the substrate, and its heat radiating is slower, which will cause the quantity of heat to accumulate and the temperature to rise. At some point for the laser to operate, the temperature of the coating from the surface to the substrate falls gradually. There is a great temperature gradient in the coating layer from its surface to the matrix. The simulated results show that the maximum temperature is higher than the melting point (1668 C) of the cladding material and substrate in the process of the laser. The whole coating is in a melting state at high temperature. Thus a molten bath is formed while the laser is scanning. The molten bath inside changes quickly and acutely. Due to the characteristic of internal molten bath, there will be a major driving force in the bath [8]. Even though the liquid phase as ceramic molten mass possesses some stickiness, under the great temperature gradient and driving at rapidly varying temperatures, it would flow definitely. Thus its composition will be well-distributed by diffusion and convection [9], providing the condition to compose the active substances, hydroxyapatite and other calcium\u2013phosphorus-based bioceramics. The structure of the hydroxyapatite has its special characteristics. In its hexagonal crystal structure, there is a major passageway paralleling the c axis. The nucleated hydroxyapatite in the molten bath at high temperature, under the actions of diffusion and convection of the substances inside the molten bath, transport Ca2+ through this passageway to provide a substantial condition for crystal growth. Therefore the synthesis of hydroxyapatite is promoted. Moreover, laser cladding is a process of rapidly melting and solidifying. Under the optimized conditions, the liquid phase in the laser molten bath is able to meet the conditions for thermodynamics and dynamics for hydroxyapatite to be synthesized. From the analysis of the thermodynamics of synthesizing hydroxyapatite, it can be found that the temperature for its synthesis should be lower than 1927 C [10]. But the maximum temperature of the simulated results is lower than this temperature. A molten bath can also be formed. This would be of great advantage to synthesizing hydroxyapatite. Therefore, the parameters optimized in the experiment are feasible. To explain the reliability of the simulated result, the microstructural analysis of SEM has also furnished strong evidence. Fig. 6 shows the bioceramic coating obtained under the optimized technical parameters. This coralline structure will be helpful for the ossifying cells growing in bioceramic coating to supply passageways. It can be seen from Fig. 7 that the structure of the short-rod piles has formed on the surface of the bioceramic coating. This is a typical structure of hydroxyapatite [11]. The structure will undoubtedly improve biocompatibility between the bioceramic coating and osteal tissue."
        ]
    },
    {
        "image_filename": "designv11_11_0002267_j.biosystemseng.2003.12.008-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002267_j.biosystemseng.2003.12.008-Figure3-1.png",
        "caption": "Fig. 3. Tractor and oscillating platform scheme: O, oscillation axis; Gp, platform centre of gravity; Gpt, platform and tractor entire centre of gravity; d, distance between the platform and O; y, inclination angle of the oscillating platform; dGpt, distance between Gpt and O; F, lateral pulling force with tractor; Fp, lateral pulling force without tractor; b, distance from the application point of F, Fp and the mean vertical plane; dGp, distance between Gp and O",
        "texts": [
            " The platform is then pulled laterally with a steel cable, the tension being measured by a loading cell (5 kN maximum load, accuracy 0 1% full scale). The load cell is joined to the platform with a low-friction link, while the steel cable passes through a wheel, thus being maintained horizontal (Fig. 2). From the measurements of the cable tension and of the platform inclination (measured with a servo-inclinometer 158 max angle, sensitivity 50 02%) it is possible to determine statically the CG position by static equilibrium considerations (Fig. 3). From the equilibrium of the momentum around the oscillating axis of the platform, being, respectively, Mt and Mr, the tractor and platform mass, the following is obtained: F d cos W b sin W\u00f0 \u00de \u00bc Mt \u00fe Mp gdGpt sin W \u00f01\u00de from which it is possible to obtain the CG position of the whole platform\u2013tractor dGpt relative to the oscillating axis: dGpt \u00bc F Mt \u00fe Mp g d tan W b \u00f02\u00de where: F is the lateral pulling force with the tractor on the platform; d is the distance between the platform and the fulcrum; b is the distance between the application point of the lateral pulling force and central axis of the platform; g is the acceleration due to gravity; and y is the inclination angle of the oscillating platform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003733_j.engstruct.2006.03.018-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003733_j.engstruct.2006.03.018-Figure1-1.png",
        "caption": "Fig. 1. (a) Pile partially embedded in the soil. (b) Internal forces and deformations of differential element in the first region. (c) Internal forces and deformations of differential element in the second region.",
        "texts": [
            " Catal and Alku have obtained the members of the second order stiffness matrix of the beam on elastic foundations [8]. Catal has obtained fourth order differential equations for free vibration of partially embedded piles with the effects of bending moment, axial and shear force [9]. Yesilce et al. have obtained free vibration frequencies of piles partially embedded in soil with different modulus of subgrade reaction [10]. The pile partially embedded in the soil whose upper end is semi-rigid connected against rotation is presented in Fig. 1. The pile parts above the soil and embedded in the soil are called the first region and the second region, respectively. The internal forces and deformations of the differential element of the pile having the length of dx1 and dx2, respectively, at the first and the second regions are presented in Fig. 1(b) and (c), respectively. Free vibration equation of motion for the partially embedded pile whose upper end is semi-rigid connected against rotation is derived under the following assumptions: material behavior of the pile is linear-elastic; axial force is constant; soil behavior coincides with the Winkler hypothesis; effect of shear foundation modulus along the pile length is neglected; the upper end of the pile is modeled with an elastic rotational spring. Each displacement function, that is y1(x1, t) and y2(x2, t) for the first and the second regions of the pile, respectively, consists of two components as: y1(x1, t) = y1b(x1, t) + y1s(x1, t) (1) y2(x2, t) = y2b(x2, t) + y2s(x2, t) (2) where y1b(x1, t), y2b(x2, t) and y1s(x1, t), y2s(x2, t) are elastic curve functions caused by bending and shear effects, respectively; x1, x2 are pile positions for the first and the second regions, respectively; and t is time variable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002085_physreve.68.061704-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002085_physreve.68.061704-Figure3-1.png",
        "caption": "FIG. 3. Definition of the flow geometry and coordinates system for simple shear flow. ~a! The lower plate is at rest and the upper plate moves in the x direction with a constant velocity V , H is the gap separation. ~b! Cartesian coordinate system with x the flow direction, y the velocity gradient direction, and z the vorticity axis. The director n is defined by the tilt angle u and the twist angle f.",
        "texts": [
            " Section V discusses the essence of the predicted results in conjunction with relevant experimental results. Section VI presents the conclusions. In this section, we present the Landau\u2013de Gennes theory for nematic liquid crystals, and the parametric equations used to describe liquid crystalline polymers texture formation. As mentioned above, the theory is well suited to simulate texture formation since defects are nonsingular solutions to the governing equations. In this paper we study a rectilinear simple start-up shear flow with Cartesian coordinates, as shown in Fig. 3~a!. The lower plate is fixed and the upper plate starts moving at t50 with a known constant velocity V; the plate separation is H . The z axis is coaxial with the vorticity axis and the shear plane is spanned by the x-y axes. The microstructure of liquid crystal polymers ~LCPs! is described conveniently in terms of a second order, symmetric and traceless tensor order parameter Q @8#: 06170 Q5E S uu2 I 3 Dvd2u, ~2! where u is the unit vector parallel to the rodlike molecules ~see Fig. 1!, I is unit tensor, and v is the orientation distribution function",
            " For rodlike molecules, a3 is always negative, while a2 can be negative for flow alignment systems (l.1) or positive for nonalignment systems @54# (0,l,1). The flow-alignment angle is known as the Leslie angle ual , and is given by 4-6 cos 2ual5 1 l ~34! and exists for l.1. As seen from Eq. ~34!, for shearaligning rods the flow tends to align the average molecular orientation along the flow direction. Next we briefly present the LE predictions to simple shear when the director is along the vorticity that are relevant to this paper. In Cartesian component form, the director is written as @Fig. 3~b!# n5(cos u cos f,sin u,cos u sin f), where u is the tilt angle and f is the twist angle. The in-plane orientation corresponds to f50, and the out-of-plane orientation corresponds to f\u00de0. The velocity gradient for shear can be assumed uniform across the sample: v5(g\u0307y ,0,0). Replacing the director and velocity fields in Eqs. ~28! in the angular momentum balance equation ~29!, and neglecting the Frank elasticity, the following coupled nonlinear differential equations result @52#: ~a32a2! du dt 1g\u0307~a3 cos2 u2a2 sin2 u"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000948_s0967-0661(02)00075-8-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000948_s0967-0661(02)00075-8-Figure2-1.png",
        "caption": "Fig. 2. Aerodynamic angles definition.",
        "texts": [
            " The spacecraft dynamic model is highly non-linear, multivariable with a significant degree of coupling between variables, and time variable (Wu, Costa, Chu, Mulder, & Ortega, 2001a). The six degree-of-freedom (DOF) re-entry dynamics consist of three DOF translational dynamics, representing the point-mass trajectory, and three DOF angular dynamics, representing the rigid-body attitude changes. The inner-loop attitude control plays a core role in the overall flight control system. To define the attitude angles used in control analyses, three coordinate axis frames need to be introduced, as illustrated in Fig. 2. The body-fixed frame (index B) is centered at the center-of-mass (c.o.m.) of the vehicle, where the XB-axis is aligned with the longitudinal axis of the vehicle pointing forwards, the ZB-axis is pointing downwards, perpendicular to the XB-axis in the plane of symmetry of the vehicle, and the YB-axis completes the right-handed system. The XT axis of the trajectory frame (index T) is along the velocity vector and the ZT-axis is pointing downwards aligned with the position vector, while YT completes the right-handed system. Its origin is in the c.o.m. of the vehicle. The aerodynamic reference frame (index A) also has its XA-axis along the velocity vector, but its ZA-axis is collinear with the aerodynamic lift force, but in the opposite direction. The origin is also in the c.o.m. of the vehicle. Then the angle of attack a is defined as the angle between ZB and ZA; the sideslip angle b is defined as the angle between YB and YA; and the bank angle s is defined as the angle between ZA and ZT; as illustrated in Fig. 2. The attitude control system discussed in this paper is illustrated in Fig. 3. Assume the guidance system provides commanded values for the angle of attack ac; sideslip angle bc (maintained at zero to minimize the side heating), and bank angle sc: A fuzzy logic attitude controller is then designed using the attitude errors and their derivatives. The errors are defined as the difference between the commanded values and the actual values, ae \u00bc \u00f0ac a\u00de; be \u00bc \u00f0bc b\u00de \u00bc b; se \u00bc \u00f0sc s\u00de: \u00f01\u00de To cover the whole re-entry flight region where different actuators could be used to perform the attitude maneuvers, the required control moments lc; mc; nc; are selected as the output of the fuzzy controller, instead of specific surface deflections or thrusters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002025_fuzzy.1996.552385-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002025_fuzzy.1996.552385-Figure2-1.png",
        "caption": "Fig. 2. Inverted pendulum.",
        "texts": [
            " However, it is pointed out that the fuzzy control has been developed but a fuzzy control theory is not discussed yet. The author e t al., have considered the one-machine infinite bus electric power model system with controllers as a decentralized model system for the decentralized control of multi-machine power systems [ 3 1 . 0-7803-3645-3/96 165.0001996 IEEE 1427 In the method, f i r s t the swing equation is 2. I n v e r t e d Pendulum and Fuzzy System rewritten i n t o a form of fuzzy system without any approximation, and the Lyapunov motor i s illustrated i n Fig. 2. The basic The inverted pendulum controlled by a DC inequalities are derived by the application equation w i t h a control input u ( t > i s given Choosing a fuzzy control input, that is, of the stability theorem. Also, using the P-region method l4 \u2019 proposed by the author e t al . , a common symmetric positive definite matrix P i s found, and the control input i s determined under the guarantee of stabil i ty[51\u2019 [ 6 1 . Generally speaking, as shown i n Fig. 1, our approach i s a way to analyze the stability of a given nonlinear control system through the fuzzy system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003816_tro.2005.853492-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003816_tro.2005.853492-Figure1-1.png",
        "caption": "Fig. 1. Two-manipulator machining system.",
        "texts": [
            " Thus, production can bemaximized without increasing the time for task completion. This paper is organized as follows. Section II provides the formulation for trajectory resolution, Section III presents the proposed method for acceleration and torque redistribution, Section IV provides simulation results to validate the proposed algorithm, and Section V provides the conclusions. When two manipulators work together in a coordinated manner, i.e., one manipulator moves the tool and the other moves the blank (Fig. 1), the relative trajectory is specified by the task, but the resolved workspace and joint-space trajectories are flexible due to the redundant DOFs. Joint trajectories can be selected, based on a cost function, to optimize the performance. In this paper, the redundancy of the system is exploited by representing the two manipulators as a single system. Using the frame and vector notation in [14], rli;j is the vector from the ith frame to the jth frame, referenced in the lth frame. The motion of the tool relative to the blank part, _xpp;t 2 Rn 1, referenced in the part\u2019s frame, is related to the joint motions, _q = [t _qT p _qT ]T 2 R(n +n ) 1, with a relative Jacobian, JR 2 Rn (n +n ), [5], [13] _xpp;t = JR _q (1) where t _q 2 Rn 1 and p _q 2 Rn 1 are the joint velocity vectors for the tool and blank robots",
            " That is, the pseudoinverse will satisfy the primary task requirements first. Considering (9) and the algorithm, it is clear that reducing the joint torques by reducing the joint accelerations will only be effective if the joint accelerations have sufficient magnitude. The effectiveness of the proposed trajectory-resolution algorithm is demonstrated through machining task simulations. One manipulator holds an object, and a second manipulator holds a tool and machines a portion of the blank\u2019s circumference with a constant relative tool velocity (Fig. 1). Four algorithms are considered: 1) the minimum-norm velocity solution, i.e., (5) withW = I; 2) the inertia-weighted pseudoinverse [25], i.e., (5) withW = M; 3) the unweighted null-space algorithm from [21], namely q = J + RW xpp;t _JR _q+Kvt _e p p;t +Kpte p p;t . . . + 1 2 M I J + RWJR + ( max + min 2 ) (10) and 4) the algorithm proposed herein. The simulations were run at a frequency of 1 kHz. The machining forces were computed analytically [30], using the characteristics of aluminum with a shear strength of 5 MPa",
            " INTRODUCTION It is believed that robotmanipulators will be appropriate for light machining tasks, such as sawing, pushing and pulling, scraping, grinding, and polishing [1]. However, for effective operation in such tasks, we have to consider the physical characteristics of such tasks. For example, in sawing, a continuous impulsive motion is required between the teeth of the saw and the object. Another important feature of manufacturing tasks is the plastic deformation of the object. The sawn parts are permanently deformed by the act of sawing. Fig. 1 shows the human sawing task. The external impulse acting on the object in manufacturing tasks is the function of the posture and the dynamic characteristic of the worker. That is, the capability to generate impulsive force depends on the dynamic characteristic of the manipulator (or worker). In most robot control problems dealing with impact, the robot is controlled to minimize the amount of external impulse transmitted to the robot upon abrupt contact, or to suppress vibration after impact. On the contrary, some manufacturing tasks require a maximum amount of external impulse"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003264_j.jmatprotec.2004.01.030-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003264_j.jmatprotec.2004.01.030-Figure2-1.png",
        "caption": "Fig. 2. The vibration system.",
        "texts": [
            " Before the finite element model is created it is necessary to simplify the actual structure. The finite element model of the gearbox auto-generated using a free meshing method [3] is shown in Fig. 1. There are 176216 tetrahedral solid elements and 62546 nodes altogether in this model. According to vibration theory, gear transmission is simplified as a vibration system with concentrated parameters, 0924-0136/$ \u2013 see front matter \u00a9 2004 Published by Elsevier B.V. doi:10.1016/j.jmatprotec.2004.01.030 shown in Fig. 2 (A: driven gear; B: driven gear). The dynamic differential equation is as follows: mx\u0308+ cx\u0307+ k(t)[x+ xs + e(t)] = ps (1) where m is the equivalent mass matrix, c the damping coefficient matrix, k(t) the gear meshing stiffness matrix, x a dynamic displacement vector, xs a static relative displacement vector, ps a static load vector, and e(t) is a gear integrate error vector. If a global equivalent excitation error is applied and high-order components can be omitted, Eq. (1) can be changed into the following form: mx\u0308+ cx\u0307+ k\u0304x = k(t)e(t) (2) where k\u0304 is the gear average stiffness matrix and k is the changeable part of the gear meshing stiffness matrix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001248_1.2826898-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001248_1.2826898-Figure4-1.png",
        "caption": "Fig. 4 The three movable branch configurations of the rhombic fourbar linkage that generate a degenerate coupler curve consisting of the three circles shown. Linkages that are dimensionally close to the rhom bic linkage have one, or two branch continuous coupler curves that closely approach the three circles. Note that, in two of the three cases, the linkage is folded upon itself and all motion takes place about two superimposed joints.",
        "texts": [
            " Of the 36 solutions expected from intersections of two sextic curves, 18 occur at imaginary double points at infinity, as governed by the circular ity property. The remaining 18 are the actual solutions. It is really not very hard to come up with a configuration in which all 18 intersections are real, and to generate the corre sponding solution positions of the Unkage. This can be done by taking advantage of the special properties of the rhombic fourbar linkage. In the case of the rhombic four-bar linkage the coupler curve for any coupler point degenerates to three circles, as is shown in Fig. 4. The 18 real configurations of a butterfly linkage that is composed of two rhombic four-bars for a specific position of joint E are shown in Figs. 5(a) through S{d). This conclusion, reached above by a purely geometric argu ment, is confirmed below by numerical solution using the poly nomial continuation method. When properly used, this tech nique can be used to find all solutions of a system of polynomial equations of unknown order, and hence can determine the order of the system (Morgan, 1987)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001623_robot.1992.220238-Figure4.1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001623_robot.1992.220238-Figure4.1-1.png",
        "caption": "Figure 4.1: Test Path",
        "texts": [
            " kp the derivative gain, b. and the command update Mod, hc. 4.0 Performance evaluation Cunently. two standards have been proposed for evaluation of robot performance: ANSI/RIA R.15.05 and IS019283. The ANSI standard considers only the point-to-point and static characteristics of robot manipulators. The I S 0 standard provides tests for evaluating both static and dynamical robot performance. The IS0 standard is used as the basis for the performance evaluation in this work. The test path, shown in Fig. 4.1, allows for the evaluation of both comering overshoot and tracking performance. The path lies in the diagonal plane of a cube, the edges of which are parallel to the base coordinate system. This cube is located within the portion of the manipulator workspace that has the greatest anticipated use. Furthermore, it occupies the maximum allowable volume. For this study, the circle was centered at the point (0.0. -0.2. 1.2) m in the base coordinate system and had a radius of 0.5 m. The speed along the trajectory was selected to be 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001708_j.1471-4159.1993.tb13392.x-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001708_j.1471-4159.1993.tb13392.x-Figure1-1.png",
        "caption": "FIG. 1. Schematic drawing of the microdialysis probe and the probe guide.",
        "texts": [
            " A stainless steel obturator was inserted into the guide cannula to prevent occlusion. The rats were allowed to recover for a minimum of 7 days before experiments were camed out. During the experiments, a dialysis probe (2 mm long, 0.25 mm o.d., 50,000-molecular-weight cut-off) was inserted into the guide cannula so that only the dialysis tubing protruded. After the experiment, the placement of the microdialysis probes was identified by histological examination. Dialysis and neurochemical measurements The dialysis probe was constructed as shown in Fig. 1: A needle for drug microinjection was attached to the removable-type dialysis probe. On the day of the experiment. the probe was inserted carefully into the conscious rat and fixed to the guide cannula by a screw. The rat was then placed in a Plexiglas box (30 x 30 cm), and the inlet and outlet tubings were connected to a swivel located on a counterbalance beam to minimize discomfort to the rat. The probe was perfused at a rate of 2.0 pl/min with Ringer\u2019s solution (147 mM NaC1, 4 mM KCI, and 2.3 mM CaCI,, pH 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003190_s10544-005-6071-1-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003190_s10544-005-6071-1-Figure2-1.png",
        "caption": "Fig. 2. External view of the flat-enzyme electrode (MP: maltose phosphorylase, RE: reference electrode, WE: working electrode, CE: counter electrode).",
        "texts": [
            "0 U, Kikkoman Co, Japan) immobilized with PVA-SbQ (CAS No. 229-47-5, Toyo Gosei Kogyo Co., Ltd, Japan) (Harrison et al., 1988) on the pre-column (MP membrane) and a flow path (volume of 60 mm3) were deposited over a MP membrane. A working electrode (WE, platinum, 2.54 mm2 area, 0.4 \u00b5m thickness), a counter electrode (CE, platinum, 0.4 \u00b5m thickness) and a reference electrode (RE, Ag, 1 \u00b5m thickness) were fabricated concentrically on the same planar surface by sputtering to make the flat-enzyme electrode (Figure 2). An enzymatic membrane including glucose oxidase (GOD, EC1.1.3.4, Amano Enzyme Inc., Japan) and peroxidase (POD, EC1.11.1.7, Wako Pure Chemistry Industries, Ltd., Japan) were immobilised on the working electrode (GODPOD membrane) (Chen et al., 1992; Cunningham, 1998). The inner volume of the flow cell was 210 \u00b5l. Using a microsyringe, 50 \u00b5l of saliva was injected and the following reactions took place at the flat-chip sensor: Maltopentaose(G5) AMY\u2212\u2192 Maltose(G2) (1) + Maltotriose(G3) \u03b1-Maltose(G2) + Phosphate (2) MP\u2212\u2192 \u03b1-D-glucose + \u03b2-D-Glucose-1 -phosphate \u03b2-D-glucose + O2 GOD\u2212\u2192 \u03b2-D -gluconic acid + H2O2 (3) H2O2 \u2192 2H+ + 2e\u2212 + O2 (4) MP is derived from Enterococcus hirae NBRC 3181 and possesses high substrate specificity for maltose and shows high thermal stability (Shirokane et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002219_1.1759342-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002219_1.1759342-Figure2-1.png",
        "caption": "Fig. 2 Geometry of cosine curvature surface pocket at center of contact",
        "texts": [
            " This approach of a global mass balance avoids the complexity associated with interacting a cavitation algorithm with the mixed lubricated-solid contact model. The results presented here represents the best performance that the lubricant trapped inside the surface pocket can achieve as all of the lubricant will participate in the pressure build-up to separate the contacting surfaces. The contact parameters and the lubricant properties are listed in Table 1. The surface pocket geometry used is as shown in Fig. 2, unless otherwise stated. This surface profile is described by Hp~X !52 Dp 2 2 Dp 2 cosS X Sp p D (22) where Dp5Sp50.6 in this study. This is a full wave length cosine curve and the overall surface profile is continuous on the two pocket edges (X56Sp). In addition, the first derivative of the surface profile is also continuous on the two pocket edges. As a result, the pressure is fairly smooth over the pocket edges. The maximum volume V00 of lubricant ~uncompressed! that the pocket can hold is then Dp3Sp50"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002491_s0022-460x(88)80114-7-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002491_s0022-460x(88)80114-7-Figure3-1.png",
        "caption": "Figure 3. Displacements and rotations.",
        "texts": [
            " Now, returning to the equilibrium equations and expressing the vector quantities in terms of their components in the local co-ordinate system and also noting that t = e3, one may write the equilibrium equations as 9 Q ' + K x Q + F = mii, M ' + K x M + e 3 x Q + C J = j 0 , (12,13) where , d M x dM~. d M , M = d--~-el+--~-s e2+-~-s e3, Q,=dQx~ . dQ,..._.:, . dQ_.__2~ elw ds e2w ds e3. Let a rod of finite length suffer some deformations in stretching, shear and bending. Then over the length of the rod the change in the rotation vector may be' expressed as (see Figure 3) Is ~2 0 2 - 0 , = k(s) ds, (14) I t It is of interest to note that this equation is analogous to that describing the velocity of a particle in a rotating frame of reference. In this analogy M becomes the position vector for the particle, while K becomes the angular velocity vector of the rotating frame. where k(s) denotes the change in the curvature-twist ofs. Following the procedure already otutlined, one may write this equation as f ~2 ( d 0 / d s - k ) ds =0 (15) l from which one deduces that 9 d0 /ds = k"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000187_20.717713-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000187_20.717713-Figure2-1.png",
        "caption": "Fig. 2. Using HA (-+ U') and vd (+ H,d) resp.",
        "texts": [
            " Benrotte et a1 [I] proposed (for the scalar hysteresis case with the VP formulation) to use the following constitutive law with H i the coercitive field of the (descending or ascending) branch and v' the associated (positive) reluctivity. (16) H = v'B + HL, 3050 HL is explicltly accounted for by means of a equivalent current density - Q x H l . The computation of HL requires an expensive iterative procedure. The approach presented in this paper is principally different and more effective. The usage of the differential tensor 5d (or .G~) results in a true linearisation of B H - tra-jectory. The associated coercitive field and the equivalent current density are implicitly accounted for. Both approaches are illustrated in Fig. 2 assuming 1D scalar hysteresis. A . Scala,i- Preisach Model If H and B are parallel and unidirectional, the hyst;eret,ic BH-relation can be described by the scalar Preisach model [a] ,[3]. Herein the material is assumed to consist of elementary dipoles, each characterised by a rectaaguhr hysteresis loop. The magnetisation hfd of the dipoles assumes the value -1 or +1, depending on the magnetic field H ( t ) and its history Hpas t ( t ) . The switching fields cv and /3 of the dipoles are distributed statistically according to the Preisach function Ps(a , P ) , which is a material parameter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000878_jsvi.1995.0088-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000878_jsvi.1995.0088-Figure2-1.png",
        "caption": "Figure 2. The free body diagram of station j(a) and field j(b) of a torsional vibration system with inner and outer damping.",
        "texts": [
            " TRANSFER MATRIX METHOD FOR UNCOUPLED TORSIONAL VIBRATION ANALYSIS For a continuous system with inner damping coefficient ci (x) and outer damping coefficient c0(x), subjected to an excitation torque with intensity mt (x, t), the relationship between the twisting angle u(x, t) and the twisting moment MT (x, t) is MT (x, t)=GJ(x)(1u(x, t)/1x)+ ci (x)(1u(x, t)/1t) (2) and the equation of motion is mt (x, t)+ 1MT (x, t)/1x= I(x)(12u(x, t)/1t2)+ c0(x)(1u(x, t)/1t), (3) where G is the shear modulus of elasticity, J is the area polar moment of inertia of the cross-section, I is the mass polar moment of inertia per unit length, x is the axial co-ordinate and t is time. If u(x, t) and MT (x, t) are harmonic functions of the forms u(x, t)= u (x) eivt and MT (x, t)=M T (x) eivt, then equation (2) reduces to M T (x)=GJ(x)(du (x)/dx)+ ivci (x)u (x), (4) where u (x) and M T (x) are the amplitudes of the twisting angle and the twisting moment, respectively, and i=z\u22121. Applying the difference form of equation (4) to field j (see Figure 2(b)) and using the relationship M L Tj+1 =M R Tj, one obtains $u M T% L j+1 = [TF ]j$u M T% R j , (5) in which [TF ]j is the transfer matrix of field j and is given by [TF ]j =$10 1/(kj +ivci ) 1 %, (6) where kj =GJj /Dxj is the average torsional spring constant of field j. The superscripts L and R in equation (5) refer to the left side of \u2018\u2018station\u2019\u2019 j+1 and right side of \u2018\u2018station\u2019\u2019 j, respectively. If the excitation torque is also harmonic and takes the form mt (x, t)=m t (x) eivt, then equation (3) reduces to m t (x)+dM T (x)/dx=\u2212I(x)v2u (x)+ ivc0(x)u (x). (7) Applying the difference form of equation (7) to station j (see Figure 2(a)), making the substitution IjVI(xj )Dxj , c0Vc0(xj )Dxj , m tVm t (xj )Dxj , and using the relationship one obtains $u M T% R j =[Ts ]j$u M T% L j , (9) where [TS ]j is the station transfer matrix, given by [TS ]j =$ 1 \u2212(v2Ij \u2212ivc0)\u2212m 't 0 1% and m 't =m t /u 1. (10, 11) The product of [TF ]j and [TS ]j yields the combined transfer matrix of field j and station j: [T]j =[TF ]j [TS ]j = &1\u2212 (v2Ij \u2212ivc0)+m 't kj +ivci \u2212(v2Ij \u2212ivc0)\u2212m 't 1 kj +ivci 1 '. (12) The relationship between the state variables of the left and right ends of a shaft, as shown in Figure 3, is $u M T% R n+1 = [T]$u M T% L 1 , (13) where [T] is the overall transfer matrix of the complete shaft, given by [T]= [TS ]n+1[T]n [T]n\u22121 \u00b7 \u00b7 \u00b7 [T]2[T]1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000499_3516.891047-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000499_3516.891047-Figure2-1.png",
        "caption": "Fig. 2. Flexpline with a pair of strain gauges.",
        "texts": [
            " The gear\u2019s nominal reduction ratio is a ratio between the number of teeth on the flexpline divided by the difference of the number of teeth on the circular spline and flexpline (1) For the designs with circular spline fixed the gear reduction ratio , and for the designs with flexpline fixed the gear reduction ratio are (2) Here, the negative sign of denotes that the output shaft of the gear rotates in the opposite direction of the input shaft. A. Initially Proposed Built-In Torque Sensing In 1989, Hashimoto first proposed a principle of torque detection from strain in the flexpline [3]. A finite-element analysis showed that the size of the strain generated in the flexpline is suitable to be detected by strain gauges [9]. Calculated strain was the highest in the diaphragm part, that is, in the bottom part of a cup-shaped flexpline; therefore, the strain gauges were cemented on the diaphragm part, as shown in Fig. 2. A pair of 90 crossing strain gauges is used in a half Wheatstone bridge configuration to cancel the normal strain, and to detect only shear strain. Such a pair of strain gauges is, in the discussion below, addressed as a single strain gauge. The finite-element analysis also showed that the signals from strain gauges are modulated by harmonic fluctuation, which is generated by deformation of the open part of the flexpline into an ellipse [9]. This modulation we call a signal fluctuation. The period of the signal fluctuation is the same as the period of major and minor axes of the ellipse. It was initially proposed to place two strain gauges, one on the major axis of the ellipse and one on the minor axis of the ellipse, to obtain two signals of opposite phases. The signal fluctuations from both strain gauges are expected to be (3) where , signal fluctuations from the strain gauges R1 and R2, respectively (Fig. 2); amplitude of the signal fluctuation; gear configuration factor: for the designs with flexpline fixed and for the designs with circular spline fixed; wave generator\u2014the gear input shaft rotation angle. Notice that the basic frequency of the signal fluctuation is times per input shaft rotation. A correction factor is needed to compensate the relative rotation of the flexpline against the wave generator in a configuration with circular spline fixed. Additionally, we need to remark that the peaks of the signal fluctuation do not match with the positions of the major or minor axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000172_s0956-5663(97)00104-8-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000172_s0956-5663(97)00104-8-Figure4-1.png",
        "caption": "Fig. 4. Transformed calibration curves (transformation 1/Ai = ill/c)) of the composite alcohol biosensors based on different SBMs (surface layer-modified: (a) CM; bulk-modified: (b) CM, (c) HXNE, (d) BRNE and (e) EINE). Hexacyanoferrate(lll) (2 mM) was used as the mediator. Conditions: 0.2 M phosphate buffer pH 8.8,",
        "texts": [
            " The dependencies of the current changes on ethanol concentration (Fig. 2(a), Fig. 3) were not linear. Similar behaviour of ADH-based biosensors in the range of ethanol concentrations 0.2- 20 mM has been described (Wang & Liu, 1993; Gorton et al., 1991). It is a typical Michaelis- transformation 1/i = f(1/c) proved suitable for the linearization. The transformed calibration curves for surface layer-modified sensors based on CM and bulk-modified sensors based on CM, HXNE, EINE and BRNE are shown in Fig. 4. The correlation coefficients of all transformed curves were never below 0-9990. The calculated repeatibilities of six successive measurements for electrodes based on various SBMs corresponded to relative standard deviations in the range from 0-9 to 3.2%. It can be seen from Figs. 3,4 that the molecular structure of SBM affected the sensitivity of sensors. The sensitivity decreased with a decreased working potential 300 mV versus SCE. was used as the mediator. Conditions: 0.2 M phosphate buffer pH 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002299_027836402761393487-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002299_027836402761393487-Figure11-1.png",
        "caption": "Fig. 11. Graphics of ADAMS during the simulation.",
        "texts": [
            " Figure 10(b) shows the result where the plate is moved in 360 sec. Since we assumed the quasi-static motion to obtain eq. (19) and since we did not use the direct feedback of contact coordinates, oscillation is caused in the motion of the object when the manipulator moves fast (Figure 10(a)). On the other hand, the object tracks the desired trajectory well when the manipulator moves slowly. In the simulation results shown in Figure 10(b), uCA and \u03d5C finally converge to uCA = [10.0602 5.1181]T and \u03d5C = \u22120.5303 rad, respectively. Figure 11 shows an overview of the graphics of ADAMS during the simulation. For manipulating an object, we used a manipulator having two direct drive motors enabling 2 DoF motion, as shown in Figure 12. The objects are two hemispheres having radii of 22.0 mm and 23.5 mm, respectively. The balls and the plate are made of rubber and plastic covered by soft paper, respectively, which prevents slipping at the contact point. We first performed an experiment by drawing one triangle on the object surface as a locus of the contact point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002001_1.1649662-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002001_1.1649662-Figure10-1.png",
        "caption": "FIGURE 10. Rig Developed for Testing Bucket Wheel Excavator.",
        "texts": [
            " This final excavator design has been built in order to test its soil excavation capabilities (Figure 9). An entire vehicle was developed, with some deletions. Not all of the wheels are currently motorized. The chassis\u2019 interior has remained largely vacant. A simplified control system was built, but not installed, and no onboard power supply was produced. Because of these deficits, it was not possible to test an intact excavator. In order to obtain test data for the soil excavation model, a special apparatus was built on which the excavator boom and bucket wheel were mounted (Figure 10). A moveable sandbox was constructed that could be pushed into the bucket wheel to simulate the forward movement of the excavator. Using two sets of liner guides, the motion of the subframe was confined to the two principal directions of the excavation forces. The guides are used to resist lateral forces (Fz), and any moments (Mx and My) that might be applied to the frame during testing. Horizontal and vertical links between the subframe and hood were used to take up any applied forces and moments in the remaining directions (Fx, Fy, and Mz)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003365_j.electacta.2005.01.017-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003365_j.electacta.2005.01.017-Figure3-1.png",
        "caption": "Fig. 3. The influence of soaking time in CHCl3 on the reduction current of the enzymatically generated o-quinone at the PPO\u2013poly1-modified glassy carbon electrode: (a) 0 min; (b) 15 min; (c) 30 min; (d) 60 min; (e) after 15 min contact with a 0.1 M phosphate buffer solution (pH 6.5). Experimental conditions: starting potential, 0 V vs. Ag/AgCl; first vertex potential, \u22120.5 V vs. Ag/AgCl; second vertex potential, +0.15 V vs. Ag/AgCl, potential scan rate, 10 mV/s, supporting electrolyte, 0.1 M TBAP in CHCl3; substrate, 0.1 mM catechol; poly1 film composition, 150 nmol 1 + 0.40 mg PPO.",
        "texts": [
            " This phenomenon, observed for three different biosensors, suggests that their electroanalytical parameters depend strongly on hydration and permeability of the biomatrix. Nevertheless, it should be noted that this optimized biosensor sensitivity (15.6 mA M\u22121 cm\u22122) remains lower than those previously reported for PPO electrodes based on sol\u2013gel or organohydrogel composites (27.5 to 785 mA M\u22121 cm\u22122) that also exhibited broader linearity ranges [10,14,17]. In order to obtain more information, the electrochemical b b c c c f t b p s p ehavior of the PPO\u2013poly1 bioelectrode was studied y cyclic voltammetry as a function of soaking time in hloroform (Fig. 3). After addition of catechol in the hloroform solution, the first cycle shows no cathodic peak orresponding to the electroreduction of the enzymatically ormed o-quinone (Fig. 3, curve a). After 15 min of soaking ime, an intense reduction peak was observed (Fig. 3, curve ). Nevertheless, the intensity of the o-quinone reduction eak decreases monotonously with further increasing of oaking time (Fig. 3, curves c and d). When the reduction eak is no more observed (Fig. 3, curve d), the electrode was the saturation of chloroform with water does not improve the biosensors sensitivity. Consequently, the strong decrease of the biosensor sensitivity observed in chloroform may be due to the decrease of poly1 matrix permeability but also to the modification of the enzyme microenvironment within the cross-linked polymer. In order to optimize the biosensor construction, the effect of the composition of the PPO-monomer 1 coatings on the biosensor sensitivity was investigated",
            " The optimum composition of the monomer 1\u2013PPO coating was chosen as 150 nmol of monomer 1 and 0.50 mg PPO. In order to examine the reproducibility of the biosensor construction, four electrodes were prepared using the same mixture of enzyme and monomer. A relative standard deviation (RSD) of 7.6% was recorded for the biosensor response to catechol (5 M), this substrate concentration corresponding to the linear part of the calibration curve. This transferred into the aqueous solution of phosphate buffer for 15 min. This regeneration process allows recovering the initial peak intensity (Fig. 3, curve e). This process can be performed at least two times without any loss of the peak intensity. The interval of time elapsed between the successive recordings of curves (a) and (b) was required by the attenuation of the biomembrane hindrance for catechol diffusion to reach the active site of PPO (phenomenon previously illustrated in Fig. 2D). The further decrease of the o-quinone reduction peak could be assigned to the alteration of the hydration microenvironment of the entrapped enzyme as a function of the soaking time in the chloroform solution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002725_cdc.2003.1272782-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002725_cdc.2003.1272782-Figure1-1.png",
        "caption": "Fig. 1. Body fixed and eanh fixed reference frames",
        "texts": [
            " PROBLEM FORMULATlON It is convenient to define the underwater vehicle state vectors according to the Society of Naval Architects and Marine Engineers (SNAMEj notation [l]. Two common vectors that being used in defining the undenvater vehicle state vector are q and U . The vector q is defined as: q = [qy $ I T , where q1 = [x y is the vehicle position vector in the earth fixed frame and q 2 = [4 6' $ I T is the vehicle Euler angle in the earth fixed frame. And the vector U is defined as: U = [UT vFlT, where q = [U U wIT is the body fixed linear velocity vector and 212 = [p q vIT is the body fixed angular velocity vector. In Fig. 1, the defined coordinate frames are illustrated. Beside the Euler angle representation, Euler parameters or unit quaternions [l], [17] can also be used. The vehicle's motion path relative to the earth fixed frame coordinate system is given by the kinematics equation [ I ] as follow: where,J(q) is a 6 x 6 kinematics transformation matrix or Jacobian matrix. The dynamics behavior of an underwater vehicle is described through Newton's laws of linear and angular momentum. The equations of motion of underwater vehicles are highly nonlinear and coupled due to hydrodynamic added mass, lift and drag forces, which are acting on the vehicle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003634_j.matdes.2006.10.008-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003634_j.matdes.2006.10.008-Figure2-1.png",
        "caption": "Fig. 2. The model of three-dimensional temperature field.",
        "texts": [
            " Taking the results obtained from the investigation for thermodynamics and dynamics of cladding gradient bioceramic coating by the wide-band laser as a guide, the technical parameters for wide-band laser cladding optimized through the orthogonal test are: output power P = 2.5 kW, scanning velocity V = 150 mm/min, facula is rectangular, size D = 16 mm \u00b7 2 mm. (Analysis about the results will be published in another paper). The schematic diagram for the experiment process is shown in Fig. 1. A commercial finite element analysis software was used to establish a mathematical model for 3-D temperature fields on a titanium alloy substrate, as shown in Fig. 2. On the basis of the symmetry, only one half of it is used for analysis here. It is hypothesized that the laser energy is partially absorbed by the powder while the main part of the laser energy transfers to the substrate. The substrate\u2019s absorbing coefficient for the laser energy is a constant. The constant obtained by analysis and calculation should be in the range from 0.2 to 0.3 [3]. For the model in the experiment, it is calculated as 0.25. Because laser cladding is a thermal current output mode for small areas with high-speed heating and uneven distribution, the preset coating powder is heat-conducted as a porous and unsubstantial material",
            " The laser beam\u2019s continuous scanning is described through a user subprogram, which makes the thermal load of the laser as a form of thermal current density exerted to the appropriate unit. With an even rectangular laser beam bombing facula distribution, its energy density distribution is [4]: I \u00bc a p=A; where a is the coefficient for the material to absorb the laser; P is output power of the laser and A is the facula area. (b) Boundary condition The bottom surface (jzj = 5.5) of a sample (as shown in Fig. 2) is taken as a mandatory condition: T \u00f0x; y; 5:5; t\u00de \u00bc 298 K; \u00f01\u00de where T(x, y, 5.5, t) means that the temperature of the model bottom surface is 298 K at any time, that is 25 C. For other surfaces, the boundary condition is k\u00f0T \u00de dT dn \u00bc h\u00f0T T 0\u00de; \u00f02\u00de where h is the coefficient of convective heat exchange on the surface, which is generally taken to be in the range of 10\u2013100 W/m2 C. On the surface making contact with the air this model, h = 30 W/m2 C. (c) Initial condition When the laser beam comes into contact with the coating surface, the temperature across the whole coating is a constant (25 C), that is Table Therm Param Therm Therm Densit U\u00f0x; y; z; 0\u00de \u00bc 298 K \u00f03\u00de (d) Master formula According to the thoughts [5] of the weighted remainder of finite element and Galerkin\u2019s method, on the basis of general formula of temperature field, a mathematical model for the 3-D temperature fields is advanced in this paper: / \u00bc P C t \u00fe 298 e K C\u00f0 \u00det ; \u00f04\u00de where K is the thermal conductance matrix and it relates to the thermally conductive properties of the coating material and the heat transfer conditions; P 1 odynamic data at various temperatures of Ti6Al4V eters of thermal properties Temperature ( C) Known 20 100 200 300 al capacity C (J/kg C) 611 624 653 674 al conductivity k (W/m C) 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003446_1.2735339-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003446_1.2735339-Figure9-1.png",
        "caption": "Fig. 9 Relative curvature between conjugate surfaces as parameterized using cylindroidal coordinates",
        "texts": [
            " An nvariant measure for the speed Vp of the pitch point p on the itch surfaces for generalized gear pairs with constant instantaeous gear ratio g is Vpf = fRf A1 Vpm = mRm A2 he two velocity components Vpf and Vpm are perpendicular to the ommon generator $p and tangent to the two hyperboloidal pitch urfaces. The speed V p of the pitch point p projected onto the lane perpendicular to the contact normal $l gives V f = fRf sin nf A3 V m = mRm sin nm A4 here n is the normal pressure angle. The speed V p of the pitch oint p in a direction parallel to the tooth spiral gives V f = fRf 1 tan pf A5 V m = mRm 1 tan pm A6 he resultant velocity Vtot defined by the two components V p nd V p determines the direction of the path of contact between he two gear surfaces in mesh. Figure 9 shows the inclination ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ash angle of the contact line relative to the pitch surface. This velocity depends on the instantaneous axial and polar displacements. The inclination angle between the resultant velocity Vtot and the tooth spiral tangency the intersection between the tooth surface and the reference pitch surface can be expressed tan = V f V f = V m V m A7 and hence tan = tan p sin n A8 A lot of attention has been directed to the relative curvature between two surfaces in direct contact outside the context of gearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000507_027836499501400207-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000507_027836499501400207-Figure9-1.png",
        "caption": "Fig. 9. Slip with infinite friction for l = 5.",
        "texts": [
            " The second condition ensures that the slider velocity vs is not equal to the pusher velocity vp: the contact is slipping. For sticking contact to occur the fence would have to apply a force f away from the slider, which is impossible without adhesion. at The University of Iowa Libraries on June 8, 2015ijr.sagepub.comDownloaded from 178 Figure 8 shows the velocity cones for infinite It and different rod lengths 1. The pusher-slider contact will slip for pushing angles just less than 180 degrees. Figure 9 demonstrates slipping contact for l = 5. The rod endpoint velocity Vg cannot equal the pusher velocity v~, because v~, lies to the left of the velocity cone. Therefore, the contact is slipping to the right and the applied force f lies on the left edge of the friction cone. This gives rise to a rod endpoint velocity v~ on the left edge of the velocity cone. The pusher, slider, and slipping velocities are illustrated in Figure 9. Note that the normal force at the pushing contact is zero, allowing the tangential frictional force to be finite during slipping. Sticking contact will always occur for infinite p, regardless of the slider\u2019s support distribution, if the pusher moves exactly in the direction of the contact normal. The velocity cone must lie within 90 degrees of the friction cone, and therefore the infinite friction velocity cone must always include the contact normal. Slip is impossible for a normal push with infinite ti, because it implies that the pusher performs negative work, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001463_robot.1990.126233-Figure3.8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001463_robot.1990.126233-Figure3.8-1.png",
        "caption": "Figure 3.8 Grasp on three vertices for case 1 and case 2",
        "texts": [
            "5 to find a force direction at each vertex. When the intersection of vertex feasible regions is not a single convex region, it is divided into several convex regions. Also if it is not bounded, the points located at large distance from the origh are assumed to make it a bounded convex polygon. To select a force focus point, the center of each bounded convex polygon is computed first. Then using each center as a force focus point, a grasp is constructed. The grasp which has the best heuristic value is selected as the final grasp. Figure 3.8 (a) shows the grasp on three vertices when three vertex ranges have normal circle as Figure 3.7 (a). 3. 4. 5. Algorithm 39 Grasp on Three Vertices : Case 2. One pair has counter overlap in normal circle as Figure 3.7 (b) where CO1 and CO2 have counter-overlap. 1. 2. 3. Same with step 1 of algorithm 3.8. Same with step 2 of algorithm 3.7. Divide normal circle into two sectors by the line which coincides with ul. Divide vertex range if it is located in more than one sector of divided normal circle",
            " If subranges CI and Cz have counter-overlap, define direction of base vector as a vector passing through the middle of CO3. Apply algorithm 3.6 to find usable region CFU of CF1. If empty, stop. Find intersection of third vertex feasible region and CFU, CF2 = CFU n CF(C3). If empty, stop. Find force focus point from CF2 and grasp points with force directions by step 4 and 5 of algorithm 3.8. When three vertex ranges have a normal circle configuration as in figure 3.7 (b). three different grasps, (Cl2 , CzJ, (CII, CZI) and (Clz, C& pair with CO,, need to be evaluated. Figure 3.8 (b) shows the grasp on three. vertices where normal circle is given in Figure 3.7 @). When two pairs have counter-overlap in normal circle as shown Figure 3.7 (c), construction of grasp can be done by following similar procedure with algorithm 3.9. For this case, normal circle is divided into four sectors. Then, for each feasible combination of subranges, a gmsp is constructed. The maximum number of feasible subranges pairs will be nine. Also, when all three cones have counter-overlap. the normal circle is divided into six sectors and the maximum number of feasible subrange pairs will be thirty six"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001409_311-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001409_311-Figure1-1.png",
        "caption": "Figure 1. Vertical bimorph actuator.",
        "texts": [
            "hermal microactuators based on the bimorph effect [1] have been used for different applications, such as fluid deflection [2], microrelays [3] and micromirrors [4, 5]. All the above actuators employ planar bimorphs for movement normal to the wafer plane. We have introduced vertical bimorph actuators that allow movement in the wafer plane [6] as shown in figure 1. They consist of silicon beams side-coated with aluminium, which bend upon heating due to the difference in the thermal expansion coefficients of aluminium and silicon. To heat the bimorphs, a driving voltage is applied between the two contact pads, which are in electrical contact with the silicon underneath. This causes an electrical current through the silicon beam dissipating power in the bimorph. In [6] we have reported on static displacement measurements. In this paper we investigate the time constant of the system when a power pulse is applied"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000981_rnc.4590030203-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000981_rnc.4590030203-Figure1-1.png",
        "caption": "Figure 1. The qualitative expected behaviour of the solution to objective (a)",
        "texts": [
            " At the same time the variable E changes sign but satisfies, however, the conditions 1 El < e and sign[E(ro)] = -sign[E(tr)]. Starting from t = tl the behaviour of trajectories of system (14) in the plane (5, E) is similar; 9 starting from zero becomes less negative than - pe/ (c, + p) and then it becomes zero again at t = t 2 . In the meantime E changes sign (sign [E(tl)] = - sign [E(t2)]) and still remains, in absolute value, less then e. This repetitive behaviour persists for the following time intervals ( t 2 , t 3 ] , ( t 3 , t 4 1 , ..., ( f k , t k + l ] , ... (see Figure 1). The time evolution of d and E will be based on the piecewise continuous virtual control input ,u obtained by the piecewise continuous signal li and therefore with continuous control u. Objective (b) In the first step starting with S(0) = 0 and E(0) unknown, but with known sign (we suppose, for simplicity E(0) > 0) we reach, at the instant t = to, with s\u0302 Q 0, the configuration $(to) = 0 and E(t0): E(to)E(O) < 0, I E(t0) I c E where e is suitably related to A. In the remaining time (to, + 00) both the variables 3 and E oscillate, from positive to negative values and vice versa, as for objective (a), but with an amplitude becoming increasingly smaller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000907_s0956-5663(01)00205-6-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000907_s0956-5663(01)00205-6-Figure1-1.png",
        "caption": "Fig. 1. (a) Schematical representation of the set-up that allows positioning of a SAM-modified Au-surface in front of the nozzle of the micro-dispenser. (b) Top view of the set-up for surface structuring by means of a micro-dispenser. The gold plate (see white arrow) is attached via double-faced adhesive tape to the positioning table of the micro-manipulator that can be moved by three micrometer screws in each direction. For fine height adjustment, an additional piezo element is integrated in the set-up. The micro-dispenser is positioned at a close distance to the gold plate allowing precise targeting onto the gold surface without disturbance by air movement.",
        "texts": [
            " The silicon plate with the SAM-modified Au-surface is mounted using doublefaced adhesive tape to the micro-manipulator stage, which allows its fine positioning in all directions. After filling the micro-dispenser with enzyme solution, droplets are dispensed by application of rectangular potential pulses to the piezo actor. The target point (which should be outside the Au-surface) can be evaluated after shooting some droplets, and hence, an x, y, z-displacement can be calculated to move the SAMmodified Au-surface with its starting point at the expected dispensing spot. A schematical representation and a photograph of this set-up are shown in Fig. 1. A single droplet of enzyme solution having a volume of 100 pl is released from the orifice of the micro-dispenser and shot onto the functionalised Au-surface. After that, the Au-plate is moved a pre-defined distance in a lateral direction, and another droplet is shot onto the surface. If the distance is large enough, patterns of single spots having a diameter of about 100 m can be obtained (not shown). If the distance moved between each dispensing cycle is smaller than 100 m, the two neighbouring points overlap"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002794_05698198708981732-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002794_05698198708981732-Figure1-1.png",
        "caption": "Fig. 1-Squeeze film damper geometry and coordinate systems for smallamplitude off-centered motions.",
        "texts": [
            " T h e approximate force coefficients a r e of extreme simplicity and of excellent accuracy when compared to a numerical solution to the problem. Force Coefficients for Open-Ended Squeeze-Film Dampers 7 1 GOVERNING EQUATIONS order of magnitude tests, convective inertia terms a re all Consider the laminar flow of an isoviscous incompressible f l~~ic l in the narrow annular region between two nonrotating cylinclers of length L and radii R and R + c , respectively. -The geometry of the system is shown in Fig. 1 . l 'he inner cylinder o r journal performs small oscillations with characteristic frequency o and maximum an~pl i tude u about the mean \"equilibrium\" o r static eccentricity e,(*u). I n lubrication applications, the thickness h of the fluid film is very sniall compared to its axial length or to its radius of curvature. Hence, the variation of (.he pressure across the film and the effects of the curvature of the film are negligible. A cartesian coordinate system {x,y,z} is prescribed in the plane of the lubricant film. As shown in Fig. 1, the fixed x axis is perpendicular to the line joining the static centers of the cylinders (along the film), and they axis is in the direction of the minimum film direction. T h e fluid-film thickness, h, is described by the relation: 11 = c + x,(t) cos 0' + yj(t) sin 0' [ I ] where x,(t),y,(t) a r e the instantaneous coordinates of the journal center in the inertial coordinate system ( X , Y ) with its origin fixed in the geometric center of the damper, and the angle 0' is nieasured from the -X axis in the direction of the whirl motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002314_1.1814390-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002314_1.1814390-Figure5-1.png",
        "caption": "Fig. 5 Rotation singularities: geometric condition \u201eb\u2026",
        "texts": [
            " When this geometric condition occurs, the platform can perform an infinitesimal rotation around an axis perpendicular to the plane, the vectors ni , i51, 2, 3, are parallel to, even if the revolute pairs adjacent to the base are locked. This result agrees with the fact that the three legs prevent the platform from rotating around axes parallel to the three vectors ni , i51, 2, 3. Unit vector ni is perpendicular to the plane, s i , located by the revolute pair axes of the ith leg\u2019s universal joint. Therefore, condition ~22! is matched when either ~a! at least two out of the three planes, s i , i51, 2, 3, are parallel or ~b! the three planes, s i , i 51, 2, 3, intersect one another in parallel lines. Figure 5 shows the geometric condition ~b!. The analytic condition that identifies the translation singularities is obtained by equating to zero the explicit expression of the determinant of the matrix that collects the coefficients of the components of P\u0307 in system ~18b!. Such a matrix coincides with the M matrix defined by expression ~13!. Thus, condition ~15! is also the singularity condition that allows all the translation singularities to Transactions of the ASME 17 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F be found and these singularities always make a finite translation of the platfom possible even if the actuated joint are locked"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000507_027836499501400207-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000507_027836499501400207-Figure12-1.png",
        "caption": "Fig. 12. A pulling example including support friction and inertial forces for I = 5.",
        "texts": [
            "comDownloaded from 180 velocity cone nor the acceleration cone is directly applicable, but it is still easy to construct examples where the initial motion involves pulling or slip with infinite friction. Again we consider the initial motion of an object starting from rest. The initial acceleration is represented by an acceleration center. This acceleration center is also the impending velocity center, from which we can derive the support frictional force. The resultant of the inertial force and the support frictional force resisting the motion must balance the applied pushing force f. Figure 12 shows a possible pulling solution for l = 5. For this acceleration center on the ring, both the inertial force and the support frictional force act along a line through the contact point and tangent to the opposite side of the ring. Whatever their relative magnitudes, the resultant must act along the same line. A dynamic balance results from an applied force f acting along the same line in the opposite direction, as shown. Notice that this acceleration center gives an initial rod endpoint acceleration away from the slider: pulling"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003606_detc2005-85337-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003606_detc2005-85337-Figure10-1.png",
        "caption": "Fig. 10 Mobility analysis of 2-R\u030cR\u030cR\u030cR\u0302R\u0302-2-RARARAR\u0308R\u0308 PKC: (a) The original kinematic chain and (b) The kinematic chain composed of two equivalent serial kinematic chains.",
        "texts": [
            " Step 3 It can be found that the PKC has a full-cycle equivalent serial kinematic chain. The full-cycle equivalent serial kinematic chain is a PPR serial kinematic chain [Fig. 9(b)]in which the axis of the R joint is coaxial with the axes of the Ra joints located on the moving platform and the directions of the P joints 8 nloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/07/2016 T are all perpendicular to the axes of the RA joints. Thus, the PKC has full-cycle mobility. Example 5 Consider the 4-legged 2-R\u030cR\u030cR\u030cR\u0302R\u0302-2RARARAR\u0308R\u0308 PKC shown in Fig. 10(a). In this PKC, the axes of all the R\u030c joints pass though a common point, the axes of all the R\u0302 joints pass though a second common point, the axes of all the R\u0308 pass through a third common point, the axes of all the RA joints are parallel. The mobility analysis of this PKC can be performed as follows. Instantaneous mobility analysis The wrench system of each R\u030cR\u030cR\u030cR\u0302R\u0302 leg is a 1-\u03b60-system in which the base wrench can be a \u03b60 whose axis passes through the common point of the axes of all the R\u030c joints and the common point of the axes of all the R\u0302 joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001965_amc.1996.509374-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001965_amc.1996.509374-Figure9-1.png",
        "caption": "Fig. 9: Rotor which has magnetization in direction of pole",
        "texts": [
            " To use the waveform for the rotor position estimation, it is desirable that the waveform is a non-distorted sinusoidal wave. Therefore, to modify the waveform, the position where the non-magnetic materials are pasted is adjusted as in the next section. 3 Position where Non-magnetic material In the preceding section, we assume that a permeance of a permanent magnet is equal to one of air. However, in some cases of small motors, there is a small difference between permeance p d of a d-axis and Pq of a qaxis, because the rotor is magnetized in the direction as shown in fig.9. Therefore, when non-magnetic materials is pasted are not pasted, an inductance of a coil changes slightly according to the rotor position. On the assumption of ( p d - p q ) / ( p d + p p ) = -0.1, a change of a reciprocal yuv of the inductance LUV against the rotor position is shown in fig.10. In fig.10, L, is shown as follows, L, = N2(P,i + Pq) /2 , According to the principle of superposition, a waveform of the reciprocal yuv of the inductance Luv is synthesized from the waveform in fig.8 and the one in fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003606_detc2005-85337-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003606_detc2005-85337-Figure11-1.png",
        "caption": "Fig. 11 Mobility analysis of two 6-legged PKCs.",
        "texts": [
            " Step 4 It is found that the PKC composed of legs 1 and 2 has a full-cycle equivalent serial kinematic chain, which can be denoted by leg 1, and that the PKC composed of legs 3 and 4 has a full-cycle equivalent serial kinematic chains, which can be denoted by leg 3. In addition, legs 1 and 3 comprise a nonoverconstrained kinematic chain. Thus, the PKC has full-cycle mobility. Example 6 Consider a 6-legged 6-RRRRR PKC. In this PKC, the axes of all the R joints are parallel to a same plane. The twists of all the R joints within a same leg are linearly independent. The axis of any R joint of one leg is not parallel to the axis of any R joint of the other legs. For clarity, only one leg of this 6-RRRRR PKC is shown in Fig. 11(a). The mobility analysis of this PKC can be performed as follows. Instantaneous mobility analysis The wrench system of each RRRRR leg is a 1-\u03b6\u221e-system in which the base wrench can be a \u03b6\u221e whose axis is perpendicular to the axes of all the R joints. The wrench system of the PKC is also the above 1-\u03b6\u221e-system. We have ci = 1, c = 1, Ri = 0. Using Eqs. (4), (7) and (8), we obtain C = 6\u2212 1 = 5 and F = C + 6\u2211 i=1 Ri = 5. The number of overconstraints of this 6-legged PKC is \u2206 = 6\u2211 i=1 ci \u2212 c = 6\u2212 1 = 5",
            " Step 4 It is found that the PKC cannot be decomposed into j mi-legged PKCs each having a full-cycle equivalent serial kinematic chain. Step 5 According to the result obtained in step 4, the PKC does not have full-cycle mobility. Generally, all the five DOF of the moving platform of this PKC are infinitesimal. Example 7 Consider a 6-legged 6-RRRARARA PKC. In this PKC, the axes of all the R joints are parallel to a same plane. The twists of all the R joints within a same leg are linearly independent. The axes of all the RA joints are parallel. For clarity, only one leg of this 6-RRRARARA PKC is shown in Fig. 11(b). The mobility analysis of this PKC can be performed as follows. Instantaneous mobility analysis The wrench system of each RRRRR leg is a 1-\u03b6\u221e-system in which the base wrench can be a \u03b6\u221e whose axis is perpendicular to the axes of all the R joints. The wrench system of the PKC is also the above 1-\u03b6\u221e-system. We have ci = 1, c = 1, Ri = 0. Using Eqs. (4), (7) and (8), we obtain C = 6\u2212 1 = 5 and F = C + 6\u2211 i=1 Ri = 5. The number of overconstraints of this 6-legged PKC is \u2206 = 6\u2211 i=1 ci \u2212 c = 6\u2212 1 = 5",
            "org/about-asme/terms-of-use The above examples show that the mobility analysis of parallel mechanisms has been well solved using the proposed method. It is noted that the mobility analysis of parallel mechanisms such as the mechanisms in Example 1 can also be dealt with using the approaches proposed in [3\u20139, 20]. However, the mobility analysis of some mechanisms such as the mechanisms in Examples 4 and 5 can not be well solved using the previous approaches at their current state of the art. It is noted that parallel mechanisms with only instantaneous mobility and mixed instantaneous and full-cycle mobility (see Fig. 11 for example) have been rarely dealt with in the literature. This paper has presented a systematic approach to the mobility analysis of parallel mechanisms. Using the proposed approach, the mobility analysis is performed in two steps. The first step is the instantaneous mobility analysis, and the second step is the full-cycle mobility inspection. The first step can be performed based on screw theory. The second step has been well solved with the aid of the concept of the equivalent serial kinematic chain and the types of multi-DOF single-loop overconstrained kinematic chain"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001699_1.1538619-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001699_1.1538619-Figure2-1.png",
        "caption": "Fig. 2 Finite element model for thermal analysis, with loads and boundary conditions \u201enot to scale\u2026",
        "texts": [
            " Also, there is dissipation of heat by convective cooling by the air within the clearance of the journal and the bushing. To represent the periodic heat dissipation in the finite element model, the nodes on the surface of the shaft are coupled. The interface temperature continuity on the surface of the journal and the contact area of the bushing is modeled by coupling the temperatures at the nodes on the interface. The outer surface of the bushing is subject to natural convection. The finite element mesh, thermal boundary conditions and the thermal loads are schematically represented in Fig. 2. For clarity, the operating clearance in Figure 2 is scaled by a factor of approximately 300. 2.2 Nonlinear Transient Elastic Finite Element Model Elastic/Thermoelastic Elements. The transient thermoelastic analysis to find the contact forces uses two types of elements in the Finite Element Program ANSYS 5.7. The solid element PLANE42 is used to model the journal and the bush. This element is a two-dimensional bilinear element with the displacements in the x and y directions as the degrees of freedom. The radial clearance between the journal and the bush is modeled using twonoded contact elements, namely CONTAC52"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000376_ma00126a027-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000376_ma00126a027-Figure1-1.png",
        "caption": "Figure 1. The star-branched pearl-necklace model. This is an \u201cf x N.\u201d star, meaning it has farms (f = 6 here) and N . sites per arm. The total molecular weight N = f x N . + f. Some number NI of sites on each arm are \u201ccore\u201d sites, N I being determined variationally as described in the text. Note the definition of the angle H between the bonds connecting nextnearest-neighbor (n.n.n.) sites.",
        "texts": [
            " In a succeeding papefi4 we will present the calculated intermolecular properties of the model star fluid, including the density-fluctuation correlation functions that are measured by labeled light and neutron scattering experiments. 11. Model Star Polymer Fluid We define a basic model of a star molecule that is a generalization of the \u201cpearl-necklace\u201d model of linear polymers studied earlier?? Attached to a branch point are f linear \u201cpearl-necklace\u201d chains ofN, backbone sites Macromolecules, Vol. 28, No. 22, 1995 each (see Figure 1). We refer to this as an \u201cf x N,\u201d star. The spherical sites have diameter u and are joined by rigid bonds of length b. The branch point consists of a rigid central structure built o f f sites located at the vertices of a regular polyhedron of edge length b. Thus for the values f = 4, 6, 8, and 12 studied in section IV the central structure consists of sites at the vertices of a regular tetrahedron, octahedron, cube, and dodecahedron, respectively. The central structure for f= 6 is shown in Figure 1. The use of the f-vertex polyhedron as a central structure instead of the more common single site has no particular significance, but js made just for computational convenience. Note that the total number of sites N on the star is The freedom of the molecule to bend and twist a t each site may be restricted locally by a bending or torsional potential. For example, we can impose this simple local bending potential, + f and not fn,. where 0 is the angle formed by neighboring bonds (see Figure l), and co is a parameter controlling the strength and general effect of the potential"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003346_j.jsg.2004.07.005-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003346_j.jsg.2004.07.005-Figure7-1.png",
        "caption": "Fig. 7. Geometrical and kinematic evolution of a curvilinear fault-bend anticline developing above a thrust whose lower and upper ramps are parallel to layering (simple step model). See text for details.",
        "texts": [
            " The circular hinge sector BP 00 is pinned at the central footwall ramp upper inflection point and is active, while the circular hinge sector FP 00 is fixed and is passively transported along the upper footwall ramp. During Step II, FP 00, FP and FL are passively transported along the upper footwall ramp and their shape and size remain unchanged, while panel CP 0 widens. The ramp geometry of the hanging wall rocks causes the continuous thickness increase in panels CP 0, BP 00 and BP (Fig. 3d). When the lower and upper ramps are parallel to layering (simple step; Suppe, 1983), such thickness increase does not occur and only CP 0 widens (Fig. 7). Adoption of circular hinge sectors in curvilinear faultbend folding imposes a transient geometric configuration in the anticlinal crest, forelimb, and foreland panels. During this transient stage, which is dictated by line-length preservation in the early stages of deformation, the stratigraphical elevation of point C2 is lower than Sc3 (Fig. 8a). The hinterlandward side of the crestal panel is characterised by a constant cutoff angle b2. The forelandward side has a variable cutoff angle, b* 2 , initially equalling a2 and then progressively lowering, to eventually equal b2",
            " (43). The geometric construction of the step II configuration starts from a3, which is obtained by linking the curvature centres of the two circular hinge sectors (Fig. 4b). Entering a3, hf and h0 c into Eqs. (42) and (43) provides b0 1 and b3, respectively. Entering b0 1, h 0 c and hb in graph (a) provides b1. Once b1 and hb are known, the solution for a2 is given by Eq. (2); a2 and b1 can be entered in graph (b) to obtain a1 and b2. The geometrical construction of the simple step construction (Fig. 7) requires one to know either the backlimb or forelimb dip, which are univocally related (Fig. 12). For small amounts of displacement, (i.e. when g7 and g8 axial surfaces still occur), the dip of the ramp (corresponding to hb) can be obtained by linking the curvature centre of the two circular hinge sectors. The mathematical description of the internal architecture in curvilinear fault-bend anticlines can be simplified without significantly altering the overall balancing of the structures, by imposing a horizontal orientation to both the CP and FL panels",
            " Development of curvilinear fault-bend anticlines above staircase thrust trajectories produces deformation panels associated with both kink-style and circular hinges (Fig. 18c). In particular, material migration about the lower ramp inflection point causes homogeneous deformation in rock folded by the straight hinge segment g1, whereas rocks rolling about the parabolic hinge g7 undergo a nonhomogeneous deformation, roughly proportional to layer dip. This implies that the backlimb of the fault-bend anticline during step I (Fig. 7) is expected to consist of a non-homogeneously deformed rock panel (BP 0) ahead of a homogeneously deformed one (BP). The completion of the structure during step II eventually results in a deformation pattern consisting of four deformation panels (Fig. 18c). The innermost one, in the backlimb, is predicted to be homogeneously deformed, analogous to the kink-style structure. Deformation in the other three panels is nonuniformly distributed and its intensity generally decreases upward and laterally"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001256_3.10686-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001256_3.10686-Figure5-1.png",
        "caption": "Fig. 5 Crane of example problem.",
        "texts": [
            " Not only is the computational cost higher if the finite element method is used, but also the accuracy of the control deteriorates due to round-off error. This is because Eq. (47) involves more calculations (and hence it is more prone to round-off) and also the condition of the equation can be deteriorated by a bad stiffness distribution. For determinate structures, stiffness information is not needed in computing the slow motion control under rigid assumptions, and hence it is more appropriate to use Eq. (6) in computing the control. As an example problem to illustrate the control algorithm, consider the crane shown in Fig. 5. It is assumed that node 7 has the end-effector attached to it and bars 2 and 7 are length-adjustable. An optimal (straight-line) trajectory of length 1.0/77 beginning at point A and ending at A ' is shown in Fig. 5. The trajectory is chosen so that point A ' is beyond the reach of the crane, i.e., lies outside the workspace of the crane. The unknown control elongations in bars 2 and 7 are to be determined so that node 7 moves along the prescribed trajectory. ... . The incremental controls are computed as in Eq. (41) where only the rigid contribution is considered and the contributions due to elasticity and support movement are, ignored for convenience. The increments are accumulated to compute the cumulative control at any instant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001413_an9911600453-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001413_an9911600453-Figure4-1.png",
        "caption": "Fig. 4 Influence of the value of the Michaelis-Menten constant, K,, on the response of the pH-bas_ed urea sensor. Phosphate buffer, pH 7.0, 0.01 moldm-3. Where kv = 0.01; 1 and l\u2019, K , = O.OOO1 mol dm-3; 2 and 2\u2019, K , = 0.001 mol dm-3; and 3 and 3\u2019, K , = 0.01 mol dm-3. Lines l\u2019 , 2\u2018 and 3\u2018, the influence of pH on enzyme kinetics was taken into account",
        "texts": [],
        "surrounding_texts": [
            "The model presented in this work for the response of the pH-based potentiometric enzymic sensors assumes that the enzymic layer is separate from the bulk solution. All of the components of the solution and the enzyme layer, except for the enzyme molecules are able to diffuse through the membrane in both directions. Realistic examples which can be described by the proposed model are enzymic sensors with pseudo-immobilized enzymes connected to the surface of the pH sensor by means of a dialysis membrane. However, the application of the model is not limited to this instance only. In several situations (including that for the hydrogen ion because of the enzymic reaction), such a membrane does not exist at all, and there is only a hypothetical border between the bulk solution and the zone where the local concentration changes, which alter the analytical signal, occur. The thickness of the enzymic layer is not defined in the proposed model. Contrary to the previously described diffusion modeIs,l2-15 this means that this model is not applicable for use in describing the concentration profiles inside the sensing layer. On the other hand, the geometry of the sensing layer does not have to be known, and this is a major advantage of the proposed model. Diffusion models cannot be used for describing the response of enzymic sensors with a monomolecular sensing layer of enzyme. Because the geometry of the enzymic layer is not Pu bl is he d on 0 1 Ja nu ar y 19 91 . D ow nl oa de d by U ni ve rs ity o f Pi tts bu rg h on 3 1/ 10 /2 01 4 15 :1 9: 36 . View Article Online 456 ANALYST, MAY 1991, VOL. 116 known it is not important to know the exact concentration of the enzyme in this layer. The enzyme concentration in the sensing layer, however, is required for a diffusion model. This becomes impossible when the enzyme is covalently bound to the surface of the sensor. Therefore, electrodes with thin enzymic layers can also be described by the proposed model. Diffusion models adequately describe the pH response of sensors with thick enzymic layers, whereas for electrodes with thin sensing layers the use of the model proposed by Morf is more plausible ,*8 after the appropriate modification for pH-based sensors. This is confirmed by the observation that the response of thin-layer sensors depends on the stirring rate, whereas with thick enzyme film electrodes this effect is not seen. The proposed model takes the stirring effect into account, as stirring modifies the respective transport rate constants. Apart from the fundamental differences in the treatment of the transport phenomena, the diffusion and kinetic models lead to the same conclusions. However, the model proposed in this paper appears to be more practicable because of the mathematical simplicity. The general equation [eqn. ( l l ) ] can be modified without increasing the mathematical complexity. This model can also be used when a polyprotic acid is used as a component of the buffer system and/or polyprotic products are formed in the enzymic reaction. This requires only small changes in eqns. (3a)-(3c), (4a)-(4c) and (5b)-(5c). The proposed model also allows for differences between the transport rate constants, which depends both on the type of substance and the type of protolytic form [eqn. (7)]. Similarly an assumption that the transport rates both to and from the sensing layer are different does not exclude the use of the equation. In this instance, only the distribution coefficients will quantitatively describe the process of species concentration. These modifications complicate the general equation [eqn. ( l l ) ] but do not cause difficulties in its use. The same modifications, when introduced to the diffusion model, markedly increase the mathematical complexity. On the other hand, some simplifications of the general equation [eqn. ( l l ) ] are possible when proper approximations [eqns. (12a)-(12c)] are accepted. If the concentration of the substrate in the sensing layer is assumed to be much smaller than that in the bulk solution, i.e., [S] << [SIB, hence, only the transport phenomena govern the response, then an equation [eqn. (12a)l is obtained, which is an explicit algebraic function [SIB = f[H]. This relationship is linear versus the transport parameters and the buffer concentration, but owing to the assumption that the substrate is totally transformed into products in the enzymic reaction, the kinetic parameter does not appear in this equation. This equation is identical with one of the equations for the diffusion model, derived with the same assumptions10211 when the kinetic parameters, kH and kw, are replaced by the partition coefficients (defined as the concentration ratio of the species at the sensing layer and in the bulk solution). An additional assumption that th_e transport rate constants for all species are the same (kH = kw = 1) leads to the transformation af eqn. (12a) into the classicial equation describing the pH value of a mixture of acids and bases. 17 Equation (12a) can be used for describing the response of pH-based sensors when the concentration of the substrate, [SIB, is low. The response calculated by using the equation agrees with the experimental response10311 for urea21 and penicillin14 sensors at low concentrations of substrate. The differences at higher concentrations of the substrate (the lack of the upper limit of determination) appear because the kinetic parameters of the enzymic reaction are not taken into account. The proposed model allows the pH at the upper determination limit to be calculated, on the basis of eqn. (12b), which was obtained with the assumption that the kinetics of the enzymic reaction are of zero order. For zero order kinetics ([S] >> Km), eqn. (12b) is obviously independent of the substrate concentration and describes only the maximum value of the analytical signal, i .e., the pH which corresponds to the concentration at the upper limit of determination. The derivation of eqn. (12c) is based on the approximation of the Michaelis-Menten non-linear equation by a kinetic equation, for the first-order reaction, ([S] << K,) . It should be noted that for large values of kv, i.e. , for a high level of enzyme activity, the simplified equation [eqn. (12c)l approaches that for the diffusion model, where [S] << [SIB. In all the instances mentioned, as for the general equation, the bisection method can be applied. The equations are linear versus the various parameters, which makes the use of linear algebra possible, and in consequence? simple numerical optimization and fitting procedures. The calibration graphs calculated for any given experimental conditions, approximate the general equation relationships in particular regions (Fig. 3). As mentioned earlier it is not difficult to take into account the influence of inhibitors on the kinetics parameter [eqns. ( l l ) , (12b), (12c) and (13a)l. Because inhibitors are neither consumed nor formed it can be assumed that their concentrations in the bulk solution are equal to that in the enzyme layer. When the solutions to be analysed contain inhibitors at equal concentrations, the use of eqn. (2) without modification except for the apparent kinetic parameters K , and V,,, ( i .e . , Pu bl is he d on 0 1 Ja nu ar y 19 91 . D ow nl oa de d by U ni ve rs ity o f Pi tts bu rg h on 3 1/ 10 /2 01 4 15 :1 9: 36 ANALYST, MAY 1991, VOL. 116 457 9.50 I 9.50 1 7.00 5.0 4.0 3.0 2.0 1 .o 0 -Log[SIB Fig. 5 Influence of normalized rate constant of enzymic reaction, k, , on the response of the pH-based sensor (urea sensor). Phosphate buffer, pH 7.0,O.Ol rnol dm-3; K , = 0.001 rnol dm-3. 1 and l ' , kv = 0.1; 2 and 2', kv = 0.01; and 3 and 3 ' , isv = 0.001. l ', 2' and 3 ' , the influence of pH o n enzyme kinetics was taken into account zv), is possible. The response of the pH-based potentiometric enzymic sensor is affected by local changes of pH within the sensing layer, because of the change of enzymic reaction kinetics. This is taken into account in eqns. (14a) and (14b) (Fig. 3). The introduction of all of the modifications discussed above causes an increase in the complexity of the final relationships, but as previously stated there are simple algebraic equations in either non-explicit [eqn. ( l l ) ] or explicit [eqns. (12a)-(12c)] forms. The introduction of these modifications to the equations describing the diffusion models requires the use of complicated numerical methods which can give only approximate solutions. By using eqns. ( l l ) , (12b) and (12c) it is possible to anticipate the influence of kinetic parameters on the shape of the calibration graphs. The value of the Michaelis-Menten constant affects mainly the upper limit of determination and only slightly changes the analytical signal. The larger the value of K,, the further the upper limit of determination is extended, but the sensitivity decreases (Figs. 4 and 5 ) . The parameter kv indicates the influence of the enzyme activity on the calibration graph (Fig. 5 ) because it has the same function 5s the 'loading factor' in the diffusion models. An increase of kv causes an increase in the sensitivity of the sensor over a range of concentrations. For all of the substances, the transport rate constants [eqns. (lOa)-(lOc)] depend on the stirring rate to the same extent, therefore, only kv takes into account the effect of stirrkg. An increase in the stirring rate decreases the value of kv and consequently, also the sensitivity of the detector (Fig. 5 ) . The proposed model allows a prediction to be made regarding the influence of the concentration and pH of the buffer used, on the shape of the calibration graph for the pH-based potentiometric enzymic sensor (Figs. 6 and 7). An increase in the concentration of the buffer, &, shifts the calibration graph towards the higher concentration range and decreases the sensitivity (Fig. 6). The sensitivity of the sensor is mainly dependent on the pH in the bulk solution, pHB. When, owing to the enzymic reaction, the pH increases, a decrease in the sensitivity of the sensor is observed for a pH-based potentiometric enzymic electrode for urea (Fig. 7). A small influence on the detection limit is primarily connected with the changes in buffering capacity. Therefore, at a pH close to the pK, of the buffer (i.e., for maximum buffering capacity) the sensor shows the worst detection limit. All of the effects mentioned above were experimentally investigated in detail and will be submitted for publication at a later date. The considerations presented in this paper refer to the steady state. When a non-steady state is considered the 5.0 4.0 3.0 2.0 1 .o 0 Fig. 6 Influence of buffer concentration, & on the response of the pH-based urea sensor. Phosphate buffer, pH 7.0; K,, 0.001 rnol dm-3; and Ev, 0.01. 1 and l', c% = 1 x 10-4 rnol dm-3; 2 and 2', cyv = 1 X rnol dm-3; and 3 and 3 ' , c\"w = 1 x 10-2 rnol dm-3. l ' , 2' and 3' . the influence of pH on enzyme kinetics was taken into account -Log[S]B 1 1' 9.00 1 3 0-- 2' r 7.50 a 6.00 5.0 4.0 3.0 2.0 1 .o 0 -Log[S]B Fig. 7 Influence of pH of the analysed solution, pHB, on the response of the pH-based urea seasor. Phosphate buffer, 0.01 rnol dm-3; K , = 0.001 rnol dm-3; and kv = 0.01.1 and l ' , pH = 8.0; 2 and 2', pH = 7.0; and 3 and 3', pH = 6.0. l ' , 2' and 3 ' , the influence of pH on enzyme kinetics was taken into account differential equations [eqns. (5a)-(5e)] have to be solved. Because the magnitude of the transport rates, for all of the substances, and the rate of the enzymic reaction are of the same order, and because the rates of protolytic reactions are much higher,l6 the consideration may be limited to a discussion of eqn. (5a) as carried out by Morf.18 Conclusion The proposed kinetic model for the response of the pH-based potentiometric enzymic sensor has the following advantages in comparison to earlier published models. (i) The model is mathematically simple, and in order to describe it only algebraic equations are required. (ii) The geometry of the enzymic sensing layer need not be defined. (iii) Stirring effects are taken into account. ( iv) Modifications of the model are possible, without further complications, and which take into account: the differences in the transport rates of the respective species; the process of concentrating the species in the enzymic layer; the decrease in enzyme activity caused by local changes in pH or by the presence of inhibitors; and all protolytic equilibria. The proposed model also leads to conclusions similar to those of the previously described diffusion models. This model can be applied not only to potentiometric sensors but generally to systems where hydrogen ions are monitored such as ISFETs (ion selective field effect transistor) and optodes. Pu bl is he d on 0 1 Ja nu ar y 19 91 . D ow nl oa de d by U ni ve rs ity o f Pi tts bu rg h on 3 1/ 10 /2 01 4 15 :1 9: 36 458 ANALYST, MAY 1991, VOL. 116"
        ]
    },
    {
        "image_filename": "designv11_11_0001888_s0142-727x(02)00176-5-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001888_s0142-727x(02)00176-5-Figure5-1.png",
        "caption": "Fig. 5. Computed temperature and velocity fields for Pr \u00bc 0:1, Hm \u00bc 0:5 and different P eclet numbers: Pe \u00bc 1:0 (a,c) and Pe \u00bc 4:0 (b,d).",
        "texts": [
            " In fact, the Prandtl number as ratio of kinematic viscosity m0 and thermal diffusivity a0 is a material property too, but the knowledge of these properties is insufficient for liquid metals, and in this context, the Prandtl number is used as model parameter. In order to enable a separate investigation of the different melt pool effects, it is useful to vary only one parameter whereas the other dimensionless groups are assumed to be constant. As a first approach, the influence of surface tension gradients, buoyancy and friction forces were neglected. This leads to Ma \u00bc Gr \u00bc Wkey \u00bc 0. The dimensionless temperature distribution is two-dimensional in this case and depends mainly on the P eclet number (Mahrle and Schmidt, 1998a,b). Fig. 5 shows calculated temperature and velocity fields for Pe \u00bc 1 and Pe \u00bc 4. The assumed values of the melting point temperature Hm \u00bc 0:5 and the Prandtl number Pr \u00bc 0:1 are approximately valid for iron and steels, respectively. For Pe \u00bc 1, the influence of the melt pool flow on the local temperature distribution and the resultant weld pool dimensions is negligible. However, as the P eclet number increases, two eddies are formed for Pe \u00bc 4. In contrast to the flow around a circular cylinder where the eddies are located behind the cylinder, the flow conditions in the fusion zone lead to the formation of eddies at the weld pool boundary"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002639_s0263574700003611-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002639_s0263574700003611-Figure5-1.png",
        "caption": "Fig. 5. Transmission in joint 1.",
        "texts": [
            " Feedback is then introduced for the deviations of joint variables from their prescribed values: Aq = q ~ qno Aq = q - qnom Au=AAq BAq + C \\Aqdt (34) Finally, a mixed approach can be used. Our intention is to consider which of these two options is more convenient from the standpoint of vibrations due to deformations in transmissions. We shall discuss eigenvalues and simulation results. A concrete numerical example is given. 5. DISCUSSION OF PRACTICAL RESULTS We consider the six DOF manipulation robot UMS-7 (Figure 4). For the numerical examination the test motion shown in Figure 5, is used. The robot has to rotate around the vertical axis in joint 1, for the angle 6 = ulA. The rotation has to be performed for T = ls with the trapezoid velocity profile having the acceleration time ta and the deceleration time td : ta = td = 0.33 s. At the end of this motion the robot has to keep the position reached. The scheme of transmission in the rotational joint 1 is shown in Figure 5. It is assumed that the deformation is concentrated in the HD reducer. The simulations are performed for the rigid reducer and for the elastic reducer having the torsion constant K* = 0.113880 x 106 Nm/rad, and the ratio N = 80. This torsion constant does not correspond to any concrete reducer but it is ten times smaller than the constant of the harmonic drive type HDUC-80 (N = 80). This constant is adopted in order to obtain a better insight into elastic oscillations. After this examination the simulation is performed for the true catalogue constant K = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000765_s0043-1648(02)00108-4-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000765_s0043-1648(02)00108-4-Figure7-1.png",
        "caption": "Fig. 7. (a) Conditions of restrain and load of wheelset and (b) finite element mesh of half wheelset.",
        "texts": [
            " Loads are applied to the tread of the wheelset in the circumferential direction, on different rolling circles of the wheel. The positions of loading are, respectively, 31.6, 40.8 and 60.0 mm, measured from the inner side of the wheel. Fig. 6 indicates the torsional deformations versus loads in the longitudinal direction. They are all linear with loads, and very close for the different points of loading. The effect of the loads on the deformation of direction of y-axis, shown in Fig. 5a, is neglected. Fig. 7 is used to determine the oblique deformation of the wheelset. The oblique deformation is unsymmetrical about the center of wheelset, so it is necessary that discretization of the whole wheelset is made. According to the situation of the loads and deformations of a wheelset moving on track, the restrain and load conditions of it are selected as shown in Fig. 7a. The center of the left nominal rolling circle of the wheelset is fixed in the directions of x-, y- and z-axis, respectively, and that of the right is fixed in the directions of x- and z-axis, respectively. The element nodes of loading should be fixed in x direction to avoid singularity of the global stiffness matrix of the wheelset. In order to find the effect of the restrain conditions above on the oblique deformation loads are applied in y direction and the opposite direction of y-axis, respectively. Fig. 7b is the finite element mesh of the whole wheelset. Fig. 8 is the oblique deformations of the left and right side wheels against lateral loads in y direction (the lines with triangle signs) and the opposite direction of it (the lines with circle and square signs), respectively. When the loads on the left and right side wheels are to be equal, or less than 45 kN, there is not much difference between the deformations of the left and right side wheels at the points of load. After 45 kN, if the load on the left side wheel is not increased and that on the right is still increased, it is found that the deformation of the left side wheel drops and that of the right keeps increasing with about the same as the previous slop"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003509_cca.2005.1507162-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003509_cca.2005.1507162-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of the servovalve-cylinder configuration (without the load mounting)",
        "texts": [
            " Thus, as starting point for derivation of the proposed controller, the considered hydraulic system is at first transformed into a suitable canonical form using differential geometric methods [13]. The effectiveness relating to the robustness against considerable parametric uncertainties and to the tracking performance of the presented nonlinear control approach is demonstrated both by simulations and experiments. H 0-7803-9354-6/05/$20.00 \u00a92005 IEEE 422 The hydraulic actuation system under consideration is available as an experimental setup at our Institute Laboratory and depicted in Fig. 1, where the valve\u2013cylinder configuration is extra shown schematically in Fig. 2. Therewith, the considered plant consists mostly of an asymmetric single-rod cylinder (also termed differential cylinder) and a servovalve. For the derivation of the mathematical model of this hydraulic system, some (simplifying) assumptions are made; among other effects of leakage flows and valve hysteresis are negligible. The piston motion equations can be written as: RBBAApg fpApAxm (1) where BAflpg VVmm is the total mass, px the piston position, iA the piston surface area in the chamber i and ip the pressure in the chamber i (with BAi , ), Rf the friction forces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001756_jsvi.2001.4016-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001756_jsvi.2001.4016-Figure2-1.png",
        "caption": "Figure 2. Virtual cylindrical gears.",
        "texts": [
            " Namely, the axial, lateral and torsional vibrations of the system may couple with each other. The present paper, therefore, is mainly concerned with the coupling among the axial, torsional and lateral vibrations due to the bevel gear transmission. 2. KINETIC CONSTRAINT FOR A PAIR OF SPUR BEVEL GEARS The tooth surface of a pair of spur bevel gears is the envelope of a family of spherical involute curves. Figure 1 shows a pair of bevel gears, whose transmission can be simpli\"ed as a pair of virtual cylindrical gears shown in Figure 2. In this study, the following assumptions upon the system of concern will be used hereinafter: and the torsional angles and can be simpli\"ed to x sin #y cos #r \"x sin #y cos #r , (1) where is the pressure angle of gear, r and r are the radii of base circles of the two virtual cylindrical gears. As shown in Figure 3, the motion described in the co-ordinate frame ox y z can be determined from x y z \" cos 0 sin 0 1 0 !sin 0 cos x y z , (2) where \" ,! , i\"1, 2 are the pitch cone angles. For the virtual cylindrical gears and the bevel gears, the following kinetic relation holds true: r \"r , (3) where r , i\"1, 2 are the radii of base circles of bevel gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003895_978-3-540-74764-2_46-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003895_978-3-540-74764-2_46-Figure1-1.png",
        "caption": "Fig. 1. The spring-mass model for running with two swing-leg control strategies: leg rotation (left) and stiffness adaptation of the leg spring (right).",
        "texts": [
            " In the present study we propose a linear stiffness change of the leg during swing phase in addition to swing-leg retraction. For periodic running (satisfying constant apex heights of two subsequent flight phases) we consider combinations of constant leg stiffness and leg angle rates that guarantee stable locomotion over a large range of speeds. The identified combintions of both swing-leg control strategies can be used in legged robots based on compliant leg behavior. Model: The planar spring-mass model is characterized by alternating flight and stance phases (Fig. 1). The body is represented as a point mass which is, during stance, influenced by gravity g and a force exerted by the leg spring (stiffness kTD , rest length l0) attached. The equation of motion is mr\u0308 = kTD ( l0 |r| \u2212 1 ) r \u2212 mg, (1) where r = (x, y) is the position of the center of mass. If the length of the massless spring reaches its rest length, the system changes into flight phase and describes a ballistic curve. Touch-down occurs if the landing condition y \u2264 l0 sin(\u03b1TD) is satisfied. Since the system is conservative and the ground is even the systems state during flight can be fully described by the horizontal velocity vX and the apex height yA , which is the upper point where the vertical velocity vY equals zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002529_j.ijsolstr.2005.03.061-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002529_j.ijsolstr.2005.03.061-Figure7-1.png",
        "caption": "Fig. 7. A SFSF rectangular plate carrying four identical 3-dof spring\u2013mass systems with their locations and physical properties shown in Table 6.",
        "texts": [
            " 4) and in such a situation, the rotational axes of the lumped mass (cf. Fig. 3) are parallel to the last node lines. Therefore, the mass moments of inertia, J \u00f01\u00de x and J \u00f01\u00de y , of the spring\u2013mass system are also the important parameters affecting the vibration characteristics of an attachment-mounted plate. To show the availability of the presented technique, the first six natural frequencies of a SFSF plate carrying four identical 3-dof spring\u2013mass systems, SM1, SM2, SM3 and SM4, as shown in Fig. 7, are investigated here. The physical properties of the four 3-dof spring\u2013mass systems are shown in Table 6 and the first six natural frequencies, xj (j = 1 to 6), of the attachment-mounted plate are shown in Table 7. From Tables 5 and 7, one finds that the influence of the four identical spring\u2013mass systems on the first six natural frequencies of the SFSF plate is little. In general, the influence of a concentrated load on the dynamic characteristics of a plate is more than that of a distributed load if the magnitude of the concentrated load is equal to that of the distributed load"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001256_3.10686-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001256_3.10686-Figure4-1.png",
        "caption": "Fig. 4 Relationship between position vector r(t) and r(0).",
        "texts": [
            " Let the q -tuple v\"\"(0 list the length changes in the q bars at time / (superscript r for rigid). The components of v'r(0 are the values of the controls at time / .Le t r denote the position vector of the attachment point (relative to an inertially fixed point 0) of the crane with the payload. The motion of the attachment point is a function of the controls, i.e., r==r[v\"XO] (11) Defining rA = r[v'r(0)] and rA> = r[v'r(T)] as position vectors of the terminal points of the trajectory AA ', and using the optimal trajectory s(t)i studied in the previous section, from Fig. 4, we may write r[v'r(0] = r[v'r(0)] + 5(0/5 0 < t < T (12) In this highly nonlinear (with respect to the unknowns listed in [v\"~(OD vectorial equation, the right-hand side is known at all times, and we are expected to solve for the controls [v/r(OJ. We will show that we can fulfill this expectation without even generating the explicit expressions for the components of the nonlinear vector equation. Let At denote a small time increment and define t' \u2014t \u2014 At. Let r and i denote the descriptions of r and i, respectively, in the inertially fixed reference frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001147_s0924-4247(00)00355-1-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001147_s0924-4247(00)00355-1-Figure6-1.png",
        "caption": "Fig. 6. The apparatus to measure the strength of adhesion in the flocculation medium.",
        "texts": [
            "2 2 3 Five hundred cube units were stirred in the solution of the flocculant with the apparatus shown in Fig. 5. The ratio of the bonded units was obtained at various pH and concentrations of the flocculant after stirring at 150 rpm for 5 min as shown in Table 1. It is shown that the units are not bonded only when both surfaces of the units are SiO at a pH of 10.5.2 The adhesion between the units and an Si wafer was measured from the force which detaches the units from the wafer by centrifugal force and the fluid flow, as shown in w xFig. 6. Smith and Kitchener 8 evaluated the strength of adhesion of particles. When the wafer was placed on the bottom of the vessel, the units adhered to the wafer with PAAM. The vessel was closed under water to eliminate air bubbles. The number of units adhering to the area from 10 to 15 mm in radius was counted while increasing the rotational speed. Fig. 7 shows the result using the surfaces Al O \u2013SiO and Al O \u2013Al O at a pH of 10.5.2 3 2 2 3 2 3 Supposing that the velocity of the fluid flow is proportional to the distance from the center of the rotation, and \u017d "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002122_s0921-5093(01)01722-1-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002122_s0921-5093(01)01722-1-Figure7-1.png",
        "caption": "Fig. 7. Numerical simulation of the experimental benchmark using the program Maxwell2D. Flux lines configuration for H=5000 A m\u22121 and interfaces between yokes and sample (a) (L, effective length of the sample; Ls, real length of the sample; Li, internal length of the yoke); existence of leakage of flux for H=10 700 A m\u22121 (b).",
        "texts": [
            " By(t)= S Sy B(t) (9) Hy(t)= S 0 rySy B(t) (10) B(t) always being smaller than 2.2 T, the maximum values of By and Hy are, respectively, 0.05 T and 13 A m\u22121. From relations (Eqs. (4)\u2013 (8)) the magnetic field strength inside the sample can be obtained. H(t)= Ni(t) L \u2212 (t) 0L Ly rySy + La Sa (11) A numerical simulation was carried out using the program Maxwell 2D\u00a9 in order to validate the hypothesis of flux conservation. A non-linear simulation under magnetostatic conditions was performed, using the standard magnetic characteristics of the alloys. For H=5000 A m\u22121 (Fig. 7a) the flux lines are homogeneous and no leakage of flux is witnessed. Fig. 7a also shows a zoom of the contact zone between the sample and the yokes. Magnetic flux enters the sample in the same way, whatever the amplitude of the magnetic field strength. This allows us to compute the effective length the conservation of the flux is no longer valid. The limitation of the experimental device is then H 9000 A m\u22121, when the leakage of flux occurs. Energy losses per unity of mass and per cycle were computed using the following relationship. W= 1 T 0 H(t) dB(t) dt dt= 1 nS T 0 H(t)+e(t)dt (12) with the density of the material in kg m\u22123",
            "25 mm) but is weaker than the total length Ls of the sample. IEC normalisation [7] and literature concerning SST devices recommend, nevertheless, the use of the internal length of the yokes [28,29]. The main difference is in the smaller dimensions of our device compared with SST (i.e. small Li/La ratio). The use of the computed value L instead of the internal length is necessary to avoid a substantial error in the calculation of the magnetic field strength. For H 9000 A m\u22121 a leakage of flux can be observed (Fig. 7b) and the hypothesis of that the degradation of the crossed behaviour (Hb ) is less pronounced than the degradation in the collinear direction (Hb // ) with = n the stress vector and n the tensile direction lying in the sheet plane (Fig. 9a and b). For (Fe,Co)\u20132wt.% V plastically strained along the rolling direction (RD) at p=1.46%, the magnetisation along the transverse direction (TD) is also less degraded than along RD (Fig. 9c). The difference between crossed and collinear behaviours decreases with increasing magnetic field strength whatever the plastic strain level"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001635_s0377-0257(00)00144-0-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001635_s0377-0257(00)00144-0-Figure3-1.png",
        "caption": "Fig. 3. (a) Definition of rectilinear simple shear flow. The discotic mesophase sample is placed between two infinitely long plates. The lower plate (y = 0) is stationary and the top plate (y = H) moves in the +x-direction with a known constant velocity V. The velocity gradient \u2207v is along the y-axis; (b) Definition of orientation angle \u03b8 that the primary eigenvector (uniaxial director) n of tensor order parameter Q makes with the x-axis.",
        "texts": [
            " (6) The dimensionless form of the above equation is obtained by scaling as follows: Er dQ dt\u2217 = Er [ W \u2217 \u00b7 Q \u2212 Q \u00b7 W \u2217 + 2 3 \u03b2A\u2217 + \u03b2 [ A\u2217 \u00b7 Q + Q \u00b7 A\u2217 \u2212 2 3 (A\u2217 : Q)I ] \u22121 2 \u03b2[(A\u2217 : Q)Q + A\u2217 \u00b7 Q \u00b7 Q + Q \u00b7 A\u2217 \u00b7 Q + Q \u00b7 Q \u00b7 A\u2217 \u2212 {(Q \u00b7 Q) : A\u2217}I ] ] \u2212R 6 (1 \u2212 (3/2)Q : Q)2 [( 1 \u2212 1 3 U ) Q \u2212 UQ \u00b7 Q + U { (Q : Q)Q + 1 3 (Q : Q)I }] + 1 (1 \u2212 (3/2)Q : Q)2 [ \u2207\u22172Q + 1 2 L\u2217 2 \u00d7 [ \u2207\u2217(\u2207\u2217 \u00b7 Q) + {\u2207\u2217(\u2207\u2217 \u00b7 Q)}T \u2212 2 3 tr{\u2207\u2217(\u2207\u2217 \u00b7 Q)}I ]] , (7) t\u2217 = \u03b3\u0307 t, A\u2217 = A \u03b3\u0307 , W \u2217 = W \u03b3\u0307 , \u2207\u2217 = H\u2207, L\u2217 2 = L2 L1 . The dimensionless quantities are represented by a superscript (\u2217) in Eq. (7), and H is the characteristic distance between the two plates (see Fig. 3). As there are three competing contributions controlling the microstructural response of discotic nematics, therefore, we have two dimensionless numbers or scaling parameters: Er = \u03b3\u0307 H 2c\u03baT L16Dr = VHc\u03baT L16Dr = VH\u00b5e L1 , (8a) \u00b5e = c\u03baT 6Dr , (8b) R = DrH 2\u00b5e L1 = H 2 6 c\u03baT L1 . (9) The Ericksen number Er is the ratio of the viscous flow effects to long-range order elasticity, whereas ratio R, introduced previously by Tsuji and Rey [16\u201318], is the ratio of the short-range order elasticity to long-range order elasticity",
            " It is noted that the L\u2013E theory has no restriction on the values of elastic constants, however, as mentioned above the present theory is restricted to K11 = K33. In the present analysis, as a first step and due to the computational complexities, known flow kinematics are assumed, therefore linear and angular momentum balance equations are not solved along with the microstructure governing equation (Eq. (3)). The complete form of the stress balance equation along with the shear properties of discotics will be presented in the following studies. The model discotic mesophases are subjected to the rectilinear simple shear flow, shown in Fig. 3a. The lower plate (at y = 0) is stationary and the top plate (y = H), at distance H from the bottom plate, moves in the +x-direction with a known constant velocity V. The velocity gradient is along the y-axis, and vorticity along the z-axis. In this study we restrict our analysis to planar orientation such that two of the three eigenvectors of Q lie in the shear plane, and as a consequence the only non-zero components of tensor order parameter are Qxx , Qxy , Qyy , Qzz. The components along the vorticity direction, Qzx and Qzy , are set to zero",
            " Expressing the components in terms of eigenvectors and eigenvalues, it is found that Qzx = \u03bbnnznx + \u03bbmmzmx + \u03bbl lzlx, (10) Qzy = \u03bbnnzny + \u03bbmmzmy + \u03bbl lzly, (11) and, it follows that the sufficient condition for both components Qzx and Qzy to be equal to zero is a = (0, 0, 1), where a =n, m, l . In this work we have never observed a director escape from the shear plane. The planar director dynamics are given in terms of one azimuthal angle \u03b8 , measured in degrees, which n makes with the x-axis as shown in Fig. 3b. One of the objectives of this paper is to analyze the distinct microstructure features of sheared discotics pertaining to different boundary constraints. Two fixed anchoring modes are possible under the planar molecular orientation assumption: BCVG: the director n is fixed along the velocity gradient direction (y-axis), such that nS,BCVG = (nx, ny, nz) = (0, 1, 0). (12) BCF: the principal eigenvector n is fixed along the flow direction (x-axis), such that nS,BCF = (nx, ny, nz) = (1, 0, 0). (13) Furthermore at the surface, it is assumed that the discotics are uniaxial (P = 0) and at equilibrium (S = Seq)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003206_j.mechmachtheory.2003.12.003-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003206_j.mechmachtheory.2003.12.003-Figure12-1.png",
        "caption": "Fig. 12. Identified motion domains of the driving link in Example 5.",
        "texts": [
            " In the case of the other closed curve of the coupler curve, the number of domains of motion is two and numbers of circuits and branches are one and two, respectively. Example 5. We identify the domains of motion of the Stephenson six-link mechanism composed of seven revolute pairs whose kinematic constants are as follows. a0 \u00bc 40; a1 \u00bc 40; a2 \u00bc 30; a3 \u00bc 40; a4 \u00bc 4; a5 \u00bc 3; a6 \u00bc 20; a7 \u00bc 20; a8 \u00bc 20 \u00bdmm a \u00bc 70 \u00bddeg The constituent four-bar linkage is the double lever mechanism and one of two closed curves of the coupler curve is similar to the 8 character as shown in Fig. 12(a). In this case, two limit points and two turning points are obtained respectively as shown in Fig. 12(a). Then, the relationship between angular displacements of the driving link FG and the link BC becomes the curve of oscillating motion with the amplitude of greater than 360 and less than 720 as shown in Fig. 12(b). The mark h in Fig. 12(a) and (c) indicates the extension point. By using the procedure in Section 5.2, two numbers 1 and 2 are assigned to two domains of motion to be mapped on four number lines as shown in Fig. 12(c). Numbers of circuits and branches are one and two, respectively. In the case of the other closed curve of the coupler curve, the number of domains of motion is two and numbers of circuits and branches are one and two, respectively. We investigate the identification of motion domains of the driving link of the Stephenson-3 sixlink mechanism. The conclusion can be drawn as follows. (1) The point on the coupler curve of the non-Grashof-type constituent four-bar linkage may be corresponded to one of the value of the argument of the point on the relationship-curve between angular displacements of two links to be revolute-paired to the stationary link"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002591_0094-114x(85)90040-0-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002591_0094-114x(85)90040-0-Figure9-1.png",
        "caption": "Fig. 9. 18-tooth gear with 20 c pressure angle, cut with a zero tip radius cutter.",
        "texts": [
            " The sum of these two arrays completely defines the profile of a single rack form generated involute tooth. To draw more than one tooth, one can sequentially rotate this array through an angle equal to the circular pitch in radians: = p c / R = 2 r r / N . (28) {X:} = [cosa sinc~ I (23) The top of the involute is at point A, the intersection of the involute with the addendum circle. This point has a pressure angle, d~, found from the gear addendum radius, R~, to be Sufficient duplication of this rotation and drawing procedure then produces a drawing of a full gear. Figure 9 shows one such drawing of a standard 20 \u00b0 pressure angle gear with 18 teeth which has been cut by a rack form with a zero tip radius. Note that this gear is undercut because the addendum on the rack is a full 1.25/Pd since there is no tip radius. cos +, = (R cos d~)/R,,. (24) Using the involute function to determine the central angle between the X.~ axis and a radial line through point A, one has where = inv(+.) - inv(6). inv(+) = t a n 6 - ~. The location of point A can now be written as ro = R~ cos(a - \"y)i3 - R,, sinlc~ - ~')j3",
            " The surface normal to the rack at the cutting point must pass through the fixed mesh pitch point. Equations for the four separate sections of the tooth f o r m - - root, fillet trochoid, involute and top l andmare developed for a family of rack form geometries from this condition. The points of demarcation between these sections are also determined. The effect of tool shift on the tooth shape is also included. The program has the ability to d ra~ individual teeth, as shown in Fig. 11 for an 18-tooth gear with three separate hob tip radii. It can also dra~' an entire gear, as shown in Fig. 9. By positioning the centers d r = 0 . 4 1 7 / P c a + + + Fig. ! 1. Individual teeth for a 20 \u00b0 pressure angle- 18-tooth standard gear. of two gears correctly and establishing the correct relative rotations of the two gears, a pair of gears in mesh can also be drawn, using this subroutine twice, as shown in Fig. 12. This figure shows a 20- tooth pinion in mesh with a 60-tooth gear. These plots should be extremely helpful to the gear design engineer by increasing his visualization of the effects of the rack form parameters on the gear shape and the effects of his chosen gear design parameters on the produced gear before it is manufactured"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001958_2001-01-1060-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001958_2001-01-1060-Figure1-1.png",
        "caption": "Figure 1. The two degrees of freedom vehicle model",
        "texts": [
            " In this section, we introduce a simple and a detailed vehicle model for design of the vehicle stability control system and for evaluation of the proposed controller, respectively. VEHICLE MODELING FOR THE CONTROLLER DESIGN - In order to design a controller, we make use of a two degrees of freedom vehicle model, which is the simplest one to presents the lateral motion of the vehicle. The model considers the lateral and yaw dynamics of the vehicle and the weight transfer of left-right wheels, which is shown in figure 1. The equations of motions are expressed by the SAE coordination standard. In figure 1, the model drawn by the dotted line is called the bicycle model. The equations of motion of the vehicle chassis system consider the plane motion of vehicle. The lateral and longitudinal equations of motion can be expressed as: ( )y x i i M v v r Y+ = \u2211 ( )y x i i M v v r Y+ = \u2211 , (1) ( ) ( ) ( ) ( ) 0.5 0.5z f fl fr r rl rr fl fr rl rr I r t X X t X X a Y Y b Y Y = \u2212 + \u2212 + + \u2212 + , (2) where the subscription expresses the location of wheels(i=fr: front right, fl: front left, rr: rear right, rl: rear left), , , , , , , , ,x y z f rv v r M I t t a b are the longitudinal velocity, the lateral velocity, the yaw velocity, the vehicle mass, the yaw moment of inertia, the front wheel tread, the rear wheel tread , the distance of the front wheel center of C"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000514_1.1286271-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000514_1.1286271-Figure3-1.png",
        "caption": "Fig. 3 Test bearing shell",
        "texts": [
            "asmedigitalcollection.asme.org/pdfaccess.ashx?url= 40\u00b0C, 3.95 cSt at 100\u00b0C and density of 873.5 kg/m3! is used for bearing lubrication. The oil feed pressure is maintained at 206.9 kPa ~30 psi!. The complete rig is supported on a rigid structure mounted on anti-vibration pads Two journal bearings with inner diameter 60 mm ~length 39 mm, diametral clearance 54 mm! and 65 mm ~length 40 mm, diametral clearance 52 mm!, with 97 mm outer diameter are tested. The copper rivets are inserted in the bearing shell ~Fig. 3! flush with the bearing inner surface for realistic temperature measurement of bearing inner wall. An oil hole ~for feeding lubricant in bearing! of 6 mm diameter is provided with its centerline located on the vertical mid plane of the horizontal bearing. Half of the depth of the oil hole is threaded ~9.5 mm, i.e., 3/8 inch! for fixing the feeding nipple. A pressure gauge attached to the filter housing indicates the requirement for filter cleaning, and another pressure gauge is provided in the lubrication circuit near the bearing to measure the feed pressure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000806_s0301-679x(00)00147-x-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000806_s0301-679x(00)00147-x-Figure1-1.png",
        "caption": "Fig. 1. Physical configuration of a finite partial journal bearing.",
        "texts": [
            " The modified Reynolds equation is obtained by using the Stokes equations to account for the influence of couple stresses resulting from the lubricant blended with various additives. The film pressure is numerically solved and applied to derive the nonlinear motion equation of the journal. The dynamic squeeze-film characteristics (such as the velocity of the journal center, the locus of the journal center, and the minimum permissible film clearance) for the bearing lubricated with a couple stress fluid will be compared to the Newtonian-lubricant case. Consider the physical configuration of a pure-squeezing partial journal bearing with length L shown as in Fig. 1. The journal of radius R is approaching the bearing surface with a velocity dh/dt. The lubricant in the system is taken to be an incompressible non-Newtonian couple stress fluid. It is assumed that the body forces and body couples are absent, the fluid film is thin as compared to the radius of journal, and fluid inertia is small as compared to the viscous shear. The velocity components of the lubricant are solved from Eq. (1). Substituting the expressions of velocity components into continuity Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003686_j.ijmachtools.2005.10.017-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003686_j.ijmachtools.2005.10.017-Figure4-1.png",
        "caption": "Fig. 4. Diagram of cross-sectional stress distribution. (a) Bending stress, (b) bending shear stress, (c) stress of press, (b) torsion stress, (e) the max. stress point.",
        "texts": [
            " The bending and shear stresses are obtained by substituting deformation from Eq. (18) into Eq. (19). From data of the axial drilling force and torque measured by Ref. [10], as shown in Fig. 3, variation of the force and torque is small. Therefore, the force and torque are taken as constant to analyze the compression and torsion-shear stresses: sew \u00bc P Ai , tej \u00bc T Ji . \u00f020\u00de The bending stress, shear stress from bending, compression stress, and torsion-shear stress are distributed on a section simultaneously, as shown in Fig. 4(a)\u2013(d). Since value of the bending stress is larger than that of the shear stress caused by the bending, stresses at M point are the largest on micro-drill section, as shown in Fig. 4(e), that is sM \u00bc sq \u00fe sw and tM \u00bc tj. From the third strength theory, the calculated stress at point M is expressed as sca \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2M \u00fe 3t2M q . (21) Dynamic stress on the micro-drill section is calculated and analyzed by substituting Eqs. (19) and (20) into Eq. (21). For the drilling process, the bend deformation and dynamic stress of the drilling system are calculated using Eqs. (18) and (21) under different eccentricities, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003250_j.ijmecsci.2006.09.021-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003250_j.ijmecsci.2006.09.021-Figure2-1.png",
        "caption": "Fig. 2. Geometry of a differential element.",
        "texts": [],
        "surrounding_texts": [
            "The governing equations are derived by considering the following simplifications and assumptions: work rolls are assumed rigid, lateral spread of material is ignored, steady state conditions are considered in the analysis, and material being rolled is assumed a rigid perfectly plastic material. Figs. 1 and 2 schematically show the geometry of the roll gap and a differential element, respectively. As it is seen, the deflection of the ingoing sheet is defined by two independent parameters Z and yi. In fact, the location of the entry section cannot be specified merely by the angle of rotation of the plate at entry as the roll gap extension is changed by the vertical movement of the sheet as well. Angle Z is considered positive if the angular rotation at entry is clockwise, and the angular extension of the roll ARTICLE IN PRESS M. Kadkhodaei et al. / International Journal of Mechanical Sciences 49 (2007) 622\u2013634624 gap, fi, is considered positive if the parameter yi is positive. The stress field applied on the vertical slabs is shown in Fig. 3. These stresses are considered positive if they are in the same directions as shown in this figure. The non-uniformity of the normal stress across the section is considered by assuming a linear distribution on the differential element. The slab selection and the stress field considered in this study are similar to those by Mischke [21]. Mischke stated the equilibrium equations in terms of the horizontal coordinate x, as an independent variable, while in this analysis these equations are derived in terms of the angular coordinate f. This leads to simplicity of applying the boundary conditions at the entry plane as the boundary conditions are all defined in terms of this angle and same values, and the set of the equilibrium equations are solved as an initial value problem. The required geometrical parameters to obtain the angle fi are: aui \u00bc cos 1 \u00f0you yi\u00de cos Z \u00f0hi=2\u00de Ru Z, (1) ali \u00bc cos 1 \u00f0yi yol\u00de cos Z hi 2 Rl \" # \u00fe Z, (2) xui \u00bc Ru sin aui, xli \u00bc Rl sin ali, \u00f03\u00de yui \u00bc you Ru cos aui, yli \u00bc yol \u00fe Rl cos ali. \u00f04\u00de Hence fi \u00bc tan 1 xli xui yui yli . (5) Moreover, au \u00bc sin 1 \u00f0yo you\u00de sin f Ru \u00fe f, (6) al \u00bc sin 1 \u00f0yo yol\u00de sin f Rl f, (7) yu \u00bc you Ru cos au, yl \u00bc yol \u00fe Rl cos al , \u00f08\u00de h \u00bc yu yl cos f . (9) The equilibrium of the horizontal and vertical forces as well as the moment about the mid point on the left hand side of the element give the following relations: su \u00fe sl 2 h sin f t sin f\u00fe su \u00fe sl 2 cos f dh df t\u00fe 1 2 dsu df \u00fe dsl df h cos f h sin f dt df \u00fe Ru pu sin au tu cos au dau df \u00fe Rl pl sin al tl cos al dal df \u00bc 0, \u00f010\u00de ARTICLE IN PRESS M. Kadkhodaei et al. / International Journal of Mechanical Sciences 49 (2007) 622\u2013634 625 su \u00fe sl 2 h cos f\u00fe t cos f su \u00fe sl 2 sin f dh df t\u00fe 1 2 dsu df \u00fe dsl df h sin f\u00fe h cos f dt df Ru pu cos au \u00fe tu sin au dau df \u00fe Rl pl cos al \u00fe tl sin al dal df \u00bc 0, \u00f011\u00de su \u00fe 5sl 12 dh df \u00fe Ru su \u00fe sl 2 sin \u00f0au f\u00de dau df \u00fe h 12 dsu df dsl df \u00fe h 2 t\u00fe Ru cos \u00f0au f\u00det dau df Ru 2 sin \u00f0au f\u00depu dau df \u00fe Rl 2 sin \u00f0al \u00fe f\u00depl dal df \u00fe Ru 2 cos \u00f0au f\u00detu dau df Rl 2 cos \u00f0al \u00fe f\u00detl dal df \u00bc 0. \u00f012\u00de The Von-Mises yield criterion for the top and bottom parts of each element taking the effect of the shear stresses into account gives [see Appendix A]: su \u00bc pu tu sin 2f ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k2 t2u q cos2 f, sl \u00bc pl tl sin 2f ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k2 t2l q cos2 f. \u00f013\u00de The frictional shear stresses are considered to be proportional to the mean yield shear stress, i.e., tu \u00bc muk, tl \u00bc mlk, \u00f014\u00de in which the frictions factors mu and ml are constant parameters. Substitution of the relations (13) and (14) into the equilibrium equations gives three first-order ordinary differential equations containing pu, pl, and t as the main unknown variables. Since the roll gap is divided into three distinct regions, in addition to the boundary conditions, the extent of each region should be evaluated. From the volume constancy of material, the following approximate relationship for the positions of the upper and lower neutral points may be considered [13,20]: V uh\u00f0fnu\u00de cos anu fnu \u00bc V lh\u00f0fnl\u00de cos anl fnl , (15) in which fnu and anu are relevant angles f and a for the upper neutral point, and fnl and anl are the ones for the lower neutral point. According to this equation, fnu and fnl are dependent variables, so if one of them is obtained the other one can be calculated from the above relationship."
        ]
    },
    {
        "image_filename": "designv11_11_0003850_elan.200503471-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003850_elan.200503471-Figure2-1.png",
        "caption": "Fig. 2. Cyclic voltammetric responses at a conventional 3-mm diameter SPE (A) and the d\u00bc 20 mm, l\u00bc 0.18 mm SPUME (B) for 1 mM ferricyanide in pH 2 KCl/HCl solution at a scan rate of 10 mV/s.",
        "texts": [
            ", in the range of 0.18 \u2013 1.35 mm length with a width of 20 mm in this study. Figure 1 shows the optical picture of a SPUME cut at SE \u00bc 3.2 mm. Different layers of the carbon, silver, and silver portions can be clearly seen from the optical microscopic picture. The microband electrodes are sandwiched between insulator layers with three electrodes stayed considerably apart from each other in the SEM morphology. The w value (i.e., electrode width) of the microband carbon electrode was measured as 20 mm. Figure 2 compares the cyclic voltammograms for the redox reaction of 1 mM ferricyanide on a macroscopic SPE strip in three-electrode configuration and the SPUME at a scan rate of 10 mV/s. As expected, a steady-state response similar to that of the reported metallic UME with a sigmoidal-shaped curve for the SPUME was observed. A more dynamic response with diffusion-controlled characteristics was observed for the macroscopic SPE strip. The halfwave reduction potential of E1/2 \u00bc 160 mV observed at the SPUME was found to match with the redox potential of ferricyanide at normal-sized SPE"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001076_1.2803542-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001076_1.2803542-Figure5-1.png",
        "caption": "Fig. 5 Relative bicoherence values for the first pattern (rollers)",
        "texts": [
            " The benefit of this bicoherence based bearing defect detec tion scheme is evaluated with a more challenging set of bearing signatures. Figure 3 shows vibration signals of a roller defected bearing (/\u201e \u00ab 90 Hz) and of the normal bearing, and their spectra are in Fig. 4. It would be very difficult to tell the differ ence between the two even for trained eyes. However, the bico herence values at all four frequency pairs (/\u201e,,fr\u201e), (2fro,fr\u201e), (3fm, fm), and (2 /\u201e , 2fro) give unmistakable indication about the state of the bearings (Fig. 5) . A bearing condition monitoring technique employing bico herence analysis is developed. It has been demonstrated, using experimental data obtained from bearings with (i) outer-race defects, (ii) roller defects, and (iii) no defects, that the bicoher ence values among harmonics of a characteristic defect fre quency are a sensitive indicator of bearing localized defects. In addition, we found that the magnitudes of these bicoherence values are consistent with the severity of defect. This means bicoherence analysis is also a competitive candidate for defect severity assessment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003634_j.matdes.2006.10.008-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003634_j.matdes.2006.10.008-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the wide-band laser scanning process.",
        "texts": [
            " The device used for the laser cladding includes a TJ-HL5000 5KWCO2 laser; a Siemens numerically controlled machine tool with 5-coordinates and 3-axis linkages; and a JKF-6 wide-band scanning rotation mirror. Taking the results obtained from the investigation for thermodynamics and dynamics of cladding gradient bioceramic coating by the wide-band laser as a guide, the technical parameters for wide-band laser cladding optimized through the orthogonal test are: output power P = 2.5 kW, scanning velocity V = 150 mm/min, facula is rectangular, size D = 16 mm \u00b7 2 mm. (Analysis about the results will be published in another paper). The schematic diagram for the experiment process is shown in Fig. 1. A commercial finite element analysis software was used to establish a mathematical model for 3-D temperature fields on a titanium alloy substrate, as shown in Fig. 2. On the basis of the symmetry, only one half of it is used for analysis here. It is hypothesized that the laser energy is partially absorbed by the powder while the main part of the laser energy transfers to the substrate. The substrate\u2019s absorbing coefficient for the laser energy is a constant. The constant obtained by analysis and calculation should be in the range from 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001081_1.1414129-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001081_1.1414129-Figure1-1.png",
        "caption": "Fig. 1 Machine tool setting for pinion teeth generation",
        "texts": [
            " A computer program, based on the theoretical background presented, has been developed for the calculation of load distribution and transmission errors in hypoid gears. By using this program the influence of machine tool setting parameters for pinion DECEMBER 2001, Vol. 123 \u00d5 579 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F manufacture\u2014as are the sliding base setting ~c!, the basic radial ~e!, the basic machine center ~f!, the basic offset setting ~g!, the basic tilt angle ~b!, the swivel angle ~d!, and the machine root angle (g1), ~Fig. 1!\u2014on maximal tooth contact pressure (pmax), load distribution factor (bF), and transmission errors (Df2) was investigated. The investigation was carried out for the hypoid gear pair of the design data given in Table 1. The starting machine tool setting parameters for the generation of the pinion and the gear tooth blanks were calculated by the method used in Gleason Works and by the method presented by Litvin et al. @3,4#, and are given in Tables 2 and 3. The results obtained are presented in Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001325_s0094-114x(02)00118-0-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001325_s0094-114x(02)00118-0-Figure4-1.png",
        "caption": "Fig. 4. Orientation capability map of the dexterous workspace of a manipulator with l1 \u00bc 230 mm, l2 \u00bc 100 mm, l3 \u00bc 60 mm and l4 \u00bc 30 mm.",
        "texts": [
            " The following example demonstrates this set of regions which give the complex angle at the virtual joint. With a manipulator of l1 \u00bc 230 mm, l2 \u00bc 100 mm, l3 \u00bc 60 mm and l4 \u00bc 30 mm in length, the full dexterous workspace given from Eqs. (8) and (9) is f100; 360g, where the virtual ground link lvg varies. Mapping the region of dexterous workspace onto the orientation capability map, a dexterous workspace annulus is produced between loci Dl and Du. From this the orientation boundary circles are obtained as loci A and B. This orientation capability map is shown in Fig. 4. The intersection between the boundary circles and the concentric circles which represent the workspace loci gives the value for the orientation range, i.e., hv ranges. When there is no intersection between the origin-centred concentric circles and the offset boundary circles, the workspace is fully dexterous, this is represented by a region between loci Dl and Du in Fig. 4. Concentric circles which represent the workspace loci between B and Dl, and between Du and A gives the partial dexterous workspace. The orientation ranges in the partial dexterous workspace can be identified through the intersections between the boundary loci A and B and concentric loci which are centred at O. These are given in Table 2. In the table, critical values give the changes from a partial dexterous workspace to a full dexterous workspace. To illustrate the use of the orientation capability map, concentric circles a0, b0, c0 and d 0 adjacent to the critical values are used to identify the orientation ranges. The dexterous workspace is then represented in the range of f100; 360g in Fig. 4. This can also be proved from [7] and further proved by applying the finite twist mapping [5,16] which produces the range as in Fig. 5. In Fig. 5, the outer profile is the reachable workspace while the inner region is the full dexterous workspace. The region with the mesh is partial dexterous workspace. In the above, the orientation capability map has been given by either mapping the graphical representation in Fig. 1 or obtaining the results from the generalised discriminant in (1) and (2). It can be seen from both Figs",
            " 6, the polar equation of the boundary locus can be given as cos h \u00bc 1 r r2ol s0 2s0 r 1 2s0 : \u00f010\u00de Similarly, the upper orientation boundary locus of radius rou can be given as cos h \u00bc 1 r r2ou s0 2s0 r 1 2s0 : \u00f011\u00de From the analysis, the offset value is s0 \u00bc le and the following is given rou \u00bc l1 \u00fe lvc; \u00f012\u00de rol \u00bc jl1 lvcj: \u00f013\u00de The intersection between the workspace loci which is centred at the coordinate origin and the two boundary loci give the orientation capability of a manipulator. When there is no intersection between the workspace loci and the orientation boundary loci, a manipulator has a full orientation and has a region of dexterous workspace as in Fig. 4. Thus a dexterous annulus can be produced in Fig. 7 in which the workspace loci do not intersect the orientation boundary loci. Suppose the radii of the lower and upper boundaries of the dexterous workspace are rdl and rdu, respectively, the relationship between the orientation boundary loci and the dexterous annulus is rdl \u00bc rol \u00fe s0; \u00f014\u00de rdu \u00bc rou s0: \u00f015\u00de To illustrate the use of the orientation capability map, the orientation capability of a five-link manipulator is being investigated. The manipulator has link lengths of l1 \u00bc 330 mm, l2 \u00bc 160 mm, l3 \u00bc 90 mm, l4 \u00bc 70 mm and l5 \u00bc 50 mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002451_0168-1656(90)90027-9-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002451_0168-1656(90)90027-9-Figure2-1.png",
        "caption": "Fig. 2. Configuration of a gas-sensing electrode.",
        "texts": [
            " (c) Liquid ion-exchange membranes electrodes, Ca 2 +, CI-, divalent cations, BF 4 , N O 3 , CIO 4-, K +. (d) Electrodes with coating over membranes of ion-selective electrodes, e.g. CO2, NH 3, H2S, NO 2, SO 2. Like other gas-sensing membrane electrodes for ammonia, hydrogen sulfide, sulfur dioxide and nitrogen dioxide, the carbon dioxide electrode consists of a hydrophobic gas-permeable membrane and a pH electrode separated by a thin layer of internal electrolyte (Orion, a). Its basic configuration is shown in Fig. 2. The differences between the several gas-sensing electrodes are mainly apparent with respect to their internal tilting solutions and their operating pH ranges. The key principles of such gas-sensing membrane electrodes can be exemplified by those of the carbon dioxide electrode. Typically, the gas-sensing electrode and an external reference electrode are immersed in a sample solution. Dissolved carbon dioxide in the sample solution diffuses across the gas-permeable membrane into the internal electrolyte layer until the partial pressures of carbon dioxide on both sides of the hydrophobic membrane are equal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001358_s0094-114x(03)00090-9-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001358_s0094-114x(03)00090-9-Figure11-1.png",
        "caption": "Fig. 11. Assembly modes of the mechanism.",
        "texts": [
            " For each real value of the displacement s, the coordinates of the internal revolute joints B (see Table 3) and E are calculated. Finally, the displacement s1 is determined. The corresponding four assembly modes of the triad with one internal and one external prismatic joint are shown in Fig. 10. Finally, the method presented in Section 5 is used for the position analysis of the one-degree-offreedom planar mechanism with eight links including a triad with three external prismatic joints. The mechanism with decoupled structure (see up part of Fig. 11) consists of the frame 0, the input link 1, an Assur group of class 2 (dyad with links 2 and 3) with three revolute joints (F , G and D) and an Assur group of class 3 (triad with links 4, 5, 6 and 7) with three internal revolute joints and three external prismatic joints. The geometrical data of the mechanism and the position angle h10 of the input link are inserted in the left part of the Table 4. The position analysis of the above-mentioned mechanism consists of the following steps: 1. Determination of the revolute joint F (see Fig. 11) coordinates with respect to the frame coordinates system of the mechanism. 2. Determination of the position angles h20i and h30i (i \u00bc 1, 2) with respect to the x-axis of the dyad links 2 and 3 respectively, using an analytical method. Two real solutions are obtained and in Fig. 11 only one of the assembly modes of dyad is presented. 3. Determination of the triad position using the procedure described in Section 5. The points A, D and F are used as auxiliary points of the triad. For each configuration of the dyad, the polynomial Eq. (61) is solved and eight solutions in the complex domain of the displacement s3 are obtained. For the dyad configuration here considered, Eq. (61) provides four real solutions and four complex solutions for displacement s3 (see Table 4). For each real solutions of the s3, using back substitution, the displacement s1 and s2 are calculated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001699_1.1538619-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001699_1.1538619-Figure1-1.png",
        "caption": "Fig. 1 Schematic of a journal bearing and its support structure",
        "texts": [
            " A transient heat transfer analysis was done to model thermal effects of dry frictional heating on the journal and the bearing. 003 by ASME OCTOBER 2003, Vol. 125 \u00d5 833 s of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F 3. A transient thermoelastic analysis was performed to study the interactions of the journal-bearing pair during bearing start-up. The variation of radial clearance, contact forces and ovalization of the bearing were studied in this analysis. Analysis Model. The model consists of a shaft rubbing on the inner surface of the bushing as shown in Fig. 1. The contact forces result in the generation of frictional heat on the entire surface of the shaft and in the area where it contacts the bushing inner radius. Due to the rise in temperature, the shaft expands and its encroachment to the bushing leads to a loss of clearance. At some point in time, the bearing clearance reduces to a minimum and shaft starts to encroach the bearing. Analyses show that typically during TIS, the following three phenomena occur: ~i! The contact forces increase, increasing the heat generated; ~ii"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001436_j.wear.2003.10.004-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001436_j.wear.2003.10.004-Figure4-1.png",
        "caption": "Fig. 4. Development of sharpness for nominally planar abrasive surfaces.",
        "texts": [
            " Ignoring the effect of truing after production, it is apparent that the surface inherits properties directly attributable to the underlying particles\u2014this relationship has been convincingly demonstrated experimentally, e.g. [7]. However, it is fair to suggest that new factors determine the effectiveness of the abrasive surface, e.g. the density of the asperities on the surface, their height distribution, and also, any bias of particle orientations arising due to shape. These factors complicate the problem of estimating surface sharpness from particle attributes. The concept of sharpness has therefore been extended to include direct analysis of surfaces, as schematically illustrated in Fig. 4. The section plane Ps is finite in this case and possesses a centroid indicated by the origin of the coordinate system o\u2013xyz. The section plane is not constrained parallel to the basal plane and is free to basculate in such a way that, as the penetration level h changes, the centroid of the observable projected penetration areas {\u21261, . . . ,\u2126N} coincides with the centroid of the plane Ps. Each asperity can be projected orthogonally onto its own projection plane Pp. Because the direction of traversal is not specified, the mean-value theorem can be implemented over the domain \u03c8 = [0, \u03c0) to give the total average groove area for the specific value of h",
            " In addition, despite the apparent planarity of the abrasive surface at large length scales, locally the average surface orientation varies with respect to the location and scale of the sampled region. The \u2018floating\u2019 polishing arrangement is a feature of the equipment used, however, it is more effective than a rigidly held specimen because it eliminates problems of alignment, which become increasingly significant with decreasing particle size and distance between successive section planes. According to Fig. 4, the section plane projects onto the basal plane, which represents a sampling window applied to the broader abrasive surface. The angle between Z- and z-axes is assumed small enough for the difference between the area of the section and basal planes to be disregarded. While Fig. 4 does not illustrate the possibility of an asperity lying on the sampling window boundary, such occurrences are either included or excluded from the sample by applying Gundersen\u2019s tiling rule [9], as illustrated in Fig. 5. This rule provides an unbiased estimate of asperity frequency. Any regions that touch the heavy lines are not included in the sample. If the regions are known to be convex then the lines extending ad infinitum are not required. Spatial sampling is further discussed in the experimental part of this paper where it is applied to sections of surfaces composed of SiC particles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003047_iros.2003.1249198-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003047_iros.2003.1249198-Figure4-1.png",
        "caption": "Figure 4: Dual arm system supparted by a vehicle.",
        "texts": [
            " Moreover note that, in order to also avoid any possible interference between ( (now smoothly generated via (28), (23) and i (it also maintained active) we should furtherly shape Z ( p ) , with respect to a(@), in such a way to be certainly unitary within the whole finite support where a ( p ) > 0 (see Fig. 3). As it can be easily realized, with such a choice for i2 and a, signal i always results in a null one, even during the smooth transition phase of 4 (and then (1. The results of the previous section will be now extended to the case of a dual arm, non-holonomic mobile manipulator of the type of Fig. 4, when performing grasping operations. As a matter of fact, a grasping operation to be performed by the overall system simply corresponds to the global task of having the two end-effector frames <el>, < e p asymptotically converging to the goal frames <gl>. <gp, respectively, while obviously maintaining the desired minimum level of manipulability for each arm. By still assuming each arm separately controlled, as done in the previous section, and in order to approach the problem, let's staR again by considering the following (tentative) global Lyapunov function (with an obvious meaning of the introduced terms) 1 v 6 - (eye1 +eTez)c + 2 p = - T "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003399_j.ijmecsci.2005.04.003-Figure15-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003399_j.ijmecsci.2005.04.003-Figure15-1.png",
        "caption": "Fig. 15. Beam and material symmetry axes.",
        "texts": [
            " Having tested the validity of the present model on the free vibration problem, the results of the forced vibration analysis are compared with those of ANSYS in graphical form and a close agreement has been observed. It should be emphasized again that the aim of the present work is to demonstrate the application of an efficient method to the transient analysis of composite cylindrical helical rods rather than reconfirming their expected response. The authors thank C- ukurova University Scientific Research Projects Directorate that supported the present work (FBE2002 D-178). The angle between the fiber direction in a lamina and the beam axis is denoted as y (Fig. 15). Stress\u2013strain and strain\u2013stress relations in 1, 2, 3 coordinates, rotated about 3-axis are written as si \u00bc C0 ij j; i \u00bc S0 ijsj \u00f0i; j \u00bc 1; 2; . . . ; 6\u00de, (A.1) where C0 ij and S0 ij are the transformed stiffness and compliance matrices, respectively, and calculated as [27,28]. \u00bdC0 \u00bc \u00bdT 1\u00bdC \u00bdR \u00bdT \u00bdR 1; \u00bdS0 \u00bc \u00bdR \u00bdT 1\u00bdR 1\u00bdS \u00bdT . (A.2) Transformation matrices T and R are defined as \u00bdT \u00bc m2 n2 0 0 0 2mn n2 m2 0 0 0 2mn 0 0 1 0 0 0 0 0 0 m n 0 0 0 0 n m 0 mn mn 0 0 0 m2 n2 2 666666664 3 777777775 ; \u00bdR \u00bc 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 2 666666664 3 777777775 , (A",
            " The elements different from zero of ~Q 0 ij are ~Q 0 11 \u00bc C0 11 \u00fe \u00f0C0 12S 0 12 \u00fe C0 13S 0 31\u00dea 0 11 \u00fe \u00f0C0 12S 0 26 \u00fe C0 13S 0 36\u00dea 0 61, \u00f0A:6a\u00de ~Q 0 12 \u00bc C0 16 \u00fe \u00f0C0 12S 0 21 \u00fe C0 13S 0 31\u00dea 0 16 \u00fe \u00f0C0 12S 0 26 \u00fe C0 13S 0 36\u00dea 0 66, \u00f0A:6b\u00de ~Q 0 22 \u00bc C0 66 \u00fe \u00f0C0 62S 0 21 \u00fe C0 63S 0 31\u00dea 0 16 \u00fe \u00f0C0 62S 0 26 \u00fe C0 63S 0 36\u00dea 0 66, \u00f0A:6c\u00de ~Q 0 33 \u00bc C0 55, \u00f0A:6d\u00de where a011 \u00bc S0 66 S0 11S 0 66 S02 16 ; a016 \u00bc a061 \u00bc S0 16 S0 11S 0 66 S02 16 ; a066 \u00bc S0 11 S0 11S 0 66 S02 16 . (A.7) For an orthotropic material, the stiffness and compliance matrices are given by Jones [27] \u00bdC \u00bc C11 C12 C13 C22 C23 0 C33 symmetric C44 C55 C66 2 666666666664 3 777777777775 6 6 , \u00f0A:8\u00de \u00bdS \u00bc S11 S12 S13 S22 S23 0 S33 symmetric S44 S55 S66 2 666666666664 3 777777777775 6 6 . \u00f0A:9\u00de After a rotation about the 3-axis (Fig. 15), the transformed stiffness, C0, and compliance matrices, S0, take the following form \u00bdC0 \u00bc C0 11 C0 12 C0 13 0 0 C0 16 C0 12 C0 22 C0 23 0 0 C0 26 C0 13 C0 23 C0 33 0 0 C0 36 0 0 0 C0 44 C0 45 0 0 0 0 C0 45 C0 55 0 C0 16 C0 26 C0 36 0 0 C0 66 2 666666666664 3 777777777775 , \u00f0A:10\u00de \u00bdS0 \u00bc S0 11 S0 12 S0 13 0 0 S0 16 S0 12 S0 22 S0 23 0 0 S0 26 S0 13 S0 23 S0 33 0 0 S0 36 0 0 0 S0 44 S0 45 0 0 0 0 S0 45 S0 55 0 S0 16 S0 26 S0 36 0 0 S0 66 2 666666666664 3 777777777775 , \u00f0A:11\u00de where C0 11 \u00bc m4C11 \u00fe 2n2m2C12 \u00fe n4C22 \u00fe 4n2m2C66, \u00f0A:12a\u00de C0 12 \u00bc n2m2C11 \u00fe \u00f0n4 \u00fe m4\u00deC12 \u00fe n2m2C22 4n2m2C66, \u00f0A:12b\u00de C0 13 \u00bc m2C13 \u00fe n2C23, \u00f0A:12c\u00de C0 16 \u00bc nm3C11 \u00fe nm\u00f0n2 m2\u00deC12 n3mC22 \u00fe 2nm\u00f0n2 m2\u00deC66, \u00f0A:12d\u00de C0 22 \u00bc n4C11 \u00fe 2n2m2C12 \u00fe m4C22 \u00fe 4n2m2C66, \u00f0A:12e\u00de C0 23 \u00bc n2C13 \u00fe m2C23, \u00f0A:12f\u00de C0 26 \u00bc n3mC11 \u00fe nm\u00f0m2 n2\u00deC12 nm3C22 2nm\u00f0m2 n2\u00deC66, \u00f0A:12g\u00de C0 33 \u00bc C33, \u00f0A:12h\u00de C0 36 \u00bc nmC13 nmC23, \u00f0A:12i\u00de C0 44 \u00bc m2C44 \u00fe n2C55, \u00f0A:12j\u00de C0 45 \u00bc nmC44 \u00fe nmC55, \u00f0A:12k\u00de C0 55 \u00bc n2C44 \u00fe m2C55, \u00f0A:12l\u00de C0 66 \u00bc n2m2C11 2n2m2C12 \u00fe n2m2C22 \u00fe \u00f0m2 n2\u00de2C66 \u00f0A:12m\u00de and S0 11 \u00bc m4S11 \u00fe 2n2m2S12 \u00fe n4S22 \u00fe n2m2S66, \u00f0A:13a\u00de S0 12 \u00bc n2m2S11 \u00fe \u00f0n4 \u00fe m4\u00deS12 \u00fe n2m2S22 n2m2S66, \u00f0A:13b\u00de S0 13 \u00bc m2S13 \u00fe n2S23, \u00f0A:13c\u00de S0 16 \u00bc 2nm3S11 \u00fe 2nm\u00f0n2 m2\u00deS12 2n3mS22 \u00fe nm\u00f0n2 m2\u00deS66, \u00f0A:13d\u00de S0 22 \u00bc n4S11 \u00fe 2n2m2S12 \u00fe m4S22 \u00fe n2m2S66, \u00f0A:13e\u00de S0 23 \u00bc n2S13 \u00fe m2S23, \u00f0A:13f\u00de S0 26 \u00bc 2n3mS11 \u00fe 2nm\u00f0m2 n2\u00deS12 2nm3S22 \u00fe nm\u00f0m2 n2\u00deS66, \u00f0A:13g\u00de S0 33 \u00bc S33, \u00f0A:13h\u00de S0 36 \u00bc 2nmS13 2nmS23, \u00f0A:13i\u00de S0 44 \u00bc m2S44 \u00fe n2S55, \u00f0A:13j\u00de S0 45 \u00bc nmS44 \u00fe nmS55, \u00f0A:13k\u00de S0 55 \u00bc n2S44 \u00fe m2S55, \u00f0A:13l\u00de S0 66 \u00bc 4n2m2S11 8n2m2S12 \u00fe 4n2m2S22 \u00fe \u00f0m2 n2\u00de2S66"
        ],
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    },
    {
        "image_filename": "designv11_11_0002506_ac00288a024-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002506_ac00288a024-Figure7-1.png",
        "caption": "Figure 7. Suggested explanation of the typical ammonia-saturation patterns obtained with \u201cflat\u201d electrodes showing three concurrent processes (these three processes overlap, producing typical plots llke those in Figure 4, to which the symbols 1, 2, 3, 4, 5 refer): (a) electrode glass, (b) electrode jacket, (c) gap between the glass and the jacket fllled with filling solution, (d) O-ring, (e) hydrophobic membrane: regions 2-3, saturation of the film of the filling solution; 2-4, saturation of the wedge-shaped part of the filling solution; 2-5, saturation into the depth of the gap between the electrode glass and the jacket, toward the reference junctlon.",
        "texts": [
            " In this way the partition coefficient, changing during the assays, produces a square-shaped curve (Figure 6), equalizing all the assays to almost the saturation level. This makes the unfavorable influence of the fillingsolution volume less significant. Typically saturation curves repeat the same pattern, as shown in Figure 4, curves A and B. The initial increase is linear (section 2-3), followed by a nonlinear increase (3-4), an inclined (almost linear) plateau (4-9, and then a steady plateau (H), Le., full saturation. A possible explanation of such a typical pattern is given in Figure 7. The film of the filling solution is not uniform, neither in its shape nor in access to the diffusing ammonia. There is the thinnest, uniform section of the film near the center of the electrode tip, a wedge-shaped ring around it, and a thinwalled cylinder between the electrode glass and the jacket. Ammonia simultaneously diffuses into all three parts, and saturation is subsequently attained. All three concurrent processes produce a curve, like the A or B curves of Figure 4, and the sections of the curve refer to the parts of the filling solution film (see Figure 7 ) . Experimental data show that the faster the response (due to the thinner film of the solution), the poorer the repeatability, when the jacket or the solution is changed. These differences can be as large as 100%. The most probable explanation is in the tolerance of the mechanical fitting of the electrode and the jacket. Let us consider an example: if the opening in the jacket is 5 mm with a tolerance f 0.5 mm, then the outer diameter of the electrodes can differ from 4.90 to 5.00 mm. Actual electrode jacket sets are machined to exact specifications, with the intention to make the gap as narrow as possible, but, instead, have gaps differing from 0",
            "2 mm), the actual gaps would be 0.1 mm to 0.3 mm larger, but more uniform (differing by a factor of 3, instead of a factor larger than 15). The conclusion is that it is better to design electrode jackets with a looser fit to the electrode glass; since even with the same jacket, it is easier to assemble the electrode in the same way each time. Porous membranes stretch against electrode tips mostly irreversibly, producing irreproducible conditions of diffusion, especially in the wedge-shaped part of the solution (area 2-4 of Figure 7). We suppose that the main source of the delay in the base line recovery in ammonia assays is the cylindrical part of the solution in the inside of the jacket (region 2-5 in Figure 7 ) . Ammonia dissolved there can only very slowly diffuse out, lagging for many minutes, especially in more concentrated samples (Figure 3). Table I and Figure 2 also explain some reasons of the delay. With enzymatic analyses, requiring two membranes with another film of sample solution between the membranes, the delay is especially prolonged. The results of Mascini and Guilbault (7) (comparatively fast base line recovery) were obtained with enzyme immobilized directly on a Teflon membrane without intestine/collagen, and thus without the additional layer of the sample solution between the membranes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002242_s0022-0728(02)01104-x-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002242_s0022-0728(02)01104-x-Figure1-1.png",
        "caption": "Fig. 1. Sketch of the cell system used for FTIR fiber-optic reflectance spectroelectrochemistry.",
        "texts": [
            " Found: C, 57.98; H, 3.30%. FT-IR (n , Nujol, cm 1) 2059, 2042, 2010 (s, n (CO)), 1820 (n (C /C). 1H-NMR (d , CDCl3, 300 MHz): 7.3 /7.6 m (5H, Ph), 5.40 (s, 5H, C5H5), 5.13 (s, 5H, C5H5). 13C-NMR (d , CDCl3, 75 MHz): 88.32 (C5H5), 88.13 (Fe /C5H5). The Remspec fiber-optic system was previously used as a remote-sensing transmission cell for the analysis of the bulk solution in controlled potential electrolysis experiments [13]. By replacing the usual stainless steel mirror with a platinum disk electrode (Fig. 1), the system can be used in reflectance mode to detect the changes which occur due to redox events at or near an electrode surface. While UV /vis fiber-optic reflectance spectroelectrochemical measurements have been performed, no reports of similar systems for IR spectroscopy have appeared. The system is able to detect small changes in absorbance, i.e. 0.02 absorbance units or greater, with a relatively low amount of noise and it yields results which clearly show the consumption of starting material with the concomitant production of new species"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002967_ip-d.1983.0048-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002967_ip-d.1983.0048-Figure1-1.png",
        "caption": "Fig. 1 Sign conventions",
        "texts": [],
        "surrounding_texts": [
            "List of symbols, nomenclature and abbreviations\nL = length of ship (generally between perpendiculars) m = mass of ship N = moment component on body relative to z-axis r = yaw rate S(a>) = wave energy spectral density K, 7; ,T2 ^3 > Ta = gain and time constants of ship equations u = forward velocity in x-axis v = drift velocity along y-axis U = speed of ship X, Y = force components on body relative to x and y-axes P = drift angle 3 = rudder angle tj/ = yaw angle\nPaper 2787D, first received 24th November 1981 and in revised form 6th October 1982\nDr. Lim is with the Electrical Engineering Department, National University of Singapore, Singapore and Mr. Forsythe is with the Department of Electronic & Electrical Engineering, Loughborough University of Technology, Loughborough, Leicestershire, England\nSelf-tuning control A slanting bar (/) in connection with E indicates that the expectation is conditional on the quantities written behind that bar.\nz = shift operator, e.g.: z~ 1u(t) = u(t \u2014 h) = polynomial of order na corresponding to\nsystem output; A(z~l) = 1 4- ay z \" 1 4- \u2022 \u2022 \u2022 4- a z~\"a\n~ una L\nB(z~1) \u2014 polynomial of order nb corresponding to system input; B(z~l) = b0 + bt z\"1 4- \u2022\u2022\u2022+bnbz-\"b C(z l) = polynomial of order nc corresponding to an uncorrelated zero mean random s e q u e n c e ; C(z~l) = \\ + c1z~1 + \u2022 \u2022 \u2022 + cncz-\"c d = constant disturbance J(z~l) = polynomial corresponding to system control law e(t) = uncorrelated zero mean noise at sample instant t h = sampling interval / = performance criterion P(t) = matrix proportional to the covariance of\nthe estimated parameter at sample instant t\nw(t), u(t), y(t)\nx(t)\na\ne\n= performance costing polynomials = time in sample instants = system set point, input and output at\nsample instant t, respectively = vector containing measured data at\nsample instant t = exponential forgetting factor = vector of controller coefficients = weighting factors = performance criterion related output\nfunction at sample instant t\n1 Introduction\nUntil recently almost all commercially available ship automatic pilots were based on the proportional integral and derivative (PID) type control [1-3]. Typically, the measured heading angle is compared with the desired course, and the difference is used as the input to the controller. The output of the controller is then fed to the rudder servomechanism interface which generates suitable control signals to drive the ship's rudder. Some parameters of the autopilot need to be specified, and this may be most conveniently carried out during sea trials, based on certain rules of thumb to obtain a good quality steering for the vessel under consideration.\nIEE PROCEEDINGS, Vol. 130, Pt. D, No. 6, NOVEMBER 1983 281",
            "However, the judgment of steering quality is itself a highly subjective matter. The common tendency of assuming good steering to be that which holds a tight course is understandable, because, for most ships, the only means of measuring steering performance is the heading error from the course recorder. It thus becomes necessary to define the efficiency of steering in quantitative terms, in order that a meaningful performance evaluation can be established, and, when necessary, a new autopilot can be designed to optimise the defined efficiency.\nThe functions of an autopilot can be divided into those of course changing and course keeping. Course changing demands a fast and accurate response especially when manoeuvring in crowded and confined waterways; course keeping requires a control that maintains a reasonable course with minimum rudder activity. Obviously, the difficulty of defining good steering is greater in course keeping than in course changing. Consequently, several attempts [4-6] have been made to derive a performance index based on propulsion losses owing to rudder and hull motions for an open-seas course-keeping system.\nAlthough it is possible to relate these losses directly to the parameters of the PID autopilot using linear quadratic optimal control theory, the derivation of controller coefficients relies heavily on a priori knowledge of the dynamics of the controlled plant, and the numerical values of each of the individual coefficients appearing in the chosen mathematical model must be known. Unfortunately, in most ships, such data is not always available completely, mainly because ship trials are expensive and time is often too short for adequate information to be obtained. Scalemodel tests [7, 8] may be used to obtain all the data, but usually they are conducted only for the ship of new design in the scale-model basin, for propulsive performance only. Theoretical estimation based on the hull geometrical data using wing and flow theories [9, 10] or some semiempirical equations [11] is possible, but the correlation between the estimated and the measured results is not always satisfactory [12]. Consequently, the concept of designing an adaptive controller that is capable of identifying its own system coefficients and then working out an appropriate control necessary to fulfil certain prespecified performance functions becomes an attractive alternative. There is another factor that establishes further the need for an adaptive autopilot. It is found that for a given sea state, the constant coefficient controller that produces minimum steering propulsion losses at a particular wave-to-ship encounter angle, may not necessarily produce minimum propulsion losses when the encounter angle changes. Thus, the maintenance of minimum propulsion losses in a changing operating environment can only be possible when the coefficients of the controller are adjusted continuously.\nNumerous adaptive control strategies such as modelreference [13, 14], adaptive filtering [15, 16], PID controller with gains varying on-line [17, 18], and self-tuning regulator to minimise output error variance [19, 20] have been employed in autopilot research in recent years. Nevertheless, work towards improved schemes using new adaptive control theories [21-23] is still going on. The approach described in the paper is developed from the selftuning control strategy of Clarke and Gawthrop [24, 25]. This technique differs from the self-tuning regulator [19, 26] mentioned above in that the controller output is explicitly incorporated in the performance criterion. This is in harmony with the course-keeping philosophy of minimising propulsion losses caused by hull and rudder drags. With minor modification of the criterion, it is possible to achieve a fast system response such as that demanded by\n282\nmanoeuvring operations. The self-tuning regulator [19], on the other hand, cannot be made to perform this manoeuvring function efficiently. Further comparison of the adopted approach with the model-reference method [13] reveals that the latter, although it works well during manoeuvring, is not suitable for course keeping because the external disturbances are not accounted for in the controller design. The self-tuning autopilot, in contrast, is explicitly designed to suppress the disturbances. Nevertheless, an extension of the method to eliminate steady-state error caused by nonzero mean disturbances is still necessary, and is reported in this work.\nThe paper is organised as follows: the different tasks of the automatic pilot are specified in Section 2, with formulation of performance criteria suitable for use in adaptive control designs; Section 3 considers the mathematical description of the ship simulation model including its steering gear. The nature of external stochastic disturbances is discussed and the mathematical model for generating nonlinear disturbing motions is given in this Section; Section 4 considers the design of the self-tuning controller with a detailed account of the extension of the self-tuning control to eliminate steady-state output errors; Section 5 discusses the simulation results of the self-tuning autopilot system, highlighting their practical significance; finally, Section 6 offers general conclusions and suggests areas for further investigation.\n2 Performance requirements\n2.1 Course keeping A straight course-keeping vessel is usually expected to keep the ship's heading deviation small, despite the external disturbances. Tight control is not recommended because the rudder would be too active in correcting zeromean heading errors, resulting in additional rudder drag, and unnecessary wear and tear on the steering gear. On the other hand, allowing the ship to yaw freely over long periods of time by introducing a dead-band mechanism (known as the yaw gap [1]) to reduce RMS rudder demand is not necessarily a better approach, because there would then be prolonged periodic yawing motions and extra hull resistance, which increase the journey time and running cost. Consequently, the control of the rudder application and the heading accuracy for this operation should be carried out in such a way that the resultant yawing and rudder motions produce as little propulsion losses owing to steering activity as possible.\nWork to express these propulsion losses analytically has been done [4-6] in the past, and it is recognised that, in general, propulsion losses arise from many different sources [6]. However, only those that are affected by steering control action concern us here. Therefore, the induced rudder drag and the added hull resistance owing to coupled sway and yaw motions are the two main losses to be considered, and are referred to collectively as the added propulsion losses owing to steering.\nIn mathematical terms, the instantaneous added propulsion losses may be expressed as\nX = (m + Xvr)vr + X 3d1 (1)\nwhere m + Xvr is the virtual mass of the ship, xsd is the force coefficient owing to rudder angle, V, r and 5 are the sway velocity, yaw rate and rudder angle, respectively.\nOn the assumption that the ship is operating on straight course and yawing at low frequency with small amplitude around a steady-state pivot point, the equation may be\nIEE PROCEEDINGS, Vol. 130, Pt. D, No. 6, NOVEMBER 1983"
        ]
    },
    {
        "image_filename": "designv11_11_0003140_bf01084139-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003140_bf01084139-Figure8-1.png",
        "caption": "Fig. 8. Plot of peak currents of monolayer peaks of Fig. 7 (a and c) with sweep rate.",
        "texts": [
            " 7 shows two representative cyclic vol tammograms obtained at sweep rates of 100 and 188mVs -L in the potential scan range of - 0 . 2 4 to 0.32V during electrodeposition of AgC1 on silver from 0.01 M KC1 in aqueous 0.1 M N a N O 3 . It is clear that a single monolayer peak occurs at 0.25 V (peak a~) much below the reversible potential of Ag/AgC1, namely 0.325V. The corresponding cathodic peak (cl) occurs at 0. lSV. The plot of peak current (ip) (measured from the base line of the corresponding charging currents) with sweep rate (v) gives a linear plot (cf. Fig. 8) for the anodic film formation (curve A) and its subsequent reduction (curve B), which clearly indicates that the anodic peak at 0.25 V is due to the monolayer formation of AgC1. This is further confirmed by the fact that the charge associated with peak a~ during anodic film formation in AgC1 is found to be 4.62 #C cm -2. It is pertinent to mention here that although the charge density associated with the anodic peak is less compared with full monolayer coverage (150/~Ccm -2) [9], the monolayer peaks are highly reproducible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000534_s1474-6670(17)47309-5-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000534_s1474-6670(17)47309-5-Figure1-1.png",
        "caption": "Fig. 1. A multi-trailer system with n (passive) trailers and m (active) steering wheels.",
        "texts": [
            " For the two input case, it has been pointed out (Martin and Rouchon, 1993; Murray, 1994) that, modulo somewhat different regularity conditions, chained forms are equivalent to fiat systems for the type of drift-free systems that arise in nonholonomic motion planning. This is not true for systems with more than two inputs with out allowing for the possibility of dynamic state feedback. Consider a multi-steering trailer system, i. e. a sys tem of n (passive) trailers and m (steerable) cars linked together at the axles by rigid bars, as shown in Figure 1. It is assumed that each body (trailer or car) has only one axle, since a body with two axles can be modeled as two one-axle bodies. The configuration of the system is defined by the angles of all the axles, the angles of the rigid bars in front of the steerable cars, and the Cartesian position of the system in the (x, y) plane. The ac tive or steering axles are numbered from front (1) to back (m), and the passive axles are numbered similarly from 1 to n . The angle of each passive axle with respect to the horizontal is 0{ where i is the axle number and j is the number of the steer- ing wheel most directly in front of that axle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002915_0301-679x(84)90078-1-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002915_0301-679x(84)90078-1-Figure1-1.png",
        "caption": "Fig 1 Arrangement o f the journal bearing test rig: (1) Test journal, (2) Driving shaft, (3) Ball bearing, (4) Test bearing, (5) Electric motor, (6) V-belt drive, (7) Lay shaft, (8) Flexible coupling, (9) Bearing block, (10) Displacement transducer, ( 11 ) Loading lever arrangement, (12) Balancing lever, (13) Weigh ts, (14) Compression spring, ( 15 ) Loading bar, (16) Graduated nut",
        "texts": [
            " Imposed deviations from the circular form of a journal bearing, being defined and identified by ripples or undulations 9 , ovality 1\u00b0 , multi-lobing ~3 , etc. show, under specified conditions, some improvement in the hydrodynamic performance characteristics. With these points in mind, the project was planned and conducted to investigate the effect of surface wave amplitude and length on journal bearing behaviour. Experimental results were obtained on a test rig specially developed for handling journals with wavy surfaces. Design of the test rig The general layout of the test apparatus is shown in Fig 1. The apparatus, developed for the present investigation, consists of a test shaft (1) which receives its drive from the main shaft (2) and which is supported by two self-aligning ball bearings (3). The test bearing (4) - 80 mm diameter by 80 mm length - is mounted freely on the test journal. Power drive is obtained from an electrical motor (5), through a V-belt drive (6), lay shaft (7) and flexible coupling (8). The test journal consists of a conically-bored sleeve tightly fitted onto the drive shaft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000739_s0094-114x(02)00097-6-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000739_s0094-114x(02)00097-6-Figure1-1.png",
        "caption": "Fig. 1. Typical variables and parameters of a spatial linkage.",
        "texts": [
            " [2], but there are alternative origins, such as the adhibition of Kotel nikov s principle of transference [14] or the vector-based scheme of Lee and Liang [15]. Also available to us are the device of the spherical indicatrix [1,16] and knowledge of already established six-bar solutions. Our basic set of six-bar closure relationships has been set down in various places, most recently as Eqs. (A1)\u2013(A12) in Ref. [13] (although helical and prismatic articulations are particularly excluded from that work). Our notation is widely used and easily appreciated by reference to Fig. 1. As usual, we abbreviate sine, cosine, tangent to s, c, t, respectively, and each of r and s stands for 1. We also find it convenient to employ the shorthand contrivances introduced in Ref. [17] whereby parallelism between joint-axes is denoted by J^J and a pair of coaxial screws functioning as a slider by H@H. We consider here the simplifications which ensue when parallelism between adjacent axes is imposed upon six-bar loops. (It will be found that we cannot readily treat all such cases.) Because we are seeking proper [1], overconstrained linkages of mobility 1, all joints will be of connectivity 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001732_bf01257995-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001732_bf01257995-Figure1-1.png",
        "caption": "Fig. 1. The model error.",
        "texts": [
            " The intersections of the horizontal and vertical strips forms the elementary cells to which a binary variable is associated depending on whether a cell is a free space portion or an obstacle. The mesh size varies with the shape of the object. Let us consider two particular distances: the minimal distance of approach and the maximal one from the center of the cells which is the through way of the robot, to the segment to model. The model error depends on the parameter a which is the angle between the segment to model and the grid (Figure 1). Let us consider L and [ as the horizontal and vertical widths of the meshes and define dmini as the minimal distance of the obstacle approach (Figure 2). dmini = dO sin(a + fl) with dO2= L2/4 q-[2/4, ct: orientation of the edges, fl: orientation defined by tan fl = l/L. 204 V. BOSCHIAN AND A. PRUSKI Let us define dmaxi as the maximal obstacle size distance approach while we are determining a path to the nearest environment. dmaxi = d 1 sin(a + 6) with d 12 = L2/4 + (3//4) 2, 6: orientat ion defined by tan 6 : 3l/4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003728_000094060-Figure17-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003728_000094060-Figure17-1.png",
        "caption": "Fig. 17. Reducing complex cell geometries involved in motility into four basic forms. The helical symmetry of a straight, dynamic helix ( A ) needs to be broken ( B\u2013D ) to allow swimming. The combination of these forms leads to motility.",
        "texts": [
            ", to both translate directionally and change direction), the helical cells need to constantly deviate, to some extent, from plain helicity and deform repeatedly [Daniels and Longland, 1984; Daniels et al., 1980; Gilad et al., 2003; Shaevitz et al., 2005; D ow nl oa de d by : O nd ok uz M ay is U ni ve rs ite si 19 3. 14 0. 28 .2 2 - 4/ 29 /2 01 4 12 :0 0: 07 P M Trachtenberg J Mol Microbiol Biotechnol 2006;11:265\u2013283278 Trachtenberg, 2005b]. However, all of these non-helical states are derived from, and can be traced back to, the basic helical state [Trachtenberg et al., 2003b]. This is depicted schematically in figure 17 B\u2013D. Reciprocating extension and contraction of a straight helix would not result a net displacement of the cell ( fig. 17 A). The complex dynamic cellular geometries leading to swimming can be reduced to a basic set of simple geometries each of which, and all of their combinations, can be generated by differential length changes of the cytoskeletal fibrils: (1) A deformation or kink traveling along the helical path ( 4.5 helical turns for an average cell) of the cell ( fig. 17 B). Travel can progress in either direction. (2) A switch of the cell\u2019s helical sense (handedness) traveling along the cell\u2019s helical path in either direction ( fig. 17 C). The deformation may start at any point along the cell. (3) Flexing. Here the cell bends, or kinks, in one or two planes about a fixed point ( fig 17 D). Flexing is effectively equivalent to tumbling in flagellated bacteria allowing for changes in swimming direction. It is important to note that the flexing point, or kink, may travel along the helical path and the hand, pitch and diameter on either side of the point may change as well combining all the reduced, basic modes described above [Gilad et al., 2003; Trachtenberg, 2005a]. In unusually long Spiroplasma cells ( 8 helical turns) a propagation of pairs of kinks was observed [Shaevitz et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001856_70.238288-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001856_70.238288-Figure6-1.png",
        "caption": "Fig. 6. Velocity polytope and ellipsoid of two 2-DOF cooperating manipulators",
        "texts": [
            " In the figure, both the velocity ellipsoid and the velocity polytope are shown, and a difference between the \u201cbest directions\u201d given by the two approaches may be appreciated. The lengths of the links are L1 = 1, Lz = 0.25, L3 = 0.5, while the joint angles are 191 = 2Oo,O2 = 50\u2019,& = 80\u2019. The best direction computed with the ellipsoid technique forms an angle of 153.57\u2019 (or -26.43\u2019) with the x-axis, while the polytope approach gives an angle of 6.88\u2019, with a difference of 33.31\u2019. Example 6: Let us examine now two cooperating 2-DOF planar manipulators, with a passive contact between the two robots modeled as an hard-finger contact. In Fig. 6 the velocity polytope and the velocity ellipsoid are shown. Also in this case, the difference between the results given by these approaches is noticeable. The best directions Authorized licensed use limited to: AT & T. Downloaded on March 23, 2009 at 15:05 from IEEE Xplore. Restrictions apply. IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 9, NO. 2, APRIL 1993 235 differ by an angle of 23.67\u2019. In the example, L1 = L:! = 1 for both the manipulators, while 811 = 10\u2019,821 = 50\u00b0, and 812 = 61.82\u2019, 8 2 2 = 109"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002364_robot.2001.933087-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002364_robot.2001.933087-Figure2-1.png",
        "caption": "Fig. 2. Change in contact geometry due to positional error 6, using finger 1 as an example.",
        "texts": [
            " This guessing process is repeated ng times to form the set of candidate grasps. This is basically a random search combined with the heuristic: spreading out the contacts produces better quality grasps. The heuristic makes this approach more efficient than a purely random search. Like a random search, a global optimum will be produced in the limit as ng-wo. It should be noted that local optimizing techniques, such as hill climbing, cannot be used here to find the global optimum, due to the presence of local extrema. The premise is shown in Figure 2 using finger 1 as an example. Finger 1 is programmed to apply a force in the nl direction at contact c l , however due to a positional error of 6, (due to the robot, hand and object in combination) it makes contact with the object at the point cl ' . This results in a change of the radius vector from r l to rl ' and a change in the direction of the contact normal to nl ' if cI is located at or near a vertex. The error 6, may be positive or negative. The same situation is assumed with fingers 2 and 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003259_095440604322900435-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003259_095440604322900435-Figure4-1.png",
        "caption": "Fig. 4 An eight-node solid element mesh representing the uid lm topology",
        "texts": [],
        "surrounding_texts": [
            "For simplicity, the actual shape of a pad is simpli ed as illustrated in F ig. 3. The radius of the four corners of a pocket is usually small compared to the width of the pocket. Moreover, the length of a land is usually much larger than its width. Thus the pad is simpli ed as a rectangular pocket combined with four surrounding rectangular lands. Pocket depth is usually much larger than the uid lm thickness and the pressure within the pocket is assumed to be constant. The ow resistance of a pad is determined by the conditions of four lands surrounding the pocket. A single layer of an eight-node solid element mesh is used to represent the uid lm topology as shown in F ig. 4. One side of the mesh is constrained to the pad surface and the other side is set in contact with the rail surface such that the relative sliding motion between the bearing block and the rail is allowed. A minimal value of Young\u2019s modulus and zero Poisson\u2019s ratio are given to the linear elastic solid elements such that the mesh has negligible stiffness in the thickness direction. With a zero value of Poisson\u2019s ratio, a change in the lm thickness does not induce lateral strains in the plane of the lm. Moreover, shear stress in the uid lm will be neglected and thus the mesh will be free from shear strains. Since the linear elastic eight-node solid elements have minimal deformation resistance, they will be called null elements in the following. F luid lm stiffness and damping in the thickness direction are implemented by one large userde ned superelement into which all the nodes in the null element mesh are incorporated {10, 11}. ABAQUS offers a set of input variables listed in Table 1 and the userde ned element is required to calculate force, stiffness and solution-dependent variables at each node in the element. Among the input and output variables (see Table 1), element properties include viscosity \u2026\u00b7\u2020, density \u2026r\u2020, ow resistance of the restrictor \u2026R r\u2020, supply pressure \u2026ps\u2020 and effective pad area \u2026A e\u2020. It is assumed that the ow in the uid lm is in the width direction of each land and can be viewed as Poiseuille ow, discussed in the previous section. F igure 5 shows a owchart of the sequence of calculations in the user-de ned element subroutine. Resistance of ow through each null element space can be obtained from equations (2) and (3) and the geometry of each element. F igure 6 illustrates an example of null elements in a mesh C12103 # IMechE 2004 Proc. Instn Mech. Engrs Vol. 218 Part C: J. Mechanical Engineering Science at Nat. Taichung Univ. of Sci. & Tech. on April 30, 2014pic.sagepub.comDownloaded from covering the uid lm space for a simpli ed pad. Flow resistance of an element Eij in the land can be expressed as R ij \u02c6 B ijh3 ij \u00b7 \u202611\u2020 with B ij and hij calculated from the geometry of element Eij. Combined resistance of adjacent elements aligned in the direction of ow is equivalent to electrical resistances in series. For example, the combined ow resistance of elements E11 and E12 in F ig. 6 is given as \u2026R 11 \u2021 R 12\u2020, where R 11 and R12 represent ow resistances of elements E11 and E12 respectively. Likewise, adjacent elements aligned normal to the ow direction are equivalent to electrical resistances in parallel and thus the combined ow resistance of elements E11 and E21 in F ig. 6 is given as R 11R 21=\u2026R 11 \u2021 R 21\u2020. The ow resistance of any of the four lands is given as R land \u02c6 1 Pm j\u02c61 \u20261= Pn i\u02c61 R ij\u2020 \u202612\u2020 where m and n represent the number of null elements in the length and width directions of the land. The total ow resistance of a pad is obtained by combining the ow resistances of the four lands in parallel such that Rp \u02c6 1 P4 q\u02c61 R land q \u202613\u2020 From equations (1), (2) and (5) pad pressure is obtained as pp \u02c6 R p\u2026ps \u00a1 R rqsqueeze\u2020 R p \u2021 R r \u202614\u2020 The value of squeeze ow can be determined from the nodal velocity input to the user element subroutine. Once the pocket pressure is known, total stiffness and damping of the pad can be determined from equations (9) and (10). The pressure is uniform in the pocket and is linear in the land, as illustrated in F ig. 2. Static nodal forces in the thickness direction are calculated from the known distribution of pressure and static equilibrium conditions at each element level. Contributions from the four surrounding elements are added to a node. Once the static nodal force FS i at each node i is determined, the static nodal stiffness K S i is assumed to be proportional to the static nodal force: K S i \u02c6 FS i ppA e K \u202615\u2020 where K represents the stiffness coef cient of the uid lm. Proc. Instn Mech. Engrs Vol. 218 Part C: J. Mechanical Engineering Science C12103 # IMechE 2004 at Nat. Taichung Univ. of Sci. & Tech. on April 30, 2014pic.sagepub.comDownloaded from For quasi-static analyses, nodal damping C i is assumed to be proportional to the static nodal force: Ci \u02c6 FS i ppA e C \u202616\u2020 where C represents the damping coef cient of the uid lm. Also, inertial effects are added to the nodal stiffness and nodal force, given respectively as K D i \u02c6 mi d u du \u00b3 \u00b4 i \u2021 C i d _u du \u00b3 \u00b4 i \u2021 K S i \u202617\u2020 FD i \u02c6 mi ui \u2021 C i _ui \u2021 FS i \u202618\u2020"
        ]
    },
    {
        "image_filename": "designv11_11_0003307_s10704-005-8546-8-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003307_s10704-005-8546-8-Figure4-1.png",
        "caption": "Figure 4. Orientation of initial cracks on driving pinion and driven gear.",
        "texts": [
            " In successive N points (from C to Z in Figure 3) ahead of the crack, pseudo T-stresses are calculated with: T (r)=\u03c3xx (r,0)\u2212\u03c3yy (r,0)+\u03c3 c yy. (19) The T-stress is then obtained by the extrapolation of pseudo-T-stresses in N points to the crack tip. 4.1. Position and orientation of initial crack Repeated rolling\u2013sliding contact causes normal pressure and sliding in contact area, which can result plastic deformation of the material in that area. This can lead to initiation of surface cracks, which are always angled in the sliding direction in relation to the contact surface (Figure 4). The initial crack angle depends on the amount of sliding, where higher sliding results in smaller initial crack angle (Joachin, 1984). Orientation and length of the crack is usually determined by means of metallographic investigations of initial cracks (Knauer, 1988; Weck, 1992). Kaneta and Murakami (1987) showed that cracks formed on the negative sliding surface grow faster than the cracks on the positive sliding surface. Murakami et al. (1997) experimentally observed that cracks, whose length is longer than half Hertzian contact width, grow only on follower surface when crack is inclined at a small angle to the surface in direction of load movement and frictional forces are opposite to this direction (region of negative sliding). Negative sliding (regions a in Figure 4 for given rotation) is characteristic for rolling\u2013sliding contact conditions in the tooth root contact area of a gear tooth. Cracks in region b in Figure 4 are closed completely when contact load approaches and passes over them. Therefore the crack cannot be completely filled with lubricant, which would cause crack propagation due to its high pressure. The conditions for crack propagation are most favourable in this region due to initial crack orientation and surface traction direction, which are opposite to the rolling contact direction, Figure 4. 4.2. Normal and tangential loading conditions The distribution of normal loading in non-lubricated contact can be estimated by using the classical Hertzian theory (Johnson, 1994). The real contact geometry (e.g. gear tooth flanks) can be transformed into a pair of equivalent contacting cylinders with the radii corresponding to curvature radii of analysed mechanical elements (Figure 5). The two cylinders are then further transformed into equivalent contact cylinder of equivalent radius R\u2217, for which the Hertzian normal contact pressure distribution p(x) can be estimated with simple analytical relationships"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.39-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.39-1.png",
        "caption": "Figure 3.39 Geometrical definitions for a thin elastomeric layer vulcanized between two stiff plates",
        "texts": [
            " In order to reduce the compression peak in the spokes while maintaining a straight winding, it is possible to increase the number of spokes or to reduce the radial stiffness of the hub, i.e. coefficient Cx. A low value of Cl can be obtained by winding the rim over steel supports attached to the tip of the spokes via elastomeric interlayers. The force-displacement characteristics of a thin rectangular elastomeric Isotropic flywheels 121 layer vulcanized between two stiff plates can be described by the equation: F=-Ga2b2(~X) 2t(a + b) (3.171) where: A=l+At/t G is the shear modulus of the elastomer and the geometrical parameters are defined in Figure 3.39. The squeezing of the elastomeric layer At, which must be added to the displacement of the tip of the spoke us can be easily obtained: At = t(X-l) (3.172) where X is the solution of the third-degree equation (3.171) and takes the value: 3/-__\u2014 IVJ?_ 3 / i_^_ / r ? _ 5 ~yJ2 27 + V4 27 + V2 27 V4 27 3 where s=-2Ft(a + b)/Ga2b2, if s<3/^4 (3.173) or ,-arcos A = -<2cos '27 - 2 s 3 H if s ^ 3 / (3.173a) Equation (3.171) is valid for compression so F, X and At are negative. The stresses in the flywheel shown on the right in Figure 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003264_j.jmatprotec.2004.01.030-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003264_j.jmatprotec.2004.01.030-Figure3-1.png",
        "caption": "Fig. 3. The 3D FE model.",
        "texts": [
            " Stiffness excitation is dynamic excitation arising from time-variation of the integrate meshing stiffness in a gear meshing process. The meshing stiffness can be calculated as follows: k = n\u2211 i=1 Fi \u03b4pi + \u03b4gi (4) where Fi is the meshing gear contact force and \u03b4pi and \u03b4gi are the distortion of the drive gear and driven gear tooth, respectively. In this paper, the meshing stiffness of all stages of the gear transmission are simulated numerically by a 3D contact FEM [4]. The second stage gear contact FE model is shown in Fig. 3. The curve of gear meshing stiffness is shown in Fig. 4(a). The gear meshing error results from both the gear machining error and the setting error. These errors lead the gear meshing profile to depart from the theoretically ideal meshing position, which destroys the proper meshing condition of involute gearing. Then, variation of the gear instantaneous transmission ratio occurs: collision and impact occur between the gear teeth, and gear meshing error excitation takes place. In the research reported in this paper, the error curves were simulated by gear backlash, which was determined by the gear precision class [5]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000762_s001580050087-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000762_s001580050087-Figure1-1.png",
        "caption": "Fig. 1 Coordinate convention (a) and stress distributions (b) for a rotating disk of constant thickness without central bore",
        "texts": [
            " Stodola\u2019s solution Within a flywheel of constant thickness without central bore, Fig. 1a, stresses are distributed as plotted in Fig. 1b. The normal stress in radial direction \u03c3r must meet the natural boundary condition at the rim. Here the circumferential stress \u03c3\u03b8 is somewhat higher than the radial stress. Both stress curves increase with decreasing distance from the centre. They actually meet at the centre with zero slopes. With regard to both normal and circumferential stress, the material of the disk of constant thickness is not economically used because of the stress value variations. Stodola (1924) discussed an optimum-strength design for the central disk of a steam turbine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002709_1.2125707-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002709_1.2125707-Figure1-1.png",
        "caption": "FIG. 1. A sketch of the MC simulation cell setup, consisting of two confining planar surfaces perpendicular to the laboratory x axis. The periodic boundary conditions have been applied along y and z directions. We also show a monomer GB particle with two embedded surface interaction sites A and B, and a vector parallel to the surface n\u0302, and the angle between the monomer axis and n\u0302.",
        "texts": [
            " The FENE pair interaction stretching Us * sij and angular U * ij energies between two reaction sites i and j can be written in general terms as:38 U * ij = \u2212 K ln 1 \u2212 ij \u2212 eq Q \u2212 eq 2 , 5 where ij =sij for the stretching, and ij = ij for the bending energy. Here eq is either the equilibrium bond length seq or bend angle eq, and K = Q \u2212 eq 2 /2, where is a stiffness parameter, and Q \u2212 eq is the maximum displacement from the equilibrium value. If the distance or the angle are equal to seq or eq, respectively, then the pair bonding energy is equal to the U0 * value. The specific anisotropic surface-monomer interaction has been taken into account by embedding two spherical sites, labeled A and B, within each GB ellipsoid see Fig. 1 . The interaction energy between the sites of particle i and the smooth wall, Uw * i , is given by a shifted n ,m potential This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 130.18.123.11 On: Thu, 18 Dec 2014 16:27:13 where Kw is the interaction strength term, f u\u0302i is an anisotropic angular term which influences particles\u2019 alignment with respect to an in-plane surface axis, i A and i B are site specific coefficients, and rwi A and rwi B are the sites distances from the wall see Fig. 1 . The w parameter has been chosen equal to s, i.e., the short axis of a GB monomer. As for the choice of the exponents, we recall that by integrating the dispersion interaction between a LJ particle and an infinite slab formed by LJ centers, an overall particle-surface potential governed by a 9,3 law is obtained. In the literature, the particle-surface energy is usually modeled with a variety of repulsive and attractive exponents, like the 10,4 exponents implemented by Steuer et al.,18 and the 9,3 used by Quintana et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001920_robot.1997.619070-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001920_robot.1997.619070-Figure7-1.png",
        "caption": "Figure 7: Model of a deformable pyramid. Figure 9: This articulated chain is subjected to a force 3 and has to reach the point M with a low velocity v'.",
        "texts": [
            " In fact, as long as the error exists, the width of the Gaussian distribution is not nil and the algorithm tries to find other solutions. This method allows us to improve the convergence of'the algorithm. A case which needed 200 generations to converge takes, with this method, only 20 generations. 4 Experimentation 4.1 Treatment of two independent criteria Rigid-deformable identification: The goal of this test is to simuhte the behavior of a. rigid object using our model. Our object, i s a. pyramid which is defined by a set of particles (figure 7) related by linear 4 , T-7- . T A - - + segments) -1 8 . nt ,r i Figure 6: The evolution Gausian distribution while looking for the value s=3.4 (MAPLE). a.nd angular springs/dampers. We consider that connectors a.re identical and their coefficients are X and p . We want that the difference between the trajectory given by the simulator and the one obtained by applying the rigid body mechanics to be less than 6 = 9eP4. to bring it to a desired position (figure 9) with a very small velocity, as fast as possible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001241_physreve.62.8141-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001241_physreve.62.8141-Figure1-1.png",
        "caption": "FIG. 1. Definitions of coordinate system and flow geometry. The liquid crystal sample is placed between two large flat parallel plates, and is sheared by moving the upper plate with a constant velocity V . At the bounding surfaces the tensor order parameter is a constant equal to its equilibrium value, and with the director parallel along the flow direction. The gap separation is H.",
        "texts": [
            " Section II presents the scaled governing equations, dimensionless numbers, parameters, initial and boundary conditions, and the numerical methods used to solve the governing equations for a given shear flow. Section III presents and discusses the results given in terms of tensor order parameter profiles, director orientation angle profiles, and rheological phase diagrams. Section IV gives the main conclusions of this work. The rectilinear simple shear flow geometry studied in this paper is shown in Fig. 1, where H is the plate separation and V is the constant and given velocity of the moving upper plate; the bottom plate is fixed and the upper plate moves in the x direction. The shear plane is the x-y plane, and z is the vorticity axis. To characterize all the possible planar orientation modes we use the following tensor order parameter: Q5E S uu2 d 3 D f du25S Qxx Qxy 0 Qxy Qyy 0 0 0 QZZ D , ~1! where u is a unit vector along a rodlike molecule, f is a orientation probability density function, and d is the unit tensor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001691_s0003-2670(02)00663-3-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001691_s0003-2670(02)00663-3-Figure1-1.png",
        "caption": "Fig. 1. Amperometric electrode prob.",
        "texts": [
            " The performance of the electrode was tested by measuring the alcohol content of commercially available beers. Polycarbonate (PC) track etched membranes with nominal pore size 0.03 m was obtained from Poretics (California, USA). Alcohol oxidase was obtained from the Institute of Biochemistry, Grodno, Belarus. Glutaraldehyde, monomer ethylendiamine, ethyl alcohol, hydrogen peroxide and the other buffer chemicals were obtained commercially (Sigma, Steinheim and Merck, Darmstadt, Germany). An oxidase based probe type enzyme electrode was used (Fig. 1). The electrode consists of Pt working electrode and Ag/AgCl reference electrode. The Pt electrode was polarized at +650 mV for H2O2 detection and the amperometer was linked to a data acquisition system and a computer. The PC membranes were treated in a glow discharge reactor by plasma polymerization technique to incorporate amino groups on the surface. Plasma polymerization system: The reactor was a glass tube with two external cupper electrodes. A 13.6 MHz radio frequency generator was used to sustain plasma in the reactor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002426_978-3-642-84379-2_1-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002426_978-3-642-84379-2_1-Figure6-1.png",
        "caption": "Fig. 6",
        "texts": [
            " The possibility of rejecting a zero measure set permits determining the velocity vector for sliding modes, too. Indeed, although in the points on the discontinuity surface vector f(x, t) in system (1.1) is uncertain, these points in an n-dimensional vicinity make a zero measure set and may be disregarded. Thus, in systems with a single discontinuity surface, the Filippov method yields the following result: (a) the minimal convex set of all vectors f(x, t) in the vicinity of some point (x, t) on the discontinuity surface (Fig. 6) is actually a straight line connecti-ng the ends of vectors f + and f - (to which vector f(x, t) tends with x tending to the point under consideration from either side of the discontinuity surface), and (b) since vector fO in sliding mode lies on a plane tangential to the discontinuity surface, the end of this vector may be found as a point of intersection of this plane and the straight line connecting the ends of vectors f + and f -. At first sight, the Filippov continuation method seems quite applicable to treat controls of the type (1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000363_s0168-874x(99)00042-6-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000363_s0168-874x(99)00042-6-Figure8-1.png",
        "caption": "Fig. 8. Load distribution in a ball bearing.",
        "texts": [
            " If an application requires that the load on the bearing be measured, then the integrated sensor module would include a load-sensing element, which can be designed to structurally support the modi\"ed outer ring. A load sensor based on the piezoelectric e!ect is an appropriate choice since its high structural rigidity can be used to carry large loads with little de#ection. Although most of the load will still be carried by the bearing structure, the rigidity of the load sensor can be utilized to reduce the ring de#ection. If the sensor provides su$cient structural support to the bearing, then the load distribution q(t) on the outer ring will take the form as shown in Fig. 8, with q(t) given by q(t)\"G q .!9 [1! 1 2e(1!cost)]n for !t - (t(t - , 0 elsewhere, (6) where q .!9 is the maximum load and e is the load distribution factor [3]. The exponent n depends on the type of bearing, and is n\"3 2 for roller bearings and n\"10 9 for ball bearings. For a bearing with nominal diametral clearance, q .!9 is given by q .!9 \" 5F 3 Z cosa (7) where F 3 is the applied radial load, Z is the number of rolling elements, and a is the mounted contact angle. The limiting angle t l in Eq",
            " For the various module dimensions analyzed, the size of the piezoceramic chip was held constant at 1.7 mm long, 2.6 mm wide, and 0.58 mm high. The outer ring, \"xtures, and module housing were modeled with the same type of solid elements as used in Fig. 4. By applying a nominal contact pressure of 100 kPa as shown in Fig. 3 and varying the size of the module, the \"nite element model produced the load sensor outputs shown in Fig. 9. (Note that the location of the sensor module corresponded to t\"0 in Fig. 8.) The charge produced by the piezoelectric force sensor is given by Q\"!d 33 F, (9) where d 33 is the piezoelectric charge constant for the sensor material and F is the force applied to the sensor. Note that the charge Q is independent of the sensor dimensions, because of the longitudinal e!ect. However, the support provided by the bearing structure varies with the module size, and the sensor output will vary with the load on the module. As expected, Fig. 9 shows that the sensor output increases with the sensor module size"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002718_20.106362-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002718_20.106362-Figure4-1.png",
        "caption": "Fig. 4 Flux distribution of end region",
        "texts": [
            " Calculation of circulating current and losses After solving the set of equations (10) and (111, the strand current can be obtained: i,=(Pr+ j qr)+(p ; + j q ; ) Introducing the average circulating coefficient K : the circulating losses is then given by P = K, I 2 R where R is the resistance of the stator bar. NUMERICAL RESULTS The method is applied to calculate the end region magnetic field and the current of the stator winding strands in a 2-pole 300MU generator. The distribution of end region magnetic field is shown in Fig.4(in Fig.4 the equipotential lines are the equal scalar magnetic potential lines). It can be seen from Fig.4 that the end region leakage flux mainly concentrate on the plate and the end winding areas, so these areas are source from which the end additional losses are generated, The distribution of peripheral flux density and the radial flux density in stator winding area at the end region along the stator bar length is shown in Fig.5 and Fig.6. From Fig.5 and Fig.6 we can see that the flux density is higher near the end surface of iron core and they decay rapidly along the stator bar length. Fig.7 shows the current distribution of the stator bar along the bar height"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003809_robot.2006.1642172-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003809_robot.2006.1642172-Figure1-1.png",
        "caption": "Fig. 1. The uncertainty in estimating the position of the target at x is given",
        "texts": [
            " The term triangulation refers to inferring the state x of a target by solving a system of simultaneous equations z = h( x) where z denotes the observation vector. In this section, by: U(s1, s2, x) = d(s1,x)\u00d7d(s2,x) sin \u03b8 we will study the process of estimating the position x = [x y] of a target (or a robot) from measurements by two cameras. We assume calibrated cameras, hence their location are known with respect to a common reference frame and their measurements can be interpreted as angles with respect to the horizontal axis (see Figure 1). In this case, we have observables \u03b81 and \u03b82 and solve for the unknowns x and y in: tan \u03b81 = y1 \u2212 y x1 \u2212 x tan \u03b82 = y2 \u2212 y x2 \u2212 x One way of establishing the accuracy of the estimation is to study the effect of small variations in the observables on the estimate. One way of formally establishing this effect is to study the determinant of the Jacobian H = \u03b4h \u03b4 x which is commonly referred to as the Geometric Dilution of Precision (GDOP). In case of cameras GDOP is given by U(s1, s2, x) = d(s1, x) \u00d7 d(s2, x) | sin s1xs2| (1) where d(x, y) denotes the Euclidean distance between x and y and \u03b8 = s1xs2 is the angle between the sensors and the target (Figure 1). The details of this derivation can be found in [7]. In general, Equation 1 suggests that better measurements are obtained when the sensors are closer to the target and the angle is as close to 90 degrees as possible. Let W be the workspace which consists of all possible locations of the robot. Let U(si, sj , w) denote the uncertainty in localization when the robot is at location w \u2208 W and queries sensors si and sj as defined in Equation 1. Let S = {s1, . . . , sn} be a set of sensors. When there is no danger of confusion, we will use si to denote the location of sensor i as well"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002787_robot.2003.1241932-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002787_robot.2003.1241932-Figure7-1.png",
        "caption": "Figure 7 The arrangement for caging relatively large object by three mobile-manipulators' hands and bodies.",
        "texts": [
            " Because both the object and robots' orientations should be considered, obtaining the pmin becomes a minimum search problem in a relatively large space. In [lo], a fast algorithm is proposed for polygon object-robot pair, but it is under the assumption that the robots group does not have non essential robots and closest pair of points between two neighbor robots can be decided. Here, we consider another special case: all robots keep the same orientation during the whole period of the object handling(simi1ar with robots' bodies in Fig.7). In this case, we just need to calculate the all orientation of the object, because the geometrical shape of the CC-Closure Object just be affected by the relative angle between object's orientation and robot's orientation. Then searching space is reduced to 2 dimensional space which is reasonable small by using numerical searching procedure in the precalculation stage. When the pmin is obtained, the testing procedure in the runtime is the same with the case of disc-shaped robots, just n times inequality checking",
            " By using this property, we consider the case that the system only consists of two different type of robot effectors working for caging the object, such as hand a,nd body of mobile-manipulator. If these two different effectors are arranged around the object alternately: Ai(\u00b6) = di+z(q) = ' ' {d. %+I (q ) = \"4i+3(9) = _ ' ' i then, C & d d = CClS.i+2(4) = ' ' _ ccl,.i+l(n) = C C l S . i + 3 ( 4 ) = _ ' ' ~ ~ c l s . i ( i + l ) ( 4 ) = 0CCClS.(i+l)(i+P) ( 4 ) The last property indicates that only one geometric data of CC,I,,, is necessary for testing Object Closure on mobile-manipulators if we intentionally arrange hands and bodies of robots alternately around the object(Fig.7) and testing process can be realized in real time too. 3.6 Object Closure Margin To control a robots team which has uncertainty on control and error on sensing, margin for realizing the Object Closure should he introduced into the testing and formation control procedure. Based on the concept on building the testing algorithm, we define the Object Closure Margin as follow: Definition: While the Object Closure is achieved, the closure margin to each neighbor pair robots in the system is defined as: '/ij = Pmin - P i j The minimum of the closure margin all pair of neigh- bor robots in the system is defined as the Object ChuTe Margin %is = yF(7l"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001516_iros.1997.649040-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001516_iros.1997.649040-Figure3-1.png",
        "caption": "Figure 3: Swing Motion Steps",
        "texts": [
            " Task B) controls the manipulator to converge to the desired swing motion in order to throw the gripper to the target precisely. The algorithm for Task B) is shown in section 4.4. Before discussing the control of swing motion, we consider several modes of swinging the casting manipulator as penodicity. The motion of modes a) and b) in Figure 2 is periodic motion, while that of modes c) and d) is not repeated periodically. Considering the stability of swing motion and throwing motion, we chose mode a) \u20acor swinging the manipulator in the first step. Figure 3 shows the steps of the swing motion. Figure 3 I), 2) and 3) represent respectively the initial state, arbitrary swing state, and desired swing state. shown in Figure 2. Roughly speaking, there are two nodes, that of pendulum motion and that of giant swing motion. Both are divided further into two modes in terms of ' I70 and where L; is the length of link i, d i is the distance between joint i and the center of gravity of link i, m, is the mass of link i, li is the moment of inertia about the center of gravity of link i , 61 is the angle of joint i, and g is the acceleration due to gravity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002314_1.1814390-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002314_1.1814390-Figure2-1.png",
        "caption": "Fig. 2 A translational 3-URC mechanism",
        "texts": [
            " Among these papers, Ref. @20# has presented a class of TPMs with linear inputoutput equations that contain some translational 3-URC mechanisms. In the next sections, at first, the demonstration that some mounting and manufacturing conditions yield 3-URC mechanisms that constrain the platform to translate will be given; then, the position and the velocity analyses of such translational mechanisms will be addressed by assuming that the three revolute pairs lying on the base are the actuated pairs. Figure 2 shows a 3-URC architecture whose configuration matches the following mounting and manufacturing conditions: ~i! In each leg, the revolute pair axis fixed in the base is parallel to the cylindrical pair axis fixed in the platform ~since this condition requires that the platform, the base, and the legs\u2019 links satisfy some geometric conditions and be properly assembled, it is a mounting and manufacturing condition!. ~ii! In each leg, the cylindrical pair axis intersects and is perpendicular to the adjacent revolute pair axis ~since the cylindrical pair and the adjacent revolute pair belong to the same link, this condition is a manufacturing condition",
            " In each leg, the axes of the two revolute pairs that are not adjacent to the base are parallel to one another ~since these two revolute pairs belong to the same link, this condition is a manufacturing condition!. The following part of this section will show that a 3-URC mechanism, manufactured and assembled so that these conditions are met, makes the platform translate when it changes its configuration under the action of the actuated pairs, provided that some singular configurations are avoided during motion. Hereafter a 3-URC mechanism that meets the above-mentioned conditions will be called translational 3-URC. With reference to Fig. 2, points Ai , i51, 2, 3, are the centers of the universal joints. Points Bi , i51, 2, 3, are the intersections of the cylindrical pair axes with the revolute pair axes adjacent to them. Moreover, Sp is a reference system fixed in the platform and Sb is a reference system fixed in the base. Point P is the origin of Sp . 004 by ASME NOVEMBER 2004, Vol. 126 \u00d5 1113 17 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F Figure 3 shows the ith leg, for i51, 2, 3, of the translational 3-URC",
            " Since the platform of a translational 3-URC translates when the mechanism is out of singular configurations, the position analysis of a translational 3-URC can be addressed by assuming that the platform orientation is constant and known with respect to the base. This assumption yields that the rotation matrix, Rbp , which transforms the vector components measured in Sp into the vector components measured in Sb , is constant and known. Therefore, the translational 3-URC DPA analytically consists of determining the positions of point P ~see Fig. 2! compatible with given values of the joint coordinates u1i , i51, 2, 3 ~Fig. 3!. On the contrary, its IPA consists in calculating the u1i , i51, 2, 3, values compatible with an assigned position of point P. With reference to Figs. 2 and 3, the constraint equations of a translational 3-URC can be written as follows: w2i\u2022~Bi2Ai!52di , i51,2,3 (9a) ~Bi2Ai! 25hi 21di 2, i51,2,3 (9b) with Bi5P1Rbp p~Bi02P!2siw4i , i51,2,3 (10) where all the vectors are measured in Sb and the bold capital letters without a left-hand superscript point out position vectors measured in Sb , whereas the left-hand superscript p, added to a vector symbol, indicates that the vector is measured in Sp ~Fig. 2!. The substitution of expression ~10! for Bi into Eqs. ~9!, by taking into account condition ~1a! and expanding the resulting expressions, yields the following relationships: w2i\u2022P1w2i\u2022@Rbp p~Bi02P!2Ai#1di50, i51,2,3 (11a) P21p~Bi02P!21si 21Ai 212P\u2022@Rbp p~Bi02P!2siw1i2Ai# 22siw1i\u2022@Rbp p~Bi02P!2Ai#22Ai\u2022Rbp p~Bi02P! 5hi 21di 2, i51,2,3 (11b) rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/22/20 The analysis of Fig. 3 reveals that the analytic expression of the unit vector w2i is w2i5cos~u1i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001993_s003320010001-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001993_s003320010001-Figure1-1.png",
        "caption": "Fig. 1. (a) Left: The physical template: spring-loaded inverted pendulum (SLIP) monoped with point mass, m, at hip and massless leg consisting of a spring with potential U (qr ). By convention, both q\u03b8 and bx are defined to be negative to the left of vertical and positive to the right. (b) Middle: Illustration of the template\u2019s correspondence to Raibert\u2019s hopper. (c) Right: Illustration of the template\u2019s correspondence to a human runner.",
        "texts": [
            " In this paper, motivated by certain questions common to both robotics and biomechanics, we develop what may arguably be construed as the simplest possible \u201cplant model\u201d1 for general dynamical locomotion behavior in both robots and animals. That such a model would even exist may seem dubious. After all, legged animals present an incredible diversity of shape, size, and morphology. In spite of these obvious and important differences, biomechanists studying running2 [1], [4], [8], [10] have identified a striking underlying uniformity in the center of mass (COM) behavior of the majority of creatures studied. This seeming unity of strategy finds its archetype, or template, in the spring-loaded inverted pendulum (SLIP) depicted in Figure 1(a). The view of 1 From the perspective of systems engineering, a particular physical phenomenon may be represented by either an input/output map or a full state internal model\u2014the latter by linear or nonlinear dynamics; and these, in turn, may be cast in continuous or discrete time; and so on. In the end, the \u201ccorrect\u201d mathematical representation is dictated by the problem of concern and the available analysis and design tools. We will honor traditional usage by calling this representation the \u201cplant model",
            " animal dexterity as arising from the orbits of strategically tuned spring-loaded actuators dates back to Bernstein [3], and contemporary biomechanists have posited the SLIP as a specific template for fast legged locomotion behavior [4], [5], [10], [28]. Specifically, Full has presented strong evidence suggesting that animals, whether using two, four, six, eight or more legs, arrange their nerves and muscles in a manner that persuades their COM it is riding on such a pogo stick [10]. This notion of a \u201cvirtual SLIP\u201d is suggested in Figure 1(c). The utility of dynamical legged locomotion was introduced to robotics by Raibert [32]. His machines were designed to be explicitly SLIP-like, incorporating a physically identifiable spring connecting the toe to the body. The SLIP mechanics afforded simple yet ground-breaking strategies that relied on the shaping of total energy and reverse time symmetries for control. These strategies yielded stunning results for the planar monoped depicted in Figure 1(b), and were extended with equal success to an entire family of one-, two-, and four-legged machines running in three-dimensional space, again using intuitive notions of a \u201cvirtual SLIP\u201d as suggested in Figure 1(c). Even subsequent to Raibert\u2019s pioneering designs, standard approaches to the control of legged locomotion have continued to employ feedback controllers to track joint space reference trajectories [23], [42], [45], [46]. A fundamental question arises regarding the origin of these reference signals. Since translation of desired body motions into joint space trajectories that achieve them represents a central unknown, a variety of different approaches have been proposed. In character animation, for example, these signals are often generated via playback of motion capture recordings from animals [13] or from interpolation of tediously assigned key frames [9]",
            " A feeling for the nature of these results is provided by a glance at the function h1 U (qr ) =  t\u0302 s 1(qr ) q\u0302\u03b8 1(qr ) p\u0302\u03b8 1(qr ) p\u0302r 1(qr )  =  tsb + m H\u22121 pert(\u03be\u0302r ,q\u0302\u03b8 0(\u03be\u0302r ), p\u0302\u03b8 0(\u03be\u0302r )) (qr \u2212 rb) \u03b8b + p\u0302\u03b8 0(\u03be\u0302r ) \u03be\u0302 2 r H\u22121 pert(\u03be\u0302r ,q\u0302\u03b8 0(\u03be\u0302r ), p\u0302\u03b8 0(\u03be\u0302r )) (qr \u2212 rb) p\u03b8b + m2g\u03be\u0302r sin(q\u0302\u03b8 0(\u03be\u0302r )) H\u22121 pert(\u03be\u0302r ,q\u0302\u03b8 0(\u03be\u0302r ), p\u0302\u03b8 0(\u03be\u0302r )) (qr \u2212 rb) H\u22121 pert(qr , q\u0302\u03b8 1(qr ), p\u0302\u03b8 1(qr ))  , (1) which we obtain by applying our approximation technique to the Hamiltonian vector field, X Hpert (q, p) =  pr m p\u03b8 mq2 r p2 \u03b8 mq3 r \u2212 DU (qr ) 0 +  0 0 \u2212mg cos(q\u03b8 ) mgqr sin(q\u03b8 )  , arising from the SLIP of Figure 1(a) forced by a spring with the potential energy function U (qr ). Here H\u22121 pert(qr , q\u03b8 , p\u03b8 ) = [ 2m [(U (rb)\u2212U (qr ))+ mg(rb cos(\u03b8b)\u2212 qr cos(q\u03b8 ))] + ( p2 \u03b8b r2 b \u2212 p2 \u03b8 q2 r )] 1 2 , and \u03be\u0302r = (1/4) qr+(3/4) rb. Additionally, the numerical subscript identifies the particular iterate\u2014both q\u0302\u03b8 0 and p\u0302\u03b8 0 are defined in (2). Other notations are defined in Table 1. Although X Hpert is nonintegrable and the spring potential, U , is not prescribed at all, h1 U closely approximates the results of numerically integrating trajectories of X Hpert from stance bottom states (where the leg spring is maximally compressed) to flight apex states (where the body\u2019s vertical height is greatest) for all instances we have examined when U is a convex function (i",
            " Simulation results presented in Section 4 demonstrate that gravity cannot be ignored in stance if a wide range of orbits is desired. We thus introduce an iteration procedure, combining Picard style iterates with the Mean Value Theorem for Integrals result of Section 3, to construct approximate solutions to the perturbed dynamics whose accuracy and complexity grow in a controlled manner as exemplified in equations (1) and (2). Again, simulation data is compared to establish the efficacy of this approach. The SLIP template, depicted in Figure 1(a), is defined according to the following assumptions. The leg is assumed to be a massless spring, with potential law U (qr ), that connects the toe to a point mass, m, at the hip. It is assumed that there are no losses during stance or flight and that the only force acting during flight is gravity. Furthermore, it is assumed that once on the ground the toe does not slip, effectively acting as a hinge about which the leg is free to rotate in the sagittal plane. The hopping cycle consists of two primary phases: the stance phase, when the foot is on the ground, and the flight phase, when the leg is airborne",
            " As mentioned above, the vector field X Hunpert (4) corresponding to the unperturbed system is completely integrable\u2014having two constants of motion: the total energy, E0 = Hunpert, and the angular momentum, L0. Integrating by quadratures,6 we use constant L0 to give p\u03b8 and this, in addition to constant E0, to give pr , p\u03b8 (qr ) = L0 pr (qr ) = [ 2m(E0 \u2212U (qr ))\u2212 L2 0 q2 r ] 1 2 . (11) 4 Here, both q\u03b8 and bx are defined to be negative to the left of vertical and positive to the right, as defined in Figure 1(a). 5 We denote the jacobian of g and all other functions by the symbol Dg. 6 Choosing qr as the dependent variable conforms to tradition [14, \u00a73\u20135] [24, \u00a71.3c] [44, \u00a748], suits well the need to leave unspecified the spring law U (qr ), and easily allows the convention of characterizing the transition from stance to flight by the achievement of a particular leg length, qr = qrl [22], [27], [32], [39], [43]. With no loss of generality, we focus attention on the decompression phase (pr > 0) in this work and, therefore, select the positive square root solution for pr "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003926_0301-679x(76)90014-1-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003926_0301-679x(76)90014-1-Figure2-1.png",
        "caption": "Fig 2 Replacement o f the original oil lubricated bearing and the associated seal (left) with a water lubricated bearing (right) resulted in a considerable simplification o f the final design era horizontal spindle pump",
        "texts": [
            " The type of material which is best suited to any particular application will depend on the quality of the water used. The water supply of a pump using river water will probably at best be filtered before use and will almost certainly contain abrasive particles and other contaminants. In other applications, eg process industries, the water may be to a very carefully controlled high purity, possibly at temperatures up to 250\u00b0C. Applications An example of a water lubricated bearing replacing a gland on a horizontal spindle pump is shown in Fig 2. The simplification achieved by removing the gland is clearly seen by comparing the original and final designs. The water in this case was of high purity and was at a temperature of about 40\u00b0C. The bearing supply was obtained by tapping water off the second or third stage outlets and returning it to the pump suction. Carbon was used for the bearings, including some internal interstage steady bearings and satisfactory performance was obtained Fig 3 shows a vertical spindle pump in which the bottom bearfng is water lubricated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000724_s1388-2481(02)00369-7-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000724_s1388-2481(02)00369-7-Figure3-1.png",
        "caption": "Fig. 3. Images of electrode configuration employed for voltammetric studies; 10 magnification, 60 magnification.",
        "texts": [
            "5 M), the aqueous solution contained no added reagents. It is apparent from the image that under conditions where the organic and aqueous streams were operating with balanced flow rates, the interface remains stable and essentially centrally located across the width of the cell. This behaviour was observed for all appropriate H:W ratio cells examined. Next voltammetric measurements were performed using a microelectrochemical reactor of design illustrated in Fig. 1. The microelectrodes were fabricated (Fig. 3) such that a set of working, reference and counter electrodes were sited in each solvent stream. A DCE solution containing 0.1 M TBAP and the reagent TMPD and an aqueous solution containing 1 M KCl and the reagent hexaamineruthenium(III)chloride were employed for the studies. Both solutions were fed through the cell and the flow rates balanced (to within 1% of one another). A set of linear sweep voltammograms was recorded in turn, for each phase, for the electrolysis occurring in that phase, using volume flow rates of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003360_s0022-0728(83)80350-7-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003360_s0022-0728(83)80350-7-Figure3-1.png",
        "caption": "Fig. 3. Variations of k s as a function of Aks/ks: (e) capillary El: (O) capillary C2; (+) HMDE; (A) GCE. The numbers are the value of v in V s - 1.",
        "texts": [
            " The differential capacity C which is proportional to the area was measured by LPSV from the residual current in the potential range of the faradaic peak in the absence of reactant. For the mercury electrodes we have C = 2.4 \u00d7 10 -5 F cm -2 and for the G C E C = 1.8 \u00d7 10 - 4 F cm -2. The high value of C for the G C E is due to the fact that the current in the absence of reactant does not have exclusively a capacitive origin, but includes a large residual current; in that case C represents an apparent capacity which can, however, be used in the calculations. The values of AEp, r given in Table 2 are calculated with an accuracy of _+ 0.2 mV. We have plotted in Fig. 3 the variations obtained with different scan rates for k s as a function of A k s / k s for the four electrodes of Table 1 by proceeding as indicated above. The number of electrons n was assumed to be one, T = 298 K and Q0 = 5 \u00d7 10 - 9 C. The latter value corresponds for most organic compounds to coverages of about 2 x 10- u to 7 x 10-13, which represents the lowest practical value giving rise to a measurable peak. If we want the error on k s to be < 10%, we see that the limiting values of k s, which are indicated in Table 1, are rather low"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002204_s1474-6670(17)31748-2-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002204_s1474-6670(17)31748-2-Figure2-1.png",
        "caption": "Fig. 2 Parallel deviation problem",
        "texts": [
            " T RUD ' Tcpp and a are time constants. The subscripts H , P, Rand Th denote the highly non-linear hydrodynamic force induced by the hull, propeller, rudder and thruster. For detail of the hydrodynamic force, see (Ohtsu et al., 1996). 2.3 Minimum-time parallel deviation maneuvering problem and the non-linearity o/its solutions In this paper, the minimum-time parallel deviation maneuvering problem and its solutions are considered as a simple example of the feasible study realised by CAMS 2004 proposed control system. Figure 2 shows the initial course line and terminal one of the minimum-time parallel deviation problem. Where .e is the distance between two parallel course lines. In this case, the boundary conditions for the two-point boundary value problem and the non differential constraint are as follows. I) The initial ship's state [x(O) y(O) u(O) v(O) reO) V'(O) 8(O)Y =given (14) 2) The final state of the ship [y(1) 1(1) r(1) 1!f(1) o(1)y =[Yf VI rf lJII oJ =0(15) 3) The non-differential constraints 8' (t) - sigmoido Dumy(t) = 0 , 0 ~ t ~ 1 (16) where, o~"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003184_2005-01-1651-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003184_2005-01-1651-Figure12-1.png",
        "caption": "Figure 12 \u2013 Diagram of interferences",
        "texts": [
            ": 2 SM SMrr 2 1 SM RV e 2 1,rf 2 22 2 cln c2 1 1 RV e 2c 1F (9) with the variable r( ) represents the distance from an asperity summit with angle at the system centre, zrms corresponds to the standard deviation of the heights of the asperity summits around the mean line of asperity summits which is denoted by SM, SM is the position of the mean line of asperity summits, is the standard deviation of the radius distribution and 1c and 2c are constants defined in the appendix. When we adopt a more macroscopic description of the surfaces, they can be represented using the diagram in Figure 12. Figure 12 shows that the distribution of the asperity heights results in contacts that vary in intensity as a function of the angle . According to this figure, an initial approximate expression of the mean line of asperity summit attitudes is: coseRr 1rSM (10) with e is the eccentricity between the axis of the small end bore and the piston pin. For an asperity summit defined by r , there will be contact if the interference S is positive, where the interference is: R-rS 0 (11) With this schematic description, it is necessary to specify the surface density of the asperities asp"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003711_j.wear.2005.01.012-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003711_j.wear.2005.01.012-Figure4-1.png",
        "caption": "Fig. 4. The measuring extent for both, the coefficient of friction and the worn surfac at the timing signal was defined as the reference point.",
        "texts": [
            " der, (3) cylinder holder, (4) CCD camera, (5) ring spring, (6) strain gauge, rotating rod, and (11) differential transformer. The sliding direction of rubber was from top to bottom in the figures. It was confirmed that large abrasion patterns were formed on both of the two specimens. Each pattern reached from one side to another side of the rubber wheel. The same area on the rubber surface was defined for measuring the time series variations of the coefficient of friction and worn surface. The measurement area for the coefficient of friction and surface profile are explained in Fig. 4. The contact area between the outermost surface of rubber specimen and the mating cylinder was defined as a reference point at the timing of synchronous signal. When the rubber wheel rotated, the coefficient of friction was measured as a function of the distance from the reference point along the circumference of the rubber wheel. The rubber rotation was also defined as r surfaces after the experiments. e profile. Contact area between the rubber specimen and the mating cylinder an angle from the reference point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000688_1.1287265-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000688_1.1287265-Figure2-1.png",
        "caption": "Fig. 2 Large scale model: \u201ea\u2026 Test section; \u201eb\u2026 configuration of the interference seal; \u201ec\u2026 configuration of the clearance seal.",
        "texts": [
            " The gas for the large scale model is air. A scale of five in geometry was chosen because it allows representative testing to be performed at close to atmospheric pressure when the Reynolds number is the same as for the engine seal. The high aspect ratio of the seal periphery to height is such that the flow is judged to be essentially two dimensional at any location. Thus a linear model was considered to be sufficient to represent the brush seal flow. The test section of the large scale model is shown in Fig. 2~a!. The cross sectional area is a parallelogram with angle of 45 deg, which is the same as the bristle lay angle. The cross section is 200 mm3115 mm. The length of the test section is 190 mm, and the bristle pack was installed in the middle. The overhang radial length of the bristles is 5 mm. Therefore, the backing ring clearance of 4.075 mm corresponds to an interference seal with the build interference of 0.925 mm; and the backing ring clearance of 6.5 mm corresponds to a clearance seal with a clearance of 1.5 mm, as shown in Fig. 2~b! and ~c!. There were 4125 bristles within the pack. The bristle pack consists of aluminum alloy wires to BS 1471 5251 H8. Table 1 gives the properties of the real engine seal and the large scale model. Aluminum alloy was chosen as the best available compromise to maintain Reynolds number and stiffness rom: http://gasturbinespower.asmedigitalcollection.asme.org/ on 02/18/20 term E/Pu , the same in the model and the engine. Also, f b and f BR were approximately the same for both cases. The seal housing was constructed from aluminum alloy plate, with the exception of the top plate which is manufactured from perspex to provide optical access"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001039_978-3-642-71949-3_17-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001039_978-3-642-71949-3_17-Figure12-1.png",
        "caption": "Fig. 12. Scheme of the one-link inverted pendulum model (a). The dashed line denotes the feedback loop with time delay T. The nonlinear properties of propri oceptors are modelled by a piecewise linear functions (b), (c) or smooth function (c).",
        "texts": [
            " Thus, the origin of the body sway while quiet standing was supposed to be a result of fluctua tions in the control and mechanical subsystems. A similar model was studied in (Matsushira et al. 1983). To account for the sensibility threshold of pro prioceptors, Matsushira et al. have also considered piecewise linearity in the feedback loop. They found that this leads to the excitation of periodic oscil lations corrupted by noise. The importance of the nonlinearity in the feedback loops was demonstra ted elsewhere (Rosenblum et al. 1989, Rosenblum and Firsov 1992a). The following model was studied numerically (Fig. 12a): <p+2h<p+.w2r,o+'Cl.r(r,o(t-T),>.t} +'C2.r(<p(t-T),>'2) =0, (7) where the piecewise linear function .r describes the characteristics of the proprioceptors with sensitivity thresholds >'1,2, .r(x, xo) = (x - xo)e(x - xo) +. (x +. xo)e ( - (x +. xo)) , (8) eo is the Heaviside step function. For this model in a broad range of pa rameters chaotic oscillations arise. It was concluded that oscillations of the center of gravity of the human body may be of deterministic origin. Another model (Rosenblum and Firsov 1992a) was proposed on the base of the so-called equilibrium point hypothesis (Feldman 1979; Hogan 1985)",
            " The sensitivity thresholds ).1,2 and the coefficients C1,2 may serve as the physiologically relevant bifurcation parameters. 4.2 Modelling Sways in Two Dimensions From the fact that body sways of healthy persons in anterior-posterior and lateral directions are independent, we can conclude that there exist two sep arate control systems governing maintainance of the upright posture. We assume that both systems can be described by equations of the form (11). 2 If the proprioceptor characteristics of Fig. 12b is used, infinitely growing unsta ble solutions may occur. As we restrict ourselves to modelling small oscillations around the equilibrium, we do not consider these solutions. We do not perform the detailed bifurcation analysis of the model because there are 6 free parameters, and the physiological meaning of two of them, Cl,2, is not clear. Of coarse, the parameters of these equations can differ. In the following we suppose that the time delay T is the same for both systems because it is determined by the length of the neural fibers and the velocity of the signal propagation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003023_001-Figure22-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003023_001-Figure22-1.png",
        "caption": "Figure 22. A schematic drawing of the end of an inflexible metal mass spectrometer intravascular blood gas catheter probe (after Hansen er al 1986).",
        "texts": [
            " Various slits or holes have been cut into the steel catheter to allow the gas molecules to diffuse to the mass spectrometer head, and the geometrical design of these catheters was examined by Seylaz and Pinard (1978) and Pinard et al(l978). In more recent years several reports (Lundsgaard et al 1980, Parker and Delpy 1983, Hansen et a1 1986) have described catheter probes with the tip consisting of a sintered, porous substrate (typically bronze) covered with a permeable membrane. Two examples are shown in figures 22 and 23. The Hansen et a1 (1986) design (figure 22) uses the conventional stainless steel tube connection to the mass spectrometer, but the Parker and Delpy (1983) design (figure 23) uses a flexible plastic catheter, coated on the inside with polyurethane to minimise the problem of water vapour diffusion through the catheter walls. This latter design also includes a bilumen tube, one lumen being used for blood sampling. 9.1.2. Non-invasive probes. A transcutaneous mass spectrometer non-invasive probe is shown schematically in figure 24. It is essentially a heated gas collection chamber, and was described by Delpy and Parker in 1975"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003310_1.2400209-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003310_1.2400209-Figure1-1.png",
        "caption": "FIG. 1. Schematic sketch showing a neutrally buoyant 2D rigid circular cylinder dynamically interacting with N pairs of point vortices symmetrically located about the direction of velocity V of the cylinder.",
        "texts": [
            " Adopting this philosophy and keeping in mind the stated advantages of having a finite-dimensional model, the Hamiltonian model developed by SMBK1,4 is considered. In this model, a 2D rigid cylinder of arbitrary but smooth cross section dynamically interacts with N point vortices external to it. In this paper, a special case of this model, which will be referred to as the half-space model, is investigated. In this half-space model, the cylinder is circular, the vortices are distributed symmetrically about the direction of motion of the cylinder, and the circulations of the vortices are reflected about the axis of motion see Fig. 1 . Thus the sum of the strengths of all the vortices in the full space is zero. The motivation for looking at this special case comes from the observation5 that the vortical structures shed behind swimming creatures are typically vortex rings, and a 2D model such as this can be thought of as a section of an axisymmetric sphere vortex rings model. The organization of this paper is as follows. In Sec. II, the Hamiltonian structure of the half-space model and the equations of motion for the general case when N vortices are present in the half-space or, equivalently, 2N vortices in the full space is presented",
            " Now consider the symmetric half-spaces Psym P defined as Psym: = p P x1 \u2212 xN+1 = 0,y1 + yN+1 = 0, . . . ,xN \u2212 x2N = 0,yN + y2N = 0,Lx = constant,Ly = 0 , where, without loss of generality, it is assumed that the vortices are indexed from left to right, going from 1 to N in the top row and from N+1 to 2N in the bottom row. In each of these symmetric half-spaces the cylinder is constrained to move along a straight line, which we have assumed to be the x axis of a body-fixed frame with its origin at the center of mass of the cylinder as in Fig. 1. The half-spaces can be thought of as being parametrized by Lx. Fact: Each Psym is an invariant subspace of Pleaf with the same value of Lx and Ly under the flow of the SMBK Hamiltonian vector field. Moreover, choosing coordinates x1 ,y1 , . . . ,xN ,yN ,Lx for Psym, the inclusion map i : Psym\u2192Pleaf, i x1,y1, . . . ,xN,yN,Lx = x1,y1, . . . ,xN,yN,x1,\u2212 y1, . . . ,xN,\u2212 yN,Lx,0 is symplectic and induces a symplectic form on Psym by pullback, Psym \u00aa i* p = j=1 N 2 j dxj \u2227 dyj . 1 Hamiltonian on Psym: Consider the Hamiltonian Hsym: Psym\u2192R obtained by the restriction of the SMBK Hamiltonian on P"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002427_50009-5-Figure7.33-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002427_50009-5-Figure7.33-1.png",
        "caption": "FIGURE 7.33 On-line testing can provide quality control on the whole strip length in the rolling mill. The strip is passed through a magnetizing tunnel where a solenoid generates the field and a non-contact flux-closing double-C yoke ensures a certain degree of homogeneity of the magnetization in the material (a) [7.105]. The induction is measured by means of an enwrapping coil and the field by means of a tangential H-coil. In the arrangement shown in (b), however, a Rogowski-Chattock coil is used in association with compensation windings (C) and copper plates to maintain uniform field in the measuring region, so that the magnetizing current provides a measure of the field (see also Section 7.1.2 and Eqs. (7.3) and (7.4))[7.106].",
        "texts": [
            " The single-sheet testing method is widely accepted in the industrial laboratories and as far as possible adopted in lieu of the Epstein strip testing method because it is quicker and easier to operate. It may be desirable, however, to make a quality assessment of the whole lamination in the plant during the final phase of production, that is, to make magnetic testing on the continuously running steel strip before coiling. This must obviously be non-contact measurement and special solutions must be devised to reliably detect B and H, which is all we need to characterize the material. Figure 7.33a provides a schematic view of an arrangement for on-line lamination testing along the rolling direction (that is, the direction of motion of the strip) [7.105]. The steel strip slips through an enwrapping magnetizing solenoid and a B-sensing coil, which are enclosed by a double-C yoke, placed at the smallest possible distance from the moving strip allowing for safe operations. A fiat H-sensing coil, placed as near the surface of the lamination as practicable, can additionally be employed. The comparatively approximate nature of the resulting measurement, which is valuable chiefly in terms of comparative testing and continuous monitoring of the lamination properties along the coil, is the inevitable consequence of the poor quality of the magnetic circuit and the tension on the strip. The effect of the latter must be accounted for by known dependence on stress of the magnetic properties of the investigated material. Figure 7.33b illustrates the realization of an on-line testing method where, in analogy with the principle of the fieldcompensated single-strip tester described in Fig. 7.6, a RCP is employed to automatically detect and compensate, via the set of supplementary 7.3 AC MEASUREMENTS 387 coils (C), the drop of magnetomotive force occurring outside the measuring region [7.106, 7.107]. In this way, the value of the magnetizing current can be taken as a measure of the field in the material (see also the discussion in Section 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003399_j.ijmecsci.2005.04.003-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003399_j.ijmecsci.2005.04.003-Figure1-1.png",
        "caption": "Fig. 1. The rod geometry.",
        "texts": [
            " Even though the natural frequencies can be calculated, because the element stiffness and mass matrices are not obtained separately, the corresponding mode shape cannot be calculated using the present method. It should be emphasized that the present work is primarily concerned with the application of an efficient method of the forced vibration analysis to composite helical rods. Consider a naturally curved and twisted spatial slender rod. The trajectory of geometric center G of the rod is defined as the rod axis and its position vector at t \u00bc 0 is given by r0 \u00bc r0\u00f0s; 0\u00de where s is measured from an arbitrary reference point s \u00bc 0 on the axis (Fig. 1a). Let, at any time t, a reference frame be defined by the unit vectors t, n, b with the origin of the axis of the rod chosen such that t \u00bc qr0\u00f0s; t\u00de qs , (1) where t, n and b are unit tangent, normal and binormal vectors, respectively. The following differential relations among the unit vectors t, n, b can be obtained with the aid of the Frenet formulas [24]: qt=qs \u00bc wn; qn=qs \u00bc tb wt; qb=qs \u00bc tn, (2) where w and t are the curvature and the natural twist of the axis, respectively. In order to take into account the initial twist of the cross-section, a second rectangular Cartesian frame \u00f0x1;x2; x3\u00de is defined such that the x1-axis is in the direction of t, and x2;x3 are the principal axes of the cross-section (Fig. 1b). Let i1; i2 and i3 be the unit vectors along x1;x2 and x3. From Fig. 1b Eq. (3) can be written as t \u00bc i1; n \u00bc i2 cosj i3 sinj; b \u00bc i2 sinj\u00fe i3 cosj. (3) Let the displacement of a point on the rod axis, and the rotation of the cross-section about an axis passing through G be denoted by U0\u00f0s; t\u00de and X0 \u00f0s; t\u00de, respectively. Assuming that the effect of warping is ignored, and that the material of the rod is homogenous, linear elastic and anisotropic the governing equations of a space rod are obtained in vectorial form as [13]: qU0 qs \u00bc A0T0 \u00fe B0M0 \u00fe X0 t; qX0 qs \u00bc F0T0 \u00feD0M0, (4a) qT0 qs \u00fe p\u00f0ex\u00de \u00bc p\u00f0in\u00de; qM0 qs \u00fe t T0 \u00fem\u00f0ex\u00de \u00bc m\u00f0in\u00de, (4b) where the inertia force vector is T0, the inertia moment vector is M0 and p\u00f0ex\u00de and m\u00f0ex\u00de are the external distributed load and external distributed moment vectors per unit length of axis, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003243_physreve.70.026222-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003243_physreve.70.026222-Figure4-1.png",
        "caption": "FIG. 4. First border-collision bifurcation at a=a1 bc=2. Shown are the system function (thick line) and its second iterated function (thin line) before the bifurcation (a) and after the bifurcation (b). (c) is a blowup of the rectangle marked in (b). The dotted lines in (b) and (c) mark the functions f l and fr outside their domains.",
        "texts": [
            " Firstly, the fixed points x4 * and x5 * vanish at the bifurcation point. Note that due to the border collision, these fixed points do not lose their stability as is typical for local bifurcations in smooth maps, but disappear altogether. Secondly, a stable limit cycle with period two emerges. This limit cycle consists of the points 1\u22121/a and 1/a, which were fixed points before the border-collision bifurcation (for this reason we denote this limit cycle hx4 * ,x5 *j). This behavior can be explained taking Fig. 4 into consideration. As one can see from this figure, before the bifurcation the functions f l and fr intersect, the angles bisector in their domains f0,1 /2d and s1/2 ,1g. Hence, these intersection points are fixed points of system (1). After the border-collision bifurcation the intersection points leave the domains where the functions f l and fr have effect, but the second iterated function now intersects the angles bisector at the same points. In addition we remark that the fixed points x4 * and x5 * collide at the bifurcation point, not only with each other, but also with the fixed point x2 *"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001058_a:1017384211491-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001058_a:1017384211491-Figure6-1.png",
        "caption": "Figure 6. Principal sketch of aircraft nose gear.",
        "texts": [
            " In Figure 5 solutions of the analytical and eigenvalue limit cycle methods are compared, showing good coincidence. The limit cycle amplitudes increase with velocity V and decrease with damping coefficient k. The model from the example (see the next section), with secondorder polynomials for the describing functions of the tire and linear functions for all other moments, and parameters of Table 1 (cg = 0, e = 0.1 m) are used. The eigenvalue method is now demonstrated by the example of self-excited shimmy oscillations of an aircraft nose landing gear (see Figure 6). This instability is caused by dynamic reaction forces between elastic tires and the ground. A third-order nonlinear model describes the torsional degree of freedom and the tire elasticity according to elastic string theory. This basic model of the torsional dynamics of the nose landing gear was derived in [11] and investigated using different mathematical methods in [16]. Typical data for an aircraft of 10 tons of weight are used (see Table 1). For yaw angle \u03c8 a second-order differential equation (28) and for slip angle \u03b1 of the elastic tire, a first-order differential equation (29) is set up: Iz\u03c8\u0308 = M1 +M2 +M3 +M4 +M5, (28) \u03b1\u0307 + V \u03c3 \u03b1 = V \u03c3 \u03c8 + (e \u2212 a) \u03c3 \u03c8\u0307"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003825_j.finel.2005.08.001-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003825_j.finel.2005.08.001-Figure9-1.png",
        "caption": "Fig. 9. The real zone of compression.",
        "texts": [
            " It is known that the external force induces in the bolt a force supplement, compared to the initial state of the preload Q. The total working force in the bolt Fb is Fb = Q + Sp2 Sp + Sb Fe (5) with the total flexibility of the part Sp = Sp1 + Sp2. (6) What complicates the computation is that the part flexibility is not uniformly distributed across the thickness. In fact, the image of the compressed zone under the head of bolt, up to the mating plane, appears as a volume approaching the shape of a truncated cone (Fig. 9). To fairly accurate the real situation, an appropriate algorithm is used to calculate the flexibility of a compressed part. Part could be made by two or multiple partitions. Considering a two parts partition case (Fig. 10), the methodology is as follows: 1. Calculate Ap cross-section by improved Rasmussen\u2019s formulation [14], then total part flexibility Ap \u21d2 Sp = Lp ApEp . (7) 2. Calculate Ap1 cross-section by improved Rasmussen\u2019s formulation [14] and the corresponding flexibility, characterized by L1 length Ap1 \u21d2 Sp1 = L1 Ap1Ep "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001931_28.108458-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001931_28.108458-Figure5-1.png",
        "caption": "Fig. 5. Regions S and T.",
        "texts": [
            " Relationship between voltage-error vector and instantaneous space-voltage vector. Fig. 3 . Space-voltage vector. In region B, the zero-voltage vector is selected because v, within H , is small, and furthermore this selection makes it possible to reduce the switching frequency of the inverter. When zero-voltage vector is applied to the induction motor, i,, keeps the almost same value as before and i , , decreases if the motor is in the motor operating region as is obvious from (8) and (9). In region C , both selection methods described in regions A and B are used, (see Fig. 5). Although v, is the voltage vector nearest to v,, this voltage vector should not be selected. Selection of v4 forms a minor loop [2] on the locus of the flux-linkage vector h defined by (17) because v, exists behind the d axis. (17) v = vu + avb + a2vc where a = eJ('*I3) and v,, vb , and vc are the respective potentials at the inverter output terminals. Appearance of many minor loops on the locus increases the switching frequency of the inverter, the iron loss, and the stray load loss P I * In order to find the appropriate selection method, this region is further divided into the two auxiliary regions-the S and T regions-as shown in Fig. 5. And if the voltage vector nearest to v, is located in the S region, this voltage vector can be selected. The voltage vector in the T region should not be selected, whereas the zero-voltage vector can be selected so as not to appear the minor loops on the locus. Consequently, the optimal voltage vector can be selected by combining the selection method based on the position angle of voltage error vector and the method based on the amplitude of voltage error vector. Fig. 6 shows all of the space-voltage vectors this current controller enables the inverter to generate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003784_1.1829070-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003784_1.1829070-Figure2-1.png",
        "caption": "Fig. 2 A schematic diagram of the five-bar linkage",
        "texts": [
            " There are special cases, for example, if the two links belong to a singledegree-of-freedom subchain, or if the two links are physically connected. Special cases, however, will not be considered in this paper by assuming that the motion of link j relative to link i depends on both degrees of freedom of the linkage. Although the instant center I i j is not a unique point in the plane, it is important to note that it is also not an arbitrary point. The two-degree-offreedom five-bar linkage shown in Fig. 2 can be used to illustrate this statement. Here the instant center I14 must lie on the line that 250 \u00d5 Vol. 127, MARCH 2005 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 02/26/20 connects the two primary instant centers I15 and I45 . The exact location of I14 on this line, however, will depend on the angular velocity ratio of the two input links ~for example, links 2 and 5!. An analytical proof that the instant center I i j , shown in Fig. 1, must lie on a unique straight line will now be presented"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002144_j.jsv.2003.05.019-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002144_j.jsv.2003.05.019-Figure1-1.png",
        "caption": "Fig. 1. Schematic cross-section diagram of electro-pneumatic hammer.",
        "texts": [
            " Although research is continuing, there is no effective treatment available for the vascular symptoms of HAVS and there is no treatment for its neurological component. Therefore, hand-transmitted vibration has gained increasing attention in the literature and is now regarded as one of the most important occupational hazards. The electro-pneumatic hammer, which is one of the most representative piston-operated vibrating tools and is widely employed as a concrete breaker, hammer-drill and impact ripper in various areas of industry and construction, is analyzed in the present study. Schematics of the electro-pneumatic hammer is shown in Fig. 1. The electric motor drives the exciting piston via the crank and connecting rod. The reciprocating piston periodically compresses and decompresses the air in the pneumatic chamber, thereby setting the striker in motion. The striker hits the intermediate piston that in turn hits the pick which then hits the material being treated. The pick has a collar that prevents it from going too far into the mechanism after rebounding against the object of treatment. The operator has to press the machine against the object of treatment thereby applying a permanent force (this is called the feed force)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002767_978-3-642-71015-5-Figure2.27-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002767_978-3-642-71015-5-Figure2.27-1.png",
        "caption": "Fig. 2.27. Distribution of magnetic flux density. (--) experimental; (- - - ) assumed",
        "texts": [],
        "surrounding_texts": [
            "r' = a; in the analogous problem this leads to the requirement Re {V~1)} = const for I w'l = a. 2.6 Unipolar Induction - Circular Motion 107 Expanding (2.6.20) for I W'l > m, we obtain [ ) ) 2 1 -(1) . Kzo R m m V z = 1-/1oR - 1 + (- + (- +.. . , 2 Wi Wi Wi (2.6.21) or, for the real component V~1) at I w'l = a, we get V\\I) ~ ~\" Po :' [ : sina'+ ( : )' sin2a' + ( : Y sin3 a'] (2.6.22) This expression is, however, nonzero. The circumference of the circle I w'l = a is thus a source of a so-called \"secondary\" fictitious potential component V~2) which, in conjunction with the \"primary\" V~1), makes the resultant potential at a vanish; in order to offset V~1), the potential V~2) must have the form V\\\" = ~ K; Po :' [ : sina'+ (:)' sin2a'+ (: Y sin3a'] . (2.6.23) The secondary complex potential V~2) must be an analytic function for I w'l < a. Thus, by the Cauchy-Riemann conditions and by (2.6.23), we have V-(2)_. Kzo R2 [(m)2 Wi (m)4(wl)2 z -1--/10- - -+ - - 2 m a m a m + (: )' ( :)' +], or 2 V- (2) _ \u2022 K zO R z - 12/10-;;; which leads to (-S'-)'(~) 1~(:)'(:) , v\\\" = ~~o PoR l : + (:)' w,~a; j (2.6.24) (2.6.25) (2.6.26) Substitution of Wi = w+ m aad expansion of the second term in the bracketed expression yield 108 2, Principles of Magneto-Electric Interactions (2.6.27) Within the pole projection, we obtain from (2.6.19,27) that the resultant complex vector potential component is given by v: - y(l) + y(2) z - z z, (2.6.28) - KzO W Kzo {R ( a )2 R Vz=-, lJ.oR---, lJ.oR --+ - 21 R 21 m m (a2Im)-m (2.6.29) From (2.5.12) - adapted to the surface-current distribution - and owing to the orthogonality of the trigonometric functions, we now obtain by con version to a line integral over the pole contour I (2.6.30) (2.6.31) The power input to the sheet obtained from (2.6.2) therefore reads p=~a..:1(DmB)2nR2(1- (Ria) 2 ) 2 z [1-(mla)2]2 (2.6.32) so that the braking torque Tbr = PI D exerted by the magnet on the rotating sheet is in turn given by T, = ~a..:1 DnR 2m2B2 (1- (Rla)2 ). br 2 z [1-(mla)2]2 (2.6.33) 2.6 Unipolar Induction - Circular Motion 109 2.6.3 Numerical Solution In practice, (2.6.13) may sometimes demand a more sophisticated approach as the spatial distribution Bz = Bz(r) cannot always be approximated by square representations (Fig: 2.27). For such cases, we now outline a numerical approach. Thus, we introduce the notation f(r', a') == - aL1 Qsina aBz(r) , ar (2.6.34) wheref(r', a') is a given function [based on measurements of Bz(r) at points r', a'J. When solving a2D' 1 aD' 1 a2D' --+- --+- --=f(r', a') , ar,2 r' ar' r,2 aa' (2.6.35) subject to the boundary condition D' = const for r' = a, we consider first the eigenvalue problem a2D' 1 aD' 1 a2D' __ + ___ + ___ = _)..2D , ar,2 r' ar' r,2 aa' (2.6.36) with).. 2 (eigenvalue) still undetermined. For symmetrical conditions with respect to the angle a', we assume a solution of the form D' = R (r') sinqa' , (2.6.37) where q is an integer and the function R (r') satisfies the Bessel equation (2.6.38) ---,.-=.---.-;---+-.--+-.--t-r--.--.---T\"'-\"!-----'3I- radius r [cmJ 6543210 3 4 5 6 R 110 2. Principles of Magneto-Electric Interactions The solution of this equation (convergent at r' = 0) is given by the Bessel function of first kind, order q: (2.6.39) where the amplitude D~, A needs still to be determined. By extending the definition of D' to the circular case, we have A ~ = - oD'/or'; vanishing of the current density at r' = a therefore imposes the condition dJq(Ar') I =0 dr' r' =a (2.6.40) Denoting by uq, n = Aq, na the nth (positively increasing) solution of this equation, we obtain A = uq,n q,n a (2.6.41) On changing the hitherto general notation D~,A to one adapted to the specific number n, we obtain D'= ~ ~ D~,nSin(qa')Jq(uq,n~) . q=On=l a (2.6.42) The functions in this equation are orthogonal, and we expand 1(r', a') in a series of this form by means of the coefficients Cq, n: 1(r', a') = ~ ~ Cq,nsin(qa')Jq (uq,n~) , q=On=l a (2.6.43) in which Cq,n = (2.6.44) The coefficients Cq,n are obtainable for given values of oBzlor. Setting now - (A q,n)2 D' = 1(r', a') , (2.6.45) we finally obtain, by means of (2.6.42,43) D~,n = _ (_a_)2 Cq,n . uq,n (2.6.46) 100 80 60 40 20 2.6 Unipolar Induction - Circular Motion 111 Fig. 2.28. Damping constant T I Q as function of dimensionless distance ml a between disk axis and pole-face centre. (a) Experimental. (b) Calculated from (2.6.33). (c) Numerical evaluation L....l_---L_J __ J ___ l_~ _ ___L__~ o 20 40 60 80 100 mjc[%J Once D' is known, the power P dissipated in the rotating disk is readily calculated, and the braking torque T = PI Q is obtained in a straightforward manner. Some relevant results are reproduced in Fig. 2.28, which is plotted in terms of the braking constant T I Q."
        ]
    },
    {
        "image_filename": "designv11_11_0002997_j.mechmachtheory.2004.02.005-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002997_j.mechmachtheory.2004.02.005-Figure10-1.png",
        "caption": "Fig. 10. Three-dimensional simulation of new type of beveloid gears.",
        "texts": [
            " The profile errors are different at the two ends of tooth of gear 2, but they can be reduced if the pressure angle can be changed. This will be difficult for the gear manufacturing, especially for tooth profile modification. By means of analysis of axial and tooth profile errors, the tooth profile of gear 2 can be determined. The paper has finished the simulation of the noninvolute beveloid gears by means of Pro/ Engineer CAD system. The steps are shown as Fig. 9 and the simulation is shown as Fig. 10. Based on space engagement theory and differential geometry, this paper has developed the noninvolute beveloid gear model with line contact in mesh with intersecting axes. Meanwhile the paper has presented the tooth profile equation and engagement equation. In particular, the paper has developed the method to calculate the axial and profile errors. From the work, we can draw the conclusion that the tooth profile errors are far less than axial errors. The profile errors are allowable in general in gearing in most machine tools"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002614_0301-679x(87)90094-6-Figure23-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002614_0301-679x(87)90094-6-Figure23-1.png",
        "caption": "Fig 23 Typical deterministic mierogeometry models o f the contact surfaces o f conventional oil seals under sealing and leaking conditions",
        "texts": [
            " (4) The interpretation of n/No > 104 is to show that the mutual interferences between microasperities is the necessary factor to maintain the sealing ability. In order to satisfy the relationship of n/No > 104 , it is necessary that the distance between two microasperities is estimated to be approximately 0.05 mm. Keeping the above four clauses in mind, and sketching the geometrical structure of the microasperities on contact surfaces under dynamic contact conditions, it is considered that the basic structure, as shown in Fig 23, will be the typical example. Conversely, limiting the object of the dynamic behaviour of contact surfaces, which create leakage, into the L2 region of Fig 14, this region will have similar parameter values to those of region S~ except that M1 will be changed from the condition of > 0 to < 0. A typical example of the model for contact surfaces, therefore, is considered to be the basic structure in Fig 23. At present, the compositions of materials for oil seals are designed in order to maintain a small value of N1/No. Unless composition design is mistaken, the leakage phenomenon of L~ region in Fig 14 will not occur. It will be sufficient, therefore, to clarify the basic structure of contact surfaces in the L2 and S~ regions. Investigation of adequacy of theoretical contact surface configuration according to model seal I I Model seals II which have a theoretical microgeometrical structure of contact surfaces as shown in Fig 24 were manufactured"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001937_7.303744-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001937_7.303744-Figure1-1.png",
        "caption": "Fig. 1. Bending structure example [5].",
        "texts": [
            "19 m in diameter and has a deformable mirror mounted upon it. Three legs (tripod) connect the bulkhead to the smaller secondary mirror assembly (SMA) which is 1.32 m in diameter and whereupon a smaller mirror is mounted. The overall height of the structure is 8.14 m. Ensuring the SMA and the bulkhead are aligned is of vital importance; thus, measuring and reducing linear and angular displacement is the purpose of the sensors and actuators. An exaggerated example of the bulkhead and SMA not being aligned is shown in Fig. 1. Note that the alignment is not altered by a pure torsional force about the line of sight (LOS) axis. The actuators employed are called proof mass actuators (PMAs). A PMA has a mass that is moved by an electromagnetic force. This mass is moved to inhibit the bending of the structure at the location of the PMA. There are 18 PMAS located on the structure. Six are mounted in a vertical position at each of the \u201chexagonal points\u201d on the bulkhead. The remaining 12 PMAs are located on the tripod. Each leg of the tripod has an x-axis and y-axis PMA located at one-third and two-thirds the length of the leg"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003701_095440705x6406-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003701_095440705x6406-Figure3-1.png",
        "caption": "Fig. 3 Power and speed characteristics for the IRC HMT",
        "texts": [
            " In the actual HMT application, the HSUand 2 and the motor, ST is the pump stroke and Z r power P h is limited due to the pressure limit andand Z s are the number of ring and sun gear teeth the HSU efficiency, so \u22122 ratio is only possible inrespectively. Efficiencies of the TM elements and theory. From SR=0 to SR=0.25, H shows a negativeHSU can be included, but in this study it is assumed value. The negative ratio means that the directionthat no loss exists in every TM element. of the HSU power is reversed; in other words, theIn Fig. 3, network analysis results for the IRC type power flows from node #5 to node #1 (Fig. 2), whichHMT in Fig. 2 are shown. In Fig. 3, the HSU power means that the power circulates, forming a closedP h , HSU motor torque T m , pump speed v p and the loop. When H has a negative value, the mechanicalmotor speedv m are plotted in non-dimensional form power P m that passes through the mechanical part isusing the input power P in , the input torque T in and represented as the summation of the input power P in the input speed v in . In Fig. 3, H is the ratio of the and P h . For instance, when H=\u22120.56 at SR=0.16HSU power to the input power and M is the ratio the mechanical power ratio is obtained as M=1.56,of the mechanical power that flows through the which is greater than the input power. This meansmechanical part to the input power. The speed ratio that 156 per cent of the input power passes throughSR is defined as the ratio of the transmission output speed to the input speed. H becomes\u22122 at a speed the mechanical part due to the negative HSU power. D20703 \u00a9 IMechE 2005 Proc. IMechE. Vol. 219 Part D: J. Automobile Engineering at UNIV OF MICHIGAN on July 14, 2015pid.sagepub.comDownloaded from At SR=0, the motor torque ratio, T m /T in , shows through the HSU becomes 75 per cent of the input power and the remaining 25 per cent flows through+2 and decreases as the speed ratio SR increases. This infinite torque ratio is obtained since the the mechanical part. From Fig. 3, it is observed that the HSU power ratio H is less than 1 for SR 0.25.HSU efficiency is not considered in the calculation. Generally, the HSU efficiency is very low at the speed In Fig. 4, the power and speed characteristics are analysed for an SRO type HMT in Fig. 1 by (a) theratio SR=0; therefore the infinite torque ratio cannot be obtained in an actual application. The high network analysis and the results are compared with those by (b) Nomura\u2019s graphical analysis. In calcu-motor torque is not acceptable from the viewpoint of the machine element design"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002688_crv.2005.81-Figure10-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002688_crv.2005.81-Figure10-1.png",
        "caption": "Figure 10. Analytical (a), inferred (b) and inferred with source/sink node (c) topological maps.",
        "texts": [
            " The data were collected during a typical weekday for a period of five hours from 10:00am to 2:30 pm. In addition to the normal traffic Proceedings of the Second Canadian Conference on Computer and Robot Vision (CRV\u201905) 0-7695-2319-6/05 $ 20.00 IEEE one or two subjects were encouraged to stroll about the region from time to time during the collection period in order to increase the density of observations. In total, about 1800 timestamped events were collected. Ground truth values were calculated in order to assess the results inferred by the approach. A topological map of the environment (Figure 10(a)) was determined based on an analysis of the sensor network layout shown in Figure 8. Inter-vertex transitions times for the connected sensors were recorded with a stopwatch for a typical subject walking at a normal speed (Table 1). The results obtained by running the new topology inference algorithm on the experimental data correspond closely to the ground truth values. Figure 10(b) shows the topological map obtained by thresholding the inferred transition matrix. 3 3The number of agents was selected to be an estimate of the most likely Disregarding self-connections, the difference between the inferred and deduced matrices amounts to a Hamming error of 1. The inferred connection from D to B was not given a transition probability large enough to be detected based on our thresholding technique. However, the opposite edge from B to D was correctly inferred. Of course, it would be easy to build into the algorithm the assumption that all edges must be two ways",
            " The selfconnection inferred to this node is due to a detected correlation in the delay between exit times and subsequent re-entry times for agent motion. In fact, this correlation is due to the tendency of subjects to re-enter the system after roughly the same time period (e.g. to use the washroom or photocopier). Therefore, the detection of this connection was actually a correct inference on the part of the algorithm. It is interesting to note that two-way connections were inferred to the source/sink node from both sensors D and F (Figure 10(c)). It was possible for subjects to pass by either of these sensors on their way into or out of the monitored region. (The exit to the far right of the area, shown in Figure 8, was little used.) This demonstrates the function of the source/sink node as a method for the algorithm to explain sudden appearances and disappearance of agents in the system. number of people in the system at any time (3), the SSLLH paramter was set to \u22125, and a threshold value of \u03b8 = 0.1 was used to obtain the topological map Proceedings of the Second Canadian Conference on Computer and Robot Vision (CRV\u201905) 0-7695-2319-6/05 $ 20"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001904_iros.2001.976254-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001904_iros.2001.976254-Figure9-1.png",
        "caption": "Figure 9: Three-link jumping machine",
        "texts": [
            " It indicates that the posture of the jumping machine was controlled well. In Fig.8, (i) shows the acceleration of the ground surface with the soft landing movement, and (ii) shows that without the soft landing movement. It is clear that the impact received from the jumping machine in (i) is smaller than that in (ii). These experimental results show obviously that the proposed scheme is effective to perform the soft landing movement. 4 Three-link Jumping Machine In the next stage of our research, the other pendulum-type jumping machine is considered as in Fig.9. The jumping machine is expected that this pendulum-type jumping machine is able to jump up a stair and move to the required direc- tion by means of the different swings of arms. It consists of three links and two servo motors. Link1 is shaped into \u2019Y\u2019 and regarded as the body of the jumping machine. The foot of the jumping machine is short. The other links are jointed to the both sides of Link-1 and regarded as the arms of the jumping machine. The both ends of the arms are equipped with weights"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002525_s0022-460x(85)80146-2-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002525_s0022-460x(85)80146-2-Figure6-1.png",
        "caption": "Figure 6. A meridionally symmetric mode for N = 0 with dominant motion in circumferential direction ( M V = i). (a) tlalf-section view; (b) side view.",
        "texts": [],
        "surrounding_texts": [
            "In the present study, a graphics software has been developed to display tire natural mode shapes in 3-D in order to interpret the eigenvectors generated by the free vibration analysis. To illustrate those mode shapes in an easy-to-visualize manner, it is imagined that a tire is cut along a meridional line and then opened up to become a rectangular plate. The two sides of the plate are either simply supported or fixed, depending on the tire boundary condition assumed at the wheel rim. The other two sides of the plate are free to move but the displacements at the corresponding positions must be compatible. As explained earlier, four modal numbers, N, MW, M U and MV, may be used, either in part or all together, to identify a mode shape. The circumferential wavenumber N indicates the number of-full harmonic variations around the tire circumference. The meridional wavenumbers MW, M U and M V designate the number of half waves in the transverse, meridional and circumferential displacements, respectively, along a bead-tobead meridional line. Figures 5(a) and (b) illustrate two meridionally symmetric mode shapes characterized by these four modal numbers. The mode shape in Figure 5(a) is dominated by transverse motion and the mode shape in Figure 5(b) is dominated by tangential motion. An odd number in M W and M V or an even number in M U signifies L. E. KUNG E T AI . . 338 a meridionally symmetric mode shape, as shown in Figures 5(a) and (b), while the opposite signifies a meridionally skew-symmetric mode shape. The 3-D graphical display software was then used to study the predicted natural mode shapes. Figures 6(a) and 7(a) display two major spin modes for N = 0. It is noted that the 3-D tire mode shapes presented in this paper are exceptionally enlarged for the purpose of illustration. Since the displacements ofthe two modes are in the circumferential direction, their side views, as shown in Figures 6(b) and 7(b), further illustrate the details of these mode shapes. In order to observe the N = 1 transverse mode shown in Figure 8(a), the same view with 90-degree rotation about the tire axis, as shown in Figure 8(b), appears to be quite informative. It is of interest to illustrate a natural mode shape composed of displacements in all the w, u and o directions. The side view of one of these mode shapes is shown in Figure 9(a), and a half-section view is shown in Figure 9(b). Since the present computer graphics software can plot the 3-D views for any mode shape from the various viewing angles, a more thorough understanding of the tire natural mode shapes can be achieved."
        ]
    },
    {
        "image_filename": "designv11_11_0002720_acc.2005.1470274-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002720_acc.2005.1470274-Figure7-1.png",
        "caption": "Fig. 7. Phase Portrait when Reference Modification is Switched Off",
        "texts": [
            " Now, the diverging tendency due to the state dominates the restoring tendency that the control can provide, and the state diverges to infinity as seen in Fig.4. From Fig.5 we see that the control also diverges to infinity and the adaptive parameters settle down to one of the parameter bounds. In this simulation the instability protection is on, but the reference modification is turned off. From Fig.6 we see that the tracking error is bounded and asymptotically approaches zero as the reference trajectory lies in the trackable region and within the estimated points of no return. Fig.7 shows that the state is restricted well within the points of no return, because the points of no return pnr and the stabilizing control us are conservatively estimated from a\u0304 and b\u0304. This is the best that can be done with the imprecise knowledge of the system parameters a\u2217 and b\u2217. The adaptive parameters oscillate haphazardly between the bounds as seen from Fig.8. However, the transition of the control uc between ut and us is smooth and no control chattering is seen. C. Case 3: Instability Protection & Reference Modification Switched On In this simulation both the instability protection and the reference modification are turned on. The tracking error is bounded and asymptotically approaches zero as the original desired reference lies in the trackable region and within the points of no return, as shown in Fig.9. From Fig.10 we see that the controller does a better job of tracking than in Fig.7. Fig.11 shows that the estimated parameters converge to the true parameters. This is because the reference is persistently exciting and may not be true otherwise. VII. CONCLUSIONS AND FUTURE RESEARCH This paper presented a methodology for stable adaptation in the presence of control position limits for scalar linear time invariant systems with uncertain parameters. For unstable systems, the paper identifies the points of no return and proposes a switching control strategy to restrict the state within the points of no return"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000765_s0043-1648(02)00108-4-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000765_s0043-1648(02)00108-4-Figure3-1.png",
        "caption": "Fig. 3. (a) Contact surfaces of bodies in rolling contact before deformation and (b) the situation after deformation.",
        "texts": [
            " The numerical results obtained show marked differences between the creep forces of wheelset/rail under two kinds of the conditions that effects of the SED are taken into consideration and neglected. In order to make better understanding of effects of the SED of wheelset/track on rolling contact of wheel/rail it is necessary that we briefly explain the mechanism of reduced contact stiffness increasing the ratio of stick/slip area in a contact area under the condition of unsaturated creep-force. Generally the total slip between a pair of contact particles in a contact area contains the rigid slip, the local elastic deformation in a contact area and the SED. Fig. 3a describes the status of a pair of the contact particles, A1 and A2, of rolling contact bodies and without elastic deformation. The lines, A1A \u2032 1 and A2A \u2032 2 in Fig. 3a, are marked in order to make a good understanding of the description. After the deformations of the bodies take place, the positions and deformations of lines, A1A \u2032 1 and A2A \u2032 2, are shown in Fig. 3b. The displacement difference,w1, between the two dash lines in Fig. 3b is caused by the rigid motions of the bodies and (rolling or shift). The local elastic deformations of points, A1 and A2, are indicated by u11 and u21, which are determined with some of the present theories of rolling contact based on the assumption of elastic-half space, they make the difference of elastic displacement between point A1 and point A2, u1 = u11 \u2212 u21. If the effects of structure elastic deformations of bodies and are neglected the total slip between points, A1 and A2, can read as: S1 = w1 \u2212 u1 = w1 \u2212 (u11 \u2212 u21) (1) The structure elastic deformations of bodies and are mainly caused by traction, p and p\u2032 acting on the contact patch and the other boundary conditions of bodies and , they make lines, A1A \u2032 1 and A2A \u2032 2 generate rigid motions independent of the local coordinates (ox1x3, see Fig. 3a) in the contact area. The u10 and u20 are used to express the displacements of point A1 and point A2, respectively, due to the structure elastic deformations. At any loading step they can be treated as constants with respect to the local coordinates for prescribed boundary conditions and geometry of bodies and . The displacement difference between point A1 and point A2, due to u10 and u20, should be u0 = u10 \u2212 u20. So under the condition of considering the structural elastic deformations of bodies and , the total slip between points, A1 and A2, can be written as: S\u2217 1 = w1 \u2212 u1 \u2212 u0 (2) It is obvious that S1 and S\u2217 1 are different"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001146_319-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001146_319-Figure1-1.png",
        "caption": "Figure 1. Deep penetration laser welding processes.",
        "texts": [
            " As a result, the measurement with only one in-line sensor is not effective in distinguishing different welding conditions unless the plasma plume is weak and the plasma inside the keyhole is distributed uniformly such as in those shallow penetration cases in Beersiek et al (1997). One way to distinguish different plasma emission contributions is to look into the keyhole from different viewing angles simultaneously. Miyamoto and Mori (1995) proposed an idea to \u2018peek\u2019 into a keyhole using not one but several photodiodes arranged at different angles (figure 1). Each photodiode provides a partial view into the keyhole and a photodiode can \u2018peek\u2019 deeper into the keyhole if it is arranged at a higher angle with respect to the horizontal axis. Because each photodiode \u2018peeks\u2019 into different portions of the keyhole, it is feasible to re-establish the plasma intensity distribution inside the keyhole by comparing the signals measured at different angles. Such a technique has been used to predict the penetration depth of thick section sheets of steels for both 20 kW CO2 and 8 kW Nd : YAG lasers (Ikeda et al 1999, Inoue et al 1999)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002687_20.42274-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002687_20.42274-Figure1-1.png",
        "caption": "Fig. 1. The pracucal machine",
        "texts": [
            " Yamamoto analysed the starting characteristics of a flat type permanent magnet pulse driven machine using equivalent magnetic circuits and analytical expressions for one-way motion [7]. Yoshida simulated the performance of a flat-type long stator linear synchronous motor analytically using per phase equivalent circuits [8]. However, the simulation is based on a preset duty-cycle and does not include the phase variables and the dynamic performance of the system. A Practical Svstem The Tubular Motor : Construction and Coeeine Forces The practical machine shown in Figure 1 has been constructed. It is a shortstator type with two poles on the stator and four on the rotor [9]. The stator has four laminated blocks and uses open slots. This facilitates construction; the blocks can be assembled over the six circular stator coils which are connected in the conventional sequence. The rotor is stepskewed in order to eliminate unwanted tooth-cogging forces. It will be observed from the figure that three segments each spanning 120\u00b0 are arranged around the periphery to form one pole of the machine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002264_0379-6779(89)90497-9-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002264_0379-6779(89)90497-9-Figure4-1.png",
        "caption": "Fig. 4. Cyclovoltammetric curves for the doping/undoping process with PPy layers, d n = 1 ~n, 0.i M NBu4BF 4 in MeCN, i0 mM HzO , v s = 20 mV s -l. The PPy was galvanostatically electrodeposited in the same electrolyte, containing 0.1 M Py in addition:",
        "texts": [
            " Nevertheless, there must be some interaction with the Py, for a comparison of the ct~rves (3a) and (3bl reveal a higher prewave for the latter, thus indicating a current _~nplification n~.chanism. A possible explanation could be a slow formation o\u00b1 ~ohlb]e prcx~tlcts under the mild conditions of oxidation. Influence on the dopinq/undopinq process To our surprise, the water effect on the electrodeposition of PPy additionally yields a very pronounced change in the reversible cyclovoltammetric curve for the doping/undoping process. Fig. 4 displays an example for the system with NBu4BF4 as the supporting electrolyte. Both polypyrrole layers are galvanostatically electrodeposited, the first with a low current density in the region of the prewave, the second with a higher current density in the region of the positive branch. In spite of the same nominal thickness d n = 1 pm /5/, it is only the former which yields the standard curve, reported very frequently in the literature /3, 4, 6, I0 - 13/. The latter has a much lo~r redox capacity and the sharp anodic peak at the beglnning of the doping process disappears. The electrodeposition at the beginning of the anodic overoxidation clearly yields a noncharacteristic material. Nevertheless, the redox process remains to be reversible. There is nearly no effect on the specific features of the corresponding curves on substituting NBu4CI04, LiBF 4 or LiCIO4 for t/~e electrolyte NBL~IBF, I employed in case of Fig. 4. (i) j = 0.2 mA ~-2 (2) j = 2.0 mAcro -2 The first discharge at 2 mV/s is drawn as a dashed line. A typical cyclovoltammetric doping/undoping curve for an analogous experiment, but with electrodeposition in the presence of 1 n%M Br-, at 2 mAcm -2 is shown in Fig. 5. A new feature appears as a second cathodic peak, just symmetrical to the anodic peak, as it is standard for an adsorbed redox system. All peaks and even that for the first discharge are sharper. Surprisingly, the redox system Br-/Brz, positive to the potential regime of the reversible curve shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002520_0005-2736(90)90004-8-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002520_0005-2736(90)90004-8-Figure1-1.png",
        "caption": "Fig. 1. Effect of iron ions, salicylate and benzoate on NADH oxidation in radish plasmalemma-enriched vesicles. Additions were: 4 mM NADH, 40 /~M FeSO4.7 HzO, 40 /~M FeCI3.6 H20 or a mixture (1 : 1) of both (trace A); 15 mM salicylate (trace B); 15 mM benzoate (trace C); 30 mM salicylate (trace D); 30 mM benzoate (trace E). Figures next to each trace are expressed in nmol O2/mg protein per min and are representative of one typical experiment.",
        "texts": [
            "7), deferoxamine melysate, EDTA, 4-aminoantipyrine, 1,10-o-phenan- throline were purchased from Sigma Chemical, St. Louis, MO, U.S.A. Sodium benzoate and sodium salicylate were from Merck, Darmstadt , F.R.G. Epinephrine was obtained from Fluka Chemic, Buchs, Switzerland. Other chemicals were reagent grade. In a preceding work we showed that radish plasma membrane vesicles sustain an NAD(P)H-dependent oxygen uptake which is stimulated by ferrous ions and inhibited by catalase or superoxide dismutase, thus indicating the involvement of the superoxide anion and hydrogen peroxide [32]. Fig. 1, trace A, also shows that NADH-dependent oxygen consumption ( N A D H oxidation) was strongly stimulated by Fe 2+ and, to a lesser extent, by Fe 3+. An intermediate value was obtained by using a mixture (1 :1) of Fe 2+ and Fe 3+. Salicylate and benzoate, two hydroxyl radical scavengers, partially inhibited the basal and the Fe2+-stimulated N A D H oxidation (traces B and C). This inhibition was also evident if the scavengers were added during Fe2+-stimulated N A D H oxidation (traces D and E). The need of trace iron ions for N A D H oxidase activity in our membrane preparat ion has been already demonstrated [32]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003091_taes.2005.1541428-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003091_taes.2005.1541428-Figure1-1.png",
        "caption": "Fig. 1. Orbital and satellite coordinate systems.",
        "texts": [
            " In the closed-loop system, prescribed pitch angle reference trajectories are asymptotically tracked in spite of the uncertainties in the system. The control system includes dynamic feedback for parameter adaptation. The organization of this paper is as follows. Section II describes the mathematical model and the control problem. A nonlinear adaptive feedback control law is derived in Section III, and simulation results are presented in Section IV. Consider an unsymmetrical satellite with its center of mass S moving in a circular orbit about the Earth\u2019s center O (Fig. 1) for simplicity. (The modification required for the spacecraft in an elliptical orbit is indicated later.) The inertial frame XYZ has its Y axis pointing towards ascending node, and Y\u00a1Z defines the orbital plane. The unit vector e\u0304 is along the Earth-Sun line. The rotating orbital frame xoyozo has its xo axis normal to the orbital plane, yo axis is along the local vertical, and zo axis is normal to the local vertical and lies in the orbital plane. The coordinate system xbybzb is fixed to the satellite body, with yb and zb axes in the orbit plane and xb axis normal to the orbit plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001820_6.2003-5727-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001820_6.2003-5727-Figure2-1.png",
        "caption": "Figure 2. Banked Horizontal Turn",
        "texts": [
            " We apply the approach described in the previous section to construct an adaptive formation controller. But first we discuss some modeling issues. The formation of vehicles is constrained to lie in a twodimensional plane. The vehicles are considered to be point-mass objects that can accelerate both along and perpendicular to the direction of motion. In the following section, the equations of motion for a single vehicle are developed. Vehicle Dynamics Consider the equations of motion of an aircraft in the horizontal plane. 6 American Institute of Aeronautics and Astronautics With reference to figure 2, the equations of motion are given by, \u03c6\u03c8 sinLmV = (21) DTVm \u2212= (22) \u03c6cosLmg = (23) where V,\u03c8 represent the heading and speed of the aircraft with respect to an inertial frame that will be specified later, \u03c6,m represent the mass and bank angle, DTL ,, represent the lift, thrust and drag forces on the aircraft and g is the acceleration due to gravity. Eliminating \u03c6 from eqs. (21) and (23), 12 \u2212= n V g\u03c8 (24) g W DT V \u2212= (25) where = W L n is the load-factor of the aircraft. Equations (24) and (25) can be non-dimensionalized by letting = o o R V tt ' and ( )oVVV =' represent non- dimensional time and speed, where oV and oR are constant quantities with units of speed and distance respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001358_s0094-114x(03)00090-9-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001358_s0094-114x(03)00090-9-Figure7-1.png",
        "caption": "Fig. 7. Triad with three external prismatic joints.",
        "texts": [
            " Also E belongs to the straight line parallel to the sliding direction of the external prismatic joint. The intersection of the sextic curve with a straight line will be at six real intersection points at most and therefore the maximum number of the assembly modes of the triad is six. This procedure can be applied for six kinds of the Assur group of class 3 with one internal and one external prismatic joint. In this section, the position analysis of the Assur group with three external prismatic joints is developed (Fig. 7). The coordinates of auxiliary points A1, A2, A3 situated on sliding direction of the external prismatic joints, with the respect to an arbitrary reference system Oxy, are known. Also, the lengths lB1B2, lB1B3, lB2B3 of ternary link, the distances d1, d2, d3 and the angles h1, h2, h3 are given. The position of the triad links is described by a small number of parameters, as the displacements s1, s2 and s3. The constraint equations to be solved are: \u00f0xB2 xB1\u00de2 \u00fe \u00f0yB2 yB1\u00de2 \u00bc l2B1B2 \u00f052\u00de \u00f0xB1 xB3\u00de2 \u00fe \u00f0yB1 yB3\u00de2 \u00bc l2B1B3 \u00f053\u00de \u00f0xB3 xB2\u00de2 \u00fe \u00f0yB3 yB2\u00de2 \u00bc l2B2B3 \u00f054\u00de In Eqs",
            " (57) and (58), using the Sylvester theorem, one can eliminate s1 from these equations yielding: F12\u00f0s2; s3\u00de \u00bc 0 \u00f060\u00de Again, using Sylvester theorem and eliminating the variable s2 from Eqs. (59) and (60) yields the eighth order final polynomial equation in the only unknown s3: X8 i\u00bc0 Pisi3 \u00bc 0 \u00f061\u00de Eq. (61) provides eight roots for s3 in the complex field from which maximum two real solutions lead to real solutions for displacements s1 and s2. This can be confirmed considering that the internal joint B3 (see Fig. 7) lies on the second order curve of the four-bar mechanism C1B1B2C2 of the PRRP type [2]. Also B3 belongs to the straight line parallel to the sliding direction of the external prismatic joint C3. The point B3 is the intersection point of the second order curve with a straight line and two real intersection points exist at most. Therefore the maximum number of the assembly modes of the triad with three external prismatic joints is two. Finally, using Eqs. (55) and (56) the coordinates of the internal joints B1, B2 and B3 are calculated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000396_(sici)1521-4109(199812)10:18<1281::aid-elan1281>3.0.co;2-i-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000396_(sici)1521-4109(199812)10:18<1281::aid-elan1281>3.0.co;2-i-Figure2-1.png",
        "caption": "Fig. 2. Magnified view of the cell set-up for application of organic solvents and aggressive materials based on an inert polymer tube and a Viton O-ring used to tighten the tube around the shaft of the working electrode. a) working electrode, b) Teflon or KelF tube, c) counter and pseudoreference electrode, d) O-ring.",
        "texts": [
            " The volume of the electrolyte is determined by a tube which is placed over the working electrode. The material of the tube has of course to be selected according to the used solvent. For aqueous solutions which are usually used for the entrapment of biological recognition elements within conducting polymer films anyway, a polyethylene (PE) tube is sufficient, while for some organic solvents the tube material has to be Teflon, KelF etc. In the latter case, the tube can be tightened around the working electrode shaft using a Viton O-ring (Fig. 2). The working electrode is placed inside the cell body of the whole set-up by means of a screw-cap. The glass body of the cell can be connected via two glass valves and vacuum tubes to a vacuum/argon line. This allows the independent evacuation of the half-cells, their flushing with argon and the connection of the top- and bottom-part of the cell under outflow of argon. This arrangement allows one to adjust the height of the working electrode inside the glass body to place the counter and reference electrodes into the microcell volume"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002348_robot.1994.351251-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002348_robot.1994.351251-Figure9-1.png",
        "caption": "Figure 9: A visualization of the evaluating function in case it is assumed that the wall can be extended.",
        "texts": [
            "1 Determining the sensing point for wall extension The first condition for the determining the sensing point is to explore along the extended line of a known wall. Our method uses the evaluating function p t l ( s , y), which becomes maximum on the line when a point extended 30cm from the known wall can be observed. d i s t ( i ) - d/30 for d 5 30, - { 1 - ( d - 30)/90 for 30 < d < 120, (2) where d is the distance between the edge of a line segment and the foot of the perpendicular drawn from the point of (x,y) to the line i. A visualization of this evaluating function is shown in Fig.9. Moreover, the evaluating function is multiplied by the distance from the robot in order to reduce the amount of the movement by the robot. p t l ( z , y) = p t l ( z , y) x (1 - d i ~ t / 5 0 0 ) , (3) where d i s t is the distance between the coordinates of the robot and the point (z,y). The robot moves to the grid in whose evaluating function has the highest value. 4.3.2 Determining the sensing point for wall flnding When no extendable wall exists or sensing the extended line of detected wall is impossible, the sensing point is determined near possible occupied area and unknown area boundary"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002171_insi.46.12.758.54491-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002171_insi.46.12.758.54491-Figure1-1.png",
        "caption": "Figure 1. Test bearing with sensors",
        "texts": [
            " The bearing test rig employed for this study had a maximum load capability of 16 kN via a hydraulic ram. The test bearing employed was a Cooper split-type roller bearing (01B40MEX). The split-type bearing was selected as it allowed defects to be \u2018seeded\u2019 onto the races, furthermore, assembly and disassembly of the bearing was accomplished with minimum disruption to the test sequence. The transducers employed for vibration and AE data acquisition were placed directly on the housing of the bearing, see Figure 1. A piezoelectric type AE sensor (Physical Acoustic Corporation type WD) with an operating frequency range of 100 kHz\u20131000 kHz was employed whilst a resonant type accelerometer, with a flat frequency response between 10 and 8000 Hz (Model 236 Isobase accelerometer, \u2018Endevco Dynamic Instrument Division\u2019) was used for vibration measurement. Pre-amplification of the acoustic emission signal was set at 40 dB. The signal output from the pre- amplifier was connected directly to a \u2018Physical Acoustics\u2019 AEDSP data acquisition card"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002698_tmag.2005.844348-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002698_tmag.2005.844348-Figure2-1.png",
        "caption": "Fig. 2. Magnetic circuit with a 3-tooth FE structure (half the actual structure on one side of symmetry plane ; dimensions are given in mm; traces of a",
        "texts": [
            " Magnetostatic and magnetodynamic applications are considered, with the aim to illustrate and validate the developed dual methods. The application examples consist of magnetic systems coupling FE and lumped element regions. Magnetic fluxes and MMFs are associated with each member in both regions and their coupling is defined through a given magnetic circuit topology. For a first problem, the 3-D FE region is chosen as a portion of a variable reluctance structure gathering three teeth and an airgap (Fig. 2), for which fluxes and MMFs are expressed as unknown nonlocal quantities depending on the whole system behavior. The complementary parts of the system are the lumped element regions including the necessary MMF sources and lumped reluctances with pre-defined values. Computed MMF-flux ratios are given in Fig. 3, which points out the correct convergence of both formulations when increasing the number of degrees of freedom. A second problem concerns a T-joint of a transformer with a particular layout of laminations (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.57-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.57-1.png",
        "caption": "Figure 3.57 Section of the 'deltawrap' flywheel designed by Union Carbide Corp. (Right) Showing thickness of the plates and angle between the fibres and the circumferential direction as functions of the radius in the flywheel. (Knight, [77-30])",
        "texts": [
            " Tension balanced spokes have low radial stiffness and are quite strong. As an example, fibreglass-epoxy spokes have a lower elastic modulus but roughly the same strength as graphite epoxy rims. With suitable design it is possible to match the hub and the rim displacements. A completely different approach is to connect the rim to the disc at the outer radius. This is done by overwrapping the rim with suitable filamentary composite materials. These overwrappings are usually made into two complete plates. The 'deltawrap' flywheel shown in Figure 3.57 is an example of this type of rotor. The advantage of overwrapping the rim with a composite material structure is that if the compatibility of the displacements between the rim and the plates is not satisfied, radial compressive stresses result in the rim. The plates will, however, be heavily loaded and their design must be extremely accurate in order to allow a regular working of the assembly. The parameters which can be used in order to achieve the stress distribution are numerous: the plates can be made with varying thickness, fibre content and orientation simply by using internal moulds and controlling the temperature, tension and winding angle during the construction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000147_s0003-2670(98)00368-7-Figure9-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000147_s0003-2670(98)00368-7-Figure9-1.png",
        "caption": "Fig. 9. Amperometric response for NH 4 at 358C and 408C. Other conditions: GLDH 1.4 U ml\u00ff1; NADH 1.7 10\u00ff4 M; 2-oxoglutarate 2.5 10\u00ff3 M; NH 4 14 10\u00ff5 M; pH 8.3.",
        "texts": [
            " Table 1 summarises the performance characteristics for the assay under the stated conditions. In the next part of this investigation the effect of temperature on the response at constant concentration of reactants was studied. We observed a linear increase 4.2 10\u00ff5 M; pH 8.3. in the reaction rate when the temperature of the solution was increased from 168C to 358C; a change in temperature of 1.08C increased the response rate by around 0.166 nA s\u00ff1. However, at 408C loss in enzyme activity occurred soon after the reaction had commenced as indicated in Fig. 9. This behaviour suggests that at temperatures >408C the enzyme starts to unfold as a result of the breaking of hydrophobic bonds as well as other structural changes. The amperometric assay was performed on samples of tap and pond water before and after spiking with ammonium ions at a concentration of 5 10\u00ff6 M. For these determinations the buffer pH was 8.3 and the temperature was 208C; the concentration of enzyme was 5.8 U ml\u00ff1, and the concentrations of 2-oxoglutarate and NADH were 2.5 10\u00ff3 and 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003335_0020-7403(81)90025-4-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003335_0020-7403(81)90025-4-Figure6-1.png",
        "caption": "FIG. 6. Quadrilateral figure. The internal velocity is assumed parallel to BC.",
        "texts": [
            "very simple way; let us consider the vectors e,. e., applied to the common vertex B of the sides AB and BC, see Fig. 5. From the end of each vector draw a line parallel to the corresponding side of the figure. The point of intersection of such parallel lines, together with the point B, determines the vector i of the internal rigid motion of the figure. Example 4. Quadrilateral figure When the material does not flow through the side BC, the direction of the internal motion is parallel to BC, see Fig. 6. When the external velocity vector is known on any other side of the figure, we revert to the first case. It will be then possible to calculate the flux of the material through the two remaining sides, considering the component of the internal vector normal to each of them. In the case of the trilateral figures the two sides bearing the starting data are obviously adjacent; this does not generally happen in the case of multilateral figures. Nevertheless no new difficulty is met due to this fact, because any two sides of the figure meet in a virtual point and from this point the graphical solution is the same as that of the trilateral figure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002638_1.1645297-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002638_1.1645297-Figure1-1.png",
        "caption": "Fig. 1 Notation for the flexible crankshaft\u00d5flexible block interaction",
        "texts": [
            " 126, APRIL 2004 rom: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Term Bampton reduction process is that the size of the generalized co- ordinate vector $x r b ab % is much smaller than the size of the physical DOF vector $xb%. Similarly, the vector of the physical flexible DOF of the crankshaft $xc% is partitioned into internal $xi c% and retained $xr c% DOF. The vector $xr c% includes the x and y DOF of three grids ~left, center and right end! on the crankshaft centerline for each bearing location as shown in Fig. 1. For one of the bearing locations, $xr c% also includes the z DOF of the center grid in order to apply an axial boundary condition. Finally the y DOF of two points on the outer crankshaft surface are also included in $xr c% in order to impose an appropriate torsional boundary condition. A right-hand coordinate system xyz is used with the x and z axes pointing in the vertical and axial directions, respectively. All the remaining DOF of the vector $xc% are included in the vector of the internal DOF $xi c%",
            " The equivalent oil film stiffness and damping matrices can be viewed as general nonlinear \u2018\u2018lubrication elements,\u2019\u2019 which can be easily added to any nonlinear structural dynamics code, in order to study the crankshaft-block interaction problem. The supporting mechanism between the rotating flexible crankshaft and the flexible block is represented by three sets of generalized nonlinear springs, at each bearing location. They are placed in the circumferential journal direction, at the two bearing ends and the middle bearing location, indicated by node #1, node #2 and node #3, respectively in Fig. 1. They connect the crankshaft centerline points with points on the inner bearing surface as shown in Fig. 2, offering support in the radial direction without restricting the crankshaft rotation. In this section, a relationship for the oil film thickness distribution h(z ,w ,t) is derived as a function of the generalized coordi- rom: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Term nates of the block ~Eq. ~3!! and the crankshaft ~Eq. ~4!!. The deformation of any point on the crankshaft is a function of its elastic curve ~deformation of its centerline!. Due to the high local crankshaft rigidity, its cross-sectional geometry is assumed to stay circular before and after deformation. Because the length of each bearing is relatively short, the deformation \u00ab of the crankshaft centerline along each bearing ~see Fig. 1! is considered to be quadratic. For each bearing, the crankshaft ~journal! eccentricities \u00ab1 , \u00ab2 , and \u00ab3 at the left end, middle and right end locations are used to define the crankshaft deformation distribution \u00ab(z) along the bearing length, as \u00ab~z !5A1~z !\u00ab11A2~z !\u00ab21A3~z !\u00ab3 (18) where, A1~z !52S z Lb D 2 23S z Lb D11, A2~z !524S z Lb D 2 14S z Lb D , A3~z !52S z Lb D 2 2S z Lb D (19) and Lb is the bearing length. Assuming, temporarily, that the block is undeformed, the radial oil film thickness can be expressed as @25# hr~z ,w ,t !5c2\u00abx~z !cos w2\u00aby~z !sin w (20) where, as shown in Fig. 1, the angle w is measured from the bearing crown, counterclockwise. The quantity c represents the original radial clearance at the undeformed state, and \u00abx(z) and \u00aby(z) represent the crankshaft deformations in the x and y directions respectively, for a particular axial direction z. Combining Eq. ~18! and Eq. ~20! yields, after omitting the parentheses for simplicity hr5c2@Tc#$xc%. (21) where, @Tc#5@A1~z !cos w A1~z !sin w A2~z !cos w A2~z !sin w 3A3~z !cos w A3~z !sin w# , (22) $xc%5$\u00abx1 \u00aby1 \u00abx2 \u00aby2 \u00abx3 \u00aby3 %T and \u00abxi and \u00abyi , i51,2,3 are the crankshaft deformations at node i in the x and y directions, respectively ~see Fig. 1!. The vector $xc% in Eq. ~21! is a part of the retained DOF vector $xr c% of the crankshaft ~see Eq. 4!. A large number of generalized nonlinear springs must be used in the circumferential direction. At each time step, the stiffness and damping of the generalized springs are calculated from Eq. ~13!. Each nonlinear spring connects a node on the crankshaft with a point on the inner bearing surface. Since the crankshaft cross section retains its circular shape during its flexible deformation, the force-displacement relationship depends on the distance between the grid point on the crankshaft centerline and the inner bearing surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002591_0094-114x(85)90040-0-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002591_0094-114x(85)90040-0-Figure4-1.png",
        "caption": "Fig. 4. Rack tip forms.",
        "texts": [
            ", vector from the fixed coordinate frame to the rotating frame attached to the gear blank, one obtains the expression for the involute on the gear blank as a function of the gear blank rotation from the pitch point mesh: {;;}= rco~ 0~ sin 021 r: = {R cos 0: + R0: sin 02 - R02 sin (b cos(02 - O)}iz + { - R sin 02 + R0,_ cos 02 + R0., sin d) sin(0, - (b)}j2. (7) or Equation (7) describes the involute profile for both positive and negative rotations of the gear blank from the pitch point mesh position. The top face of the tooth is generated for negative values of 02, and the involute portion of the tooth flank is generated for positive values of 0,. The generation of the gear tooth fillet is produced by the rack form tip. This tip can take on a sequence of different shapes for the same gear dedendum, as shown in Fig. 4. The maximum dedendum that can be produced would be made by a pointed rack form tooth and would have the value d = pc/(4 tan 6) = ~r/(4Pd tan d~), (8) where Pc is the circular pitch in inches and Pd is the diametral pitch in inch- ~ of the teeth. For a pressure angle of 20 \u00b0, the maximum dedendum possible is 2.158/Pd. For dedenda less than this, one has a choice of three rack form tip shapes. The basic shape is shown in Fig. 4(b) with two rounded corners and a small bot tom land. The two limits of this shape are shown in Fig. 4(a) with a full radius tip, which has the maximum possible tip radius for the given dedendum, and in Fig. 4(c) with the maximum tip bottom land. For this family of rack form tips the cutter tip radius, rack form addendum and gear dedendum are related as shown in Fig. 5. Note that the rack form addendum is not normally the same as the gear addendum. It should be equal to or greater than the gear addendum to produce a truly interchangeable gear with a full active involute. This cutter addendum is ac = d - rc(l - sin (b). (9) For standard AGMA 20 ~ full-depth teeth, d = 1.25/ Pd, rc = 0.3/Pd and ac = 1.053/Pdma value slightly higher than the gear addendum of 1",
            " Unfortunately, this tip radius will produce a cutter ad- dendum of 0.939/Pa for the standard dedendum of 1.25/Pd. Since this addendum is less than the standard 1.O/Pa. gears cut with a full tip radius cutter cannot mesh with a standard rack. Since the cutter tip forms of Figs. 4(a) and 4(c) are limits of the cutter tip with both a bottom land and a tip radius, generation of gear tooth fillets by these two cutters is not treated separately from the generation of a gear tooth fillet by the rack form tip of Fig. 4(b). For a cutter of this form the tip has two distinct surface normals: one for the bottom land. and one for the tip radius. For the bottom land the surface normal is and the tooth root base has the values r_, = (R - d) cos0.,i_~ - (R - d) sin0,,j.~ (15) for the start of the right side root. The second tip surface normal is for the section of tip produced by the radius, r,. This normal passes through the arc center, C, as shown in Fig. 6. As the gear blank rotation angle. 0,,, decreases past R-I(Pc/4 - ~/2), the angle that this normal vector makes with the Y, direction",
            " Q, expressed in the fixed coordinate frame at the gear blank center is given by r: = {R - a~ + rc sin 6 - r, sin 13}1o2 + {R0: - ac tan 6 - r, cos 6 + r, cos 13}jo:. (19) Rotating this description of the fillet cutting point to the (X:, 1'~) coordinate frame yields the following expression for the trochoid on the gear blank r., = {R cos 02 + R02 sin 0_- cos(0: - 6) a t rc sin(0: - 6) cos 6 + rc sin(0: - 13)}i: + { - R sin 0: sin(0z - 6) + R02 cos 02 + a t cos 6 - rt cos(0; - 6) + rc cos(0z - 13)}j2. (20) Even in the case of Fig. 4(c) with a zero value for re, eqn (20) describes the trochoid portion of the tooth flank which blends the bottom land arc into the bottom of the tooth 's involute profile. The presence of undercutting on the gear tooth can be determined by comparing the rack form addendum to the location of the tangent point, B, between the gear 's base circle and the line of action, BO, of the cutting mesh. If the perpendicular dis. tance from the rack 's pitch line to point B is greater than the addendum on the rack form, then no involute interference will occur"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000976_20.728299-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000976_20.728299-Figure2-1.png",
        "caption": "Fig. 2. Process of magnetic anisotropy.",
        "texts": [
            " From the measurement results of a prototype hysteresis motor using a diametrally magnetically anisotropic Fe\u2013Cr\u2013Co magnetic ring, this paper quantitatively substantiates the position that the new hysteresis motor using Fe\u2013Cr\u2013Co magnetic material is superior in characteristics to the conventional hysteresis motor using Alnico magnetic material. Further, this paper makes it clear that the characteristics of the radial flux type motor can be improved largely by using the radially magnetically anisotropic hysteresis ring. Fig. 1 shows a cross section of sample motor. OF ITS APPLICATION TO THE ROTOR RING The Fe\u2013Cr\u2013Co magnet can be made to have the property of magnetic anisotropy in the direction of the magnetic field by heat treatment, 30 min at 640 C in a magnetic field [6], [7]. In this experiment, as shown in Fig. 2(a) and (b), a simple method was adopted to give the property of magnetic anisotropy to a Fe\u2013Cr\u2013Co magnetic rotor ring. With this method, magnetic flux passes in the direction of the dotted lines, thereby enabling the rotor ring to have nearly ideal diametral and radial magnetic anisotropy. Additionally, the method shown in Fig. 2(a) was used to give the property of nearly circumferential magnetic anisotropy to the rotor ring. However, this property is somewhat different from the ideal circumferential magnetic anisotropy. Therefore, this property is hereinafter referred to as diametral magnetic anisotropy. In order to obtain the magnetic characteristic of the rotor ring, we toroidally wound exciting coils and search coils on the magnetic ring and measured the circumferential dc hysteresis loop. In this method, the radial hysteresis loop of a radially anisotropic sample shown in Fig. 2(b) cannot be measured. However, since the radially anisotropic magnetic rotor ring is prepared in exactly the same manner as that for the diametral anisotropic magnetic rotor ring shown in Fig. 2(a), the radial hysteresis loop of the radial magnetic anisotropic rotor ring is considered to have nearly the same magnetic characteristic as that of the diametral anisotropic magnetic rotor ring. Fig. 3 shows the measurement results of the alternating hysteresis losses of various rotor ring material. For the sake of comparison, in addition to the characteristic of Fe\u2013Cr\u2013Co material, Fig. 3 also shows the magnetic characteristic of isotropic Alnico 5 which has an energy product equal to that of Fe\u2013Cr\u2013Co material, together with the magnetic characteristic of magnetically semihard Alnico material kA/m) which is the most widely used in hysteresis motors",
            " 5(c)] and the other having isotropy. OF Fe\u2013Cr\u2013Co MOTORS, ALNICO 5 MOTORS, AND SEMIHARD ALNICO MOTORS In this section, we compare and discuss characteristics of motors made of anisotropic Fe\u2013Cr\u2013Co magnetic material, isotropic Alnico 5 magnetic material, and the most widely used semihard Alnico kA/m) magnetic material. We quantitatively made clear that a motor using anisotropic Fe\u2013Cr\u2013Co magnetic material is far superior to others. In this section, we deal with Fe\u2013Cr\u2013Co magnetic material having only diametral magnetic anisotropy [Fig. 2(a), hereinafter abbreviated to CF anisotropy]. Hereafter, a motor with its rotor ring made of Fe\u2013Cr\u2013Co magnetic material is referred to as motor A, a motor with its rotor ring made of Alnico 5 (isotropically processed) as motor B, and a motor with its rotor ring made of semihard Alnico as motor C, respectively. Additionally, the ring support material of the rotors being discussed in this section are all made of nonmagnetic material of circumferential flux type (CF-type). It is well known that motor characteristics are the best when the number of poles of the rotor due to magnetic anisotropy is equal to the number of poles of the stator. However, the equipment which gives anisotropy of multiple pole to the rotor is complicated. The equipment shown in Fig. 2, on the other hand, is comparatively simple for a two-pole machine. It seems, then, that it would be very useful in practical terms if the motor characteristics of a stator with four or more poles could be improved by using a rotor with magnetic anisotropy by means of simple equipment. Therefore, the motor characteristics were measured both when the number of poles of the rotor due to magnetic anisotropy was equal to the number of poles of the stator and when it was different. Figs. 6 and 7 show synchronous pull-out characteristics",
            " In general, a RF-type motor, in comparison with a CF-type motor, is characterized by smaller input current, higher efficiency, etc., whereas the RF-type motor has the disadvantage that the RF-type motor is smaller in pull-out torque. This section of the study clarifies from a series of experimental results that this disadvantage can be improved upon by using radially anisotropic magnetic material for the rotor ring of a RF-type motor. The magnetic anisotropy of the rotor ring was applied by the method shown in Fig. 2(b). Fig. 17 shows pull-out characteristics of three-phase, twopoles radial anisotropic, RF-type and three-phase, two-poles isotropic CF-type motors, respectively. Fig. 20 shows the torque ratio . From these figures, the key points are enumerated as follows. 1) Except in the high input voltage range of , the RF-type motor is greater in pull-out torque than the CF-type motor because reaction torque (difference between and hysteresis torque adds considerably more to the hysteresis torque when compared to the CFtype motor",
            " (5) Although the RF-type motor is experimentally slightly smaller in pulsation than the CF-type motor, it is reasonable to consider that both the CF-type and RF-type motors are nearly the same in pulsation. Fig. 22 shows the respective pull-out characteristics of three-phase, four-poles, radial anisotropic, RF-type motors and three-phase, four-poles, isotropic CF-type motors. Fig. 21 shows the torque ratio. The tendency toward considerable torque improvement being obtained from the two-poles motors at a low voltage, as outlined in the previous section A, cannot be seen in the four-poles motors. The reason is that, as shown in Fig. 2, with the magnetic anisotropy of the rotor ring for two-poles motors being applied to the four-poles motors, the reaction torque is too small to cope with the four-poles motors. However, due to the increase in hysteresis loop area by magnetic anisotropy, the radial anisotropic, RF-type motor obtains a torque equal to or somewhat greater than that of the isotropic CF-type motor. The starting characteristic shown in Fig. 23 indicates a tendency similar to the synchronous pullout characteristic except in the extremely high input voltage range",
            " This study experimentally examines how much the hysteresis motor is practically serviceable and to what extent its characteristics can be improved upon when magnetically anisotropic Fe\u2013Cr\u2013Co magnetic material is used for the rotor ring. The results of the experimental examination done are as follows. 1) Coercive force was suppressed to 31.8 kA/m which is relatively low as for an anisotropic Fe\u2013Cr\u2013Co magnet and was set to as high as allowable in order to enlarge the hysteresis loop area. 2) The hysteresis rotor ring was made to magnetic anisotropy in such a manner as shown in Fig. 2(a) and (b) to add reaction torque to hysteresis torque We have clarified that with the aid of (1) and (2), a compact, large output power, and highly efficient hysteresis motor can be realized. Although the method shown in Fig. 2(a) and (b) adopted in this study to make the rotor ring have magnetic anisotropy is suitable for a two-poles motor and can be expected to have a certain effect on a multi-poles motor, however, it cannot be said that this method is sufficient for the multi-poles motor. For the multi-poles motors, it is desirable to apply the method introduced in [9] for making the multi-poles motor have multi-poles anisotropy. The authors deeply appreciate Mr. Yazaki of Tokin Metal Industry Co., Ltd. and Mr. Iwasa, Mr"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001358_s0094-114x(03)00090-9-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001358_s0094-114x(03)00090-9-Figure6-1.png",
        "caption": "Fig. 6. Triad with one internal and one external prismatic joint.",
        "texts": [
            " C is the intersection point of the sextic curve with the circle and 12 intersection points exist at most. Due to the fact that this intersection contains two imaginary points as triples points, there will be at most six real intersection points. Therefore the maximum number of the assembly modes of the triad is six. The proposed method can be applied for the other two kinds of triad with one internal prismatic joint, where the internal joint B or C is prismatic and the other joints are revolute. Consider the Assur group with one internal and one external prismatic joint shown in Fig. 6. Without loss of generality, a local Cartesian coordinate system, with origin the joint A and x-axis from A to D is chosen. The position of the external joints A\u00f00; 0\u00de and D\u00f0d; 0\u00de and of the auxiliary point F \u00f0xF ; yF \u00de situated on sliding direction of the external prismatic joint are known, as well as the length of links lAB, lBE and the angle h. The distances d1 d2, d3 and d4 are also given. The position of the triad links is described by the coordinates of the internal joint B\u00f0x; y\u00de and the displacement s",
            " (7)\u2013(9), (49)\u2013(51) depend only on the triad geometry and external joints position and include the unknown s. Similarly to the procedure previously adopted for eliminating to the unknowns x and y, a final polynomial equation of sixth order with only variable s is derived, which is free from extraneous roots and whose coefficients depend only on the Assur-group data. The six order of the final polynomial equation is minimal. This is confirmed using similar considerations as at the previous triads: For a given position of the external joints of the triad (see Fig. 6), the internal joint E lies on the tricircular sextic curve of the four- bar mechanism ABCD of the RRPR type. Also E belongs to the straight line parallel to the sliding direction of the external prismatic joint. The intersection of the sextic curve with a straight line will be at six real intersection points at most and therefore the maximum number of the assembly modes of the triad is six. This procedure can be applied for six kinds of the Assur group of class 3 with one internal and one external prismatic joint",
            " The solving of the final sixth order polynomial leads to four real roots and two complex roots (see Table 2) for the input data here considered. For each real value of the displacement s, using back substitution, the coordinates of the internal revolute joints B (see Table 2), C and E are calculated. The corresponding four assembly modes of the triad with one internal prismatic joint are illustrated in Fig. 9. The procedure proposed in Section 4 for the position analysis of the triad with one internal and one external prismatic joint (see Fig. 6) is applied in the third numerical example. The input data of the triad are given in the left part of the Table 3. By solving the sixth order polynomial equation, four real roots and two complex roots are obtained (Table 3). For each real value of the displacement s, the coordinates of the internal revolute joints B (see Table 3) and E are calculated. Finally, the displacement s1 is determined. The corresponding four assembly modes of the triad with one internal and one external prismatic joint are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001735_s0020-7683(01)00198-6-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001735_s0020-7683(01)00198-6-Figure8-1.png",
        "caption": "Fig. 8. Ansys solution for step 5.",
        "texts": [
            " Small oscillations are visible in the diagram, which depend on the discretization of the FEM mesh, and may be a consequence of the Lagrange method. Another difference is a small asymmetry in the traction, which results from the shift of the stick area. This is clearly visible for the frictional traction marked with crosses for a =2 \u00bc 5:4, where the tip of the traction is larger on the left side. The reason of this discrepancy is the analytical assumption of an undeformed contact surface, which neglects the geometrical non-linearity produced by the moving stick zone. The interior stress field of the numerical (Fig. 8) and analytical solution (Fig. 9) is illustrated for step 5 in the regime of partial slip \u00f0a =2 \u00bc 5:4\u00de. The maximum and the form of the contours are the same for both methods, but the discrete FEM mesh produces some corners in the contours. The interior stress field differs characteristically from the classical Hertz solution, because the stress concentrations appear at the discontinuities of the curvature. This effect is important for non-Hertzian surfaces with discontinuous curvatures. Finally, the numerical (markers) and analytical (full line) tangential surface displacements are compared in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000615_rnc.4590050410-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000615_rnc.4590050410-Figure1-1.png",
        "caption": "Figure 1. A multi-trailer system with n (passive) trailers and rn (active) steering wheels",
        "texts": [
            " 0 Although this is a very specific form of prolongation of a Pfaffian system, and the conditions of the theorem must be checked in a specific coordinate system with a given independence condition, there do exist practical systems which can be converted into extended Goursat form using this type of prolongation, as will be seen in the following section. 4. A MULTI-STEERING N-TRAILER SYSTEM Consider a multi-steering trailer system, i.e. a system of n (passive) trailers and m (steerable) cars linked together by rigid bars. A sketch of such a system is given in Figure 1. It is assumed each body (trailer or car) has only one axle, since, as has been shown in Reference 23, a twoaxle car is equivalent (under coordinate transformation and state feedback) to a one-axle car towing one trailer. This system was originally proposed and examined in Reference 25, where it was shown how to convert the system into chained form using dynamic state feedback. Once the system is in chained form, there are several different algorithms available for steering or stabilizing the system; many of these are discussed in Reference 25 and will not be investigated further here"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000309_la010456+-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000309_la010456+-Figure6-1.png",
        "caption": "Figure 6. Chemotactic direction vectors.",
        "texts": [
            ",17 bacterial motion is modeled as being entirely self-generated, equating s to the chemotactic direction. In this model, motion is caused by the combination of swimming and the physical and chemical forces described by CFT. Therefore, s in this case is the overall direction in which the bacterium is moving as a result of swimming, advection, etc. Note that the likelihood of a turn decreases as the s component of \u2207C increases. The radial and angular components, respectively, of the chemotactic direction vector are where \u03b3 is the last angle in which the bacterium has turned (see Figure 6). The overall expressions for radial and angular velocity are The overall unit direction vector, then, is \u00e2(r,\u03b8) ) \u00e2o exp[-\u00f8o v Kd (Kd + C(r,\u03b8))2 s\u201a\u2207C(r,\u03b8)] (20) sr ) -cos(\u03b8 + \u03b3) (21) s\u03b8 ) sin(\u03b8 + \u03b3) (22) vr ) ur-LO + (srv) (23) v\u03b8 ) u\u03b8 + (s\u03b8v) r (24) The decision of whether to turn is made at each time step as follows. A random number (called F) is chosen on the interval [0,1]. A turn will be made if \u00e2\u2206t > F. Otherwise, the bacterium\u2019s existing swimming direction is maintained. If a turn is made, its magnitude \u03b3 is chosen from the bacterium\u2019s turn angle distribution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003507_jsen.2006.881421-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003507_jsen.2006.881421-Figure5-1.png",
        "caption": "Fig. 5. Modeling of time-variant bearing defect position due to inner raceway rotation.",
        "texts": [
            " Given that the major function of the two pillow blocks was to support the driving shaft, they were modeled as solid cylinders without considering the relative degrees of freedom of the rolling elements within the pillow blocks. The pillow blocks were retained in the model since they present a source of structural noise for the bearing system being monitored. The position of the localized defect on the inner raceway of the bearing varies with time as the inner raceway rotates. To model the resulting position-variable interactions between the rolling balls and the defect, eight representative positions, each is 45\u25e6 apart from the adjacent positions, were placed around the bearing periphery. These are labeled in Fig. 5 as \u201cPos 1\u201d through \u201cPos 8,\u201d respectively, starting from the horizontal axis position. At each representative defect position, the transient dynamic force Fb was applied (e.g., to Pos 3 as shown in Fig. 5) to simulate the impulsive interactions between the rolling element and the defect. Given a bearing rotation speed of 900 r/min (experimental condition), a bearing inner raceway diameter of 46.5 mm and a ball diameter of 7.5 mm, the contact time between the ball and the inner raceway was calculated to be approximately 1 ms. Given the presence of a background noise, selection of the optimal sensor locations needs to consider nodal responses both to the signal input Fb and to the noise input Fa. Certain sensor locations, while showing large nodal displacements responding to defect-induced signal input in the simulation, may also be sensitive to noise input, resulting in an overall low signal-to-noise ratio (SNR) that render the particular location unfavorable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000363_s0168-874x(99)00042-6-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000363_s0168-874x(99)00042-6-Figure2-1.png",
        "caption": "Fig. 2. Wireless communication between a sensor-integrated `smarta bearing and an external data receiver.",
        "texts": [
            " To maintain the generality of the structural analysis, an outer ring-modi\"ed bearing with an empty slot was \"rst analyzed. The results provided input to help design a bearing that may have any type of sensor module integrated. Based on the general structural model, a further analysis was conducted to determine how much a load sensor would support the modi\"ed section of the bearing outer ring. The analyses were based on a commercially available radial ball bearing with a bore of 100 mm and an outer diameter of 180 mm. The width of the raceway was 34 mm. In Fig. 2, the scheme of data communication between a sensor-integrated bearing and an external data receiver is illustrated. As stated above, the outer ring is assumed to be \"xed while the inner ring rotates. Thus, no inertia forces are associated with the outer ring. It is further assumed that the bearing carries a pure radial load. If gravity is neglected, then the outer ring is loaded only on its inner surface (raceway) and outer surface. The load on the outer surface is the reaction force between the ring and the housing",
            " While bearing vibration analysis is indeed a crucial element for a successful condition monitoring system, it involves many variables (e.g., number of defects, size of defects, bearing geometry, etc.) and is thus too lengthy a subject to be included in this paper. Therefore, the vibrational analysis of a sensor-embedded bearing will be presented in separate papers which focus on the e!ects of bearing structural defects on the bearing's vibrational behavior. Another important aspect under development is wireless data transmission from the embedded sensor to an external receiver via RF telemetry, as illustrated in Fig. 2. It can be predicted that a compact bearing with self-diagnostic capabilities will be of great relevance to a wide range of industrial and commercial applications. The authors sincerely appreciate the funding provided to this research by the National Science Foundation under CAREER award DMI-9624353 and by the SKF Condition Monitoring Company. [1] M. Becker, K. Jaeker, F. Fruehauf, R. Rutz, Development of an active suspension system for a Mercedes-Benz coach (O404), Proceedings of the IEEE International Symposium on Computer-Aided Control System Design, Dearborn, MI, USA, Sep"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003712_cl.2006.326-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003712_cl.2006.326-Figure1-1.png",
        "caption": "Figure 1. Schematic showing the procedure of immobilizing Pt-DENs onto MWCNTs (a) and the preparation for enzyme electrode (b).",
        "texts": [
            " The hybridized nanocomplex can combine the advantages of Pt-DENs and MWCNTs to improve the enzyme electrode\u2019s electroactivity for glucose. MWCNTs can not only be as a solid phase for adsorption and concentration of metal nanoparticles,7 but also have the ability of promoting electron-transfer reactions with enzyme and other biomolecules.8 Thus, the nanocomposite can be assumed as an attractive immobilization matrix for glucose oxidase (GOx), chosen as an enzyme model. Our strategy to design Pt-DENs nanoparticles incorporated with MWCNTs conjugates is depicted in Figure 1a. Briefly, carboxylic acid groups were introduced onto MWCNTs by acid treatment as described elsewhere.9 Dendrimer encapsulated Pt nanoparticles was attached covalently onto these cut MWCNTs via 1-(3-dimethylaminopropyl)-3-ethylcarbodiimide hydrochloride (EDC) to yield stable conjugates. A concentration of 10mg/mL of MWCNTs was usually used, and the volume of Pt-DENs nanoparticles stock solution was varied to optimize the dendrimer encapsulated Pt nanoparticles concentration. As shown from the TEM image in Figure 2a, a high and homogeneous dispersion of spherical Pt-DENs nanoparticles was prepared, which is in good agreement with Crooks et al.10 The nanoparticles dispersed well on the surface of MWCNTs with a dense distribution (Figure 2b), which show that dendrimer is a good template for metal nanoparticle avoiding agglomeration even conjugated on the CNTs, and our method is convenient and effective for CNT supported metal nanoparticles compared with other preparation for biosensor platforms using Pt nanoparticles and CNTs.11,12 The fabrication of MWCNTs/Pt-DENs modified enzyme electrode has been described in Figure 1b. Briefly, Pt electrodes (2 4mm2) were carefully polished, cleaned with concentrated H2SO4, rinsed with water and ethanol. The electrode was then Copyright 2006 The Chemical Society of Japan transferred to the electrochemical cell for cleaning by cyclic voltammetry between 0:5 and \u00fe1:2V versus Ag/AgCl at 100mV/s in 50mM phosphate buffer, until a stable CV profile was obtained. For the activitation of the electrode\u2019s surface as well as the improvement of MWCNTs and Pt-DENs adhesion on the Pt electrode surface, the cycling was terminated by stepping the potential to \u00fe1:2V for 2min"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003089_tmag.2005.846230-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003089_tmag.2005.846230-Figure1-1.png",
        "caption": "Fig. 1. Structure of FRM.",
        "texts": [
            " Compared to rectangular wave drives, sinusoidal wave drive need expensive position sensors and is consisted of a rather complicated drive system. However, we can expect less torque ripples. Two models, skewed and nonskewed, have been also investigated to confirm the performance with the driving techniques. In this paper, we used two types of models. Model 1 has rotor that is 15 skewed. By skewing the rotor, it is expected to have Digital Object Identifier 10.1109/TMAG.2005.846230 less torque ripple. Model 2 is a model with no skews. The shape of FRM is shown in Fig. 1 and the main specifications are shown in Table I. The basic operating principle of the FRM is similar to that of the brushless dc motor. Compared to the BLDC motor which has a cylindrical structure, FRM has a doubly salient structure. Due to this difference, the reluctance force is much larger of FRM than that of BLDC motors. In an FRM, the stator self inductance is dependent on rotor position and stator PM contributes to the air gap variable flux linkage. This relation can be described using the following equation: (1) 0018-9464/$20"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003606_detc2005-85337-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003606_detc2005-85337-Figure5-1.png",
        "caption": "Fig. 5 Mobility analysis of 3-PR1R1R1 PKC: (a) The original kinematic chain and (b) The kinematic chain with an equivalent serial kinematic chain added.",
        "texts": [
            " Then, we obtain the mobility (or the degree of freedom) F of the PKC as F = C + R = 6\u2212 c + m\u2211 i=1 Ri. (7) 5 wnloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/07/2016 Te In addition to the mobility, another important index of a PKC is defined as \u2206 = m\u2211 i=1 ci \u2212 c (8) where \u2206 is called the number of overconstraints (also passive constraints or redundant constraints) if \u2206 > 0. In the mobility analysis of parallel mechanisms, not only F but also C and \u2206 should be revealed. These indices can be calculated using Eqs. (4), (7) and (8). Consider the 3-PR1R1R1 PKC shown in Fig. 5(a). The mobility analysis of this mechanism has been discussed in [6, 20]. In this PKC, all the axes of the R joints within a same leg are parallel. The axis of a P joint is not perpendicular to the axes of the R joints within the same leg. The axes of the R joints on the moving platform are not all parallel. The wrench system of each leg is a 2-\u03b6\u221e-system, which is composed of all the \u03b6\u221e whose axes are perpendicular to the axes of all the R1 joints within a same leg. The wrench system of the PKC is the 3-\u03b6\u221e-system",
            " Step 4 For j to 2 to m\u2212 1, check if the PKC can be decomposed in to j mi-legged PKCs which all have full-cycle equivalent serial kinematic chains and whose full-cycle equivalent serial kinematic chains comprise a not-overconstrained kinematic chain. Here, \u2211j i=1 mi = m. If yes for any one j, the PKC has full-cycle mobility and inspection ends. Otherwise, go to the next step. Step 5 The PKC does not have full-cycle mobility2 and inspection ends. We have found that the instantaneous mobility of the 3- PR1R1R1 PKC shown in Fig. 5(a) is 3. Now, let us discuss the full-cycle mobility inspection. Following the above procedure, we have Step 1 Since \u2206 = 3 6= 0, go to the next step. Step 2 There are no inactive joint in this PKC. Step 3 It can be found that the PPP equivalent serial kinematic chain [Fig. 5(b)] and each PR1R1R1 comprise a 3-DOF single-loop kinematic chain. Thus, the PPP equivalent serial kinematic chain of the 3-PR1R1R1 PKC is its full-cycle equivalent serial kinematic chain. Then we conclude that the PKC has full-cycle mobility. The method of the mobility analysis proposed above will now be illustrated using the following seven examples. Example 1 Consider the PR1R1R1R-2-PR1R1R1 PKC shown in Fig. 6. In this PKC, all the axes of the R1 joints within a same leg are parallel. The axis of a P joint is not perpendicular to the axes of the R1 joints within the same leg"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002426_978-3-642-84379-2_1-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002426_978-3-642-84379-2_1-Figure2-1.png",
        "caption": "Fig. 2",
        "texts": [
            " 1) described by equations of the type (1.1) and (1.2): mx + P(x) + kx = 0, where x is displacement, m is mass, k is the spring rigidity, P(X) = { Po with x > 0 -Po with x <0 (1.3) (1.4) and Po is a positive constant. It is quite obvious that the discontinuity surface (1.2) in this case is the x-axis S=x =0. (1.5) Notice the fact that the Coulomb friction P(x) is not defined in points where velocity x equals zero. Consider the behaviour of the mechanical system (1.3)-(1.5) on the plane with coordinates x and x (Fig. 2). As evidenced from the figure, the description of this behaviour may be obtained quite easily if Ixl > Polk, i.e. if the discontinuity points are isolated. In this case one may apply, for instance, the point-to-point transformation technique. If the state vector appears to stay within the segment.lxl ~ Polk of the discontinuity straight line (1.5) (stagnation zone, as termed by A.A. Andronov in [8]), it will not leave this segment. Since in this case the function P(x) is not defined on the discontinuity straight line, an immediate problem of an appropriate description of this motion arises"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000983_icsmc.1991.169801-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000983_icsmc.1991.169801-Figure1-1.png",
        "caption": "Figure 1. Biped robot model and coordinate configuration.",
        "texts": [
            " The location of the ZMP of a planned biped trajectory affects the stability during locomotion. The nearer the location of ZMP to the perimeter of the support region, the less control error allowed. In this work, we define an optimal biped trajectory to occur when the ZMP is at the center of the supporting region. A computer simulation of the optimal biped trajectory is obtained. The optimization is performed sequentially for each time interval. 2. Model of the biped robot The analysis described in this research is based on a biped model shown in Fig. 1. The origin of the fixed base reference coordinate B is located under Leg 1 on the ground plane. The x-axis points forward, the z-axis points upward, and the y-axis is the cross product of z and x axes. The biped robot can be modeled as a kinematic chain of (2n+l) links connected by 2n revolute joints, where n=6 is the number of degrees of freedom of each leg. Fig. 1 shows the link and joint coordinate assignments and their Denavit-Hartenberg parameters are shown in Table 1. The joint angle i is the rotation of frame i relative to frame (i-1) about axis Zi. Each link has its mass mi concentrated at its center of mass ri = [xi,yi,zilT, and the inertial matrix Ii according to its principal axes at the center of mass. Table I1 displays these physical data. The inertial force Fi = [Fix,Fiy,FizlT and moment Mi = [Mix,Miy,MizlT acting at the center of mass of link i are expressed by where Oi is the instantaneous absolute angular velocity of link i",
            " Inverse kinematics To describe the specific configuration of the biped robot, we assign the motions of link 0 (foot I), link 6 (body), and link 12 (foot 2). By fixing both the position and the orientation of these three links, the configuration of the biped robot is established. For simplicity, we assume that no rotational motion occurs for these three links during walking. In order to compute the joint motion, the inverse kinematic model is needed for given PO=(PO~,PO~,PO~) . P6=(P6x,P6y,P6~), and P12=(P12x,P12y,P12z) where Pi is the reference point of link i as shown in Fig. 1. Because there is no rotation, the joint angles can be expressed by 03 = -K + 8, e4 = o es = K - e, - e2 06 = - 81 el = - e12 es = -(K - e, - ell) e9 = o el0 = K - e, - 6 d ell = -sin-' Xr 8, = COS -1 x?+y?+z?dd -2 dl d2 d l is the length of the upper leg, and d2 is the length of the lower leg. Therefore, the biped motion can be expressed solely by positions Po, P6, and P12. A flowchart for computing the ZMP from the trajectories of Po, P6, and Pi2 is shown in Fig. 2. 4. Optimization of the biped robot trajectory The trajectory optimization is based on an objective functional, involving the ZMP, with the position of body Pg as free variables"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002653_1.7420-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002653_1.7420-Figure1-1.png",
        "caption": "Fig. 1 DDP basic geometry.",
        "texts": [
            " II presents the guidancebased approach for the formation control problem and discusses the DDP for N followers in formation. Section III deals with the stability analysis of the proposed guidance law. In Sec. IV we propose a control configuration in which each follower measures its position relative to the preceding one. The simulation results for a formation flight of five F-16 fighters are presented in Sec. V. Finally, conclusions are given in Sec. VI. The guidance law used for the formation control is based on DDP. Figure 1 describes the basic geometry associated with the DDP approach. It shows a two-vehicle formation consisting of a leader (L) and a follower (F). VL and VF are linear velocities, and \u03b3L and \u03b3F are the corresponding path angles. Using the notation presented in Fig. 1, the following conditions define a DDP: 1) The follower (F) keeps the range r constant by controlling its own speed (detective condition). 2) The follower\u2019s velocity VF leads the line of sight (LOS) by a constant angle \u03b4 (deviation condition). We limit \u03b8 to be \u2212\u03c0/2 < \u03b8 < \u03c0/2. The imposed limits guarantee that the leader\u2019s velocity has no components along the LOS vector in the direction of the follower. Note the following: 1) If the leader moves on a straight line, then \u03b3L = constant and \u03b3\u0307L = 0",
            " 2) If the leader follows a circle of radius R at constant speed, then \u03b3\u0307L = \u03c9 = VL/R = constant. In this discussion we will always assume \u03b3\u0307L \u2265 0; the discussion for negative \u03b3\u0307L is identical. The constant range requirement leads to the condition r\u0307 = 0 (1) which is equivalent to VL cos \u03b8 \u2212 VF cos \u03b4 = 0 (2) hence \u2212\u03c0/2 < \u03b4 < \u03c0/2. The LOS angular rate \u03bb\u0307 is calculated by \u03bb\u0307 = (1/r)(VL sin \u03b8 \u2212 VF sin \u03b4) (3) Using Eq. (2), Eq. (3) can be rewritten as \u03bb\u0307 = (VL/r)(sin \u03b8 \u2212 cos \u03b8 tan \u03b4) (4) From the geometry of Fig. 1, the leader\u2019s path angle \u03b3L satisfies \u03b3L = \u03b8 + \u03bb (5) Equations (4) and (5) lead to the DDP differential equation \u03b8\u0307 + (VL/r)(sin \u03b8 \u2212 cos \u03b8 tan \u03b4) \u2212 \u03b3\u0307L = 0 (6) The solution \u03b8 of Eq. (6) is used to calculate the follower path angle \u03b3F : \u03b3F = \u03b4 + \u03bb = \u03b4 + \u03b3L \u2212 \u03b8 (7) Remarks: 1) \u03b3\u0307L = 0 (straight path) implies that \u03b8 = \u03b4. 2) \u03b3\u0307L = \u03c9 = const (circular path) implies that \u03b8\u0307 + (VL/r) sin \u03b8 \u2212 (VL/r) tan \u03b4 cos \u03b8 \u2212 \u03c9 = 0 (8) Equation (8) can be rewritten in terms of the nondimensional parameter defined by = r\u03c9/VL = r/R (9) where R is the radius of the circular path performed by the leader"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003634_j.matdes.2006.10.008-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003634_j.matdes.2006.10.008-Figure5-1.png",
        "caption": "Fig. 5. The result of t = 11.6 s.",
        "texts": [],
        "surrounding_texts": [
            "Fig. 3\u20135 are the simulated results for the temperature field at the times of the laser operating of t = 2 s, t = 6 s, and t = 11.6 s, respectively. The figures show that the maximum Unknown 400 500 600 700 800 900 1700 691 703 710 712 712 712 712 10.3 11.8 12.8 24.3 lt of t = 2 s. temperature rises with time. When t = 2 s, the maximum temperature is 1833 C. But, when t = 11.6 s, the maximum temperature has reached 1919 C. The reason for this is that the thermal conductivity of the ceramics is less than that of the substrate, and its heat radiating is slower, which will cause the quantity of heat to accumulate and the temperature to rise. At some point for the laser to operate, the temperature of the coating from the surface to the substrate falls gradually. There is a great temperature gradient in the coating layer from its surface to the matrix. The simulated results show that the maximum temperature is higher than the melting point (1668 C) of the cladding material and substrate in the process of the laser. The whole coating is in a melting state at high temperature. Thus a molten bath is formed while the laser is scanning. The molten bath inside changes quickly and acutely. Due to the characteristic of internal molten bath, there will be a major driving force in the bath [8]. Even though the liquid phase as ceramic molten mass possesses some stickiness, under the great temperature gradient and driving at rapidly varying temperatures, it would flow definitely. Thus its composition will be well-distributed by diffusion and convection [9], providing the condition to compose the active substances, hydroxyapatite and other calcium\u2013phosphorus-based bioceramics. The structure of the hydroxyapatite has its special characteristics. In its hexagonal crystal structure, there is a major passageway paralleling the c axis. The nucleated hydroxyapatite in the molten bath at high temperature, under the actions of diffusion and convection of the substances inside the molten bath, transport Ca2+ through this passageway to provide a substantial condition for crystal growth. Therefore the synthesis of hydroxyapatite is promoted. Moreover, laser cladding is a process of rapidly melting and solidifying. Under the optimized conditions, the liquid phase in the laser molten bath is able to meet the conditions for thermodynamics and dynamics for hydroxyapatite to be synthesized. From the analysis of the thermodynamics of synthesizing hydroxyapatite, it can be found that the temperature for its synthesis should be lower than 1927 C [10]. But the maximum temperature of the simulated results is lower than this temperature. A molten bath can also be formed. This would be of great advantage to synthesizing hydroxyapatite. Therefore, the parameters optimized in the experiment are feasible. To explain the reliability of the simulated result, the microstructural analysis of SEM has also furnished strong evidence. Fig. 6 shows the bioceramic coating obtained under the optimized technical parameters. This coralline structure will be helpful for the ossifying cells growing in bioceramic coating to supply passageways. It can be seen from Fig. 7 that the structure of the short-rod piles has formed on the surface of the bioceramic coating. This is a typical structure of hydroxyapatite [11]. The structure will undoubtedly improve biocompatibility between the bioceramic coating and osteal tissue."
        ]
    },
    {
        "image_filename": "designv11_11_0002949_bf00251489-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002949_bf00251489-Figure1-1.png",
        "caption": "Fig. 1. A sketch showing the vector R v obtained by rotating a unit vector v through an angle ~ and the vector/~ representing the difference of v and the rotated vector R v .",
        "texts": [
            "23) to the order of magnitude Co, an additional assumption must be made concerning the relation between the orders of magnitude of g and E,K or equivalently between eo and el. But, prior to such an undertaking, we need to dispose of some geometrical preliminaries and definitions. Consider now any unit vector v and rotate this by the rotation tensor R through an angle o~ resulting in the vector R v . Since the proper orthogonal tensor R is length preserving, the magnitude of v remains unchanged upon rotation and we have cos o~ = v 9 R v , (4.27) which represents the projection of the rotated vector R v along v (see the sketch in Fig. 1). With the use of (2.13), it can be shown from (4.27) that cos o~ is bounded f rom below by cos 0 in (2.14), i . e . * , cos o~ ~> cos 0. (4.28) To continue the discussion, let/3 stand for a vector defined by (see also the sketch in Fig. 1) /3 = R v - - v or R v : v + /3 . (4.29) * Details of the argument are given following (Bll) in Appendix B. Keeping in mind that both v and R v are unit vectors, f rom the inner p roduc t o f (4.29) with itself we arrive at 1 I -~--/3-/3-----'~-[/312 = I - - v . R v = 1 -- c o s ~ , (4.30) which shows that ~ 11312 is the difference between unity and the projection o f in Fig. 1. Then, by (4.29)~, we have /3. v = !/31 cos ~ = --(1 - - v . R v ) . (4.31) Before proceeding further, it is instructive to consider the case o f classical infinitesimal kinematics in which both the strain and rotat ion are small. Thus, we introduce the following Definition 4.1. Given E = O(eo), a proper or thogonal tensor R is said to be an infinitesimal rotation with respect to eo if for any unit vector v, the vector /3 defined in (4.29) satisfies /3 ---- O(eo) as eo -+ 0. (4.32) 1 - - v . R v = O(e02) as eo --~\" 0, (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003198_s10846-004-7196-9-Figure13-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003198_s10846-004-7196-9-Figure13-1.png",
        "caption": "Figure 13. The manipulability forced and collision-free mobile manipulator motion.",
        "texts": [
            " As is seen from Figures 10, 13 the mobile manipulator must more decrease its holonomic manipulability as compared to that obtained from the second experiment (see Fig- ure 6) to avoid collisions with obstacles. Nevertheless, in the neighborhood of the final end-effector position, where collision avoidance constraints are not active, the holonomic manipulability reaches desirable value. Compared to the first experiment, performance time T in the manipulability forced and collision avoidance task has increased approximately by 1 second. This increase is the result of active collision avoidance constraints (see Figure 13) since the mobile robot has to decrease its velocity in neighborhoods of obstacles. Moreover, Figure 14 shows distances dm\u2212i , i = 1, 2, between the mobile manipulator and the centers of obstacles 1 and 2, respectively. As is seen from Figure 14, the manipulator penetrates the safety zone of the 1st obstacle for t belonging approximatelly to intervals [0.4, 1] \u222a [1.8, 2.8] and the safety zone of the second obstacle is penetrated for t \u2208 [1.4, 2.5], respectively. Consequently, both safety zones are simultaneously penetrated in time interval [1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002085_physreve.68.061704-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002085_physreve.68.061704-Figure2-1.png",
        "caption": "FIG. 2. ~a! Schematic of a twist inversion wall in which the director rotates by p radians when traversing the wall. ~b! Schematic of the unit sphere description of the director field @10# with respect to rectilinear simple shear flow. The x axis is the flow direction, the y axis the velocity gradient direction, and the z axis the vorticity axis. The equator lies in the shear (x-y) plane and the north pole and the south pole are located on the vorticity (z) axis. The director trajectory for two twist inversion walls, of charge C 521, and C511, is according to the rotation sense in going from the vorticity axis to the flow direction.",
        "texts": [
            " Defects are classified according to dimensionality (D) in terms of points (D50), disclination lines (D51), and inversion walls (D 52). Disclination lines can have singular or nonsingular cores @2#. The charge of a disclination line is defined by a sign (1 ,2) and a magnitude ~1/2,1, . . . !. The sign indicates the sense of rotation when encircling the defect, and the magnitude, the amount of rotation. Inversion walls are twodimensional nonsingular defects, in which spatially localized director gradients occur. Figure 2~a! shows an schematic of a twist inversion wall @1# in which the director rotates by p radians when traversing the wall. The continuous director rotation is localized in a thin region that defines the inversion wall thickness j. The surface tension of the wall is K/j , where K is the Frank elastic constant @8#. Inversion walls form either loops, are attached to other defects, or to the bounding surfaces. Once nucleated, inversion walls can shrink, pinch, or annihilate with other walls or other defects @9#",
            " Twist inversion walls are characterize by a topological charge C , given by C5 Dc p , ~1! where Dc is the total director rotation while traversing the wall. As in disclination lines, the sign of the charge define the sense of rotation. Since sheared flow-aligning nematic polymers orient very close to the velocity direction, an inversion wall formation is expected if the initial orientation is orthogonal to the imposed flow. In addition, if the flowaligning angle is sufficiently small, say less than several degrees, the walls are essentially twist walls. Figure 2~b! is a schematic of the unit sphere description of the director field @25#, where the x axis is the flow direction, the y axis the velocity gradient direction, and the z axis ~out of the plane of the paper! the vorticity axis. The equator lies in the shear (x-y) plane and the north pole and the south pole are located on the vorticity (z) axis. The figure shows the director trajectory for two twist inversion walls, of charges C521 and 11, according to the rotation sense in going from the vorticity axis to the flow"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001499_20.877692-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001499_20.877692-Figure2-1.png",
        "caption": "Fig. 2. Deformation caused by the 5th harmonic (1250 Hz) of the magnetic forces.",
        "texts": [
            " With the forces and the 3D mechanical model, the forced vibrations are obtained using Modal Superposition Method. In this method the response of a continuous structure to any force can be represented by the superposition of the various responses in their individual modes. These responses can be nodal displacements, velocities and accelerations. This method requires a natural response calculation prior to further solution steps [4]. As an example, the forced deformation caused by the th harmonic (1250 Hz) of the magnetic forces is presented in Fig. 2. In this work an average damping is considered when calculating mechanical deformations, as presented in [4]. 0018\u20139464/00$10.00 \u00a9 2000 IEEE The sound power radiated by a electric machine vibrating in a mean rms surface spatial velocity (spacelly average) , can be calculated as follows [2]: (2) where is the frequency of vibration, is density of the air, is the velocity of the propagation of sound in air, is the radiation efficiency, is the area of the machine surface contributing to sound radiation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003190_s10544-005-6071-1-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003190_s10544-005-6071-1-Figure3-1.png",
        "caption": "Fig. 3. Schematic diagram of a flow-injection-type amylase activity system used for analysis of salivary amylase activity.",
        "texts": [
            ", 2000). Following the reaction in equation (2), \u03b1-D-glucose is converted to \u03b2-D-glucose and the reaction reaches equilibrium when \u03b1 : \u03b2 = 36.4 : 63.6. In other words, while the sample solution flowed from the pre-column to the flat enzyme electrode, non-enzymatically modification from \u03b1-D-glucose to \u03b2-D-glucose occurred. POD acted as a mediator in equation (3) (Kinoshita et al., 1997). A flow-injection-type device was used as an analytical system of salivary amylase activity (flow-injectionsystem, Figure 3) (Yamaguchi et al., 1998). Maltopentaose as a substrate of \u03b1-amylase (C30H52O26, Nacalai Teque, Inc. Japan, G5) was dissolved in a phosphoric acid buffer solution (pH 7.3). A mixing coil was shaped using a tube of 630 mm length, and it was attached in order to reduce the pulsation of the buffer solution caused by a rotary pump (U4 \u2013 XV, Alitea, Swaden). When a salivary sample was injected using a sample injector (model 7125, Rheodyne, USA), it flowed on to the MP membrane of the flow cell. After that, it flowed on to the GOD-POD membrane (25\u25e6C)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001536_cdc.1995.479070-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001536_cdc.1995.479070-Figure3-1.png",
        "caption": "Figure 3 Innovative aerodynamic control effectors",
        "texts": [
            " Thrust vectoring, reaction control systems, pneumatic devices, and vortex control surfaces are commonly being used to augment conventional aerodynamic control surfaces. The design of flight control systems for these configurations is complicated by both the number of control effectors and their highly nonlinear response characteristics. The challenge is to meet stability and flying qualities requirements while fully realizing the performance capabilities of the vehicle. An example of a conceptual high performance fighter aircraft with multiple control effectors is shown in Figure 3. This figure illustrates many of the candidate aerodynamic control effector technologies available. Control effector technologies not illustrated in the figure include thrust vectoring, pneumatic devices (other than shown in the figure), the use of micro element machines (MEMs), passive porosity, and flexible wing control. Advanced aircraft will require superior mission performance, agility, and stealth levels of operation. Innovative aerodynamic control effectors, as shown in Figure 3, 75 1 can help achieve these goals. Advanced effectors that manipulate the aircraft forebody/lex/wing vortex system offer improved high angle-of-attack (a) pitch and yaw control authority, resulting in increased agility and controllability at high- a conditions. The incorporation of advanced low- a yaw and roll effectors can enable the reduction or elimination of the vertical tail and rudder control surfaces. This can significantly improve the aircraft survivability by reducing observability. It also results in reduced weight and costs",
            " As new aircraft designs progress towards tailless versions, the integration of aerodynamic controls and alternate controls (pneumatic, thrust vectoring, MEMs. passive porosity, active flexible structure control) becomes more critical. In new aircraft designs there are strong incentives for minimizing weight, costs, and maintainability requirements while maximizing system reliability. Conventional control surfaces are ineffective at high a's and also create signature problems. Non-traditional control effectors (such as shown in Figure 3) for achieving flight control need to be optimized and integrated within design constraints of the total weapon system so that the aircraft meet stealth requirements without compromising maneuverability and agility goals. This problem of control integration is a relatively new problem and has not received adequate attention (because it is so application dependent). Only in the newest fly-by-wire aircraft i s this an issue (in older aircraft mechanical linkages between effectors and the pilot stick is used)",
            " Mode logic and blending logic (on the control effector level) is usually determined in an add hoc fashion. The recent dynamic inversion [7,8] based control law thrusts [9-191 further complicate this problem. Consider the aircraft dynamics modeled by the equations of the form with n-dimensional state x and m-dimensional control U. A dynamic inversion control law which achieves the desired response characteristics may be formulated as where v specifies the desired response. The number of controls available (m > 20) on the aircraft shown in Figure 3 does not directly (easily) support the use of dynamic inversion. Typical aircraft applications of dynamic inversion [9-191 use a two time scale approach in which control surface commands (aa, Se, 6,) are calculated in order to generate desired angular accelerations (j, q, i ) . This inner loop inversion (fast time scale) requires all m controls surfaces in U to be chained (ganged) together into a form for roll, pitch, and yaw control. Outer loops are then wrapped around these inner loops to achieve aircraft flying qualities (slow time scale)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.31-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002755_b978-0-408-01396-3.50008-4-Figure3.31-1.png",
        "caption": "Figure 3.31 Rim-spoke interaction. Geometrical definitions",
        "texts": [
            "132) has been obtained by neglecting the terms of the order of Jr compared with the term of the order of Srrf. The force F exerted by the rim on the spokes can be easily obtained by equating the radial displacement of the spoke expressed by equation (3.124) to that of the rim expressed by equation (3.131). If the expression (3.130) is used for the circumferential stress, the following value can be obtained: F = co2 PS? ~C: Of ETIT + Q (3.133) Such force induces bending stresses in the rim which can be quite dangerous. The bending moments at points A and B (Figure 3.31) have been calculated as:* M M, =Frr_j \\ 1 ' r|_2sin(cp/2) cp(l+IJSTrf)j -Fr\\ 1 1 1 1 l2tgfo>/2) cp(l+IJSrr?)] (3.134) (3.135) 2tg(cp/2) As the rim can be considered a curved beam, the stresses due to the bending moment M in a generical cross-section of the rim can be expressed as a * See note on page 110. Isotropic flywheels 109 function of the distance r from the axis of rotation by the formula: M r, Sr 1 + ^ y/r (3.136) where \\f/ is linked to the profile h(r) of the rim by the equation: 1 P\u00b0 \u25a0r, i A = - - lhdr (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001549_1.1576428-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001549_1.1576428-Figure2-1.png",
        "caption": "Fig. 2 Schematic of damage to pad in Fig. 1\u201eb\u2026",
        "texts": [
            "1576428# Older bearing designs as found in the hydro industry can often be improved through the application of state of the art design tools. This is particularly the case with pump-turbine installations, which are often required to switch modes several times daily. Each change of mode requires a reversal in the direction of rotation. Figure 1~a! from Pistner @1# and Fig. 1~b! show examples within the industry of bearing pads that have wiped during a cold start. Both are from pump-turbine units. The damage in Fig. 1~b! has progressed beyond the stage of Fig. 1~a!, and is shown schematically in Fig. 2. Both pads show a central, semi-elliptical area of severe wear. In Fig. 1~b! the babbitt has smeared and aggregated in a collection of discrete particles on the trailing side of the worn area. A \u2018\u2018shelf\u2019\u2019 or cantilever of babbitt has accumulated at the trailing edge. Part of a similar shelf of babbitt on the upstream pad has broken away and jammed at the leading edge of the film. Similarly, debris from the pad that is shown broke away and interfered with the pad downstream, which showed almost identical damage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001463_robot.1990.126233-Figure3.2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001463_robot.1990.126233-Figure3.2-1.png",
        "caption": "Figure 3.2 Grasp on three edges",
        "texts": [
            " Grasp synthesis code is written in C language and run on a MicroVax II(KA630-A microprocessor running 4.3 BSD UNIX). To find three grasp points on two edges with force directions, it lakes about 0.006 second. 6. 3.2 Grasp on Three Edges When three edges are used to grasp an object, we can have either parallel or triangle grasp depending on the arrangement of the three edge normal vectors. Parallel grasp is possible when three edge normal vectors are parallel to each other and one edge normal is in the opposite direction to the other two edge normal vectors. Figure 3.2 (a) shows construction of parallel grasp on three edges. Since the procedure to construct a parallel grasp on thee edges is very similar to algorithm 3.1, we omit it for the lack of space.(For more detailed procedure, refer WI.) Algorithm 3.2 describes the construction of viangle grasp on three edges. Algorithm 3.2 Triangle Grasp on Three Edges: 1 . 2. 3. 4. Check whether three edge normal vectors make vector closure. If not, stop. Find intersection of three edge feasible regions, EF = E F ( E , ) n EF (Ed n EF ( E 3 ) ",
            " force direction vectors applied at each grasp point will intersect at the center of the convex polygon. That is, if the center of intersection of the feasible regions is selected as force focus point and grasp points are identified by projecting the force focus point on each edge, the final grasp would be the one that is safest in terms of possible errors. Even hough accurate center of a convex figure is defined in terms of centralness coefficient, the arithmetic average of vertices is used in this work as the center of intersection of feasible regions. Figure 3.2 @) shows construction of a triangle grasp on three edges. Computation of three grasp points with force directions takes 3.3 Grasp on Two Edges and One Vertex When two edges and one vertex are used to construct a force closure grasp, either parallel or triangle grasp is possible. To identify relative arrangement on edge normal vectors and vertex range as graspable configuration, define the normal circle first. Definition 3.2 Normal Circle : Normal circle is a unit circle with all edge normals and vertex range vectors starting from center of circle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002001_1.1649662-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002001_1.1649662-Figure3-1.png",
        "caption": "FIGURE 3. Early Simulation of Bucket Wheel Excavator. FIGURE 4. Blown-up View of Grate.",
        "texts": [
            " Our basic approach was to adapt a conventional terrestrial bucket wheel excavator design to use in planetary applications. An excavator scale that would be amenable to demonstration on Mars using a typical planetary mission scale, such as the Mars Exploration Rover Mission (MER), was adopted as a goal. This sets the excavator mass at approximately 50 kg, assuming that a complete demonstration mission would also include a reactor of similar mass. The MER spacecraft carry an Athena rover, which has a mass in the vicinity of 150 kg. Figure 3 shows an early simulation of the planetary bucket wheel excavator. The chassis is a six-wheel system similar to the Athena rover, derived from its rocker-bogie system, but with a fixed front wheel assembly. A boom is mounted on this chassis that allows the bucket wheel be positioned upward or downward and to move from side to side so that the wheel can excavate a swath the same width as the chassis. The boom also provides a pathway for material to move . The bucket wheel rotates counter clockwise as it is pushed through the regolith, lifting material FIGURE 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003606_detc2005-85337-Figure6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003606_detc2005-85337-Figure6-1.png",
        "caption": "Fig. 6 Mobility analysis of PR1R1R1R-2-PR1R1R1 PKC: (a) The original kinematic chain and (b) The kinematic chain with inactive joints removed.",
        "texts": [
            " Step 2 There are no inactive joint in this PKC. Step 3 It can be found that the PPP equivalent serial kinematic chain [Fig. 5(b)] and each PR1R1R1 comprise a 3-DOF single-loop kinematic chain. Thus, the PPP equivalent serial kinematic chain of the 3-PR1R1R1 PKC is its full-cycle equivalent serial kinematic chain. Then we conclude that the PKC has full-cycle mobility. The method of the mobility analysis proposed above will now be illustrated using the following seven examples. Example 1 Consider the PR1R1R1R-2-PR1R1R1 PKC shown in Fig. 6. In this PKC, all the axes of the R1 joints within a same leg are parallel. The axis of a P joint is not perpendicular to the axes of the R1 joints within the same leg. 2Although there may exist paradoxical PKCs, they are excluded from the scope of this paper. ownloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/07/2016 The wrench system of the PR1R1R1R leg is a 1-\u03b6\u221e-system, in which the base wrench is a \u03b6\u221e whose axis is perpendicular to the axes of all the R joints within the same leg",
            " We have c1 = 1, c2 = c3 = 2, c = 3, Ri = 0. Using Eqs. (4), (7) and (8), we obtain C = 6\u2212 c = 3 and F = C + 3\u2211 i=1 Ri = 3. The number of overconstraints of this 3-legged PKC is \u2206 = 3\u2211 i=1 ci \u2212 c = 1 + 2 + 2\u2212 3 = 2. Following the procedure for the full-cycle mobility inspection, we have Step 1 Since \u2206 = 2 6= 0, go to the next step. Step 2 For this PKC, the R joint in the PR1R1R1R leg which is located on the moving platform is inactive [20,21]. Remove the inactive joint, one obtain a 3-PR1R1R1 PKC shown in Fig. 6(b). Step 3 As we have found above, the 3-PR1R1R1 PKC has full-cycle equivalent serial kinematic chain. The full-cycle equivalent serial kinematic chain can be represented by a PPP serial kinematic chain. Thus, the PKC has full-cycle mobility. Example 2 Consider the 3-R\u030cR\u030cR\u030cR\u0302R\u0302 PKC shown in Fig. 7. In this PKC, the axes of all the R\u030c joints pass through one common 6 Copyright  2005 by ASME Terms of Use: http://www.asme.org/about-asme/terms-of-use Dow point, while the axes of the R\u0302 joints pass through another common point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000909_tsmc.1995.7102305-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000909_tsmc.1995.7102305-Figure1-1.png",
        "caption": "Fig. 1. Geometry of 3 link, revolute, planar manipulator in terms of (a) absolute angles, or (b) relative angles. All link lengths are equal.",
        "texts": [
            " Section III shows how pseudoinverse control can be formulated for an arbitrary set of joint angles and describes the conditions for a conservative solution in the control of these angles. The following section uses a combination of analytical and numerical methods to attempt to find conservative cases, and the last section presents implications of the results and conclusions. In this section the mathematical conditions for a repeatable config uration will be established for arbitrary joint angles for the equallength, planar, 3 joint, revolute manipulator. Fig. 1(a) shows the geometry of this problem in terms of absolute joint angles ^. It is very easily shown [6], that for these angles the Jacobian relationship is , \u2022. [ -s in^i - s i n ^2 - sin V>31 \\ . /AS [ COS^i COS \"02 COS^3 J where x is the rectilinear end effector velocity in the plane. Fig. 1(b) shows the geometry of this same problem in terms of the more familiar relative joint angles 0. Noting that each absolute joint angle is the sum of the corresponding relative joint angle plus all inboard joints, a simple relationship between the joint vectors is $1 ^2 J03. = Qr 'Ol' 02 03 = ' 1 0 0\" 1 1 0 1 1 1 0i\" 02 03 Since Qr is a constant matrix, the derivative of (5) can be substituted into (4) to get the Jacobian relationship for relative joint angles in terms of the 0 Jacobian matrix Je"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002189_mech-34368-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002189_mech-34368-Figure5-1.png",
        "caption": "Fig. 5 The Y-axis should be the X-axis, the X-axis should be the Y-axis in the opposite direction.",
        "texts": [],
        "surrounding_texts": [
            "Standard test plane and standard test path are used as two important steps in reducing the amount of testing work involved in testing and comparing the performance of different industrial robots from different manufactures. Both standard test plane and standard test path are defined based on the concept of working space center point. A wrong working space center point will waste the tremendous amount of testing work, and should be avoided. Most of the errors in the standard, unfortunately, are related to working space center point. Working space center point plays a very important role in this standard. 2.1 Center Point Location in Working Space On page 11 of the standard, in figure 4, the position of the working space center point is positioned incorrectly. Along the same x-axis shown, Cw should be located at the midpoint of the x-axis line and not off centered. . 1b) After corrected 1a) Original figure 4 Fig. 1 Cw should be located at the midpoint of that X-axis li 2 2 Copyright \u00a9 2002 by ASME tp://proceedings.asmedigitalcollection.asme.org/ on 04/11/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: ht 2.2 Coordinate Associated with Center Point Definition On page 11 of the standard, in figure 4, X1Y1 coordinate is needed. 2.3 Standard Test Plane and Its Reference Plane On pages 21and 22 of the standard, figures 12 and 13 are both mislabeled. They are not standard test plane and exception test plane, but the standard reference plane and exception reference plane respectively. The standard test plane is the plane that parallel to the standard reference plane and passes through the work place center point. 3 3 Copyright \u00a9 2002 by ASME tp://proceedings.asmedigitalcollection.asme.org/ on 04/11/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: htt The planes are not Standard Test Plane and Exception Test Plane, but the Standard Reference Plane and Exception Reference Plane respectively. 2.4 Location of Standard Test Plane in Working Space On page 22 of the standard, in figure 14, the Y-axis should be X-axis, the X-axis should be the Y-axis and in the opposite direction as shown. The standard test plane should be flipped to the other side of the robot. The first segment is smaller than the other segments. 4 4 Copyright \u00a9 2002 by ASME p://proceedings.asmedigitalcollection.asme.org/ on 04/11/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: htt 2.5 Location of Standard Test Plane and Coordinate System On page 23, Figure 15 has the same errors as figure 14 mentioned above. 5 5 Copyright \u00a9 2002 by ASME p://proceedings.asmedigitalcollection.asme.org/ on 04/11/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: ht Table 1. List of Errors page No. Before Revised After Revised 11 In Fig. 4, the position of the working space center point is positioned incorrectly. Along the same x-axis See Fig.1 See Fig. 2. 11 X1Y1 coordinate is needed. See Fig. 3 See Fig. 4. 22 In Figure 14, the Y-axis should be X. The X-axis should be Yaxis in the opposite direction. See Fig. 9 See Fig. 10 23 Figure 15 has the same errors as Figure 14. See Fig. 11 See Figure 12. 25 In item 4. STP Cycle Test, Deviation From STP, Section is \"8.4.2.8\". There is no section with that number. It should be \"8.4.2.7\". 26 Section 7.3 second line is \"(Table 2)\". Table 2 should be \"(Figure 17)\""
        ]
    },
    {
        "image_filename": "designv11_11_0002629_pime_proc_1987_201_156_02-Figure12-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002629_pime_proc_1987_201_156_02-Figure12-1.png",
        "caption": "Fig. 12 Alternator speed rlmin",
        "texts": [
            " The effective friction increase expected from wedging the belt in the pulley groove has been completely offset by the reduction caused by belt radial movement. It is commonly recommended in design guides (16, 17) that for a nominal contact arc of R radians, FJF, should not exceed 5, whatever the pulley radius. Figure 7 shows that this is extremely conservative for largeradii pulleys as far as efficiency is concerned. Finally, it is instructive briefly to extend the discussion to consider the matching of the raw-edged belt's power transmission capacity to the power requirements of a typical medium car alternator. Figure 12 shows the input power typically required for full output from a modern medium-sized (55 A) alternator (from private communication, Lucas CAV Limited, 1986). It also shows the power that can be transmitted by an AVlO raw-edged belt without excessive power loss, assuming an angle of wrap of 18W, F, + F, = 500 N, an alternator pulley radius of 30 mm and taking F J F , to equal 7 (from Fig. 7); driving between pulleys on fixed centres has been assumed (in contrast to the present experiments) and the loss of drive at high speed stems from centrifugal effects calculated for the belt's measured mass of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001056_robot.1998.680759-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001056_robot.1998.680759-Figure2-1.png",
        "caption": "Figure 2 : Cases when the conditions are and are not satisfied.",
        "texts": [
            " With the second condit,ion, any point on the hyperplane xi = 0 (:an be represented a nonnegative linear combination of vertices of H ( V ) . Note that all vertices of H ( V ) belong to the convex hull H ( N ) , and thus they are convex combinations of the N original points. Therefore, any point on the hyperplane x, = 0 can be represented by a nonnegative linear combination of t,he N points and so can the point 'U. This implies that the convex hull W ( N ) contains the origin point of Rd. 0 In Figure 2a, the t,wo conditions are satisfied for all i . In Figure 2b, the first condition is satisfied but the second is not for s i = 2 ; the second condition is satisfied but the first, is not for i = 1. If for an i the two conditions are satisfied, the conditions hold for all other i. Similarly, if for an i the two conditions are not, simultaneously satisfied, for any other i the conditions cannot be simultaneously satisfied. From Theorem 1, it is possible to recursively transform the problem of qualitative test in Rd to a problem in R1. In detail, we first slice the convex hull H ( N ) by the hyperplane x d = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002299_027836402761393487-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002299_027836402761393487-Figure1-1.png",
        "caption": "Fig. 1. Manipulation under neighborhood equilibrium.",
        "texts": [
            " If a robot hand can manipulate an object skillfully under the equilibrium grasp, we can expect that the object manipulation can be realized with a smaller number of fingers. Based on these considerations, we focus on the equilibrium grasp separate from the force-closure grasp. Now, let us introduce an interesting behavior which can be observed under the equilibrium grasp. To understand the simplest case of the equilibrium grasp, imagine that a spherical and an ellipsoidal object are placed on a table (Figure 1(a)). Suppose that the table is slightly inclined. With this small inclination of the table, both objects will lose the initial equilibrium state and start rolling motions. Once the spherical object starts a rolling motion, it never stops and finally falls off the edge of the table. Under the same situation, the ellipsoidal object will also start a rolling motion. However, it soon stops and results in another equilibrium state, while it may not stop for a larger inclination angle of the table. Corresponding to this phenomenon, we will define that an ellipsoidal object satisfies the Neighborhood Equilibrium (NE) for a small inclination of a table. Whether or not the object satisfies NE depends on the local shape of the object around the contact point. If the object satisfies NE, it is considered that the object manipulation under the equilibrium grasp can be realized easily compared to the manipulation of an object without satisfying NE, since the equilibrium can be easily satisfied. This is a motivation to focus on the manipulation of an object under NE in this paper. Figure 1(b) shows an example of manipulation. It can be simplified as shown in Figure 1(c) where the inclination of the table is controllable. For a 3D object with pure rolling contact, we have three constraints for the relative velocity at the contact point, i.e., the 463 at UNIV OF WISCONSIN MADISON on July 19, 2012ijr.sagepub.comDownloaded from two dimensional translational velocity and one dimensional rotational velocity about the contact normal become the same for two rigid bodies contacting each other. These constraints are known as the nonholonomic constraints. Also, the contact configuration is expressed as five dimensional variables, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002346_robot.1991.131953-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002346_robot.1991.131953-Figure1-1.png",
        "caption": "Figure 1: Planar kinematic chain",
        "texts": [
            " Background (Anholonomy) This paper is a continuation of [GI. Consider a robot (kinematic chain of n rigid bodies) floating in zero gravity. For convenience, assume that the bodies (and the assembly) are planar and the assembly is initially at, rest (angular momentum p = 0) as in Figure 1. Suppose the joint angles are varied continuously and brought back to rest in a prescribed manner. There will be a net displacement (say of body 1) from its absolute initial orientation. This phase shift is given by a n integral formula [GI 'Supported in part by the National Science Foundation's Engineering Research Centers Program: NSFD CDR 8803012, and by h e AFOSR URI Program under grant AFOSR-90-0105 where e = (1 ,1 , . . . , l ) , M is an n x ( n - 1) milt,rix 0 , i = l Mij = 1, i > j given by { 0 otherwise, and J denotes the n x n kinetic energy quadratic form associated to the planar n-body system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003606_detc2005-85337-Figure7-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003606_detc2005-85337-Figure7-1.png",
        "caption": "Fig. 7 Mobility analysis of 3-R\u030cR\u030cR\u030cR\u0302R\u0302 PKC.",
        "texts": [
            " Following the procedure for the full-cycle mobility inspection, we have Step 1 Since \u2206 = 2 6= 0, go to the next step. Step 2 For this PKC, the R joint in the PR1R1R1R leg which is located on the moving platform is inactive [20,21]. Remove the inactive joint, one obtain a 3-PR1R1R1 PKC shown in Fig. 6(b). Step 3 As we have found above, the 3-PR1R1R1 PKC has full-cycle equivalent serial kinematic chain. The full-cycle equivalent serial kinematic chain can be represented by a PPP serial kinematic chain. Thus, the PKC has full-cycle mobility. Example 2 Consider the 3-R\u030cR\u030cR\u030cR\u0302R\u0302 PKC shown in Fig. 7. In this PKC, the axes of all the R\u030c joints pass through one common 6 Copyright  2005 by ASME Terms of Use: http://www.asme.org/about-asme/terms-of-use Dow point, while the axes of the R\u0302 joints pass through another common point. The mobility analysis of this PKC can be performed as follows. Instantaneous mobility analysis The wrench system of each leg is a 1-\u03b60-system in which the base wrench can be a \u03b60 whose axis passes through the above two common points. The wrench system of the PKC is a still a 1-\u03b60-system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001516_iros.1997.649040-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001516_iros.1997.649040-Figure2-1.png",
        "caption": "Figure 2: Swing Modes",
        "texts": [
            " The swing motion will be divided into the following two subtasks: A) generation of swing motion, and B) control of swing motion. Task A) is necessary to add the dynamic energy to the gripper. Details will be shown in section 4.3. Task B) controls the manipulator to converge to the desired swing motion in order to throw the gripper to the target precisely. The algorithm for Task B) is shown in section 4.4. Before discussing the control of swing motion, we consider several modes of swinging the casting manipulator as penodicity. The motion of modes a) and b) in Figure 2 is periodic motion, while that of modes c) and d) is not repeated periodically. Considering the stability of swing motion and throwing motion, we chose mode a) \u20acor swinging the manipulator in the first step. Figure 3 shows the steps of the swing motion. Figure 3 I), 2) and 3) represent respectively the initial state, arbitrary swing state, and desired swing state. shown in Figure 2. Roughly speaking, there are two nodes, that of pendulum motion and that of giant swing motion. Both are divided further into two modes in terms of ' I70 and where L; is the length of link i, d i is the distance between joint i and the center of gravity of link i, m, is the mass of link i, li is the moment of inertia about the center of gravity of link i , 61 is the angle of joint i, and g is the acceleration due to gravity. 4 Swing Motion Control Before casting the gripper, it is necessary to give the gripper the motion \u20acor casting",
            " When O2 approaches the desired motion, the motion of joint 1 follows the non-holonomic restriction given by equation (2)[7]. By substituting 02 =o, 8 2 =o, 82 =a into equation (2), we obtain Differential equation (8) can thus be rewritten as a canonical equation; the phase portrait of this case is shown in Figme 5 . Figure 5 shows that joint 1 can make four kinds o f motion, \\~htch are respectively the state of rest, periodic oscillation, rotation in the constant direction, and motion on the orbit behveen the states of rest. The periodk oscillation corresponds to mode a) in Figure 2, and the rotation in the constant direction corresponds to mode b). Since we select mode a) as mentioned in section 2, we choose the periodic oscillation, namely the motion on the orbit that is similar to the elliptic orbit in Fijpre 5 , for the motion of joint 1 as the method of swinging the manipulator. On this orbit, the manipulator swings like a pendulum. In this paper we call this orbit an elliptic orbit and we call the motion of the manipulator on the elliptic orbit pendulum motion, for convenience"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003518_00207170600708699-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003518_00207170600708699-Figure1-1.png",
        "caption": "Figure 1. Performance funnel F\u2019",
        "texts": [
            " The basic problem addressed there was that of approximate tracking (with prescribed transient behaviour), by the system output y, of any absolutely continuous and bounded function r with essentially bounded derivative: the terminology \u2018\u2018approximate tracking\u2019\u2019 means that, for any prescribed >0, a control structure can be determined which ensures that the tracking error e \u00bc y r is ultimately bounded by (that is, ke\u00f0t\u00dek for all t sufficiently large); the terminology \u2018\u2018with prescribed transient behaviour\u2019\u2019 means that, for some suitable prescribed function \u2019, the error function is required to satisfy ke\u00f0t\u00dek 1=\u2019\u00f0t\u00de for all t > 0. The choice of \u2019 determines the transient behaviour; moreover, by imposing the property lim inft!1 \u2019\u00f0t\u00de 1= > 0, the approximate tracking objective is assured. For example, with \u2019: t minft=T, 1g= , the approximate tracking objective is achieved in prescribed time T>0. Figure 1 encapsulates the approach: the function \u2019 determines the performance funnel F\u2019, which may be identified with the graph of the set-valued map t fvj \u2019\u00f0t\u00dekvk < 1g. Simply stated, the control objective is to maintain the evolution of the tracking error in the funnel F\u2019. For reference signals of the generality considered in (Ilchmann et al. 2002) (namely, signals of classW1,1), the function \u2019 is required to be bounded and hence exact asymptotic tracking cannot be achieved. The purpose of the present note is to demonstrate that the boundedness condition on \u2019 may be relaxed if one restricts the class of reference signals to coincide with the set of solutions of a fixed, stable, linear, homogeneous differential equation and confines attention to minimum-phase linear systems with sign-definite high-frequency gain"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001157_jsvi.1998.1528-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001157_jsvi.1998.1528-Figure3-1.png",
        "caption": "Figure 3. Constructional variants of columns of the same boundary conditions and loading, but different way of force application: (a) load passing through a fixed point and; (b) column loaded by a moment.",
        "texts": [
            " Two different variants of the system are schematically drawn in Figures 3(a) and (b). Experiments presented in this study concern the column from Figure 2(b); the second boundary condition for x= l is given in the third part of the work [equation (7)]. In this work the stability and natural vibration of a cantilever column subjected to a follower force passing through a fixed point has been considered. This load can be realised in two constructional variants shown in Figures 3(a, b). Column I [Figure 3(a)] is loaded by a force P tangent to the deflection at the point of the force application (x= l), and passing through a fixed point O. A stiff element 1 of the length lc of column II\u2014Figure 3(b), is carrying a vertical force P. Hence for these columns the boundary conditions are W(l, t)= lcW'(l, t) (1) W(0, t)=W'(0, t)=0. (2) At the free end of both columns a concentrated mass m is mounted. For column II mass m is composed of the concentrated mass M and the reduced mass Mzr of the element 1. The point of reduction is the point of mass M fixing. The present investigation has been directed toward the following objectives: , in the field of theory \u2014to analyse the total elastic energy of columns from Figure 3 to verify whether each system is conservative or nonconservative; \u2014to evaluate the divergence critical force and its maximum as a function of the length lc . \u2014to reveal on the basis of eigenvalue curves that the columns are the divergence\u2013pseudo-flutter systems (D-PF); , in the field of experiment and numerical calculations \u2014to present an experimental and construction of the column from Figure 3(b); \u2014to perform experimental investigations of the natural vibration frequencies as a function of an external load for two columns of different geometrical and physical properties; \u2014to analyse the change in vibration modes along the eigenvalue curves. For the foregoing system the Hamilton principle has the form [32] d g t2 t1 $s 2 i=1 (Ti \u2212Vi )+L% dt=0 (3) where T1 = 1 2rA g l 0 [W (x, t)]2 dx (3a) is the kinetic energy of the column, T2 = 1 2m[W (l, t)]2 (3b) is the kinetic energy of the concentrated mass, V1 = EJ 2 g l 0 [W0(x, t)]2 dx (3c) is the energy of the elastic deformation, V2 =\u2212 P 2 g l 0 [W'(x, t)]2 dx (3d) is the potential energy of the vertical component of the force P, LA =\u2212PW(l, t)W'(l, t), LB =\u2212PW(l, t)W'(l, t) (3e, f) are the work of the horizontal component of the force P for column from Figure 3(a), or the work of the bending moment for column from Figure 3(b), respectively, rA is the mass per unit length, EJ is the flexural rigidity. Taking into account the geometric condition (1), one obtains LA =LB =L=\u2212P W2(x, t) lc . (3g) Due to the form of equation (3g), an analogous derivation as in reference [33] makes it possible to establish the potential of the horizontal force P component or the bending moment as follows V3 = P 2 W2(x, t) lc (4) with dV3 =\u2212dL, dL=\u2212PWdW. (5a, b) Existence of the potential (4) indicates that the foregoing system is conservative"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001332_s0925-4005(96)02008-4-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001332_s0925-4005(96)02008-4-Figure4-1.png",
        "caption": "Fig. 4. (a) Schematic view of the solid-contacted ISVE with (1) membrane area; (2) conducting track; (3) heat-sealing film', (4) paper disk coated with a silver layer containing membrane cocktail; (5) front opening towards analyte solution; (6) contact area at the back side (b) Cross-section of the sensor with (7) spacer; (8) silver/silver-tetrakis-(4chlorophenyl)-borate-layer.",
        "texts": [
            " The silver-coated paper disks were placed between the prepared sheet of heat-sealing film and a second, nonperforated one so that the silver layer and the conducting track were connected. The electrode was encapsulated by heat and pressure in a lamination process. The membrane cocktail of the described composition was deposited on the smaller front area. Due to this construction, the silver layer was placed near the working interface in order to obtain a thin membrane with a low iR-drop within the organic phase. A schematic view of the solid-contacted sensor is shown in Fig. 4. After evaporation of the organic solvent, the back side contact was prepared by electrolysis within the membrane. In order to obtain a coating of the silver area with silver-tetrakis-(4-chlorophenyl)-borate, the electrode (connected as a combination of reference and counter electrode) was polarised three times for each 30 s at a potentiai o f -650 mV against a silver/silver chloride-electrode in the presence of nitrate or perchlorate ions. Measurements were carried out in a two-electrodearrangement with a potentiostat/gaivanostat (PG28, HEKA, Lambrecht, Germany)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001157_jsvi.1998.1528-Figure4-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001157_jsvi.1998.1528-Figure4-1.png",
        "caption": "Figure 4. Columns of different length of the loading link: (a) lc =0; (b) 0Q lc Qa; and (c) 1/lc =0.",
        "texts": [
            " (14) In the above expression the differential notation replaces the variational notation. Substituting (9) into (14) for l:lc one may write dV dl =\u2212 fl 0 [y0(x)]2 dx lc0fl 0 y2(x) dx+ m rA y2(l)1 Q 0. (15) It it obvious from (15) that for l:lc the slope of the eigenvalue curve l= l(V) is always negative. The deflected shapes of columns for the extreme values of the length of the stiff element lc are sketched in Figures 4(a) and (c). In a certain range of lc $(lc1, lc2) the column must have the deflected shape as in Figure 4(b), for which the first derivative y'(x) is monotonic for the external load parameter l growing from zero. On the basis of the theorem of the average value of an integral of the monotonic function, the numerator of expression (14) is greater than zero and can be presented in the following form N=\u2212g l 0 y'2(x) dx+ y'(l)y(l)= y'(l)y(j)q 0 (16) where j$ 0, l . For the increasing value of l, the variation of y'(x) changes from monotonic to non-negative, and hence the numerator of expression (14) takes the form N=[\u2212y'(j)+ y'(l)]y(l) (17) and can be less, or greater, or equal to zero",
            " The link is joined by a needle bearing to the beam (10), which is mounted in the holder (11) pinned to the plate 4(2). A force created in the head 1(2) is transferred to the column (5) by means of the beam (10). Vibration tests were performed with the use of a two-channel vibration analyser (12) of 2035 type and the accelerometer (13) of 4381 type made by Bru\u0308el & Kjaer. The system was activated by the manual impactor (14). In order to study the experimental vibration modes, the virtual discrete model of the system composed of 19 elements joined by 20 nodes adequate to the real system was created also [Figure 4(b)]. An accelerometer (4381 type) was mounted at the node number 11 to collect system responses for the excitement of nodes 1\u201320. The measured band of both the excitement and responses was in the range 0\u2013400 Hz within the measuring resolution of 1 Hz. Five natural frequencies were identified within the obtained response band. The modal analysis was done with the help of the PC MODAL program (Vibration Engineering Consultants, U.S.A.) run on a personal computer (15) coupled to the analyser (12). The equations of motion and boundary conditions for the column of the bending rigidity EJ are stated in the first part of the work (1, 2, 6, 7)",
            " Results concerning the third vibration frequency for column A are marked with bars because there T 1 Geometrical and physical parameters of column Rod\u2019s diameter E1 =E2 r1 = r2 m Column (m) (MPa) (kg/m3) (kg) A 0\u00b7012 7\u00b75\u00d7104 2790 0\u00b759 B 0\u00b7014 7\u00b75\u00d7104 2790 0\u00b760 l=0\u00b763 m; lc =0\u00b731 m were no one peak values on the analyser display for these frequencies. The length of each bar is equal to the width of the measured frequency band. In Figure 8 the dimensionless critical load parameter l*c versus the relation of c= lc /l is given (l*= ll2). The values l*ca and l*cc are the critical parameters for columns from Figures 4(a) and (c), respectively. The solid line represents the change in the critical parameter for the considered column [Figure 4(b)]. Accordingly to both the formula (11) and Figure 8, the maximum critical force exists for lc = l/2. In Figure 9 the dimensionless natural frequencies V* are plotted against parameter l* for columns from Figures 4(a, b, c) of different dimensionless length c of the loading member (V*=VrAl4, c= lc /l). All curves related to the symmetric modes Mne are not affected by the length lc so they overlap each other. The change in the modes appears along curves obtained for c=0\u00b7687 only, because only this system belongs to the class of divergence\u2013pseudo-flutter systems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003154_3-540-28247-5_19-Figure19.5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003154_3-540-28247-5_19-Figure19.5-1.png",
        "caption": "Fig. 19.5. Instantaneous translation as rotation about an axis at infinity",
        "texts": [
            " If A is a line at infinity (thus both a and b are points at infinity), then A represents a translation in terms of Euclidean geometry. Indeed, using Pl\u00fccker coordinates, A \u2228 p is represented by the 3\u00d7 3 minors of b1 b2 b3 0 p1 p2 p3 1 \u23a4\u23a6 . Now we see that the first three components of A \u2228 p, namely P2,3,0 = a2b3 \u2212 a3b2, P3,1,0 = a3b1 \u2212 a1b3, P1,2,0 = a1b2 \u2212 a2b1, are independent of p1, p2, p3; thus every point p has the same velocity vector, and the result is a translation. As a result, in a very real sense, a translation is a rotation with an axis at infinity. This is fairly easy to visualize intuitively, as shown in Fig. 19.5. Imagine a point being rotated a fixed arc length l about an axis. Now keep the point\u2019s position fixed, but move the axis farther away. The point\u2019s trajectory is still a circular arc of length l, but with a larger radius. In the limit, as the axis moves away infinitely far, the trajectory becomes a straight line segment of length l. Since the axis is now infinitely far from all points in Euclidian space, all have the same direction of motion, and the result is a translation of Euclidian space. Consider now a robot arm with k revolute joints serially connected, which we consider to be in a certain position at time 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001914_isic.1994.367814-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001914_isic.1994.367814-Figure2-1.png",
        "caption": "Figure 2: Cargo Ship",
        "texts": [
            " Multiple steps into the future associated with any of the variables y, i , or U will be demarcated by N j as in y(k) , . . . , y(k + N j ) . We will use a model of the plant denoted by P and defined by f(k + 1) = f ^ ( i ( k ) , i(k)) (3) Y(k) = iqf (k) , Q(k . ) ) . (4) in our model based controller. To clarify how P, C, and M in Figure 1 are chosen for GMRAC we use a cargo ship steering problem where we seek to adaptively control the heading of the ship, $ by manipulating the rudder angle, 6. A coordinate system fixed to the ship is shown in Figure 2 and the problem was taken from [15, pp. 355-3591. The cargo ship is described by a third order nonlinear equation [16, p. 271: . . where H ( $ ) is a nonlinear function of $ ( t ) . The function H ( 4 ) can be evaluated from the relationship between 6 and $ at steady state such that *= 4 = $ = 0. An experiment. known as the \u201cspiral test\u201d approximates H ( $ ) by + b 4 . The real valued constants a and b are assigned a value of one for all simulations. The constants K , 71, 7 2 , and 5 are defined as K = KO"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003282_0301-679x(83)90043-9-Figure11-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003282_0301-679x(83)90043-9-Figure11-1.png",
        "caption": "Fig 11 Load carrying capacity plotted against attitude angle",
        "texts": [],
        "surrounding_texts": [
            "Jain and Sinhasan - Journal bearings with variable viscosity lubricants\nand the friction coefficient parameter also compared well with those of Conway and Lee a3 for different values of deformation coefficient, as shown in Table 1.\nTile rigorous 3-d and simple thin (Eq (7)) structural models were used to calculate the deformations in a bearing liner of unit aspect ratio. The radial deformations (Vb)obtained by both models were compared for different tc~ ratios of a liner which had a value of Poisson's ratio of 0.3 leg steel, brass). The upper limit of liner thickness, below which the deformation ( V b) obtained by both models matches closely is presented in Fig 6. The effect of Poisson's ratio on radial deformation is demonstrated in Fig 7. Up to the value of t~ =- 0.1 (7 = 0.3), the results obtained by both models are identical. The computation time (on a Dec-20 system) required for a particular piece of data using the 3-d model\n5 0\ncL o~\noJ (3. E 2.0 r\n~0\nLine\n0\n2\n3\n050 l - - 4\nr\n055~ 2\n% 0 0 0 0 0 1 0 03\n0 0 5 0 07\n0 1 0\nI I 1 I I 03 04 05 06 07\nHmm Fig 8 The effect o / d e f o r m a t i o n s o n the maximum p r e s s u r e\nis, however, about 8 - 10 times greater than when using the thin structural model. In the present analysis, therefore, assuming the liner thickness to radius ratio to be as high as O. 1 (a reasonably practical value 2\u00b0), V b was calculated using the 'computationally economical' thin structural model. Including these values of radial deformation, new values for film thickness (Eq (1)). pressure distribution, and static characteristics were computed for a wide range of eccentricity ratios. The performance is reported for different values of deformation coefficient (Figs 8 11) and for pressure-viscosity coefficients of 0.00, 0.05 and 0.10 (Fig 12).\nP and V b were computed for difl'erent liner thicknesses using gqs (2) and (10). The deformations (Vb) obtained l'or t a = 0.1 and t~ = 0.4 are compared with those given by",
            "Jain and Sinhasan - Journal bearings with variable viscosity lubricants\nEq (7) of the thin liner model in Fig 5. In view of the geometric and loading symmetry about the centre line (Z = 0), the deformations are shown only for half bearing. The deformations are given along the circumference at Z = 0, X/3, 2X/3 and X, for e = 0.9. Fig 5 shows that for a relatively thin liner (t~ = 0.1) the deformations obtained using both types of elastic model are quite close.\nFig 6 indicates the limit for ta below which values of Vb at any point, obtained using the 3-d elastic model, are proportional to the pressure and satisfy Eq (7). This figure presents the ratios between Vb andPin terms of V~ (=Vb/ (~o P)), for eccentricity ratio 0.6 and a Poisson's ratio of the liner material of 0.3. For a reduced liner thickness (t~ ~< 0.i), Vb andP are linearly related over a large arc of positive pressure film, as indicated by nearly constant values of V~ - unity for the thin liner approximation. With an increase in liner thickness, V~ does not remain unity and varies in the circumferential as well as in the axial direction. For large re, greater deviation from unity is observed in the value of V#.\no\n24 - Line ~o 0 0.00 2 0.05 k 3 0.05 / 5 o. I0 / / / 2 2o / / -\n1 6 ~ 5\n12t I I I I I I I i I riO 20 50 I0\nLoad capacity W r\nFig 10 The effect o f deformations on the power loss\nThe effects on V b of variations of Poisson's ratio o f the liner material (3') and of t~ may be studied on the basis o f the results presented in Figs 6 and 7. For small liner thickness and 7 between 0.3 and 014, the deformation o f the bearing liner computed using the simplified thin structural model is quite close to that Obtained using the more rigorous 3-d analysis.\nWithin the established limits of liner thickness and Poisson's ratio, and when the simple elastic analysis is applicable to the bearing deformation calculations, Vb is related to fie by Eq (7) and t o e andTh by Eq (8).iTh\u00a2 effects of liner thickness and E could thus be studied with reference to different values of ~o.\nWhen a liner deforms, the variation of V b along the bearing axis changes the film thickness (from Eq (10)) at any value of 0. Moreover, the value of the minimum film thickness - which is constant along axial length for a rigid liner and occurs at 0~ = 180 \u00b0 - appears at the bearing sides when liner flexibility is considered. For thin liners (t~ ~< 0.i)~ since the magnitude of V b at the sides is insignificant, the minimum film thickness does not change appreciably from that of a rigid bearing and can be estimated with sufficient accuracy by Hmi n = 1-e.\nFigs 8-11 present the performance characteristics of \"dae journal bearing system, in terms of maximum pressure, load capacity, attitude angle and power loss, for an isoviscous lubricant (a = 0.0). The common range of operative eccentricities is considered. Because the minimum film thickness is an important criterion in journal bearing \u0300 design, the plots of performance characteristics are drawn with respect to Hmin. Power loss and attitude angle of journal bearings of different flexibilities are then compared over the range of load capacity.\nC\n%\nd % Fig 12 The effect of viscosity variations on the performance characteristics: (aJ pressure distribution at the centre line (Z--O), full journal bearing,\" ( b ) maximum pressure; ( c ) load capacity; (d) power loss\n336 December 1983 Vol 16 Number 6",
            "J a i n a n d S inhasan - J o u r n a l b e a r i n g s w i t h va r i ab l e v i s c o s i t y l u b r i c a n t s\nof flexible journal bearings presented in Fig 10 show that for any load capacity the power loss P1 decreases with an increase in ~o. This is an important finding for bearing design. The decrease in attitude angle with increase in ~o for any load capacity (Fig l 1) is an indication of the improvement in dynamic stability of the journal bearing system brought about by a flexible bearing liner. To confirm this, however, a dynanic analysis needs to be made. The performance characteristics related to the bearing shell"
        ]
    },
    {
        "image_filename": "designv11_11_0000442_ma961333c-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000442_ma961333c-Figure2-1.png",
        "caption": "Figure 2. Picture of the Lewis structures of the electronic configurations which correlate to the surface radical of acrylonitrile proposed by Mertens et al.2 (Figure 1) at infinite organics/surface separation (see text).",
        "texts": [
            " Mesomeric forms (or configurations) stemming from electronic rearrangements inside the organic itself or inside the metal itself are not considered, as we are mainly interested in the description of the interface* Corresponding author: e-mail: christophe.bureau@cea.fr. S0024-9297(96)01333-2 CCC: $14.00 \u00a9 1997 American Chemical Society region and more particularly in the charge transfer. We first note that the {molecule + surface} system depicted in Figure 1 is a spin doublet (S ) 1/2). Several alternatives can be considered and are presented in Figure 2: (a) The interface bond is dissociated so that the two electrons of the single C/surface bond are kept on the surface: the resulting organic moiety is a spin doublet, but constitutes a radical cation. There has been no net electronic transfer from the surface to the molecule, but rather from the molecule to the surface. In other words, configuration a alone would correspond to an electron counted in an anodic current and to a highly excited situation where the charge transfer is forced to be opposite to what electronegativities would impose;6 (b) The interface bond is dissociated so that the two electrons of the single C/surface bond are kept on the molecule. The electron transfer does give rise to a cathodic current, and the resulting fragments at infinite separation are an organic radical anion and a (locally) cationic site on the surface (Figure 2b). As mentioned above, this \u201chole\u201d is not filled by electrons coming from the potentiostat, as we are performing our formal dissociation at constant overall number of electrons. An electron vacancy is thus created in the metal. Moreover, the radical anion then has a charge distribution which is opposite to that expected for its ground state,7 and thus also corresponds to a highly excited state. In addition, if this structure were to give rise to the adduct shown in Figure 1, this would mean that it is the anionic end of the molecule which has chemisorbed on the surface: one can imagine that the electrostatic interaction between this anionic end and the (local) cationic site present on the surface upon formal dissociation is favorable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002427_50009-5-Figure7.48-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002427_50009-5-Figure7.48-1.png",
        "caption": "FIGURE 7.48 (a) The medium-to-high frequency equivalent circuit of test sample and measuring setup arrangement shown in the previous figure is simplified under the assumption that leakage inductances, winding resistances and interwinding capacitances play a negligible role. This circuit is somewhat idealized and is useful to single out the effect of the self-capacitances of windings and connecting cables. It can be emulated by eliminating the interwinding capacitance by means of an electrostatic screen inserted between primary and secondary windings. (b) Associated vector diagram. Under rated flux conditions the measured power loss is not affected by the presence of C1 and C s = C2 + Cj and it differs from the actual loss in the material only by the power Ap consumed in the load, exactly as obtained with the circuit of Fig. 7.27 (Eqs. (7.52) and (7.56)). The measured apparent power is instead changed by a quantity depending on the leakage currents ic1 and ics (Eq. (7.57)).",
        "texts": [
            "27a is of limited validity at medium and high frequencies and we should try to make our evaluation of AP/P and AS/S having in mind the complete circuit shown in Fig. 7.47. We start by assuming that either an electrostatic screen is used or the windings are 420 C H A P T E R 7 Charac te r iza t ion of Soft Magnet ic Mater ials laid upon the specimen in such a way that the interwinding capacitance Co is negligible. We equally neglect the leakage inductances and the winding resistances, so that the equivalent circuit and the associated vector diagram become as shown in Fig. 7.48. Here, we have posed Cs -- C2 + Cj. The magnetizing current im(t) is related to the supply current ill(t), the secondary current i2(t), and the leakage current icl(t) by Eq. (7.51), now written in vector notation as im --\" iH + jtoC1 N1 N2 ~22U2 -{- ~11i2 9 (7.55) The measured power loss is given by the usual expression Pmeas---- f N1 f ~ u2(t)iH(t) dt = 1 NI ~ , -- m---a N22 - m--~ ~ 'HU2 cos r and is related to the actual power loss P via Eq. (7.55). We obtain, for a given value Jp of the peak polarization, Pmeas -- - ~ 1 N I _ ~ 1 N I ~ ~ m a N---2 IHU2 COS q::~12 = ma N2 lmU 2 COS q0 q- ~ ~ 1 2 ma R2 = P + AP",
            " The example reported in Fig. 7.45 is one such case where the change of the hysteresis loop shape after addition of a small capacitor in parallel with the magnetizing winding leaves the loop area unchanged. The measured apparent power is instead affected by the presence of C1 and Cs. Starting from the definition of Smeas and S provided by Eq. (7.53), we find again the relationship between Zm and iH through Eq. (7.55), based on the analysis of the equivalent circuit and the vector diagram shown in Fig. 7.48. It turns out, provided the conditions l~C1 <<lm N2 N2 ' N1 iCs << G, N1 iR2 << Zm, are satisfied, that Smeas S + AS ~ S 1 ~ 2 -- -- COS q0 ma R2 _ 1 ( ( N 1 / N 2 ) 2 C 1 n u Cs)tO~22 s in qo. ma (7.57) 7.3 AC MEASUREMENTS 421 422 CHAPTER 7 Characterization of Soft Magnetic Materials The example reported in Fig. 7.45 does not satisfy the condition ic1 <K im, but AS can still be calculated, although with slightly involved mathematics. Let us now consider the role of winding resistances and leakage inductances by noting first that it is often possible to achieve effective minimization of the interwinding capacitance and its effect by use of single-layer windings, having an equal and small number of well separated turns",
            "47, that the reactance jcoCw2 and the resistance Rw2 provide a negligible voltage drop on the secondary circuit because of the high value of the input impedance of the measuring instrument (typically 1 Mf~ with 10 pF in parallel). If, under practical circumstances, it is suspected that this is not the case, we might add a second instrument in parallel with the first one using similar connecting cables and look for a possible change of the reading. We will then consider a simplified equivalent circuit, similar to the circuit in Fig. 7.48a, but for the addition of the leakage inductance Lwl and the resistance Rwl in the primary circuit. The vector diagram in Fig. 7.48b is correspondingly modified in the diagram shown in Fig. 7.49. Again, we wish to relate Prneas and P, Smeas and S, which calls for determination of the relationship between the magnetizing current im(t), the supply current ill(t), and the secondary current i2(t). Based on the vector diagram of Fig. 7.49 and the equivalent circuit, we write im --- iH + jcoC1 N1 N2 ~ U 2 -}- ~ 1 1 i 2 - jtoCl(Rwl +jwLwl)il, (7.58) where the current il = im + i2 / -- im -- (N1/N2)i2. If we substitute il in Eq. (7.58), we obtain the desired relationship between the quantities appearing in the definition of Pmeas and P"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000684_mech-34251-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000684_mech-34251-Figure3-1.png",
        "caption": "Fig. 3 A single-loop chain with variable connectivities of the pairs.",
        "texts": [
            "\" Therefore, in branch \"b\" the complete chain has 2nb = 2na degrees of freedom, hence it is kinematotropic. a) KPa b) KPa Fig.2 Change of mobility in a kinematic chain. It is worth noting that the approach proposed here is based on the possibility that a chain may maintain the same mobility nb = na in two different branches, but that the connectivity of at least one pair may change when the chain is displaced to different branches. In other words, the pair is mobile in a branch and locked in another branch. Figure 3 shows a single-loop chain of this kind. It is a four bar linkage with 2 revolutes and 2 prismatic pairs. One of the prismatic pairs is adopted as KPa. In branch \"a,\" the mobility of the chain is equal to 1, and the connectivities (co) of the pairs are: co(KPa)=1, co(B)=1, co(C)=0, and co(D)=0. From this branch, the chain can be displaced to a singular position, where C and D coincide, then to a second branch \"b.\" In the latter branch the mobility of the chain is still equal to 1, but the connectivities are exchanged: co(KPa)=0, co(B)=0, co(C)=1, and co(D)=1",
            " Otherwise, relation \"b\" is not satisfied, the group intersection is empty and no mobility for GR1 and GR2 can occur. In order to \"toggle\" the relation between the IPs of the groups from \"b\" to \"not b,\" it is necessary to provide a displacement between the two axes of GRc and GRd. This can be done in various ways, the simplest one lying in forming a closed chain RPRP with two prismatic pairs inserted between GRc and GRd. Rows 1 and 2 of Table 1 show that two prismatic groups with parallel axes have a nonempty intersection P, then they can be moved. This leads us to the chain in Fig. 3. In branch \"a,\" the pairs P are parallel and (row 1 of Table 1) they can be displaced. In the same position, the pairs R have non-coincident axes and (row 6 of Table 1) they cannot move. By displacing the pairs P, the IPs of the pairs R are changed until their axes coincide so that these pairs become mobile (row 5 of Table 1). The displacement of the pairs R makes the relation between the IPs of the pairs P change so these pairs cannot further move (row 2 of Table 2): the chain is displaced to branch \"b",
            " In summary, the degrees of freedom of the composed chain change as follow: \u2022 na in the starting branch; \u2022 2*nb when L1 and L2 change their branches simultaneously: \u2022 3*nb when L3 and L4 change their branches. Note that the chains that change their numbers of degrees of freedom suddenly from na to m*nb must be formed with m basic chains; the chains that change their numbers of degrees of freedom gradually require a larger number of loops. An example of a chain with 1, 2 and 3 degrees of freedom is shown in Fig. 8, where the chain in Fig. 3 is used as the basic chain. For the sketch clarity, in Fig. 8 the basic chain is viewed from a point of view different from that of Fig. 3. The label M identifies pairs with connectivities equal to 1. Unlabelled pairs have connectivities equal to zero. M M M a) L1 L2 L3 L4 M M M L1 L2 L3 M L4 M M M M M b) 4 Copyright \u00a9 2002 by ASME s of Use: http://www.asme.org/about-asme/terms-of-use Downlo In the branch shown in Fig. 8-a, the loops L1 and L2 are mobile, theloops L3 and L4 are locked, and the chain has 1 degree of freedom. This is the same situation as shown in Fig. 4-a. From this position, the chain is driven to the singular position in Fig",
            " All the chains presented in the previous sections and many others that can be realized by applying the proposed approach to the basic chains obtained from Table 1 have a common feature. When the multiloop chain reaches a branch that gives the maximum number of degrees of freedom, the resulting chain performs as an open chain (see, for instance Fig. 4). It is possible to arrange basic chains in order to obtain a different aded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/08/2016 Ter result. Figure 9 presents a spatial arrangement of 6 basic chains of the type shown in Fig. 3. Here the 6 basic chains are connected by their prismatic pairs in a closed path in such a way as to form a hexagonal prism. The axes of the 6 revolutes on the top of the chain intersect at a point, and the same holds for the 6 revolutes at the bottom. In the branch \"a\" shown in Fig. 9-a, the prismatic pairs are mobile and the revolutes are locked: the hexagonal polygons that form the bases of the prism are rigid and the chain has 1 degree of freedom. When translations of the prismatic pairs make the top hexagon coincide with the bottom hexagon, all the revolutes can be displaced and the chain reaches a branch \"b\" where the prismatic pairs are locked"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002301_a:1023275502000-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002301_a:1023275502000-Figure2-1.png",
        "caption": "Figure 2. Three-link 3R planar robotic manipulator.",
        "texts": [
            " Hence, the blimp is a mechanical control system with symmetry. Given G-invariant vector fields X = (g\u03be, v), Y = (g\u03b7,w), from Proposition 1 one can easily obtain, \u3008X : Y \u3009G = g   \u22125293 \u22125392 5193 +5391 0 \u2202w \u2202\u03b3 v + \u2202v \u2202\u03b3 w \u2212 ( I\u22121 L s 0 ) , (10) where L s = \u2212  m ( \u2202\u03be 1 \u2202\u03b3 w + \u2202\u03b71 \u2202\u03b3 v ) m ( \u2202\u03be 2 \u2202\u03b3 w + \u2202\u03b72 \u2202\u03b3 v ) (J1 + J2) ( \u2202\u03be 3 \u2202\u03b3 w + \u2202\u03b73 \u2202\u03b3 v ) \u2212 mJ2 J1 + J2  52w +92v \u221251w \u221291v 0  . Planar robotic manipulator with a passive joint. Consider a three joint robotic manipulator operating on a horizontal plane (see Figure 2). We have taken this example from [11], where its kinematically controllability properties have been studied. The configuration of the manipulator is given by a triple (\u03b8, r2, r3) \u2208 S 1\u00d7 S 1 \u00d7 S 1, where \u03b8 is the angle of the first link with the plane, and (r2, r3) are the joint angles between the links. The control inputs are the torques F 1 and F 2 which actuate the shape angles (r2, r3). The Riemannian metric of the system has the following structure, see [11] for the explicit expression of the coefficients: G = M11(r2, r3) M12(r2, r3) M13(r2, r3) M12(r2, r3) M22(r3) M13(r3) M13(r2, r3) M23(r3) M33  "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003779_s11044-006-9028-0-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003779_s11044-006-9028-0-Figure3-1.png",
        "caption": "Fig. 3 Planar 4-bar mechanism in a singular configuration",
        "texts": [
            " The considerations made so far can be summarized in the following three main steps: (1) Find all spanning trees G for . For each cotree H ( , G) (a) construct involutive closures of D\u03b1 , \u03b1 \u2208 H , and the matrices C\u03b1 (b) determine rank (P\u03b1C\u03b1) (2) Choose cotree H\u2032 such that rank (P\u03b1C\u03b1), \u03b1 \u2208 H \u2032 are the minimal for all possible H (3) For each FL \u03b1 of the chosen cotree H\u2032 (a) compute SVD of P\u03b1C\u03b1 = U T V (b) construct reduced matrix U\u0304 \u21d2 Result: reduced coefficient matrices U\u0304 P\u03b1 L\u03b1, \u03b1 \u2208 H \u2032 4.1 Planar 4-bar mechanism The planar 4-bar mechanism in Figure 3 is a standard example for the occurrence of dependent constraints, when using MBS dynamics simulation tools (algorithmic redundancies). Any revolute joint chosen as cut-joint yields five constraints of which three are identically zero. Evaluating the constraint algebra shows that clos D\u03b1 = se(2), the algebra of planar motions, for all possible cut joints. The selector removes one component, so that with d = dim clos D\u03b1 = 3, d \u2212 1 = 2 constraints are sufficient. For the 4-bar mechanism the GKC formula holds and the mechanism\u2019s DOF is n \u2212 (d \u2212 1) = 3 \u2212 2 = 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002287_0301-679x(88)90121-1-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002287_0301-679x(88)90121-1-Figure1-1.png",
        "caption": "Fig 1 Narrow, rough, plane face ax i symmetr ic seal mode l",
        "texts": [
            "0 i, o p, m p , t Face area Balance ratio for an outside pressurized seal Equivalent balance ratio Friction coefficient Friction coefficient for solid contact Friction force due to fluid friction Friction force due to contact Spring force on the seal Nominal film thickness Nominal film thickness at contact Film thickness at the inside edge Minimum film thickness, minimum of h o or h i Film thickness at the outside edge Pressure-caused rotation coefficients Total pressure-caused rotation coefficient Thermal rotation coefficients Pressure Sealed pressure at the inside Contact pressure Sealed pressure at the outside Average face pressure due to spring load Friction power of the seal Radial flow per unit length Total radial flow (leakage) Radius at the inside of the face Mean face radius Radius at the outside of the face Face width Average sliding speed Load supported by fluid pressure Maximum and minimum possible fluid load support Load supported by contact pressure Applied load Absolute viscosity Combined RMS roughness of the two seal surfaces Relative radial taper angle between the faces Initial radial taper of the faces Pressure-caused radial taper of the faces Thermally-caused radial taper of the faces Total thermally-caused taper Angular velocity Subscripts for inner and outer Subscripts for primary and mating rings Subscripts for pressure and thermal this model is simple to use and yet provides meaningful results for certain aspects of seal design. The model As described above, the problem of interest is axisymmetric. Further simplifications are obtained by assuming that the seal has a narrow, plane face. To be realistic, however, roughness must be included. Fig 1 shows the essence of this simple model. In general, the faces present themselves to each other at some angle as shown where one may have a convergent or divergent gap. A convergence going radially inward will be considered positive. The average level of the face surfaces is on a straight line but a roughness is superimposed over this straight line. The model is derived for an outside pressurized seal but a similar derivation can be made for an inside pressurized seal, if needed. The pressure between the two faces consists of both fluid pressure and mechanical contact pressure in the general case",
            " The assumption made is reasonable in view of the fact that contacting seals do leak at least a small amount. It is likely for highly divergent contacts that the amount of flow estimated herein will be higher than reality because some localized high penetration of the surfaces into each other could actually close the gap. At the other extreme, limiting the minimum film thickness for the convergent case shows that complete lift is far less likely to occur than if an ideal zero roughness is assumed. Pressure, load support, and leakage Fig 1 defines the geometry of interest for this model. The most important parameter, \u00a2, is composed of several different parts. Fig 2 shows how the components of q5 are defined. Each ring has three sources: initial taper, thermal taper, and pressure moment caused taper. All of these components are defined as positive if they tend to make the seal convergent from the outside in. The angle, ~, of interest is simply the sum of the six components. \u00a2 = (\u00a2ip + ~bim) + (~bpp + g)pm) + (~btp + qStm) (1) The angle, \u00a2, may also be defined in terms of film thicknesses, thus h o - h i - (2) r o - r i To find the fluid pressure distribution, one can start with the equation for radial flow between two closely spaced bearing surfaces t\u00b0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003842_cdc.2006.376730-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003842_cdc.2006.376730-Figure2-1.png",
        "caption": "Fig. 2. The cone C ( \u03b8L(t) + \u03c6, arcsin(Kd cos \u03c6) ) .",
        "texts": [
            " (9) Furthermore vF and \u03c9F are given by vF = vL cos(\u03b2 \u2212 \u03c6) cos\u03c6 \u03c9F = vL sin \u03b2 d cos\u03c6 (10) where \u03b2 = \u03b8L \u2212 \u03b8F and, \u2200 t \u2265 0 |\u03b2(t)| \u2264 arcsin(Kd cos\u03c6) . (11) Remark 1: A consequence of property (11) is that the angle \u03b2 is bounded. This implies the following geometric property L(t) \u2212 F (t) \u2208 C ( \u03b8L(t) + \u03c6, arcsin(Kd cos\u03c6) ) (12) where \u2200 \u03b8, \u03b3 \u2208 [0, 2\u03c0], C(\u03b8, \u03b3) = { x \u2208 R 2 \u2223\u2223\u3008x , \u03c4(\u03b8)\u3009 \u2265 \u2016x\u2016 cos\u03b3 } is a cone of aperture 2\u03b3 centered in the origin, whose symmetry axis is given by \u03c4(\u03b8) = (cos \u03b8, sin \u03b8)T (see Fig. 2). Differently from [3], the followers are not rigidly disposed with respect to the leader reference frame, but their relative positions vary in time in suitable cones and only these cones remain stable with respect to the leader reference frame. To prove (12) remark that, from (11) \u3008L \u2212 F , \u03c4(\u03b8L + \u03c6)\u3009 = = \u3008d \u03c4(\u03b8F + \u03c6), \u03c4(\u03b8L + \u03c6)\u3009 = = d cos\u03b2 \u2265 d cos(arcsinKd cos\u03c6). Proof of Theorem 1 \u2013 Sufficiency: Let \u03b1 = arcsin(Kd cos\u03c6) and xL, yL, \u03b8L, xF , yF , \u03b8F be the solutions of systems (1), (2), with the initial conditions such that (11) is verified at t = 0 and where vF and \u03c9F are given by (10)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003184_2005-01-1651-Figure17-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003184_2005-01-1651-Figure17-1.png",
        "caption": "Figure 17. Worn bush",
        "texts": [
            " With this characterization, we can estimate the global wear rate of the small end bush and the location of the wear assuming the wear rate in elastic, elastoplastic and plastic contact are be Ke, Kep and Kp, the expression of the wear intensity for a point of the bush, called w( ) becomes: d,PrK ,PrK,PrKR 4 1w pp epepee0r 4 0 (19) with ,Pre = elastic contact pressure ,Prep = elastoplastic contact pressure ,Prp = plastic contact pressure With previous numerical data, we calculate the wear intensity and obtain the wear intensity curve given on Figure 17. Figure 16 shows that the wear pattern is asymmetric which give us information to compare with results from the field. Figure 18 displayed a worn small end bush showing that the wear pattern also asymmetric is quite uniform across the width of the bearing. For this case, where the pin is very stiff with respect to the load, the pin bending effect does not appear in this damage. It is interesting to stress the fact that the wear across the bush is highly related to the contact forces but nearly not sensitive at all to the pin speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003219_1.2113823-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003219_1.2113823-Figure2-1.png",
        "caption": "Fig. 2. pH electrode ond mount",
        "texts": [
            " potential behavior were recorded on an X-Y recorder. From these plots, the impedance of the sensors was determined. At low temperatures, the pH response is a low frequency phenomenon. At 368 K, the ac response is independent o f p H at frequencies above 10 -2 Hz. The two major problems with mounting the ceramic pH sensors are their fragility and high impedance. Polytetrafluorethylene (PTFE) is used as the pressure sealant in a Conax (Model PG2-250-B-T; Buffalo, New York) packing gland. This design is shown in Fig. 2. The soft sealant applies the compressive load in a uniform manner to minimize tube breakage. Unlike Niedrach's (1-4) early designs, the electrical termination region of the sensor was moved outside the PTFE pressure sealant region to ensure that any traces of moisture leaking out of the seal could not shunt the pH signal. A ceramic collar is cemented to the sensor barrel (Cotronics 940; Brooklyn, New York) to prevent the sensor from being extruded out of the pressure fitting. Belleville spring washers are used to spring load the PTFE sealant to improve the seal reliability during temperature cycling"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002090_j.scriptamat.2004.08.003-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002090_j.scriptamat.2004.08.003-Figure2-1.png",
        "caption": "Fig. 2. Poisson s ratio (right) as a function of the directional parameters a and h 2 [0,p] for the case in which the unit vectors n and m lie on a plane containing x3 (left: the shaded plane is the plane of elastic mirror symmetry). The crystal is the monoclinic cesium dihydrogen phosphate (CsH2PO4, piezoel.): s11 = 1820.0, s22 = 103.0, s33 = 772.0, s44 = 133.0, s55 = 450.0, s66 = 117.0, s12 = 219.0, s13 = 1170.0, s23 = 138.0, s15 = 249.0, s25 = 150.0, s35 = 181.0, s46 = 33.0, units in (TPa) 1 (Data from Landolt\u2013Bo\u0308rnstein [20]). The surface of the Poisson s ratio intersects the horizontal plane mnm = 0.",
        "texts": [
            " Three crystal classes exist in the monoclinic system: the domatic, spheroidal and prismatic: all these classes are associated to the same structure of the elasticity matrix [sij] and the number of independent elastic constants is reduced from 21 (complete anisotropy) to 13 (Cowin and Mehrabadi [21]). The sij are the reduced compliances according to the Voigt s notation: s11 = S1111, s12 = S1122, s13 = S1133, s22 = S2222, s23 = S2233, s33 = S3333, s15 = 2S1131, s25 = 2S2231, s35 = 2S3331, s44 = 4S2323, s46 = 4S2312, s55 = 4S3131, s66 = 4S1212. Due to the presence of the plane of elastic reflective symmetry x1x3, the loading cases of Fig. 1 are assumed with i = 1, j = 2 and k = 3. As an example, the behavior of Poisson s ratio is shown in Fig. 2 for cesium dihydrogen phosphate, when both the unit vectors n and m lie on the plane containing x3. The surface representing the function mnm intersects the horizontal plane mnm = 0 and the Poisson s ratio results to be negative, for every h, in a rather wide range of values for the angle a. In Fig. 3, three particular cases of the loading condition of Fig. 2 are shown. In the case where both n andm are on the plane of elastic symmetry (Fig. 3, left) the expression for the Poisson s ratio takes the following form: If the unit vectors n and m lie on the plane orthogonal to the symmetry plane (Fig. 3, center), the Poisson s ratio is given by: mnm \u00bc 1 8 s22 \u00fe s33 s44 \u00fe 6s23 \u00f0s22 \u00fe s33 s44 2s23\u00de cos 4h s22cos4h \u00fe \u00f0s44 \u00fe 2s23\u00desin2hcos2h \u00fe s33sin 4h : \u00f06\u00de Finally, if n lies on the plane x1x2 and m is directed along x3 (Fig. 3, right), the Poisson s ratio becomes mn3 \u00bc s13cos2a \u00fe s23sin 2a s11cos4a \u00fe \u00f0s66 \u00fe 2s12\u00desin2acos2a \u00fe s22sin 4a : \u00f07\u00de The behavior of the Poisson s ratio corresponding to these three cases is shown in Fig",
            " Polar representations of the Poisson s ratio for the monoclinic cesium denote auxetic domains. it is negative when it is internal. The grey areas indicate the ranges of the relevant angles corresponding to the auxetic behavior. Note that when the crystal is stretched in a plane orthogonal to the material symmetry plane and mnm is measured in the same plane (case of Fig. 3, center), the Poisson s ratio is always negative (Fig. 4, center) with minimum value mmin = 1.41. This situation can be recognized in the plot of Fig. 2, when a = p/2 and h is varying over its range. The depth of the region in Fig. 2 where the Poisson s ratio is always negative is shown in the right plot of Fig. 4, corresponding to the third loading case of Fig. 3. Here the function mnm becomes negative for values of the angle a belonging to the interior of a wedge having amplitude Da = 0.66 rad (in the figure, a1 = 1.24 rad and a2 = 1.90 rad); in this case, the minimum value of the Poisson s ratio is mmin = 1.34. For cesium dihydrogen phosphate, Fig. 5 shows the function representing the Poisson s ratio and its intersection with the horizontal plane mnm = 0 for the case (b) of Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000213_978-1-4419-8710-5-Figure4.6-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000213_978-1-4419-8710-5-Figure4.6-1.png",
        "caption": "Figure 4.6. Enhanced current mirror topologies, (a) active, (b) cascode, (c) regulated cascode output, and (d) active regulated cascode",
        "texts": [
            "9) The error of the negative current Tj at the current comparator inputs results from a single n-mirror reflection, A HIGH-PRECISION CURRENT-MODE MULTI-CHIP WTA-MAX CIRCUIT 97 The total current error at the input of each current comparator is therefore given by, (4.11) However, the error introduced by a current mirror is not only the random mismatch contribution, as considered in eqs. (4.9)-(4.11), but also its systematic error contribution, which results from different drain-to-source voltages at the reflecting transistors and poor impedance coupling. Fig. 4.6 shows several current mirror topologies which intend to improve precision performance with respect to the simple current mirror. The active-input current mirror idea (see Fig. 4.6(a)) [Nairn, 1990al was introduced as a need to maintain a constant voltage at the input of a current mirror in order to avoid current subtraction errors in previous stages. This technique allows the Vcs voltage of the current mirror input transistor M1 to be independent of its VDS voltage, which will be kept constant, and therefore lowers the mirror input impedance which minimizes loading effects on previous stages. The current mirror will be operative as long as transistors M1 and M2 are kept in saturation",
            " The higher the reference voltage VD is, the more current is allowed through the mirror with M1 operating in saturation. The drain-to-source voltage of the output transistor depends on the load of the mirror and will be dependent on the mirror current. If the load impedance is not sufficiently low M2 will suffer of large drain-to-source voltage variations, which through the channel length modulation effect, will cause a systematic mismatch error between the input and output currents of the mirror. Such a circumstance can be avoided by using the cascode current mirror of Fig. 4.6(b). However, this mirror has a smaller output voltage swing and requires a high input voltage drop for high currents (which are needed for maximum accuracy) [3.16]. The regulated-cascode output stage (see Fig. 4.6(c)3) [Sackinger, 1990] would allow to maintain the VDS of transistor M2 constant and to increase significantly the output impedance of the mirror, while not sacrificing voltage range at the input of the current mirror. This current mirror will be operative as long as transistor M2 remains in saturation, which depends on VD and the input current, as well as on the load impedance at the output of the mirror. By combining the active current mirror input of Fig. 4.6(a) with the regulated cascode output in Fig. 4.6(c), the active-input regulated-cascode current mirror 3 Although we are showing a differential input voltage amplifier, iill the original paper [Sackinger, 1990] a single input amplifier was used. In this case the voltage VD would be set through process and circuit parameters. of Fig. 4.6(d) results [Serrano-Gotarredona, 1994). This current mirror has a very low input impedance, a very high output impedance and is operative if transistors M1 and M2 are either in saturation or ohmic region (because their VDS voltages are always equal). Therefore, the gate voltage of transistors M1 and M2 can change almost from rail to rail. However, this current mirror will A HIGH-PRECISION CURRENT-MODE MULTI-CHIP WTA-MAX CIRCUIT 99 fail to operate with high accuracy if the output voltage approaches VD. But, on the other hand, VD can be made smaller than for Fig. 4.6(a) because M1 and M2 can operate now in ohmic regime. When cascading current mirrors, the regulated-cascode output is not needed and the configuration of Fig. 4.6(a) can be used. The virtual ground effect at the drain of transistor M2 is produced by the active input of the next current mirror. However, in this case VD has to be set equal for all PMOS and NMOS active current mirrors. Also, care has to be taken by choosing the value of VD in order to respect the output voltage range of the circuit at the input of the first mirror, and to respect the input voltage range of the circuit at the output of the la.st current mirror. As has been previously explained, the accuracy limitation of current mirrors has two main types of sources, systematic errors and random errors",
            " We will consider that the total precision of a current mirror is given by (4.12) where D.1sys is the systematic error contribution (which can be evaluated through a single nominal Hspice simulation) and (1/ is the standard devia tion of the output current (which can be evaluated through 30 Hspice Monte Carlo simulations). The statistical significance of (1/ is that 68% of the sam ples have an output current error within the range (D.1sys - (JJ,D.Isys + (1/). Fig. 4.7 shows a comparison of the precision performance of the topologies in Fig. 4.6, based on electrical simulations. For random mismatch errors Hspice simulations, it is considered that the only sources of random mismatch are the differences in threshold voltage (VT ) and current factor ({3 = Cox/-lW/L), and that their standard deviation is given by [Pelgrom, 1989], (4.13) where Wand L are the sizes of the transistors, D( '\" M') their separation, and AVT = 15mV/-lm, SVT = 2/-lV//-lm, A,13 = 2.3%/-lm, S,13 = 2 x 1O-6/-lm 100 ADAPTIVE RESONANCE THEORY MICROCHIPS (parameters given in [Pelgrom, 1989] for a 1",
            " In both cases the decrease in precision above ~ 300f-tA is because transistors M1 and M2 enter their ohmic region of operation. A simple current mirror has a resolution below 8-bit for the complete current range. This is mainly due to poor impedance coupling, which can be avoided with regulated cascode outputs, achieving 8-bit resolu tion between 45f-tA and 150f-tA. The cascode mirror suffers from large voltage drops at its input, thus offering the 8-bit resolution only between 40f-tA and 70f-tA. The active-input mirror (Fig. 4.6(a)) has low resolution because its output voltage was set to 2.5V, hence rendering an important systematic error contribution. Also shown in Fig. 4.7 is the random mismatch error contribution (0\"1 in eq. 4.12), which is approximately the same for all topologies. Note that all topologies suffer from loss of precision at high currents. This is produced because the increasing voltage drops at the different nodes approximate the limit of available voltage range. Table 4.1 shows the transistor level simulated transient times of our des ign when using a regular OTA [Degrauwe, 1982) as the active device"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002290_j.ijadhadh.2003.10.004-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002290_j.ijadhadh.2003.10.004-Figure5-1.png",
        "caption": "Fig. 5. The line-rigid model for a DLS specimen. The adhesive bond is modeled as a line of rigid links (arrow). Note: only a half of the DLS specimen is modeled and a symmetrical boundary condition, u3 \u00bc 0; is imposed.",
        "texts": [
            " / International Journal of Adhesion & Adhesives 24 (2004) 239\u2013246242 model for a DLS specimen, this is equivalent to defining rigid links between the nodes of mating substrate pieces along a line across the width of the DLS specimen through the center point of the overlap. To investigate this method, the line-rigid model was implemented in ABAQUS and LS-DYNA. In the line-rigid model for ABAQUS, rigid beam elements of type RB2D2 were used as the rigid links. In the model for LS-DYNA, rigid links were defined as constrained-nodal-rigid-body node sets. Fig. 5 shows the line-rigid model for a DLS specimen in ABAQUS. ABAQUS simulations for a SRIM/LESA DLS specimen. The simulations were carried out using the shell/solid model, the contact model and the line-rigid model. The two simplified models were compared with the baseline FE model and the analytical solutions for the SRIM/LESA DLS specimen. Fig. 6 plots the load displacement response of the DLS specimen obtained from the ABAQUS simulations, in comparison to those predicted by analytical solutions. It is interesting to see that the three FE models agree with the corresponding analytical solutions for three cases: the shell/solid model agrees with the analytical solution of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002767_978-3-642-71015-5-Figure2.24-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002767_978-3-642-71015-5-Figure2.24-1.png",
        "caption": "Fig. 2.24a, b. Finite-width sheet: (a) Geometry; (b) Infinite series of images",
        "texts": [
            " It is seen that for a wide range of 1 Fbr I, a minimum production cost value is obtained within the range (bl h) =::: 0.3470.44. Another finding of practical significance is that with increasing values of 1 Fbr I, the minimum cost point is shifted towards increased values of 2 h which is the pole dimension perpendic ular to the direction of motion. Having outlined the general approach to the problem of pole optimization in the case of a sheet of much larger dimensions than those of the pole cross section, we proceed to the case of a sheet of finite width 2A (Fig. 2.24a). The boundary condition precluding current outflow from the sheet at y = \u00b1 A is here again satisfied with the aid of a series of images; the relevant electro magnetic analogy, comprising a series of infinite current-carrying bus-bars, is reproduced in Fig. 2.24 b, with the fictitious surface current Kz obtained by integration of (2.5.4), i.e., 00 00 8B flo Jjzdx = (0\"..1) v S __ Z dx , o 0 ox (2.5.20) so that \u00b1Kz = + (0\"..1) v Bo. (2.5.21) f.lo Once more the braking force is obtainable from (2.5.6) which, in turn, leads to (2.5.15), so that the problem is actually again reduced in effect to calculation of 2. The solution of the boundary value problem defined by Fig. 2.24 b yields (Sect. 2.5.3) sin2 [(2n+ 1) .!:.~] f.lo 00 2 A 2=- I 2 7Cn=O[ 7Ch] (2n+l) 2A l-exp [ -(2n+l)X\u00b1] (2n+ 1) (2.5.22) 100 2. Principles of Magneto-Electric Interactions a t -r a I-- .r;:; N _1 L2bJ Fig. 2.22. Coil spacing around iron core Fig. 2.23. Cost C of electromagnet (adapted units) per unit length as function of dimen sionless bl h ratio for fixed values of braking force I Fbr I (adapted units) C 2000 1000 o ~~--~---T--~--~-o 2 3 4 5 90 80 70 60 50 40 30 20 10 2.5 Optimal Dimensions for Braking Electromagnet 101 As regards the optimal shape, calculations based on the same approach as before show that, for 2A = 1 > 2 h (adapted units) the minimum cost C now corresponds to a ratio 2b/2h::::: 0",
            "2); the analogy with a linear motor is more pronounced than with an ordinary induction motor, since the drag force is due to the interaction with eddy currents in a sheet of much larger dimensions than those of the core. The braking-force calculation presented here indicates an optimum ratio for a single electromagnet only; extension to an array is nevertheless obtain able by means of the main results derived in Sect. 2.4. Adapting the notation Kz for one current-carrying bus bar to the present case, i.e. defining, see (2.5.21), Kz == Ko, the spatial distribution of the surface current density Kz (y) at x = + b reads (Fig. 2.24 b) sin [(2'+ 1)-\"-1 Kz(Y) = Ko~ E 2 A cos [(2n+ 1) ~~]. (2.5.23) n n = \u00b0 (2 n + 1) 2 A In the region x::: b the z-component Vz of the vector potential linked to Kz (y) satisfies the Laplace equation (2.5.24) The solution of this equation coherent in y, bounded for 1 x 1-+ 00 and satisfying at the interface z = b the condition Hylb+O-Hylb_O = Kz(y) , reads (2.5.25) 4A \u2022 sin [(2,+1) ~ ~] [ n y] Vz =I-lOKO- 2 I: 2 cos (2n+l)-- n n = \u00b0 (2 n + 1) 2 A xexp [ +(2.+1) ~ (X~b)], x .. b. (2.5.26) In order to calculate the \"self\" component Wms of the magnetic energy per unit length of one bus bar of width 2 h in the b = x plane, we write 102 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000319_b008036p-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000319_b008036p-Figure1-1.png",
        "caption": "Fig. 1 Exploded structure of the needle-type biosensor. 1 = Pt for counter electrode (250 nm); 2 = Cr for adhesion layer (15 nm); 3 = glass substrate (0.15 mm); 4 = Cr for adhesion layer (15 nm); 5 = Pt for working electrode (250 nm); 6 = Ag/AgCl for reference electrode (250 nm); 7 = polyimide (5000 nm); 8 = acetonitrile plasma-polymerized film (device 1), introducing amino groups on to the surface, 8A = 3-(aminopropyl)triethoxysilane layer (device 2); 9 = glutaraldehyde reacted with the amino groups on layer 8 or 8A; 10 = immobilized glucose oxidase via glutaraldehyde.",
        "texts": [
            "4, type VII-S, 181 600 units g21) L-ascorbic acid, urea and acetaminophen were obtained from Sigma (St. Louis, MO, USA). 3-(Aminopropyl)triethoxysilane (APTES) was supplied by Aldrich (Milwaukee, WI, USA). All reagents were used without further purification. All solutions were prepared with de-ionized water obtained from a Millipore Milli-Q system. The arrayed needle-type sensor, which consists of a threeelectrode system, was fabricated on the basis of semiconductor and micromachining layer-by-layer processes as shown in Fig. 1. The device was formed on a 150 mm thick glass substrate. Glass slides used to make thin film electrodes were cleaned in 50% nitric acid for 1 h and then rinsed with water and acetone. Its planar dimensions were approximately 0.7 mm wide and 50 mm long. To fabricate arrayed electrodes, all the metal layers were sputter-deposited with a Model CFS-4ES-231 apparatus manufactured by Shibaura Engineering Works (Tokyo, Japan) and patterned by a lift-off process. Each layer thickness was measured using a surface profile meter (Dektak ST, Veeco Instruments, Tokyo, Japan)",
            " Table 2 Errors in glucose determination caused by interfering agentsa Error (%)b Interferent Device 1c Device 2d 0.2 mM ascorbic acid < 1 4.3 0.3 mM ascorbic acid 2.6 6.9 0.6 mM ascorbic acid 3.5 10.7 0.1 mM acetaminophen 23.6 75.1 0.2 mM acetaminophen 36.6 99.4 0.3 mM urea 4.8 9.1 1.2 mM urea 5.4 15.4 a Oxidation current (I) at +700 mV vs. Ag/AgCl is used. Sweep rate 50 mV s21. b Error (%) = 100 3 (I12I0)/I0, where I1 is I(interference + 10 mM glucose) and I0 is I(10 mM glucose). c Immobilization of GOD based on PPF (see Fig. 1).d Immobilization of GOD based on APTES (see Fig. 1). 662 Analyst, 2001, 126, 658\u2013663 Pu bl is he d on 2 3 A pr il 20 01 . D ow nl oa de d by U ni ve rs ity o f C hi ca go o n 26 /1 0/ 20 14 1 4: 41 :1 5. 21 W. H. Scouten, J. H. Luong and R. S. Brown, Trends Biotechnol., 1995, 13, 178. 22 G. F. Khan and W. Wernet, J. Electrochem. Soc., 1996, 143, 3336. 23 E. I. Iwuha, D. S. de Villaverde, N. P. Garcia, M. R. Smyth and J. M. Pingarron, Biosens. Bioelectron., 1997, 12, 749. 24 J. J. Gooding, V. G. Praig and E. A. H. Hall, Anal. Chem., 1998, 70, 2396"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003335_0020-7403(81)90025-4-Figure8-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003335_0020-7403(81)90025-4-Figure8-1.png",
        "caption": "FIG. 8. Multilateral figure. The construction of the internal vector is the same as that given in Fig. 5.",
        "texts": [
            " We must nevertheless consider that, if the sides AB and CD are parallel, the information is not sufficient to solve the problem, because the normal components of the entrance velocities are now parallel. Analysis of. plastic deformation according to the SERR method 133 Example 7. Multilateral figures The case of plane figures with a higher number of sides can be immediately solved, in a manner analogous to that of Example 3. when the entrance vectors are given on two of the adjacent sides, or to that of Example 4 in the other cases, see Fig. 8. 2. ANALYTICAL TREATMENT OF THE SPATIAL MODEL We now consider the general three-dimensional case of two contiguous rigid blocks, for which the plane, defined by the external and internal velocity vectors e and i, is not perpendicular to the discontinuity plane (shear plane), separating the two rigid blocks. With reference to Fig. 9, call a the discontinuity plane e. the normal component of the entrance velocity e, and i. the normal component of the exit velocity i; e, and i, are respectively the tangential components of e and i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002378_robot.1998.680881-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002378_robot.1998.680881-Figure2-1.png",
        "caption": "Figure 2. Reference frames used for simulation.",
        "texts": [
            " Two displacement representations are used for these simulations: homogeneous matrices and dual quaternions. 2. Mobile manipulator Figure 1 shows the mobile manipulator available at LIRMM. It is able to move outdoors. The arm is a PUMA 560 and we will consider for our simulations such a sixrevolute-axis manipulator. In this case, the number of degrees of freedom of the mobile manipulator is 9. The operational space is of dimension 6 (position and orientation of the arm end-effector). Therefore, the considered system is redundant with respect to a positioning task of the end-effector. Figure 2 represents the mobile manipulator considered for our simulations and the relevant reference frames. Our goal is to bring the end-effector to a given position and a given orientation represented by the desired reference frame Medrs. The actual position and orientation of the end-effector in the world reference frame F is represented thanks to that of the reference frame Me. The vehicle considered in this paper is a fourwheeled cart with a non-holonomic constraint. The vehicle can move either along its longitudinal axis, or along an arc of a circle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0000141_s0043-1648(97)00190-7-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000141_s0043-1648(97)00190-7-Figure3-1.png",
        "caption": "Fig. 3. Schematic view of the rotary stick-slip tester.",
        "texts": [
            " (2) and (3) results in the condition for velocity reversal during stick-slip: t\u00a2 _ 2---\"-'ff~ 1 4 ) From this equation it can be derived that velocity reversal can occur during the siip-plm.~ of a stick-slip cycle if the static friction force is sufficiently larger than the friction during the slip-pham [ F( t.r\u00a2 ,) ) and the friction at the moment of possible velocity reversal F ( t , ) . 3 . E x p e r i m e n t a l 3. L Test rig and lesI preparat ion A schematic view of the rotary stick-slip tester used in the premnt research is presented in Fig. 3. The test rig basically 140 F. Van De Velde et al. / Wear 216 t1998~ 138-149 consists of a rotating bath ( l ) driven by a frequency controlled a/c. motor, in which a ring (2) is mounted. Two centre-pivoted sliding shoes ( 3 ), with dimensions as shown in Fig. 4, are connected to an arm (4) by means of pins (5) and are pressed against the ring by a dead weight-lever system (6-7) . The arm (4) is connected to the frame by a roller bearing with the same centre as the bath and ring. Rotation of the arm is prohibited by a linear spring (8), connected to the frame. Three springs with different stiffness can be mounted: the most flexible one is a torsion bar (shown in Fig. 3 ), the stiffer two are leaf springs Fig. 5b. Rotation of the bath causes sliding of the ring against the shoes. Due to the bath the sliding contact can be immersed in a lubricant. The (small) rotation angle of the arm caused by the friction force between the shoes and the rotating ring is determined by means of laser intefferometry, measuring the angle between the optical prism (9) and a reference prism mounted on the frame. This equipment is very accurate ( +0.2% of the measured value), has a resolution of 0",
            " the tangential inertia m differed from the normal load w; the former resulting from the moment of inertia of the mm Parameter Stribcck test Sl ick-sl ip test Vibration test Normal load w ( N ) Stiffness k ( N m ' } Dimensionless damping coefficient Impn.-s.~d veh~.'ity ( mm s 0 ) Impreg~ed displacement I mm) Sampling frequency ( Hz ) 1 01) 1 01) I O0 h l . 3 X I(P 4 . 8 x IO ~ 4.8X I0 ~ I O.(X)7 0.007 I}-67 0.33 o - - 10.5-21 I 201) I (100 with dead weights and sliding shoes, the latter from the weight of the dead weights and levers (Fig. 3). The damping coefficient c was negligible as the damping component of the friction force, which was not known in advance, was not considered as a part of c, but was treated as a whole within the friction force F. The friction coefficient during the slipphases of stick-slip was then calculated as follows: m.g+k. . l\" g = (6) I1 - ~v The sampling rate was chosen 200 Hz because of the quick changes in the friction force and the position of t h e arm ( sliding mass m ). Apart from the rotation of the arm ( displacement, velocity and acceleration), two additional measurements were conducted: the electric contact resistance between the ring and one of the sliding shoes and the tangential acceleration of the bath"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003206_j.mechmachtheory.2003.12.003-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003206_j.mechmachtheory.2003.12.003-Figure1-1.png",
        "caption": "Fig. 1. Six-link mechanism composed of one prismatic pair and six revolute pairs.",
        "texts": [
            " This procedure is equivalent to the determination of points of intersections between the coupler curve of the constituent four-link mechanism and the end pairing point circle of the second link of the external dyad. The number of solutions (points of intersection) of angular displacements of moving links at any positions of the driving is even and less than six because the coupler curve of the four-link mechanism is a tricircular sixtic. As many six-link mechanisms of different link-chain configurations are constructed as the number of solutions. Letting the kinematic constants, the displacement of the driving slider and angular displacements of moving links be lengths and angles as shown in Fig. 1. The set of closed loop equations of the Stephenson-3 six-link mechanism becomes following four equations. a0 \u00fe a1 cos h1 \u00bc a2 cos h2 \u00fe a3 cos h3 \u00f01\u00de a1 sin h1 \u00bc a2 sin h2 \u00fe a3 sin h3 \u00f02\u00de s cos a2 \u00fe a5 cos h5 \u00bc a3 cos h3 \u00fe a4 cos\u00f0h2 \u00fe a1\u00de \u00f03\u00de a6 \u00fe s sin a2 \u00fe a5 sin h5 \u00bc a3 sin h3 \u00fe a4 sin\u00f0h2 \u00fe a1\u00de \u00f04\u00de If a value of the displacement s (the input variable) of the driving slider is given, Eqs. (1)\u2013(4) become the set of non-linear simultaneous equations with four unknowns h1, h2, h3 and h5 and these equations are reduced to the algebraic equation of the sixth degree with the unknown t \u00bc tan\u00f0h2=2\u00de",
            " 3(b) and (c) are five domains of motion of the driving link on the coupler curve and five relationships between the input angle and the coupler angle of the constituent four-link mechanism, respectively. That is, the number of domains of motion of the driving link is accounted to five. Besides, a more valid variable than the output angle is adopted for discriminating domains of the driving link, which corresponds one to one to the point of the coupler curve. So, two circuits to be illustrated one over another in the Chase and Mirth Fig. 1(b) can be separated automatically. Fig. 4(a) is the Stephenson-3 six-link mechanism of the Watanabe et al. example [4]. Fig. 4(b) and (c) are two domains of motion of the driving link on the coupler curve and two relationships between input and output angles, respectively. Then, the driving link oscillates within an interval of the input angle such that 2p < h6 < 4p. In the six-link mechanism of Fig. 4, the number of domains of motion is two, and numbers of circuits and branches are one and two, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001343_1.2832457-Figure5-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001343_1.2832457-Figure5-1.png",
        "caption": "Fig. 5 Interference variables for resisting (a) and assisting [b] contact regions",
        "texts": [
            " The negative of the + in the parentheses is used for resisting contacts, while the positive sign is for assisting contacts, [k and 20 / Vol. 119, JANUARY 1997 Transactions of the ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use / represent the total numbers of resisting and assisting contact regions, respectively.) Separation and Interference. Deformation of asperities may also be represented by defining an interference function e(x) as a measure of the difference between undeformed surface functions zt(x) and Z2ix) as shown in Fig. 5. The interference function e is equal to the sum of interferences ci and \u00a32 corre sponding to surfaces 5, and ^2, respectively. In accordance with the definitions illustrated in Fig. 5 and utilizing the deformed surface functions Z, and Z2, separation h both for resisting and assisting contact regions can be ex pressed as /i = Z,(.%t,f)+Z2(,%'^, 0 (5) where, the deformed-surface functions are defined as ZdX\\,t) = z>(X\\)-\u20ac\\(X\\,t) (6) Z2(.%1, f) = Z2(>%'\u0302 ) - e^iX^, t) (7) and, X\\ = x - t e = ti + \u20ac2, e a: 0 where rj and (, are the tangential displacements in bodies fl, and B2, as before. The indices i have the same representations de fined earlier. Equation (2) for tangential motion remains un changed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002781_iros.2004.1389341-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002781_iros.2004.1389341-Figure2-1.png",
        "caption": "Fig. 2. Thc robot model and ils paramelen",
        "texts": [
            " For the modeling, we establish a world coordinate frame whose original point is located at the sole of the rear leg at the heginning of stepping-over, with X-axis pointing horizontally fonvards a n d p a x i s vertically up. This frame is fixed on the ground, with which all following calculations are respect to. For the sake of simplicity, and without loss of generality, we do not consider the motion of head joint and arm joints. Rather, we take the head and the chest fixed together, and each straight stretched arm as rigid bodies. The arms can rotate about the shoulder joints, and the chest can also mate about the 131 chest joint. The hip is supposed to be vertical constantly. Fig. 2 shows all geomeuic parameters, where d l and dz are the horizontal distances of the toe and heel from the ankle joint, respectively; e 15 the height of ankle joint; s is step size; 1l,1z,lp and 1, are the lengths of the thigh, the shank, the hip and the chest, respectively; and qto.qtl and r ~ , ~ (i = 1,Z) are three of leg joints (their positive directions are defined in the figure) of the two legs. In the following, we examine each phase of the steppingover to setup the corresponding GO models, and then integrate them",
            " Now to get the maximum height of the obstacle in tbis phase, we have the following GO model: nmx h d i 5 x i smor - (dz + W) (1) (z - xP.)* + (h - zPr)' 2 r2rcl (x + w - z.,)' + (h - z,,)' 2 r:yc3 s.t. (5 + + ( h - e)* 5 r?,,z 1 -dz i xCom 5 dl where (xp,, zp,) and (xn2,zn2) are the cwrdinates of the hip and the front knee in the world frame, respectively, and smor is the maximum step size of the robot, which is 132 obtained hy the following GO model: max s Q 5 Q S G s.t. { - ZP, = ZP. -d2 5 ~ c o m 5 di where the step size s can be calculated as (see Fig. 2): s = - IlsiW(q1, + 412) - l?sin(qlz) + lisin(q21 + 4 2 2 ) + Izsin(q22). Q is the vector of all of joint angles involved, Q and are its lower and upper bounds, rrspectively. Anczp , and zp, are the hip height calculated according to the two legs, respectively: zpt = e + Ilcos(qii + q i 2 ) + lzcos(qi2), (i = 1: 2). In Phase 2 of the stepping-over, we can get the corresponding GO models in the similar way. At the beginning, the robot is still supported by the rear foot (Fig. 3(b)). The GO model is as follows: niax h Q 5 Q 5 Q I - d l 5 z 5 s - (d2 +U) where the inequalities with max( ",
            " NUMERICAL EXAMPLE To verify the proposed approach, we give a numerical example in this section. In the example, we take the humanoid robot HRP-2 developed by AIST as the robot model, and use the open architecture simulation software OpenHRP [61 to show some of the robot configurations during the stepping-over. HRP-2 has 30 degrees of freedom (DoF) in total. Each leg has six DoF's: three in the hip joinf one in the knee joint and two in the ankle joint: the chest has two DoF's: the neck also has two DoF's, and each arm has seven DoF's. The relevant parameters (as shown in Fig.2) are as follows: 11 = /2 = 300.0, d l = 135.6, dZ = 105.6, e = 105.0; qin E [-125', 12\"], qii E [0, 150\"], pi2 6 [ - 7 5 O , 42'1, (i = 1,Z); qc E [-5', 60'1, q,, E [-180\u00b0, 60\u00b0], I , = 347.7, 1, = 181.0; where lengths are in unit of millimeter, the same hereafter. Note that some parameters are just estimated values, obtained by measuring HRP-2. The total mass of the robot is about 58 kg, the mass of each part and its center (CoM) with respect to the local frame are omitted here for the sake of paper space"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002025_fuzzy.1996.552385-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002025_fuzzy.1996.552385-Figure3-1.png",
        "caption": "Fig. 3. Weight (membership) functions wl(xl> and w2(xI) .",
        "texts": [
            " The swing of the electric power system must be converged to a stable equilibrium point, but that of the inverted pendulum to an unstable one. Finally, control responses are discussed for linear and fuzzy control inputs. (2) w i t h X = [ X I x z x 3 I T and I ; , = [ f , l f , z f , , l , we f i n d that the feedback gain F1=Fz yields a linear control input u( t )=-FlX. Here, weight (membership) functions w l ( x l ) and w 2 ( X I ) are given by, using the nonlinear function siml i n eq. (11, depending on x I 20, where k l x l and k z x l are straight lines shown i n Fig. 3. Also, the nonlinear function siml can be expressed as 2 2 siml =- { C w I (xl )k I X I I / { Cw ( X I )}. i- 1 i = l (5) Therefore, i n the restricted interval L of wi th x1 for the slope k~(0 .218 , W I ( X I > and W Z ( X I ) 1 satisfy W i ( x l ) ) O and wl(xl)twz(xl>)O. Then, substituting eqs. (2>-(5) into eq. (1) gives the following form of fuzzy system: 3. S t a b i I i t y A n a l y s i s 2 2 i= 1 i= 1 i={ c w i ( X I ) A i R o / I C w i ( X I ) ) (6) Assuming a scalar function V=XTK>O i n order t o discuss the stability of the fuzzy system (61, and taking the time derivative, we obtain the Lyapunov inequalities as I f there exists a common symmetric positive definite matrix P between two inequalities, the stability of the fuzzy system (6) and then the original eq",
            " Similarly, we have P t z ) -region from AZTP2t P2Az=-Q2<0, and can obtain the P-region as a common region between P Here, it should be noted that the feedback gain F, i n A , i s determined under the existence of a P-region. - and P (') -ones. 4. Control Responses Control responses for u ( t ) = O are shown i n Fig. 4, where init ial values x1O=xl(t=O), xzo=xz(t=O) and x30=x3(t=0). The responses converge t o stable equilibrium points ( x l = -n, K , 2 >, depending on the init ial velocity x z o . Next, choosing kz.O.218 (tangent slope) i n Fig. 3, we have -m<L<m as a restricted condition, t h a t is, i f there exists a P satisfying eq. (8) under this condition, the stability of eq. (1) can be guaranteed i n the whole region of dependent variables ( X I , XZ, x3}. Actuslly, setting feedback gains as (a) linear control input: F,=F2=[33.4 9.75 0.9871, and (b) fuzzy control input; F1=[33. 4 9.75 0.9871 and F2=[85.4 22.1 1.691 i n eq. (2). we f i n d each P-region shown i n Fig. 5. I n this case, the control responses are represented i n Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003209_j.jsv.2004.12.011-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003209_j.jsv.2004.12.011-Figure1-1.png",
        "caption": "Fig. 1. Outline of journal bearing test rig.",
        "texts": [
            " Based on the linear theory, the oil-film force increment of journal bearing is the linear algebraic function of displacements \u00f0x; y\u00de and velocities \u00f0 _x; _y\u00de with respect to the journal\u2019s static equilibrium position \u00f0x0; y0\u00de; it can be written as D ~f X D ~f Y \" # \u00bc k1 x x0 y y0 \" # \u00fe d1 _x _y \" # \u00bc kXX kXY kYX kYY \" # x x0 y y0 \" # \u00fe dXX dXY dYX dYY \" # _x _y \" # , (1) where D ~f X ;D ~f Y are the oil-film force increments in the horizontal and vertical directions. k1 and d1 are the linear stiffness and damping coefficient matrices. They have their respective four linear coefficients. It is noted that once multi-sets of displacements \u00f0x; y\u00de; velocities \u00f0 _x; _y\u00de and oil-film force increments are obtained from the experiment, the linear oil-film coefficient matrices k1 and d1 can be identified. Fig. 1 shows a schematic diagram of the test rig. The test shaft (5) is supported by two identical five pad tilting-pad journal bearings (6) at both ends. A test bearing (13), diameter 152mm, width 88.3mm, radial clearance 0.114mm, is mounted between the supports. The test bearing along with the bearing housing (11) and the metal gasket (16) sits on the bottom splint (17). The bottom splint is dragged by four steel rods (9) which are screwed on the top splint (12). The top splint is hung over the spring-opposed bellows (14) which sits on a stiff supporting framework (8)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001713_s0167-2789(01)00281-0-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001713_s0167-2789(01)00281-0-Figure1-1.png",
        "caption": "Fig. 1. Sketch of the system: a disk of radius a rolls without slipping on a rough horizontal plane.",
        "texts": [
            " A uniform disk rolling on a rough horizontal plane is a nonholonomic system, i.e., the dynamical system that has three degrees of freedom, but to define its configuration we need five Lagrangian coordinates. The procedure of finding the equations of motion from the Lagrangian function and equations of constraint is well known (for details, see [4]). We will not repeat the derivation here. Our starting point is these equations of motion themselves. In our consideration we will use McDonald\u2019s notations [6]. As it is shown in Fig. 1, the axis z\u0302 is vertically upwards. A right-handed coordinate triad of unit vectors (1\u0302, 2\u0302, 3\u0302) are the moving axes (not fixed in the disk). Axis 1\u0302 being along the symmetry axis of disk is chosen so that the component \u03c91 of the angular velocity vector \u03c9 of the disk about this axis is positive. Axis 3\u0302 is directed from the center of the disk to the point of contact with the horizontal plane, and makes angle \u03b1 to the horizontal, where 0 \u2264 \u03b1 \u2264 \u03c0 . Having the direction of the velocity of the point of contact, axis 2\u0302 = 3\u0302 \u00d7 1\u0302 lies in both the plane of disk and the horizontal plane",
            " Now we suppose that \u03b1, \u2126 and \u03c91 undergo small oscillations about their equilibrium states: \u03b1 = \u03b10 + (\u03b1 \u2212 \u03b10) = \u03b10 + \u03b1, (15) \u2126 \u2248 \u21260 + a1 \u03b1, (16) \u03c91 \u2248 \u03c910 + a2 \u03b1, (17) where a1 and a2 are some constants. Let \u03b1 be small so that cos \u03b1 \u2248 1 and sin \u03b1 \u2248 \u03b1. Inserting (16) and (17) in Eqs. (4) and (5) and equating terms of first order of smallness, we find the coefficients: a1 = \u2212 2 sin \u03b10 (\u21260 cos\u03b10 + \u03c910), (18) a2 = \u2212\u21260 sin \u03b10 2k + 1 . (19) Using the equality (13) and the fact that \u03c910 = (b/a)\u21260, where b is the distance from the axis of the instantaneous motion to the center of mass of the disk (see Fig. 1), we get V dV d\u03b1 = V dV d(\u03b1 \u2212 \u03b10) = B(\u03b1 \u2212 \u03b10), (20) where B = g a ( sin \u03b10 \u2212 [ 4k + 1 2 + 2k \u2212 1 2 cos 2\u03b10 + 2(4k + 1) b a cos\u03b10 + 2(2k + 1) b2 a2 ]) is a constant for the given steady state. Let us observe that Eq. (20) is nothing else as a standard equation of linear oscillations. When B > 0, it has a saddle fixed point, and for B < 0, the fixed point becomes a center. As it is well known [9], the linear approximation of a nonlinear system is not sufficient for defining the global phase plane plot in the latter case"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0002758_jahs.49.109-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0002758_jahs.49.109-Figure1-1.png",
        "caption": "Fig. 1. Spur gear fatigue rig gearbox.",
        "texts": [
            " Vibration data were collected from accelerometers and used in previously validated gear vibration diagnostic algorithms. Oil debris data were collected using a commercially available in-line oil debris sensor. Oil debris and vibration data will be integrated using fuzzy logic analysis techniques. The goal of this research is to provide the end user with a simple tool to determine reliably the health of this geared system. Experimental Investigation Experimental data were recorded from 24 experiments performed in the Spur Gear Fatigue Test Rig at NASA Glenn Research Center. A sketch of the test rig is shown in Fig. 1. The facility operates on the torque regenerative principle. Torque is applied by a hydraulic loading mechanism that twists one slave gear relative to its shaft. The power required to drive the system is only enough to overcome friction losses in the system (Ref. 6). The test gears are standard spur gears having 28 teeth, 3.50 inch (8.89 cm) pitch diameter, and 0.25 inch (0.635 cm) face width. The test gears are run offset to provide a narrow effective face width to maximize gear contact stress while maintaining an acceptable bending stress"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0003686_j.ijmachtools.2005.10.017-Figure2-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0003686_j.ijmachtools.2005.10.017-Figure2-1.png",
        "caption": "Fig. 2. Diagram of a shaft element.",
        "texts": [
            " This is because the measured axial force and ARTICLE IN PRESS Nomenclature A cross-sectional area of a shaft element Ai cross-sectional area of various shaft segments A1 cross-sectional area of the checked shaft C the bearing damping cx, cy the bearing damping coefficient in x- and ydirections E the Young\u2019s modulus ex, ey eccentricities of an element centroid with respect to the turning axis in x-and y-directions de diameter of a shaft element G the Shear modulus L length of a shaft element Lc length of the checked shaft L1 span between the two bearings L2 length from drill tip to the bearing positioned down L1/L2 cantilever ratio of the drilling system I inertia moment of a shaft element I1 inertia moment of the checked shaft Id quadrate moment of the shaft per unit length Ip quadrate-polar moment of the shaft per unit length k Shear coefficient of the material kx, ky the bearing stiffness in x- and y-directions Ji polar inertia moment of various shaft segments P axial drilling force r radius of the checked shaft s axial position from an element end, seeing Fig. 2 T drilling torque Te kinetic energy of a shaft element t time Ue potential energy of a shaft element x, y the deformed displacements of the drilling system in x- and y-directions xb, yb displacements from the bending deformation in x- and y-directions xs, ys displacements due to shear deformation caused by the bending in x- and y-directions xc; yc; _xc; _yc displacements and velocities of the bearing center in x- and y-directions r mass density of the material yx, yy angle displacements in x- and y-directions O the spindle speed o the natural frequency o\u0304 dimensionless form of the natural frequency sca the calculated stress seq and teq bending and shear stresses of a shaft element from the bending dWb virtual work produced by the bearing force dW e virtual work produced by centrifugal force of an element Ce 1 damping matrix of a shaft element F e 1sin n o and F e 1cos n o the generalized force vectors of a shaft element Ke 1 stiffness matrix of a shaft element Ke p1 h i an element stiffness matrix due to the axial drilling force Me 1 mass matrix of a shaft element fNg; fNyg vectors of the shape functions qe u ; qe v the generalized displacement vectors of any element nodes in x- and y-directions f \u20acqug; f _qug; fqug acceleration, velocity, and displacement vectors of all element nodes of the drilling system in x-direction f \u20acqvg; f _qvg; fqvg accelerate, velocity, and displacement vectors of all element nodes of the drilling system in y-direction {A} amplitude vector of the bending deformation at any position of the spindle-drill system [C] matrix of the system damping {Fsin} and {Fcos} vectors of the generalized forces of the system [K] stiffness matrix of the system [Kp] the system stiffness matrix due to the axial drilling force [M] mass matrix of the system {Q} the system generalized forces in the complex form {z} the system generalized displacements in the complex form P",
            " Since the stiffness of micro-drills is small and there is eccentricity in the drilling system, the micro-drill and spindle bend when the axial drilling force acts. The bend causes the drill and spindle to deform elastically although the spindle deformation is very small. The elastic deformation makes the drill and spindle displace in radial and axial directions, respectively. Since the radial displacement is larger than axial one, axial displacement of the drill and spindle is neglected in this work [6\u20138]. Fig. 2 shows that a shaft element subject to axial force P is rotating at a constant speed O. Assume that the deformed displacements at any position of the element axis in x- and y-directions are x(s, t) and y(s, t), respectively, and that angle displacements of any cross-section of the element are yx(s,t) around the x-axis and yy(s,t) around the y-axis. ARTICLE IN PRESS P. Yongchen et al. / International Journal of Machine Tools & Manufacture 46 (2006) 1892\u20131900 1895 From the Timoshenko beam theory, the displacements, x and y, consist of displacements (xb, yb) from the bending and displacements (xs, ys) due to the shear deformation caused by the bending, and the angle displacements, yx and yy, are just related with the bending displacements (xb, yb)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_11_0001223_10402009508983385-Figure3-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0001223_10402009508983385-Figure3-1.png",
        "caption": "Fig. 3. T h e contributed forces are the resultant force of gas and elastic pressures Fy and hydrodynamic force Py, where Fy = (Prb + Pr)w and P,b = max{P,( t ) , Pb(t)}, where P,( t ) and Pb(t) are combustion chamber pressure and blow-by pressure, respectively.",
        "texts": [],
        "surrounding_texts": [
            "An Elastohydrodynamic Cavitation Algorithm for Piston Ring Lubrication 99\nthat was proposed by Jakobson and Floberg (21) and Olsson (22), is known as JFO condition. Through application of this theory, a mass conservation algorithm proposed by Elrod and Adams (23), Elrod (24), and later modified by Vijayaraghavan and Keith (25), (26) to a hydrodynamic cavitation algorithm, provides an effective tool to predict lubricant pressure in all regions of a bearing o r seal. Elrod's method (24), which is known as the Elrod algorithm, is an approxin~ate method that assumes an incompressible fluid exists in the full-film region and an incompressible fluid exists in the cavitated region for shear induced flow, and a compressible fluid exists for pressure-induced flow. Although this algorithm is efficient, it does not clearly portray the flow physics because it was developed through numerical experimentation. The modified cavitation algorithm developed by Vijayaraghavan and Keith (25), (26) is a method that employs a transonic flow concept to obtain a physically plausible model. Their method produces an equally efficient approach compared with the Elrod algorithm. The results predicted by this method are slightly more accurate than those by using the Elrod algorithm (27). The cavitation theory has been successfully used in a number of different cases, especially for journal bearings in hydrodynamic lubrication.\nIt does not appear that a comprehensive cavitation theory has been applied in elastohydrodynamic lubrication to date. 'The reason is that when the contact surfaces are considered to be smooth and the pressure acting on the trailing edge is low, a solution obtained using the Reynolds boundary condition has enough accuracy. However, when the pressure is high at the trailing edge, such as the position after piston rings just pass TDC in the expansion stroke, the hydrodynamic pressure distribution will be greatly different from that obtained through the employment of the Reynolds boundary condition. Because the elastic deformation strongly relies on hydrodynamic pressure, the film thickness which relies on both hydrodynamic pressure and elastic deformation will be greatly affected. Thus, an understanding of the elastohydrodynamic cavitation mechanism for a piston ring becomes critical.\nThe objective of the current research is to develop an elastohydrodynamic cavitation algorithm to predict film thickness and pressure distribution for piston ring lubrication. Instead of using a constant bulk modulus, which was used by Elrod and Adams (23), Elrod (24), and Vijayaraghavan and Keith (25), (26), a variable modulus, which is based on compressible mineral oil proposed by Dowson and Higginson (28), and a viscosity-pressure relation is used in the current research to simulate more realistic situations.\nANALYSIS\nThe Governing Equation for EHL\nThe unsteady Reynolds equation for one-dimensional lubrication can be written as:\nAnd one can define:\nwhere p, is the lubricant density at cavitation pressure and 0 is non-dimensional density in the full-iilm region or fractional-film content in the cavitated region.\nSubstituting Eq. [2] into Eq. [I] produces:\nIt is assumed that the viscosity of the lubricant can be predicted via the well-known pressure-viscosity relation:\nSubstituting Eq. [4] into Eq. [3] yields:\nAccording to Dowson and Higginson (28), the film density can be related to the pressure by the following:\nwhere po is the lubricant density at atmosphere pressure, 1 1 A. = 0.6 x lo-' - and Bo = 1.7 x lo-'-, while P is Pa Pa in Pa. Because po = p,, Eq. [6] can be expressed as:\nThus, pressure P can be written in terms of 0 as:\nAccording to Elrod (24), a switch function g based o n 0 call be defined as:\ng = 1.0 when 0 > 1 in full-film region,\ng = 0.0 when 0 < 1 in cavitated region.\nSubstituting Eq. [a] into Eq. [5] and eliminating p,. ~,rotlucc*s:\nA reduced bulk modulus is deli~ictl ;IS:\nD ow\nnl oa\nde d\nby [\nU ni\nve rs\nity o\nf Il\nlin oi\ns at\nU rb\nan a-\nC ha\nm pa\nig n]\na t 2\n2: 46\n1 6\nM ar\nch 2\n01 5",
            "100 Q. YANC AND T. G. KEITH, JR.\nthus, Eq. [9] can be expressed as:\nEquation [I I] is the EHL governing equation which will permit consideration of both elastohydrodynamic and cavitation effects.\nElastic Deformation\nThe elastic displacement of the piston ring and cylinder wall due to hydrodynamic pressure within the lubricant film can be found from the elastic equation, Eq. [28]:\n2 U ( X ) = -z jp ( ~ ) h ( x - u2d( + constant [12]\nLubricant Film Thickness\nWith the assumption of perfectly smooth surfaces, the lubricant film thickness h for a piston ring with a symmetric parabolic face subject to local elastic deformation can be expressed in terms of minimum film thickness h,( t ) , x and elastic deformation v ( x ) as:\n6 where y = 7, w is the width of the ring and 6 is the (w/2) crown height of the ring shown in Fig. 1.\nPiston Ring Velocity\nThe piston ring velocity is assumed to be the same as the piston velocity. I t can be developed from the engine crank mechanism shown in Fig. 2:\n2 m where: o = -\n60\nBoundary Conditions\nInstead of applying pressure boundary conditions, 0 boundary conditions, written in terms of pressure acting on both leading and trailing edges, can be used for the compressible lubricant model.\nBy substituting PI- and PT into Eq. [7], the 0 boundary conditions can be written as:\nand\nwhere XI- and x-,. are the leading and trailing edge positions, respectively, and PL and PT are the leading and trailing\nedge pressures, respectively.\nEquilibrium Condition\nWhen an engine is operating, the net resultant radial force of a piston ring must be in equilibrium, as shown in\nWu and Chen (18) used a more detailed method to account for the bending effect for force equilibrium. Their results showed that the effect is small enough to be neglected. Accordingly, the current method employs Eq. [17].\nInitial Condition\nSince the piston ring velocity and combustion chamber pressure change periodically, the oil film thickness will also vary in a cyclic manner. T o begin the analysis, a guessed initial condition is needed for the initial time step in the first cycle and the determined result can be used as the initial guessed film thickness for the next time step in the first cycle calculation. Usually, h(x,to) can be expressed in terms of an arbitrarily guessed minimum film thickness and parabolic profile without elastic deformation, i.e.:\nNUMERICAL METHOD\nFinite Differencing\nT o begin, Eq. [ l I] is rearranged as:\nD ow\nnl oa\nde d\nby [\nU ni\nve rs\nity o\nf Il\nlin oi\ns at\nU rb\nan a-\nC ha\nm pa\nig n]\na t 2\n2: 46\n1 6\nM ar\nch 2\n01 5",
            "An Elastohydrodynamic Cavitation Algorithm for Piston Ring Lubrication\nTDC\nFlg. 3--Radial forces acting on a plston ring.\nThe right hand side of Eq. [I91 can be written as:\nThe term is based on the method of Vijayaraghavan and Keith (25) by applying central differencing in the full-film region and upwind differencing in the cavitated region. There are six possibilities depending on whether a grid point is within the full-film or cavitated regions. These can be incorporated into the following general expression:\nThe coefficients of Eq. [21] for the six cases are as shown in Table 1.\nSix different, combined-switch functions based on the switch function g may be written as follows:\nF = full-film region (AmX).hea, = PLU [o(Ob)i+ 1 + b(8h)i + r(8h)i- [2 11 c = cavitated region\n2\nD ow\nnl oa\nde d\nby [\nU ni\nve rs\nity o\nf Il\nlin oi\ns at\nU rb\nan a-\nC ha\nm pa\nig n]\na t 2\n2: 46\n1 6\nM ar\nch 2\n01 5"
        ]
    },
    {
        "image_filename": "designv11_11_0000220_acc.1999.786185-Figure1-1.png",
        "original_path": "designv11-11/openalex_figure/designv11_11_0000220_acc.1999.786185-Figure1-1.png",
        "caption": "Figure 1: Coordinate Systems",
        "texts": [
            " Finally, section 5 contains the main conclusions and discusses theoretical and practical issues that deserve further consideration. 2 Problem Formulation. This section describes the navigation problem that is the main focus of the paper and formulates it mathematically in terms of an equivalent filter design problem. For 0-7803-4990-6199 $10.00 0 I999 AACC 1910 the sake of clarity we first introduce some required notation and review the kinematic relationships of an aircraft / ship carrier ensemble, where the former is equipped with a vision based system. 2.1 Notation Consider Figure 1, which depicts an aircraft equipped with a vision camera operating in the vicinity of the ship. Let {Z} denote an inertial reference frame, {a} a bodyk e d frame that moves with the aircraft, and {C} a a camera-fixed frame. The symbol { S } denotes a shipfixed body frame. The following symbols will be used: PB = [zb yb .?&IT - position of the origin of {a} measured in {Z} (i.e., inertial position of the aircraft). ps = [zc. yB z.]\u2019 - inertial position of the ship. PSB (a .bh. p = [z y Z I T ) - relative position of the ship with respect to the aircraft, resolved in {Z}"
        ],
        "surrounding_texts": []
    }
]