[
    {
        "image_filename": "designv11_28_0003211_detc2007-34379-Figure11-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003211_detc2007-34379-Figure11-1.png",
        "caption": "Figure 11 : Discretization and element deformations",
        "texts": [],
        "surrounding_texts": [
            "% thi ber can be adjusted to cope with 3D codes possibilities -35,20,NN); N,NN); NN);xwh=zeros(NN,NN); ); zx end; t=linspace(-pi/20,pi/20,NN); ugh volume for FEM /50,pi/50,100); % for zooming M(I,:)=ycom(I);end \u2013 equal lines % for I ;for J=1:NN;xwh(J,I)=(Ro-zxo(J))*sin(t(I));end;end for I ;zwh(I,:)=(Ro-zxo).*(1-cos(t(I)))+zxo;end; f;surface(xwh,YCOM,zwh); R,YCOM);%zr=zr'; zr xp % fo p( M % 0 Copyright \u00a9 2007 by ASME ?url=/data/conferences/idetc/cie2007/71022/ on 02/20/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloade ANNEX 2 : Dynamical S The Rigid Multi-Hertzian Method has been impleme s f one simulatio 40) in d having an ini k: 1360 DB) IZ=IX, IY= tical equ tial roll v ck. Figure 10 : Dynamic te, looking at these un-filtere are no such seen with this profiles pai uous. The small e to 250 Hz is due to the large Hertzian stiffness of the contact and is excited by the pproximations. Note that there is abso ping at all in the mechanism. imulation Example nted in the dynamical code \u201cOCREC\u201d that u es it \u201conline\u201d. Following Figure shows the results o n using the pair S1002/UIC60(1/ conditions of the LD Benchmark [7]: Isolated Wheelset without friction an tial lateral velocity. No damping at all. Track Gage:1435.1mm, Wheels Back to bac mm (instead of 1352.14mm in L Wheelset mass: 1568kg, IX=656kg.m2, 168kg.m2, Ro=0.457m Initial wheelset position: centered and in ver ilibrium, total load on rails: 180kN Initial wheelset lateral velocity : 0.1m/s, ini elocity: 1/180 rad/s, adhesion: 0, rigid tra al Simulation It is interesting to no d elementary forces, that there discontinuities as often r. Vertical loads are contin ripple clos numerical a lutely no dam 11 Copyright \u00a9 2007 by ASME d From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/idetc/cie2007/71022/ on 02/20/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloade ANNEX 3 : FEM Calculation using ANSYS One FEM calculation of the test case was made on a PC_Pentium4 at LMGC using the ANSYS software. The model has 19163 tetrahedral 10 nodes elements and 1151 triangle surface elements ith 6 nodes. Quasi-static calculation lasted 1h36 with 100 time steps of 0.01s. d the ented Lagrangian. w Wheel and rail are elastic materials (E=2.1E11Pascal, sigma=0.3). There is no friction an contact is according to a method of augm Resulting normal force is calculated at F=(0 ; -10308 ; 184905) Newtons 12 Copyright \u00a9 2007 by ASME d From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/idetc/cie2007/71022/ on 02/20/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: h Figure 13 : Undeformed Longitudinal model 53mm 54,72mm 54,72mm Figure 14 : Undeformed Lateral model 13 Copyright \u00a9 2007 by ASME ttp://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/idetc/cie2007/71022/ on 02/20/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Do 14 Copyright \u00a9 2007 by ASME wnloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/idetc/cie2007/71022/ on 02/20/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use"
        ]
    },
    {
        "image_filename": "designv11_28_0001538_bm049793y-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001538_bm049793y-Figure4-1.png",
        "caption": "Figure 4. Cross-section profiles of structures containing nipplelike features in a 1:1 ratio of unpolymerized DELT and L-tyrosineamide comonomer mixture (arrowheads) are shown. Two scan lines labeled a and b run through these structures. We show the cross section profiles obtained by measuring along scan lines a and b and the vertical dimensions of the structures.",
        "texts": [
            "8 The one striking feature of the images in Figure 3b is the presence of the smooth but sharp spike or nipplelike structures that rise occasionally from the overall smooth, unstructured aggregate surface. These are not regular features but are observed to occur sporadically, without ever being too close in proximity. In some instances, these structures are significantly smaller than the two nipplelike structures seen in panel b. The prominent nipplelike structures rise to significant heights from the aggregate surface. In Figure 4, we present measurements through two regions containing a few nipplelike structures. The cross section profiles are shown for the scan lines a and b through the aggregate structures. It is clear from these profiles that the aggregates rise into the range of 100-300 nm in height. The nipplelike structures themselves rise sharply from the aggregate background structure. In the instances shown, the nipplelike structures rise distances of from 50 to 180 nm higher than the underlying aggregate surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003435_s10778-009-0150-6-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003435_s10778-009-0150-6-Figure2-1.png",
        "caption": "Fig. 2Fig. 1",
        "texts": [
            " These robots consist of a driving link (its position is defined by the segment AB of length L 1 ) and a driven link (its position is defined by the segment BD of length L 2 ). The segments AB and BD make angles 1 and 2 , respectively, with the OX-axis. In both models, the velocity of the point A is determined by an angle 1 (the rotation angle of the first steerable wheel). In the first model (Fig. 1), the velocity of the point B is determined by angle 2 (the rotation angle of the second steerable wheel), and the velocity of the point D is directed along BD. In the second model (Fig. 2), the second steerable wheel is at the point D and, thus, the velocity of the point B is directed along AB, and the velocity of the point D is determined by an angle 3 (the rotation angle of the second steerable wheel). Denoting by x and y the coordinates of the point B, and byV V x V yx y, , the velocity of the point B and its projections onto the OX- and OY-axes, we can write equations describing (in kinematic approximation) the motion of these mobile compound robots. For example, for model I (Fig",
            " 44, No. 12, 2008 1063-7095/08/4412-1413 \u00a92008 Springer Science+Business Media, Inc. 1413 S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine 03057, e-mail: model@inmech.kiev.ua. Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 111\u2013120, December 2008. Original article submitted October 11, 2007. V Vx cos( ) 2 1 , V Vy sin( ) 2 1 , sin( ) cos( )cos 1 1 2 1 1 2 1 V L x , sin( ) cos( ) 2 1 2 2 2 1 2 V L x . (1.1) For model II (Fig. 2) we have V Vx cos 1 , V Vy sin 1 , sin cos cos 1 1 1 1 1 V L x , sin( ) cos cos 2 1 2 3 2 3 1 V L x . (1.2) 2. Reduction of the Models. Assume that | | , | | , | | , | | 1 2 1 2 1 , | | , | | / 1 2 3 2 in (1.1) and (1.2). Also assume that controls u 1 , u 2 , and u 3 determine the rotation rate of the steerable wheel: 1 1 V ux , 2 2 V ux , 3 3 V ux . (2.1) Let also x 0. This makes it possible to choose the coordinate x as an independent variable in Eqs. (1.1), (1.2), and (2.1) and, thus, to reduce the order of the system. In this case, the motion of the robot shown in Fig. 1 is described by the following equations (prime denotes differentiation with respect to x): y tan( ) 1 2 , 1 1 2 1 1 2 1 sin( ) cos( )cosL , 2 1 2 2 2 1 2 sin( ) cos( )L , 1 1 u , 2 2 u . (2.2) For the robot shown in Fig. 2, such equations are y tan 1 , 1 1 1 1 tan L cos , 2 1 2 3 2 1 3 sin( ) cos cosL , 1 1 u , 3 3 u . (2.3) The system of equations (2.2) can be rearranged as y v 1 , 1 2 v , 2 2 2 2 2 cos sin L y L , (2.4) v u L 1 2 1 2 2 1 2 1 1 1 2 3 (cos( )) sin( ) cos (cos( )) , v u L u 2 1 2 1 1 2 1 2 2 1 1 1 cos cos( )(cos ) cos( ) cos (c os( )) 1 2 2 . (2.5) For system (2.3), such equations are y v 1 , 2 2 v , (2.6) v u L L 1 1 1 1 3 1 2 1 2 1 1 2 1 5 3 1 (cos ) (cos ) (sin ) sin (cos ) (cos ) 1 2 , v u L L L 2 3 2 1 2 1 3 2 2 3 1 1 cos( ) cos (cos ) cos( )sin 2 1 3 1 3 2 1 3 2 2 1 2 2 2 2 2cos cos (cos ) sin( ) (cos ) (c L os ) 3 3 ",
            "7), of the controls u 1 and u 3 as functions of y, 1 , 2 , 1 , and 3 , we can use (2.1) to find the dependence of 1 and 3 on the current phase coordinates, i.e., to synthesize a nonlinear real-time feedback. Note that it is the easiest to determine the velocityVx when the system is coasting. Therefore, let us solve the stabilization problem for model II that is coasting. The fact that the kinetic energy of a coasting system remains constant (the constraints imposed on the system are perfect) can be used to findVx . Let the centers of gravity of the links of the model shown in Fig. 2 be at their middle (i.e., at the middle points of the segments AB and BD). The masses and central moments of inertia of the driving and driven links are denoted by m 1 , m 2 and J 1 , J 2 , respectively. We can use (1.2) to derive expressions for the kinetic energy of the driving (T 1 ) and driven (T 2 ) links: 2 1 4 1 1 2 1 1 1 1 2 1 2 T V m J m L ( )tan , (7.1) 2 2 2 2 2 2 3 2 2 1 3 2 3 2 T V m (cos ) (cos( )) cos (cos( 1 2 2 2 1 3 2 2 2 2 4 )) (sin( )) J m L , (7.2) where, as in (1.2),V is the velocity of the point B ( )V V Vx y 2 2 2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003762_026635108785260588-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003762_026635108785260588-Figure2-1.png",
        "caption": "Figure 2. Discrete model and continuum model.",
        "texts": [
            " We use the same method to calculate the flexural stiffness EI, the shear stiffness GA and the coupling terms between them. For more details, the reader may refer to the reference [16]. Three tensegrity cells are concerned in this study, the simplex, the regular quadruplex (vertical quadruplex) and the half-cuboctahedron quadruplex (horizontal quadruplex). Before developing the numerical applications, it is important to remember that the notion of repetitive cell is defined as the assemblies of two cells for the first two cases (Fig 2 and 9). The third case is devoted to only one cell (Fig 15). For the three cells, the geometrical and mechanical characteristics of the struts and cables are: Cable cross-section: Ac = 0.28 cm2 ; Strut cross-section: Ab = 3.25 cm2 Young\u2019s modulus: Ec = 40 000 Mpa (cables); Eb = 200 000 Mpa (struts) EA h d C d C d GJ h d \u2032 \u2032 \u2032 \u2032 1 16 6 16 1 6 0 1 + = + = 108 International Journal of Space Structures Vol. 23 No. 2 2008 In order to validate the suggested approach, the results obtained are, first of all, compared to those obtained with the finite element method (Table 2b), and those for the following initial selfstress tension vector (T\u00b0): Examining this table, the coupling terms can be noted to be null and the equivalent rigidity of flexion (EIy=EIz) and of shearing (GAy=GAz) are identical according to y and z"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001155_s0022-0728(01)00380-1-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001155_s0022-0728(01)00380-1-Figure7-1.png",
        "caption": "Fig. 7. Y vs. E curves for a pH 4.1 aqueous solution of 0.1 M NaClO4 on: (a) bare mercury and on mercury coated with mixed L16\u2013DOPC monolayers containing (b) 0; (c) 20; (d) 50; and (e) 100 mol% L16.",
        "texts": [
            " A self-organized monolayer of pure DOPC turns the polar heads toward the aqueous phase and the hydrocarbon tails toward the hydrophobic mercury surface. Over the potential range from \u22120.20 to \u22120.75 V versus SCE this monolayer behaves like a half-membrane [14,51,52]. Thus, it is practically impermeable to inorganic ions and its differential capacitance amounts to 1.7\u20131.8 F cm\u22122, namely it is twice that of solvent-free black lipid membranes. At more negative potentials, the quadrature component of the electrode admittance shows three peaks (see curve b in Fig. 7), which are due to different degrees of reorientation of the lipid molecules. Fig. 7 illustrates the changes in Y of mixed L16\u2013DOPC monolayers when passing from pure DOPC to pure L16. An increase of the L16 content in the film narrows the potential range over which Y coincides with the differential capacitance of DOPC alone. Naturally, over the potential range in which L16 is electroactive, its reduction current also affects Y , which can no longer be identified with the differential capacitance. The increase in Y observed at potentials positive of \u22120.25 V is to be ascribed to the electroreduction of the L16 molecules and to their reorganization as well"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003459_iciea.2008.4582679-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003459_iciea.2008.4582679-Figure1-1.png",
        "caption": "Fig. 1 Schematic diagram of turbomolecular pump with active magnetic bearings.",
        "texts": [
            " It should be hoped, from what has been said above, that the turbomolecular pump with active magnetic bearings will decrease the influence of unbalance or external disturbance, overcome the uncertainty on the physical parameters, work in wide operational rang with adaptive variable structure controller. Simulation results serve as evidence of proposed turbomolecular pump with high robustness and disturbing resistibility. In this paper, we designed adaptive variable structure controller for turbomolecular pump with active magnetic bearings. The center of gravity that located below the blades of the turbomolecular pump could be schematized as Fig. 1. There were five degree of freedoms controlling by large, small, and thrust active magnetic bearings in this system; two radial displacements, one axial displacement, and two angles of the mass center were x, y, z, \u03b8x, and \u03b8y, respectively. The basic structure of turbomolecular pump with active magnetic bearings could be represented diagrammatically as Fig. 2. The symbol O meant the mass center of the rotor; a and b meant the distance from the large and small magnetic bearing to the mass center in the z direction, respectively; 1 to 10 meant the magnetic poles for magnetic bearings; F1 to F10 mean the magnetic forces for magnetic bearings; the directions of the five degrees of freedoms and the direction of the magnetic forces also showed in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001075_cm0208004-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001075_cm0208004-Figure3-1.png",
        "caption": "Figure 3. Schematic diagram showing the relative orientations of the sample and the polarization axes of the excitation and emission polarizers. The sample was mounted with the shearing direction along (a) the z-axis and (b) the x-axis.",
        "texts": [
            " The quantum yield of 1 in the solid films was very low, estimated to be about 10-8, presumably due to selfabsorption and self-quenching in the solid phase. Nevertheless, fluorescence emission from the films can be observed because of the high density of 1 (\u223c1 \u00d7 10-7 mol/cm2) in the films in addition to the large extinction coefficient of 1.33 Polarized fluorescence emission from the oriented films of 1 was examined with the polarization axes of the excitation and emission polarizers set in the same direction (horizontal, \u03b8 ) 90\u00b0). Initially, the films were mounted in an orientation (shearing direction along the z-axis as shown in Figure 3a) such that the highest absorption of the polarized incident light occurred. When excited at 457 nm, intense fluorescence emission was observed. The films were then rotated 90\u00b0 (as shown in Figure 3b)38 such that the absorption transition dipoles of the majority of the molecules were oriented perpendicular to the polarization axis of the incident light. Consequently, the emission intensity decreased dramatically. Representative spectra of the polarized emission of the films studied are shown in Figure 4. At 690 nm, the ratio of the emission intensity Iz90 (when irradiated perpendicular to the shearing direction) to Ix90 (when irradiated parallel to the shearing direction) for this film was calculated to be 30 ( 2",
            " (38) By rotating the solid sample instead of the emission polarizer, the effect of the polarization bias of the emission monochromator was minimized. ratio (Az/Ax) of the same film at 457 nm was determined to be 36 ( 1. To further examine the anisotropic fluorescence properties of oriented films of 1, we studied the angular dependence of emission intensity upon excitation with incident light linearly polarized along the x-axis (horizontal). Figure 5 shows the results for the same film that was used to obtain the spectra shown in Figure 4. Again, the film was mounted in an orientation (as shown in Figure 3a) such that the highest absorption of the polarized incident light occurred. The emission intensities at 690 nm were collected at different angles (\u03b8 ) 0\u00b0-120\u00b0) of the emission polarizer and plotted as a function of \u03b8. The highest emission intensity of the film was observed when \u03b8 was \u223c90\u00b0 (the angle at which the polarization axes of the emission and excitation polarizers were parallel). After correction for background and the polarization bias (caused by differences in the transmission of horizontal vs vertical polarized light) of the fluorometer, the emission intensity at 90\u00b0 (Iz90) was found to be about 4",
            " This result is expected for compounds that have their emission dipoles aligned with their absorption transition dipoles.37 The value of the fluorescence anisotropy39 (calculated as (Iz90 - Iz0)/ (Iz90 + 2Iz0)) was 0.52 ( 0.03, indicating that significant fluorescence depolarization occurred. The values of Iz90/ Iz0 and anisotropy obtained for the other films studied were as high as 5.0 and 0.57, respectively. We also attempted to determine the fluorescence anisotropy of the film when its shearing direction was along the x-axis (as shown in Figure 3b). However, the emission intensity was too low to allow reliable determination of the anisotropy. The fluorescence depolarization observed was presumably caused by three factors. First, as for most compounds, the radiating dipole may not be collinear with the absorption transition dipole (a small angle may exist between these vectors).39 Second, differential reabsorption of the emitted light may occur. Third, although these solid films of 1 were highly oriented, the presence of molecules aligned at different angles to the z-axis was expected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001726_978-1-4684-3776-8_1-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001726_978-1-4684-3776-8_1-Figure4-1.png",
        "caption": "Fig. 4. Immobilized enzyme stirrer. Reprint ed with permission from reference 117.",
        "texts": [
            " Nitrite levels in the range 1 x 10-4 to 5 X 10-2 M could be determined. The immobilized enzyme was stable for at least three weeks and could be used repeatedly for about 100 determinations. A more convenient method of utilizing immobilized enzymes in sta tionary solutions was described by Guilbault and Stokbro.(117) Com mercially available immobilized urease was placed onto a Teflon-coated magnetic stirring bar and was held in place by means of a nylon net. The \"immobilized enzyme stirrer,\" shown in Fig. 4, both stirs the solution and 26 Robert K. Kobos affects the enzymatic transformation. Urea in blood serum was determined with an accuracy and precision of approximately 2 % using an air gap electrode to measure the ammonia formed. After the analysis was completed the immobilized enzyme stirrer was removed, washed with distilled water, and patted dry. It was then ready for the next assay. Linear calibration curves for urea solutions were obtained from 1 x 10-4 to 5 X 10-2 M. The stirrer could be used for 450 assays or a period of four weeks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001349_amc.1998.743536-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001349_amc.1998.743536-Figure1-1.png",
        "caption": "Fig. 1. Voltage vectors of a two-level voltage source inverter along with the sectors for the selection of the voltage vectors",
        "texts": [
            "1 The selection of the proper stator voltage vector The basic principle of the DTC is to select proper voltage vectors from an optimum switching table. The selection is based on the hysteresis control of the stator flux linkage and the torque. The stator flux linkage is calculated with $, = [ + A T (E, - R,;,) dt (8) where the voltage vector can be written as Sa, Sb and S, represent the states of the three phase legs, 0 meaning that the phase is connected to the negative and 1 meaning that the phase is connected to the positive leg. The voltage vectors obtained this way are shown in Fig. 1. No motor parameters except the stator resistance is needed. The voltage vector plane is divided into six sectors so that each voltage vector divides each region into two equal parts. In each sector, four of the six non-zero voltage vectors can be used. Also zero vectors can be used. All the possibilities can be tabulated into an optimum switching table. The optimum switching table presented in [ 11 is in Table I. 3.2 Estimation of the rotor angle In DTC the calculations are done in the reference frame fixed to the stator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003363_isorc.2007.32-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003363_isorc.2007.32-Figure4-1.png",
        "caption": "Figure 4. Forwarding of sensed values.",
        "texts": [
            "val, m carries the backup data m.data = \u3008data1, \u00b7 \u00b7 \u00b7 , datamxD\u3009 to the sensor node si. Each backup tuple m.datak includes values of attributes \u3008sid, seq, val, state\u3009, where each tuple shows that a sensor node sid sends a message with a sensed value val whose sequence number is seq. If state = ON , the source node of m informs si that the actuator node a has received the sensed value val. Here, a tuple \u3008seq, val, state\u3009 for the backup tuple is also enqueued into RQik for a sensor node sk(= sid). In Figure 4, a node si sends a message m1 with a sensed value vi where m1.seq = 4. A node sj receives the message m1 but sk fails to receive m1. The node sj sends a message m2 with not only a sensed value vj but also a backup tuple \u3008si, 2, OFF \u3009. On receipt of m1 from si, a node sk stores a tuple \u30084, vj , OFF \u3009 to a receipt subqueue RQkj . \u30082, vi, OFF \u3009 and \u30084, vi, OFF \u3009 are stored RQki and RQki, respectively in sk on receipt of m2. If a sensor node si takes a value v by sensing an event, si sends a message m with the sensed value v as follows: [Transmission of a message m with a sensed value v] { SEQ := SEQ + 1; m"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000297_s0736-5845(01)00037-0-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000297_s0736-5845(01)00037-0-Figure6-1.png",
        "caption": "Fig. 6. Angular rotation of camera.",
        "texts": [
            " The remaining parameters Cn 5 and Cn 6 can be approximated using only this information, by considering first that the cameras are placed far from the region where the actual positioning task takes place and therefore only a small increment in the pan or tilt rotation is enough for encompassing a large volume of the manipulator\u2019s workspace. Secondly, according to Eqs. (3) and (4), the point \u00f0C5;C6\u00de represents the approximate camera-space location of the origin of the coordinate system xyz (see Fig. 6), used to define the physical location of the manipulated visual features. Thus the following approximate relationship exists if an orthographic projection is assumed, C5pX0; C6pY0: \u00f014\u00de And since the following is true for small pan and tilt rotations: DX0pDa; DY0pDb: \u00f015\u00de The increment in the value of C5 and C6 from one position to another can be defined in terms of the increment in pan and tilt rotations as follows: DC5pDa; DC6pDb: \u00f016\u00de The proportionality constant corresponding to the two previous expressions can be evaluated experimentally considering different values of the last two view parameters at different, reoriented locations of the cameras"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002998_robio.2006.340097-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002998_robio.2006.340097-Figure3-1.png",
        "caption": "Fig. 3. Illustration of the shortest distance between link i and obstacle j.",
        "texts": [
            " Apart from determining if two rigid bodies are in contact, the gap function will also be used as a basis for calculating the direction and size of the forces involved in the contact. Link i can, at each time-instance, only touch a convex obstacle j at one point, resulting in a contact point that may move across the entire surface of a link. Hence, by inspecting the shape of the surface of a link, we need to consider the distances between two cylinders, and a cylinder and a sphere to calculate the shortest distance (i.e. the gap functions) between the link and the obstacle, see Fig. 3. 1) Cylinder - Cylinder Contact: If the part of link i which is shaped as a cylinder is closest to the obstacle (also being a cylinder), then the gap function for object contact is defined as the distance between these two cylinders. The distance between two infinitely long cylinders equals the distance between their mid-lines minus the sum of their radii. The normal vector to the mid-lines of both the obstacle j and the link i cylinder is nij = eI z \u00d7 eBi z \u2016eI z \u00d7 eBi z \u2016 . (5) The shortest distance between the two mid-lines can now be found as dij = ( rGi \u2212 rHj )T nij , (6) Hence, the gap function is gHij = |dij | \u2212 ( LHj + LSC ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001669_03093247v204217-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001669_03093247v204217-Figure3-1.png",
        "caption": "Fig. 3. Radial clearance between pin and lug",
        "texts": [
            " In the example only contact at node 1 was considered, and after solving the equations and calculating the percentage changes of nodal loads and clearances, the highest negative percentage change occurred at node 2. cos a1 0 0 0 0 1 0 cos a2 ca 0 0 0 - 1 -cos x 5 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 a12 0 a22 a 3 2 a 4 2 a 5 2 1 0 0 1 0 0 0 0 0 0 After solving for the changes in nodal load and clearance, they must be divided by the non-zero initial nodal loads and clearances. All the initial nodal loads are zero and only the clearances at nodes 2, 3, 4, and 5 have an initial value, C, as shown in Fig. 3 and which can be calculated from equation (10) CT = r 2 - ( r 2 - r l ) cos x i - r f - ( r : - r f ) sin\u2019 %i (10) where Cy is the initial radial clearance at the ith node; r 2 is the radius of the hole; r 1 is the radius of the pin; x 1 is the angle that the ith node subtends with the axis With engineering fits between the pin and the hole, it can safely be said that rz - r l is so small compared with r l that the above expression can be reduced to ( 1 1) So the initial percentage change of clearance will be given by C,/C:"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001403_027836498900800504-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001403_027836498900800504-Figure5-1.png",
        "caption": "Fig. 5. Pllickercoordinates.",
        "texts": [
            " 2 This configuration was obtained by noticing that in this case two lines of the determinant were constant, but outside these two particular configurations, no systematic method was proposed to find all the singular configurations of a parallel manipulator. Let us investigate now a geometric approach. 2. Plfcker Coordinates of Lines, Rigidity, and Geometry It is well known that a line can be described by its Plucker coordinates. Let us introduce briefly these coordinates. We consider two points on a line, say M, and Ma , and a reference frame Ro whose origin is 0 (Fig. 5). Let us consider now the two three-dimensional vectors S and M defined by: If we assemble these vectors to form a six-dimensional vector we get the vector U of the Plfcker coordinates of this line: It is useful to introduce the normalized vector U\u2019 defined by: It may be seen that the first three components of this vector are the components of the unit vector ni of the line. The last three components are given by: with M being any point of the line. Let us consider now the matrix P defined by: where U\u00a7 is the coordinate vector of line i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001411_a:1015685325992-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001411_a:1015685325992-Figure2-1.png",
        "caption": "Figure 2. The simplest walker: typical gait cycle.",
        "texts": [],
        "surrounding_texts": [
            "Human walking was traditionally thought of as a neuromuscular process. However, McGeer [1, 2] demonstrated that human walking might be a largely passive mechanical process strongly influenced by the geometry and inertia distribution of the human body. In other words, walking can also be viewed as largely a natural motion of the human body. Since then, the dynamics of passive walking machines have been studied by a number of authors [3\u20137]. Garcia et al. [4] showed that two rigid massless rods connected frictionlessly at a point-mass \u2018hip\u2019 and with two infinitesimal foot masses can exhibit motions like human walking. They called this mechanism the simplest walker. In that paper, a largely numerical and partly analytical study demonstrated the stability of the simplest walker. Here, we study its stability analytically in greater detail (upto second order). We also use an alternative expansion which has some conceptual advantages which we explain below."
        ]
    },
    {
        "image_filename": "designv11_28_0001872_s0022-0728(77)80109-5-FigureI-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001872_s0022-0728(77)80109-5-FigureI-1.png",
        "caption": "Fig. I. Working principle of coulometric thin layer flow cell. (A) Auxiliary electrode, (RE) reference electrode. Additional symbols explained in text.",
        "texts": [],
        "surrounding_texts": [
            "A flow cell assembly is described featuring ultra-low electrolyte flow propulsion rates (10 - 5 to 10 - 3 cm 3 s -1 ) in combination with a working electrode compartment of thin layer dimensions (thickness < 10 - 2 cm), enabling thus the exhaustive electrolysis of electroactive species at a potential-controlled detector electrode. The cell can be used to detect trace amounts (> 10 - 1 2 mol) of electroactive species delivered into or withdrawn from the streaming electrolyte, such as compounds adsorbed at or desorbed from an ideally polarizable electrode, allowing the independent determination of Aq. and F-isotherms of cation adsorbates. The flow cell has been used to study the adsorption of T1 on polycrystalline Ag in KCI solution. The isotherms obtained can be interpreted in terms of competitive C1- adsorption within the T1 + adsorption range.\nINTRODUCTION\nThe principle of forced electrolyte flow along one or several working electrodes has been applied repeatedly for various electroanalytical purposes and electrosynthesis [1--7 ] using the working electrode(s) as detector(s) for electroactive components already present in the electrolyte or electrogenerated within the flow stream. Electroanalytical applications are based on exhaustive electrolysis of selected electroactive species by a detector electrode process of known charge stoichiometry, the amount of reacting material being determined by coulometric evaluation of the detector current observed.\nCoulometric flow cells reported so far are based on electrolyte flow through a porous detector electrode matrix made from granular packed beds [1], porous electrode blocks [2,3] or a series of parallel micromeshes [4].\nThe electroanalytical cell described in this report is characterized by forced electrolyte flow through an electrode compartment of thin layer dimensions [8] allowing the detection and quantitative determination of trace quantities (picomoles) of electroactive species with reasonable precision. The method is considered a potentially valuable tool for the study of electrosorption processes involving reducible metal ions (\"underpotential deposition\" [9] of metals) unfit for investigation by conventional electroanalytical adsorption techniques such as twin electrode thin layer voltammetry [ 10].",
            "OPERATING PRINCIPLE OF COULOMETRIC THIN LAYER FLOW CELLS\nThe working principle of the coulometric thin layer flow cell to be described is shown schematically in Fig. 1.\nThe sample solution containing the electroactive species M ~+ in addition to a suitable supporting electrolyte is pumped at constant integral volume flow rate J = d V / d t into the thin layer compar tment (TL) defined by two insulating walls positioned in parallel at a small distance (8 ~< 100 #m). The solution flows past a potential controlled detector electrode (D) scavenging the species M z+ under limiting current conditions (E D --> +c\u00a2) by electrochemical reduction or oxidation according to\nM z+ + n e - ~ M (z~n)+ {i)\nThe cell is supposed to ensure exhaustive scavenging of M ~+ at the detec tor electrode, i.e., the depolarizer entering the cell compar tment at the initial concentration c = c o is quantitatively converted to M (z-+n)+ so that its downstream residual concentrat ion remains negligible across the entire cross section of the flowing electrolyte:\nc = c o o - ~ O f o r r > R (1)\nUnder this condition and in absence of interfering additional faradaic reactions a limiting steady state current is established at the detector electrode, which is directly proportional to the total flux of M z\u00f7 defined by the volume flow rate J:\niD = i D , s s = -+ n F c o J (steady state) (2)\nIt is assumed now that an additional electrode (SD) is located somewhere between the flow entrance and the inner edge (R0) of the detector electrode, acting as a source or drain of the depolarizer M z\u00f7. Any amount of M z+ withdrawn from, or injected into, the electrolyte flow by SD at t >/to will cause the detec tor current to deviate from its steady state value, the difference [ iD( t ) - - ides] depending upon the rate ](t) by which M ~+ is produced or consumed at SD. Detailed knowledge of the t ime dependence of iD (t), of course, would require the exact analysis of the convective diffusional transport regime established within the",
            "thin layer compartment . If, however, ]it) exhibits the proper ty\n](t) -~ 0 for t > to, t -* ~o (transient behaviour o f / ( t ) ) (3.1)\nt\nlim / j(t) dt = A N (finite total amount of M z\u00f7 produced or consumed at SD)\nto (3.2)\nit is evident that the original steady state of the system is restored after the disappearance o f j ( t ) , as soon as the amount of M z+ produced in excess (or deficit) to the depolarizer influx at the thin layer entrance has been scavenged by the detector process.\nPresuming ideal scavenging efficiency (1), the overall charge flux at the detector electrode is given by\nt t\nlim f iD(t) d t = lim f +- nF[coJ+j( t ) ] dt t - + o o t - - ~\ntO t o\nwhence, by virtue of (2) and (3.1),\nt\nAQD,1 --= lim f [iD(t ) -- iD,ss] dt= + n F A N (4) to\nAs long as the transient conditions (3.1) and (3.2), respectively, are met, the production or withdrawal of M z+ at SD, therefore, may be investigated experimentally in a very simple way by coulometric evaluation of the de tec tor current signal.\nNotice that neither the charge balance of the source/drain reaction nor any mechanistic details of the detec tor process need to be known for this t ype of coulometric analysis. The only prerequisite for the validity of (4) is the existence of a well defined charge stoichiometry (n) of the detec tor process in combination with the coulometric function (1) of the cell.\nAs to the equilibration time T of the system, i.e. the t ime required for attaining steady state conditions and ensuring exhaustive electrolysis within the portion of electrolyte flowing along the detector , an inverse dependence upon the thickness 5 of the electrolyte layer may be expected, thus favouring thin layer configuration instead of macroscopic electrolysis cells. If, in a first approximation, T is equal to the diffusional relaxation time of a stationary thin layer,\n7\" ~ 62/D [11]\na value of approximately 3.5 s is expected for a typical thin layer dimension (5 = 6 \u00d7 10 - 3 cm, D = 10 - 5 cm 2 s-Z), which should ensure proper functioning of the cell within the t ime scale of ordinary voltammetric experiments.\nDue to the small volume of electrolyte in direct contact with the working electrodes (10 - 3 cm3--10 - 2 cm3), considerable changes in the concentrat ion are brought about even by very small values of AN, thus enhancing the sensitivity o f the method."
        ]
    },
    {
        "image_filename": "designv11_28_0002015_j.mechmachtheory.2004.03.003-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002015_j.mechmachtheory.2004.03.003-Figure1-1.png",
        "caption": "Fig. 1. Topological structure of the roller drive.",
        "texts": [
            " Compactness, large speed reduction ratio, and high efficiency are the advantages of this type of reducers. Such mechanisms must be manufactured to exact standards to offer high performance levels. A roller * Corresponding author. Fax: +886-5-6321571. E-mail address: kbsheu@sunws.nhit.edu.tw (K.-B. Sheu). 0094-114X/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2004.03.003 drive with the advantages of easy manufacture and low cost has been created [5,6]. The topological structure of a typical single-stage roller drive is shown in Fig. 1. A crank, which is eccentrically mounted on the planet gear set serves as the input. A ring gear that has cylindrical rollers as its teeth is mounted on the housing; and a planet gear that has cylindrical rollers as its teeth engages with the ring gear. A constant velocity joint consisting of a set of pins attached to a disc plate and mated with an equal number of holes in the planet gear is used for converting the rotary motion to the output shaft. In the past, the kinematic analysis of the planetary gear trains has been the subject of a number of studies [7\u201313]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002852_iros.2006.281799-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002852_iros.2006.281799-Figure3-1.png",
        "caption": "Fig. 3 FTW of each joint",
        "texts": [
            " The workspace of the reduced manipulator with the locked joint 3 can be achieved by rotating the end-effector three times about joints 4,2 and 1 in sequence. The first rotation about joint 4 results in a circle; the second rotation of the circle about joint 2 results in a finger ringlike cured surface; the last rotation about joint 1 yields a solid of rotation, which is the workspace of joint 3. Fig. 2 shows a graph of this process. For a fixed motion range of joint 3, the intersection of its maximum workspace and minimum workspace, the FTW of joint 3 shown in Fig. 3(a), can be determined. Following this procedure, we can determine the FTW of joint 2 and 1 respectively, as Fig. 3(b) and 3(c) show. Thus, if the fault tolerance with respect to any one joint of the manipulator is considered, the final FTW shown in Fig. 4 can be obtained by calculating the intersection of all joints' FTW. Lon (b) Second rotation (c) Third rotation For a given end-effector's motion, a redundant manipulator has an infinite of joint motions that will result in different reduced manipulability and FTW. When two redundant manipulators perform a specific task in a coordinating way, the end-effector's trajectories of master and slave manipulators are different, but can be determined uniquely"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002797_j.wear.2005.11.009-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002797_j.wear.2005.11.009-Figure1-1.png",
        "caption": "Fig. 1. Contact between a rough surface and a flat plane producing isolated contact area.",
        "texts": [
            " The physical significance f these parameters is that as D increases the high frequency omponents become comparable in amplitude with the low freuency ones, and as G is reduced, the roughness amplitude educes over the entire frequency range. Majumdar and Tien [19], Majumdar and Bhushan [22] have sed the fractal concept in contact mechanics problems elegantly nd some of the main conclusions from their work are described elow. Considering the interface between a statistically isotropic ough surface and a rigid flat plane with mean separation, d, as hown in Fig. 1, for a given contact spot area, a, the deformation f an asperity, \u03b4, is given by = GD\u22121a(2\u2212D)/2 (4) fractal contact theory relies on the size and distribution of ontact spots produced during loading. The contact spot distri- bution, n(a), is given by n(a) = D 2 a D/2 L aD/2+1 (5) where aL is the largest contact spot area. The real area of contact over the surface, Ar, can be given by Ar = \u222b aL as n(a)a da (6) where as is the smallest contact spot area. Since as approaches zero in the limit, Ar reduces to Ar = D 2 \u2212 D aL (7) The radius of curvature, R, of an asperity producing contact spot area, a, is given by R = aD/2 \u03c02GD\u22121 (8) However, the fractal contact theory [22] has a drawback that the distribution of contact areas is assumed geometrically and not taking into account actual elasticity",
            " Persson argued that in all eal systems lower and upper cut-off lengths occur and, when the ower cut-off length has been found, the fractal models should e applied at that scale. The same reasoning holds in case of he fractal contact theory used here. However, in absence of any eliable and generally accepted fractal theory, the present analsis uses the fractal contact theory developed by Majumdar and hushan [22]. s the impact velocity is increased. For the impact between rough surfaces, the mean plane of sperity heights before impact is used as reference plane (Fig. 1). f z and d are the asperity height and separation between suraces, respectively, measured from reference plane, the number f asperities in contact may be found as 0 = N \u222b \u221e d \u03c6(z) dz (9) here N is the number of asperities per unit area; \u03c6(z), the sperity height distribution function before impact and the intererence of an asperity is \u03b4 = z \u2212 d. Assuming that there is no nteraction between adjacent asperities, the deformation of each sperity will depend on its interference only and contact area nd contact load may be written as = A(\u03b4) (10) = P(\u03b4) (11) here the contact area A and load P on an individual asperity are o be determined from a suitable mode of asperity deformation uring impact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000546_cdc.1993.325853-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000546_cdc.1993.325853-Figure1-1.png",
        "caption": "Figure 1: A five-axle, two-steering mobile robot",
        "texts": [
            " However, a method using a partial prolongation of the exterior differential system which more readily yields Goursat normal form coordinates is developed in the next section in the context of an example. 4 Application to Multi-steering, Mult i-trailer Systems In this section we demonstrate in detail how the algorithm described above can be used to put a five-axle, two-steering mobile robot into extended Goursat normal form. The algorithm is followed until we run into a problem. We then suggest a procedure to fix the problem and find the coordinates. As shown in Figure 1, the first steering train consists of three axles: the front steering wheel and the next two passive axles. The second steering train consists of the second steering wheel and the passive axle behind it. The one-form constraints for this system, labeling the axles with the constraints ao to a4 from right to left, are a0 = sin Bo dxo - cos Bo dyo = 0 a' = sin B1 d ~ , - cos el d y , = 0 a' = sin 0 2 dxz - cos tJ2 d y z = 0 a3 = sin85 dx3 - cos& dy3 = 0 a4 = sin B4 dx4 - COS e4 d y , = 0 . The Pfaffian system associated with this mobile robot is I = {a0,",
            " In exterior differential algebra, augmenting the system corresponds to adding the new constraints of the virtual axles. Moreover, the derived flag changes to our advantage, allowing us to use more forms to modify the constraints to get the form of equation (8). We now write the constraints using the Cartesian coordinates ( x , y ) = ( x 4 , y 4 ) and we use partial prolongation to add two new spond to the two virtual axles with angles 0, and 07, respectively, added onto the second steering train as shown in Figure 1. In We scale U: and use Gi to eliminate the dy term constraints to the system. These constraints, U' and U', corre- these coordinates, the constraints are written as ij: = -- sec2 o4 sec(~, - 0,) (U: + cos es .:I L4 1 = sec' B4de4 - - sec3 O4 tan(& - 0,) dx = dz; - - sec3 e4 tan(& - 0,) dzo L4 1 L4 a0 = sin 0, dx - COS eo dy - L4 cos(eo - 04) de4 -L3 cos(00 - 03) de3 - LZ cos(80 - 02) dB2 - L ~ cos(eo - e , ) de1 d = sin81 dx COS^^ dy - L4c0s(B1 - 0,) de4 -L3 cos(& - 03) de3 - L2 cos(01 - 02) d& and set the coefficient of dzo to be 2;"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001067_095441002760179771-Figure12-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001067_095441002760179771-Figure12-1.png",
        "caption": "Fig. 12 Bottom half of the global \u00aenite element model",
        "texts": [],
        "surrounding_texts": [
            "The global FE model used in the present analyses can be seen in Fig. 11 with the bottom half only shown in F ig. 12. In FE contact analysis, a contact de\u00aenition is applied at the contact surface between the two contacting bodies, allowing nodal sliding at the contact surfaces. By using this technique, it is possible for the two coupling halves to behave realistically when a load is applied, thus producing an accurate representation of the displacements and the stresses of a Curvic coupling under load. ABAQUS input \u00aeles were generated by the use of FEMGV 5.1-01 [17] Femsys pre- and post-processor. The three-dimensional mesh used in the FE analyses was based on a mesh convergence study using two-dimensional and three-dimensional FE models [18] and is considered acceptable for comparison with photoelastic results. The contact surfaces were constructed as perfectly conforming because the difference in the radius of curvature between the two surfaces is very small and hence dif\u00aecult to model accurately. The ABAQUS 5.8 commercial FE package used for the present analyses was installed on a Silicon Graphics Origin20002 server. The material properties used to obtain the results presented in the \u00aegures, for the FE models, are those of Araldite, which at a temperature of 135 8C has a Young\u2019s modulus of 10 N/mm2 and a Poisson\u2019s ratio of 0.499. Although the value of Poisson\u2019s ratio is very close to an incompressib le value of 0.5, the FE analysis can be executed with conventional continuum elements without the need for special hybrid elements [3]. The FE models used quadratic 20-noded reduced integration hybrid brick elements. When de\u00aening the contact pairs in ABAQUS, the user must decide whether to specify relative sliding as small or \u00aenite. Small sliding formulation is used for contact situations in which the relative motion of the two surfaces is small, i.e. a small proportion of the characteristic length of an element face. Finite sliding allows a large amount of sliding but requires much more complex calculations, particularly for two three-dimensional deformable bodies in contact [3]. All contact analyses in this paper have used the small slid ing option. The analyses in this paper have all used a non-linear geometry parameter. This is used in the small sliding algorithm to account for any rotation and deformation of the master contact surface and updates the load path through which the contact forces are transmitted. An isotropic Coulomb friction model was used with the Lagrange multiplier contact method, which uses additional solution variables for each surface node with frictional contact. Alternatively, it is possible to use a penalty friction formulation, which is easier to converge but allows a small amount of elastic slip when the surfaces should be sticking. The Lagrangian contact formulation is considered to be more accurate for stickslip problems [3]. Proc Instn Mech Engrs Vol 216 Part G: J Aerospace Engineering G01102 # IMechE 2002 at The University of Iowa Libraries on July 1, 2015pi .sagepub.comDownloaded from The ABAQUS FE package allows interpolation of the solution of a `global\u2019 model on to the relevant parts of the boundary of a submodel. This is used to study a local part of a model with a re\u00aened mesh based on interpolation of the solution from an initia l, relatively coarse, global model. This method has been used in the present analyses and the submodel can be seen in F ig. 13 with a close-up view in Fig. 14. G01102 # IMechE 2002 Proc Instn Mech Engrs Vol 216 Part G: J Aerospace Engineering at The University of Iowa Libraries on July 1, 2015pig.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv11_28_0002056_iros.1992.594512-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002056_iros.1992.594512-Figure1-1.png",
        "caption": "Figure 1: Link Coordinate Frames",
        "texts": [
            " 6 1 cond W = - un here, U,, is the maximum singular value, 6 1 is the minimum singular value. Equation ( 12 ) indicates that it is necessary not only to drive each joint independently but also to give no large imbalances between joints in the following experiment, therefore, special attention was paid to maintain the above conditions. Furthermore, a recursive least squares method requiring no inverse matrix computation was used to avoid restriction in the sampling number. 2.3 Parameter coefficient of manipulator Figure 1 shows a schematic diagram of the manipulator ( PUMA260 ) tested here and its link coordinates. Only three basic joints from the manipulator base that can cause large non-linear dynamic effects were considered for the identification. The dynamic modeling of the power transmission mechanisms such as reduction gears was ignored. Using equations (6) - ( 8 ) , the parameter coefficients of the manipulator were analytically derived. The coeficient equation for joint 3 is given as follows. The Y-axis of joint 3 is a rotational axis, therefore, the coefficient of 342, an element of the 1st order moment of joint 3 becomes zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002954_1128888.1128914-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002954_1128888.1128914-Figure10-1.png",
        "caption": "Figure 10: The \u2018pawn\u2019 example. The large \u2018pawn\u2019 is fixed and the small one is movable. (a) shows the colliding placement of the \u2018pawn\u2019 at t = 0. (b) shows its corresponding collision-free placement, which is computed based on UB1(PDg).",
        "texts": [
            " If the separator is farther away from the object A than the current upper bound, we can discard this separator. We use the PDt between the two convex hulls of input models as an initial upper bound of PDg. We have implemented our lower and upper bound computation algorithms for generalized PD computation between non-convex polyhedra. We have tested our algorithms for PDg on a set of benchmarks, including \u2018hammer\u2019 (Fig. 6), \u2018hammer in narrow notch\u2019 (Fig. 9), \u2018spoon in cup\u2019 (Fig. 8) and \u2018pawn\u2019 (Fig. 10) examples. All the timings reported in this section were taken on a 2.8GHz Pentium IV PC with 2 GB of memory. Lower bound on PDg. In our implementation, the convex covering is performed as a preprocessing step. Currently, we use the surface decomposition algorithm proposed by [Ehmann and Lin 2001], which can be regarded as a special case of convex covering problem. In order to compute the PDt between two convex polytopes, we use the implementation available as part of SOLID [van den Bergen 2001]",
            "5, and t = 1.0, respectively. At all these placements, the \u2018spoon\u2019 collides with the \u2018cup\u2019. The right column of this figure shows the collision-free configurations that are computed based on UB1(PDg) in each case. We also compare our computed lower bound and upper bounds over all the samples (n=101), which is shown in Fig. 8. The timing performance for this example is also listed on Tab. 1. \u2018Pawn\u2019 example. The last benchmark used to demonstrate the performance of our algorithm is the \u2018pawn\u2019 example. As Fig. 10 shows, the large \u2018pawn\u2019 is fixed, while the small one is moving. The \u2018pawn\u2019 model has 304 triangles and is decomposed into 44 convex pieces. The large \u2018pawn\u2019 has 43 convex separators. Fig. 10(a) shows the colliding placement of the \u2018pawn\u2019 at t = 0. Fig. 10(b) shows its corresponding collision-free placement, which is computed based on UB1(PDg). 13 compares the lower bound and upper bounds over the sampled configuration (n=101). Tab. 1 shows the average time to compute the lower and upper bounds over all configurations. In this section, we apply our lower bound on PDg computation algorithm for complete motion planning of planar robots with 3- DOF. The complete motion planning checks for the existence of a collision-free path or reports that no such path exists"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002777_3.49761-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002777_3.49761-Figure1-1.png",
        "caption": "Fig. 1 Model surface schematic.",
        "texts": [
            " Cf = skin-friction coefficient, ij-^p^ U^2 Cfo \u2014 smooth-wall skin-friction coefficient k = roughness dimension, peak-to-valley M = Mach number Po, To = stagnation pressure, temperature Re/ ft = unit Reynolds number, p^ U^/Hao Rek = roughness Reynolds number, kUJvw U = velocity Ur = friction velocity, (Tw/pw)1/2 U+ = law-of-wall coordinate, (U/Ur) y ^ vertical coordinate, from (k/2) y+ = law-of-wall coordinate, (yUJvw) d = boundary-layer thickness esw> \u00a3iw \u2014 short, long waveform amplitude ^sw,^w = short, long waveform wavelength H, v = viscosity, kinematic viscosity p = density T = shear stress oo = local freestream condition w = at wall, or based on wall properties THE objective of this research was to investigate experimentally effects of roughness and roughness superimposed on single and multiple, shallow, periodic waveforms on turbulent boundary-layer skin friction and velocity profile in compressible, adiabatic flow. Results were generated in support of the Trident missile development program, which required information on effects of fiberglass-wound motor case (i.e., random rough/wavy) surface conditions on missile range performance. Surface contour traces taken from an actual motor case showed the existence of three dominant features: 1) a roughness scale; 2) a short wavelength scale; and 3) a long wavelength scale. In an attempt to simulate these features, several rough/wavy patterns were created. Figure 1 schematically shows the most complex simulation, wherein roughness was superimposed on a short wavelength waveform, both of which were superimposed on a long wavelength waveform. All machined waveforms were periodic and shallow, with slopes less than two degrees. Table 1 summarizes the physical scales of all surfaces tested, including basic sand grain roughened surfaces and a full-scale planar mold of the motor case roughness (#9). Table 1 Summary of surfaces tested\" Model smooth 24 grit 36 grit 50 grit 80 grit #6 #7 #8 #9 #10 #11 #12 Type machined sand grain 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001118_bi00364a032-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001118_bi00364a032-Figure6-1.png",
        "caption": "FIGURE 6: Visible absorption spectrum of cobalt carboxypeptidase,> 35 pM, in the presence of 2.5 mM Z-Sarc-Ala and 50 mM (A) L-Ala, (B) L-Val, (C) L-Leu, and (D) L-Phe. Samples were prepared at 20 OC in 15 mM Hepes and 0.4 M NaC1, pH 7.0, and spectra recorded in a cuvette with a path length of 5 cm.",
        "texts": [
            "8 exhibits hyperfine splitting, a characteristic of both peptide and depsipeptide intermediate spectra, and the apparent g values and hyperfine coupling constants for the enzyme in the presence of the product mixture are close to those detected transiently for the intermediate of Dns-AlaAla-Phe hydrolysis under cryospectrokinetic conditions. Thus, the intermediate-like spectral properties of the cobalt enzyme that arise from the enzyme-product reaction are identifiable both in its EPR and in the visible absorption spectrum. The preceding data were obtained with a single pair of products. Intermediate-like absorption spectra (Figure 6) are also obtained with other N-blocked dipeptides and other amino acids. Thus, Z-Sarc-Ala, 2.5 mM, one of a class of peptide substrates that are hydrolyzed particularly slowly (Snoke & Neurath, 1949), in the presence of L-Phe, 50 mM, results in an absorption spectrum characteristic of a fully formed peptide intermediate (Figure 6). HPLC analysis confirms the formation of Z-Sarc-Ala-Phe. Similarly, the EPR spectrum of the cobalt enzyme in the presence of Z-Sarc-Ala and L-Phe 4672 B I O C H E M IS TRY G E O G H E G A N E T A L . is that of a peptide intermediate (not shown). Importantly, use of the carbobenzoxy N-blocking group confirms the existence of the 480-nm transition characteristic of the absorption spectrum of the peptide intermediate (Auld et al., 1984). Replacement of L-Phe by L-Leu, L-Val, or L-Ala results in formation of the intermediate-like enzyme-peptide complex but in decreasingly lesser fractions of the total enzyme, likely due to higher dissociation constants for the peptides synthesized (Figure 6). Cobalt carboxypeptidase A exhibits a weak CD spectrum with a single negative band centered at 538 nm (500 deg cm2/dmol) (Latt & Vallee, 1971). L-Phe perturbs this spectrum as shown in Figure 7A, changing the line shape in a characteristic fashion that has been reported (Latt & Vallee, 1971), whereas 2.5 mM Z-Sarc-Ala has no effect. The CD spectrum of the intermediate formed from 6.9 mM Z-Sarc-Ala and 50 mM L-Phe is marked by a 10-fold enhancement in negative ellipticity at 578 nm (Figure 7A). The CD spectrum of the intermediate resulting from 20 mM Dns-Ala-Ala and 50 mM L-Phe is nearly identical (Figure 7B)",
            " Geoghegan, unpublished observations) largely overcomes this effect, since peptides whose penultimate peptide bond is N-methylated are hydrolyzed very slowly by carboxypeptidase A (Snoke & Neurath, 1949). The absorption and EPR spectra of the ES2 intermediate of Z-SarcAla-Phe show it to be a tightly bound substrate of the enzyme. The intermediate is less fully formed when the L-Phe is replaced by an equivalent concentration of L-Leu or L-Val and is scarcely detectable when L-Ala is the amino acid product (Figure 6). It seems likely that the use of slowly hydrolyzed components such as Z-Sarc-Ala in conjunction with the use of subzero temperatures will provide authentic intermediates of peptide hydrolysis for periods long enough to permit structure analysis by almost any experimental method (e.g., NMR or EXAFS). New routes to the detection, stabilization, and characterization of enzymatic intermediates continue to be sought as valuable approaches to mechanistic questions. The present data show that carboxypeptidase A can serve as an \u201cequilibrium trap\u201d for one of its own very highly specific substrates"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001930_s10665-005-9007-0-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001930_s10665-005-9007-0-Figure6-1.png",
        "caption": "Figure 6. The distal triangle.",
        "texts": [
            " If the angles measured between the projections of the rod onto the zx, zy and yx-planes and the corresponding z, z, y-axes are denoted by \u03b2AP , \u03b2L, \u03b2Ax , respectively, as shown in Figure 5, then the following relationships can be written: Cx =CL cos\u03b2L tan \u03b2AP ; Cy =CL sin \u03b2L; Cz =CL cos\u03b2L, (A-1) where CL is the length of the projected rod in the yz-plane. Now, in the light of the relationships (A-1), Equations (1\u20134) can be obtained by successive substitutions among the following relationships written from Figure 5: tan \u03b2Ax = Cx Cy ; tan \u03b2wz = Cx Cz sin \u03b2Ax , (A-2) tan \u03b2wy = \u221a C2 z +C2 x Cy ; tan \u03b2wx = \u221a C2 y +C2 z Cx , (A-3) where \u03b2wx , \u03b2wy , \u03b2wz are direction cosine angles of the axis w in the Oxyz-reference system. The distal triangle B1B2B3 is drawn in Figure 6. Given the sides b1, b2, b3 of the triangle, the angles \u03d51, \u03d52, \u03d53 can be determined by the application of the cosine law, leading to the equation set (23). Since points B1, B2, B3 are on a circle with center at G1 and with radius R1, it follows that the triangles B1G1B2, B2G1B3, B3G1B1 are isosceles triangles. Hence, the following equations are written from Figure 6: \u03b43 + \u03b41 =\u03d51, \u03b41 + \u03b42 =\u03d52, \u03b42 + \u03b43 =\u03d53. (B-1) The solution of (B-1) for \u03b41, \u03b43 yields (22). The following solution procedure is applied to arrive at Equations (59\u201364). First, subtract (16) from (17) and from (18) side by side to yield the following: GBk \u2212GB1 =G1Bk \u2212G1B1, k =2,3. (C-1) Then substitute G1Bk k = 2,3 from Equations (19\u201321) in (C-1) to get two vector equations with two vector unknowns eu, ev. Note that, since by direct kinematics the point Bi i =1,2,3 co-ordinates (Bix,Biy,Biz) have been determined in the fixed Gxyz co-ordinate system for a given set of leg lengths, the unit vectors eu, ev are solved from the linear equation (C-1) in terms of the unit vectors i, j, k defined in the fixed Gxyz-system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003180_1.2980380-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003180_1.2980380-Figure2-1.png",
        "caption": "Fig. 2 Sensor casing details",
        "texts": [
            " Their characteristics are as ollows: \u2022 Motor: Single phase type MY 90L-4, 2 HP power, operates at 220 V and 9.0 A with a current frequency of 50 Hz and rotates at a maximum of 1500 rpm. \u2022 Generator: Single phase, rotates at 3000 rpm. Under an operating voltage of 115 V produces 36.5 A current, whereas at 230 V produces 18.3 A. igure 1 depicts the experimental setup. The AE sensor is directly ounted on the gear through a special casing see details in Fig. . The design incorporates two hollow steel cylinders Fig. 2 : the ne is mounted onto the gearbox case 1 and the other 2 slides nside the first one until its outer face 3 contacts the surface of he gear. The constant contact force needed is applied through a pring 4 located inside the first cylinder, which pushes the maller cylinder against the contact surface 3 . This contact surace of the small cylinder is made out of bronze to reduce wear nd local temperature increase due to friction. The AE sensor 5 64502-2 / Vol. 130, DECEMBER 2008 om: http://vibrationacoustics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003245_acc.2008.4586956-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003245_acc.2008.4586956-Figure3-1.png",
        "caption": "Figure 3: Inertial disk considering the balancing mass of the active disk.",
        "texts": [
            " In our analysis the rotor-bearing system has an active disk mounted on the shaft and near the main disk (see Fig. 1). The active disk is designed in order to move a mass m1 in all angular and radial positions inside the disk, which are given by \u03b1 and r1, respectively. In fact, these movements can be got with some mechanical elements such as bevel gears and ball screw (see Fig. 2). The mass m1 and the radial distance r1 are designed in order to compensate the residual unbalance of the rotor bearing system. An end view of the whirling rotor is also shown in Fig. 3, with coordinates that describe its motion. The coordinate system (\u03b7, \u03be, \u03c8) of this figure is fixed to the active disk, and the coordinate system (X,Y,Z ) is an inertial frame with Z the nominal axis of rotation. The mathematical model of the five degree-of-freedom rotor-bearing system with active disk was obtained using Euler-Lagrange equations, which is given by (M +m1) x\u0308+ cx\u0307+ kx = px (t) (M +m1) y\u0308 + cy\u0307 + ky = py (t) Je\u03d5\u0308+ c\u03d5\u03d5\u0307 = \u03c41 + p\u03d5 (t) m1r 2 1\u03b1\u0308+ 2m1r1r\u03071\u03b1\u0307+m1gr1 cos\u03b1 = \u03c42 m1r\u03081 \u2212m1r1\u03b1\u0307 2 +m1g sin\u03b1 = F (1) with px (t) = Mu \u00a3 \u03d5\u0308 sin (\u03d5+ \u03b2) + \u03d5\u03072 cos (\u03d5+ \u03b2) \u00a4 +m1r1 \u00a3 \u03d5\u0308 sin (\u03d5+ \u03b1) + \u03d5\u03072 cos (\u03d5+ \u03b1) \u00a4 py (t) = Mu \u00a3 \u03d5\u03072 sin (\u03d5+ \u03b2)\u2212 \u03d5\u0308 cos (\u03d5+ \u03b2) \u00a4 +m1r1 \u00a3 \u03d5\u03072 sin (\u03d5+ \u03b1)\u2212 \u03d5\u0308 cos (\u03d5+ \u03b1) \u00a4 p\u03d5 (t) = \u2212My\u0308u cos (\u03d5+ \u03b2)\u2212m1y\u0308r1 cos (\u03d5+ \u03b1) +Mx\u0308u sin (\u03d5+ \u03b2) +m1x\u0308r1 sin (\u03d5+ \u03b1) Here J and c\u03d5 are the inertia polar moment and the viscous damping of the totor, \u03c41(t) is the applied torque (control input) for rotor speed regulation, x and y are the orthogonal coordinates that describe the disk position, r1 and \u03b1 denote the radial and angular position of the balancing mass, which are controlled by means of the control force F (t) and control torque \u03c42 (t) (servomechanism)",
            " The proposed control objective consists of reduce as much as possible the rotor vibration amplitude, denoted in adimensional units by R = p z21 + z23 u (3) for run-up, coast-down or steady state operation of the rotor system, even in presence of small exogenous or endogenous perturbations. In the following table are given the rotor system parameters employed troughtout the paper: Table 1: Rotor system parameters M = 1.2 kg m1 = 0.003 kg a = b = 0.3m \u03b2 = \u03c0/6 rad \u03b1 = 0 rad rdisk = 0.04m u = 100\u03bcm c\u03d5 = 1.5\u00d7 10\u22123 N m/ s D = 0.01m We are proposing to use an active disk for actively balancing of the rotor (see Fig. 1 and Fig. 3). We can see that if the mass m1 is located at the position\u00b3 r\u0304 = Mu m1 , \u03b1\u0304 = \u03b2 + \u03c0 \u00b4 the unbalance can be cancelled. In order to design the position controllers for the balancing mass m1, consider its associated dynamics: z\u03077 = z8 z\u03078 = 1 m1 \u00a1 F \u2212 gm1 sin z9 +m1z7z 2 10 \u00a2 z\u03079 = z10 z\u030710 = 1 m1z27 (\u03c42 \u2212 gm1z7 cos z9 \u2212 2m1z7z8z10) y2 = z7 y3 = z8 From these equations, one can get the following nonlinear controllers with integral compensation to take the balancing mass to the equilibrium position (y\u03042 = r\u0304 = Mu m1 , y3 = \u03b1\u0304 = \u03b2 + \u03c0): F = m1v2 + gm1 sin z9 \u2212m1z7z 2 10 (4) \u03c42 = m1z 2 7v3 + gm1z7 cos z9 + 2m1z7z8z10 (5) with v2 = y\u0308\u22172 (t)\u2212 \u03b321 [y\u03072 \u2212 y\u0307\u2217 (t)]\u2212 \u03b321 [y2 \u2212 y\u22172 (t)] \u2212\u03b320 Z t 0 [y2 \u2212 y\u22172 (\u03c3)] d\u03c3 v3 = y\u0308\u22173 (t)\u2212 \u03b332 [y\u03073 \u2212 y\u0307\u22173 (t)]\u2212 \u03b331 [y3 \u2212 y\u22173 (t)] \u2212\u03b330 Z t 0 [y3 \u2212 y\u22173 (\u03c3)] d\u03c3 where y\u22172(t) and y\u22173 (t) are desired trajectories for the outputs y2 and y3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002955_tasc.2005.864335-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002955_tasc.2005.864335-Figure1-1.png",
        "caption": "Fig. 1. A magnetic dipole in an externally excited field.",
        "texts": [
            " In this paper it is shown that the Kelvin\u2019s formula with virtual air-gap provides consistent numerical results of force calculation whether or not a magnetic body is in contact with another. Firstly, in this paper, the derivation of Kelvin\u2019s formula and the summary of virtual air-gap are reviewed. And direct calculation of external field from virtual air-gap scheme is introduced. Secondly, the validity of this proposed method for magnetic force is shown by numerical comparisons with other wellknown methods such as Maxwell stress tensor, virtual work and equivalent source methods. As shown in Fig. 1, the force on the dipole is summation of force on each magnetic charge . Its formulation is as follows, (1) 1051-8223/$20.00 \u00a9 2006 IEEE where and are field intensities at the location of and respectively. If the distance between two magnetic charges is very small, the x-component of can be written as, (2) Using vector expression and magnetic momentum, (2) is rewritten as, (3) By introducing the magnetization which means volume density of magnetic momentum, the Kelvin\u2019s formula is finally acquired as follows, (4) Here, it should be noticed that the field intensity is the field before the dipole exists"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002825_j.chaos.2006.01.110-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002825_j.chaos.2006.01.110-Figure4-1.png",
        "caption": "Fig. 4. The simple pendulum system with friction.",
        "texts": [
            " Therefore, we can combine the designs of feedback linearization control and fuzzy control to construct the overall controller as follows: ufe\u00fefu ufeedbackus\u00f0t\u00de \u00fe ufuzzyus\u00f0t t1\u00de \u00bc \u00bdLgLr 1 f h\u00f0bX \u00f0t\u00de\u00de 1 Lr f h\u00f0bX \u00de \u00fe y\u00f0r\u00ded e ra1\u00bdL0 f h\u00f0bX \u00de yd n e1 ra2\u00bdL1 f h\u00f0bX \u00de y\u00f01\u00ded e 1ar\u00bdLr 1 f h\u00f0bX \u00de y\u00f0r 1\u00de d \u00fe KT x\u0302 bXous\u00f0t\u00de \u00fe ufuzzyus\u00f0t t1\u00de \u00f092\u00de where us(t) denotes the unit step function and t1 is the time that the tracking error of system touches the global final attractor Br. Consider the simple pendulum system with friction subjected to a control moment u (per unit mass) and a disturbance shown in Fig. 4. From Khalil [17], the equations of motion are _x1\u00f0t\u00de _x2\u00f0t\u00de \u00bc x2 g \u2018 sin x1\u00f0t\u00de k m x2 \" # \u00fe 0 1 m\u20182 \" # T \u00fe 0 0:1 sin\u00f0t\u00de cos x1\u00f0t\u00de l \u00fe sin\u00f0t 12\u00de \" # \u00f093\u00de y\u00f0t\u00de \u00bc x1\u00f0t\u00de \u00fe x2\u00f0t\u00de :\u00bc h\u00f0X \u00f0t\u00de\u00de \u00f094\u00de where m denotes the mass of the bob, h1 denotes the angle subtended by the rod, g denotes the gravity acceleration, k denotes the coefficient of friction, T denotes the supplied torque, x1 h1; x2 _h1 and u = T. The following physical parameters are chosen in our simulation: g \u2018 \u00bc 1; 1 m\u20182 \u00bc 0:01 and k m \u00bc 0:5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001128_38.20335-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001128_38.20335-Figure6-1.png",
        "caption": "Figure 6. Relation between the path and a moving object.",
        "texts": [],
        "surrounding_texts": [
            "An articulated kinematic chain is built of several segments connected by translational or rotational joints. The one end is articulated with a reference system. We can use a notation similar to that proposed by Denavit and Hartenberg.' 0 For each segment there is a Cartesian coordinate system. The segment is described in its own coordinate system. 0 The joint axis of the following segment is the z axis of this coordinate system. 0 There is a reference coordinate system for the kinematic chain. Its z axis is the joint axis of the first segment. We note the transformation from the coordinate system of segment No. i -1 into that of No. i by A, and the transformation from the coordinate system of segment j into i by IT,. For j =O-that is, the reference coordinate system-we write just TI . ' The joint variables q,, i = 1 , 2 ,..., n, for a chain with n segments, can be expressed in the joint vector: Each point P of the segment is originally described in the segment coordinate system with 'l? It can now be described in any coordinate system ip = V; 'p = T''T)p (6) The matrix IT, is dependent on the joint variables (I!,, k = j , j + l , ..., i or i , i + l , ..., j. The inverse kinematic transformation In the other case, if the position and orientation of segment i , described in a coordinate system T,, are known, and one wants to get the configuration of the chain, the inverse kinematic problem is to be solved. For an arbitrary kinematic chain, numerical method is necessary.4 ' Here we need the generalized coordinates (1) The transformation matrix T corresponding to s fol- lows the roll-pitch-yaw principle: T = puns(x,ys)ror(x,a>rot(r,P)rot(z,y) ( 8 ) The forward kinematic transformation The joint variables being known, the position and orientation of any part of the chain can be estimated. This is the forward kinematic transformation. Presenting the segments in the Cartesian coordinate system and representing the coordinate systems by (4 x 4) with trans (x,Y,z) for the translation about (x,y,z)' and rot(e,8) for the rotation about 8 relative to e . Given the goal coordinates of the top segment sgoni, the inverse kinematic problem is to solve the equation 19) matrices, the coordinate system of segment i is then s = Sgod 1 Ti = T,,A; = n Ak (2) The transformation matrix A, can be split into two parts: This is a nonlinear equation which can be solved by iterative interpolation with the generalized Newton method. The iteration is as follows: k l where A,,i contains the constant transformation and A,,, contains the variable part dependent on 9,. For a transwith the functional matrix or Jacobian matrix J defined as the matrix of the partial derivative of s lational joint it is the translation along the z-axis z , - , . 15116, I h < i Ai,v = pa~(0.0.qi) (4) I F In case there is no exact solution of Equation 10, we can use the generalized inverse of J,4 ,6 to get an approx- and for a rotational joint it is the rotation about z,- I with the angle q1 imate solution. January 1989 71 The motion of an articulated kinematic chain Usually the original specification of a task is the goal position and orientation of the top of the chain, such as the robot's effector. The job now is to generate joint trajectories, which allow the top to reach the goal. There is an initial path for the top segment. It is either specified as a continuous path or is, usually, the linear interpolation of the current and goal position in the reference system. The generation of a collision-free path takes place iteratively. At first the existing path will be tested incrementally. If there is a collision detected, a new motion path should be generated. The new path will be tested and modified again until a collision-free path is found. This process is outlined in Figure 1. The collision probability Now we can move the chain along this path and find out the possibility of collision between its segments and the environmental objects. The position of the segments can be calculated by the inverse kinematic transformation. The path is split into increments. To reduce the amount of computation, we change the increments dynamically, according to the collision probability. The collision probability of a segment is antiproportional to the smallest distance between the segment and its environmental objects. The collision probability of the chain is then the highest of them. Here, a segment must be tested against all environmental objects and all other segments unless they are neighboring segments. The neighboring segments cannot collide with each other because of the motion restrictions of the joints. To simplify the calculation, we use the distance between the centers of objects minus the sum of the radii of their hull sphere. While the values are positive, we can take the increment to the smallest of them and continue the next step. Otherwise collision is possible. Then the possible intersections must be detected. The smaller increment will be chosen to get accuracy (see Figure 2). Using this distance function, we can usually eliminate most objects. After this elimination there are only local objects to consider, which will often be only one object. To calculate the possible intersection of two objects, we can now use their geometrical models. But in the most likely case it is sufficient to use a simplified model, such as the hull volumes. Three simple geometries are useful: the convex hull, the hull sphere, and the hull cylinder. The choice of one of them depends on the geometry of each object (see Figure 3). Modifying the path If there is a collision with an environmental object, we must modify the path. Before the modification we have to analyze the collision of the path with the object. There are two important questions: 0 For what distance does it collide with the object? 0 How deep is the collision? To answer these questions, we can estimate the start, middle, and end of the collision position of the path for each segment and calculate the distance between the middle collision point and the surfaces of the object. The modification can be done as described in Myers and Agin.' This sets an intermediate position on the plane, which goes through the middle collision position and perpendicular to the path. If the starting and ending positions of collision lie on two surfaces, which do not intersect with each other, it will be better to set two or more intermediate positions (see Figure 4). There are the following criteria for setting the intermediate positions: 0 to the nearest surface 72 IEEE Computer Graphics & Applications 0 to the direction with the highest freedom of motion 0 to the shortest path, or other heuristc criteria, such as 0 behind, around, or over the colliding object Generally, the first criterion compares all possible directions. Here, the colliding segment has the most chance to avoid the colliding object. But an articulated kinematic chain has constraints in its motion. Therefore, the second criterion is also important. The third criterion allows optimization in Cartesian space. It is only an additional criterion because the optimal motion in Cartesian space for the colliding segment is often not the optimal one in the configuration space of the chain. Heuristic methods are often better, especially faster, as in the first method, if the geometry of the colliding object is complex. For this, just three directions are compared with each other. These criteria are to be combined with each other. The distance of an intermediate point to the original path is a function of both the length and the depth of the collision. If there are several objects colliding with the same segment, we can take the convex hull of all these objects to do the analysis and modification of the path as described above. If it is the collision of a segment, which is not the top segment, the kinematic solutions can be used to get the new configuration of the chain. If the calculated intermediate position of one segment is unreachable, the inverse kinematic solution supplies an appropriate position, which is nearest to the position proposed. The priorities of the segment All segments of the kinematic chain may collide with the environmental objects during the motion. For an articulated chain, the freedom of motion of the segments decreases from the top to the base segment. Therefore, the first segment must get the highest priority of collision freedom. For the collision detection, a segment must be tested only against the environmental objects and the segments with higher priority. For the modification of the motion, the segments with higher priority are considered first. Considering the movement of environmental objects To consider the movement of the objects, we can use generalized hull volumes of an object. For the distance calculation, the swept volume of the object during one increment must be taken into consideration, because we want to know if there is a collision during the iiicrementing process. The generalized hull sphere of the object is then the common hull sphere of the object at the time of calculation and at the position moved during this incrementing. At the time of intersection calculation, it is not necessary to modify the hull volumes or the geometrical models of the object. We calculate just the intersection of the segment and the colliding object at a certain moment for each increment. The result is the intersection of the path with the colliding object, where the geometry of the segment is effectively considered. For the modification of the path, the movements must be considered again. That is, for the calculation of the modification vectors, we have to use the starting, middle, and ending position of the colliding object. The motion direction and velocity of the object are further criteria for the choice of the intermediate positions (see Figures 5 and 6). lanuary 1989 73 final position of collision Implementation This method is implemented at our institute for the collision-free motion planning in a robot programming and simulation software.\u2019.\u2019 Because most of the robot\u2019s segments are built of two parts-a part on the joint axis and another part perpendicular to it-the robot\u2019s segments are usually modeled with two hull cylinders. To simplify the problem, the environmental objects are modeled with polyhedrons. In this implementation, objects\u2019 movements are considered through the incremental computations (see Figure 7). The calculation of intersections between polyhedrons and cylinders can be simplified to the calculation of intersections between line segments and planes. We assume that the approximation of robots\u2019 geometry with cylinders and the modeling of environmental objects with polyhedrons are accurate enough for gross motion planning. The amount of computation is reduced rapidly, so the algorithm is fast enough for interactive motion planning of robot manipulators. Conclusion The method described above uses numerical solution of the inverse kinematic problem and analyzes the path incrementally. It is therefore generalized for arbitrarily configured kinematic chains. Using dynamic incrementing according to the probability of collision reduces the amount of computation. The dynamic change of environmental objects that are in the near region of a chain segment is considered in the calculation of collision-free motion. This method can be further improved by consideration of collision-free motion direction into the inverse kinematic solution. The principal advantage of this method is that it is independent of the configuration of the object to be moved, and it is efficient for a dynamic changing environment. Additionally, it can be used for autonomous robots working in an unknown environment, because such robots can only get local information through their sensor systems. The disadvantage of all methods that consider only the local objects to generate the motion path is that the avoidance of one colliding object can cause a collision with other objects. The collision-free motion is also often not the optimal one. But for an arbitrarily configured object and for a dynamic environment, other methods are too inefficient. References 1 J K Myers and G J Agin, \u201cA Supervisory Collision Avoidance Sys tern for Robot Controllers,\u201d Proc Robotics Research and Advanced Applicutions Symp , ASME, New York, 1982, pp 225-232 2 I Denavit and R S Hartenberg, \u201cA Kinematic Notation for Lower Pair Mechanisms Based on Matrices,\u201d J Applied Mechanics, Vol 22 Trans ASME, Vol 77, June, 1955, pp 215-221 3 R P Paul, Robot Manipulators Mathematics, Programming and Control, MIT Press, Cambridge, Mass, 1982 4 F Dai, \u2018 On the Use of Numerical Methods for the Inverse Kinematics in Robot Simulation,\u201d Internal Rpt , FG GraphischInteraktive Systeme, Fachbereich Informatik, Technische Hochschule Darmstadt, 1986 5 D E Whitney, \u201cThe Mathematics of Coordinated Control of Prosthetic Arms and Manipulators,\u201d Trans ASME, J Dynamic Systems, Measurement and Control, Vol 122, Dec 1982, pp 6 A Ben-Israel and T N E Grenville, Generalized Inverses Theory and Applications, Wiley-Interscience. New York, 1974 7 F Dai and L Encarnacao, \u201cGraphical Interactive Robotics Core System for Supporting Flexible Robot Applications, Proc Advances in CADICAM, Technical Univ of Berlin, 1987, pp 8 S Baierl, Collision Detection and Avoidancefor Robot Motion, doc- 303-309 375-383 toral dissertation, Technical Univ of Darmstadt, 1987 Fan Dai is a research assistant in the Graphical Interactive Systems Group of the Department of Computer Sciences at Technical University of Darmstadt, West Germany His research interests a r e robotics, CAD/CAM/CIM, computer graphics, and artificial intelligence He is working on an off-line programming and simulation system for robot systems Dai received the Dip1 Ing degree from the University of Saarland in Saarbrucken, West Ger- many, in May 1985 Fan Dai can he contacted at Fachgebiet Graphisch-Interaktive Systeme, Fachbereich Informatik, Tehnische Hochschule Darmstadt, Wilhelmininstr 7, 6100 Darmstadt. West Germany. 74 IEEE Computer Graphics & Applications"
        ]
    },
    {
        "image_filename": "designv11_28_0002559_tmag.2005.846213-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002559_tmag.2005.846213-Figure3-1.png",
        "caption": "Fig. 3. 3-D finite-element mesh (off-centered). (a) Birds-eye view. (b) Enlarged figures (z = 58 mm).",
        "texts": [
            " The electromagnetic force is given as follows: (3) where is all the nodes contained in an object to calculate the force. Fig. 1 shows the analyzed model of an IPM motor with a cantilevered rotor, which is used for compressors of air-conditioners. The analyzed region is the whole region in order to carry out the dynamic calculation taking into account the off-center of rotor. Fig. 2 shows the position of the rotor with off-center. The parameter is the distance from the original position to the off- 0018-9464/$20.00 \u00a9 2005 IEEE center position. Fig. 3 shows the 3-D finite-element mesh, which rotor is off-centered. Fig. 3(b) shows the meshes near the air gap with off-center. Table I shows the analyzed conditions. We analyzed with and without the off-center. Fig. 4 shows the calculated waveforms of torque and electromagnetic force acting on the rotor when the parameter of is 0.0 and 0.4 mm using the Maxwell stress tensor method and the nodal force method. From Fig. 4(a), although the torque of the nodal force method is larger than that of the Maxwell stress tensor method, it is found that they agree well with each other, and the average torque is almost the same in the state of off-center too"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000426_s0020-7403(02)00136-4-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000426_s0020-7403(02)00136-4-Figure1-1.png",
        "caption": "Fig. 1. The side view and cross section of the V-belt drive system: (a) side view; and (b) cross section.",
        "texts": [
            " The results achieved are very helpful for the estimation of operation e9ciency of the V-belt drive system. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: V-belt drive system; Frictional contact analysis; Friction angle; Finite element analysis Owing to the advantages of light weight and convenient operation, the V-belt drive system has been widely applied in scooters, recreational vehicles and various types of agricultural equipments. When the V-belt drive system operates at a high angular speed !, as shown in Fig. 1(a), the centrifugal force Fr on an arc portion of the V-belt is known as R!2. is the density of the belt and R is the radius of the arc portion of the belt. As a torque is transmitted from the driver pulley to the driven pulley, the frictional contact occurs on the contact surfaces between both sides of the V-belt and the 2anges of the pulley. The di erence of belt tensions arises from the tight-side tension FT and slack-side tension FS . For the driven pulley of the V-belt drive system, the slack \u2217 Corresponding author",
            " PII: S0020-7403(02)00136-4 Nomenclature Ea vector of internal degrees of freedom Bq;Ba strain\u2013displacement relation matrices d;Ed small extension of belt and its increment Eijkl tensor of elastic constants Et; Er Young\u2019s moduli of tension member and rubber layer Fn; Ft normal and tangential contact forces Fri;Fr centrifugal force FT ; FS tight and slack side tensions g acceleration of gravity G transformation matrix h gap displacement vector I unit matrix K sti ness matrix n outward unit normal vector Nq the assembled matrix of conventional interpolation functions Na the assembled matrix of internal modes (1\u2212 2), (1\u2212 2), and (1\u2212 2) HP;E HP prescribed nodal force and its increment Eq incremental nodal displacement vector Eqs incremental relative sliding displacement vector Q resultant nodal force R radius of belt arc portion s the assembled matrix of relative sliding directions SC possible contact surface S part of element boundary under prescribed traction T (N ) Ci resultant contact traction at state C(N ) ETCi incremental resultant contact traction from state C(N ) to state C(N+1) HT (N ) i prescribed surface traction at state C(N ) E HTi incremental prescribed surface traction from state C(N ) to state C(N+1) T\u0302 (N ) Ci contact traction at state C(N ) ET\u0302Ci incremental contact traction from state C(N ) to state C(N+1) Eui;Eu incremental element interior displacement vector EuAri;EuBi incremental displacements of contact points on rubber layer Ar and pulley B Greek letters (N ) ij stress tensor at state C(N ) wedge angle of V-belt E ij incremental strain tensor from state C(N ) to state C(N+1) angular position #;E# small rotation of pulley and its increment \" arc of frictional contact weight of the belt per unit arc length #d dynamic friction coe9cient $t; $r Poisson\u2019s ratios of tension member and rubber layer % transmitted torque friction angle ! angular speed 'i element domain Subscripts A belt B pulley C contact surface tension FS is near the entry point, where the V-belt starts to run into the driven pulley. But, the tight tension FT is near the exit point, where the V-belt runs o the pulley. Fig. 1(b) displays the cross section of the V-belt, which consists of a tension member, a rubber layer, and a textile top cover. The tension member provides the V-belt with a high tensile strength and carries up to 95 percent of the torque loading [1] during the operation of the V-belt drive system. The rubber layer provides the V-belt with frictional and absorbing shock properties and transmits the torque between the pulley and the tension member. The textile top cover is located on the top surface of the V-belt to protect the V-belt during the V-belt drive system operation",
            ", in general, the normal and tangential contact forces can be obtained from the force equilibrium for an element section of the V-belt [2]. The modi6ed Euler formula, which constructs the relation among the tight and slack tensions, FT and FS , and the arc of frictional contact of the belt (\"), can be derived as [2] FT \u2212 R!2 FS \u2212 R!2 = e#d\"=sin ; (1) where #d represents the dynamic friction coe9cient on the contact surfaces between the V-belt and the pulley. is the wedge angle of the V-belt as shown in Fig. 1(b). Virabov [3] investigated the centrifugal force e ect on the 2at belt tension induced by the angular speed, but neglected the frictional contact behaviors between the belt and pulley. Kim and Marshek [4] studied the e ect of the angular speed on the contact forces from the equilibrium of normal and tangential forces for an element section of a 2at belt on the contact surfaces. However, the work on the frictional contact behaviors for the V-belt has not been tackled. Gerbert [5] calculated the distribution of the contact forces on the contact surfaces between the V-belt and pulley by a two-dimensional 6nite element analysis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002852_iros.2006.281799-Figure11-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002852_iros.2006.281799-Figure11-1.png",
        "caption": "Fig. 11 Virtual prototype of a coordinating system",
        "texts": [
            " These results indicate that reducing the sudden change in joint velocity by optimizing the initial posture can obviously decrease the displacement error of the object and the sudden increase in the reaction, and so improve the operational accuracy in fault tolerance. joit 1 joit2 ,. ....--- joiit3.---joit4 2 3 4 5 1Thnrt/s (a) Master manipulator 0.8 0.6 0.4 ;i 0.2- t 0.0 -0.2- -0.4 06. 100 --j oir1 jot3 *--- -J- /.. 90 N an - _ -~~~~~ bU 7C 0 1 2 3 4 5 T1r t/S (b) Slave manipulator Fig. 10 Joint velocity at optimal initial posture B. Solid Simulation The aim of this section is to reveal the effect of sudden change in joint velocity on the operational accuracy of above coordinating system. For this purpose, we should obtain its virtual prototype shown in Fig. 11 by building its solid model with Pro/E soft package, importing the solid model into ADAMS soft package and exerting motion constraints on every joint. To study the reaction between the end-effector and the grasped object, two spherical pairs are imported to simulate the hard point contact. Next, in the cases of arbitrary initial posture and optimal initial posture, solid simulations will be executed with this virtual prototype. J _ 70 80 90 100 X (cm) (a) X-Z plane 1 2 3 4 Time (t s) 5 (b) Y plane Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002015_j.mechmachtheory.2004.03.003-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002015_j.mechmachtheory.2004.03.003-Figure2-1.png",
        "caption": "Fig. 2. Mathematical modeling for kinematic analysis.",
        "texts": [
            " In this work, firstly, the mathematical model for analyzing the kinematics is introduced; secondly, models for kinetostatics and mechanical efficiency of roller drives considering friction are developed. The forces on various elements of the roller drive as well as the mechanical efficiency are then presented. Finally, an experimental testing is used to verify the analysis results. The following is a discussion of the angular velocity and acceleration of the roller drives and the relative speed at the contact point of the conjugated pairs. As depicted in Fig. 2, for an individual contact roller pair of the planet gear and ring gear, if we connect the four centers of the crank O4 (which is also coincident with the ring gear center, O2), a roller of the ring gear O2i , the planet gear O3, and a roller of the planet gear O3i , the quadrilateral O4O3O3iO3i forms a 4-bar equivalent linkage. By using the vector loop approach [23], the position vector loop equation can be expressed as R * 4 \u00fe R * 3i R * a R * 2i \u00bc 0 \u00f01\u00de where R * 4, R * 3i , R * a and R * 2i represent the vectors from O4 to O3, O3 to O3i , O2i to O3i , and O4 to O2i , respectively",
            " In order to investigate the influences of the geometric parameters on the speed fluctuation and mechanical efficiency of the roller drives, curves of further results are given in Fig. 14. It is shown in Fig. 14(a)\u2013(e) that reducing R2 (radius of the ring gear) and R4 (crank eccentricity), and increasing R3 (radius of the planet gear), r2 (radius of the ring gear roller) and r3 (radius of the planet gear roller), respectively, can reduce the speed fluctuation of the roller drives; unfortunately, in gaining lower speed fluctuation we suffer a reduction in the mechanical efficiency. Furthermore as shown in Fig. 2, the model of the 4-bar equivalent linkage is adopted to analyze the kinematics of the roller drive. It can be observed that link R4 is always located on one side of the link R2i while the roller drive is running. Therefore, the 4-bar linkage is not a Grashof mechanism and the relationship of the 4 link lengths can be expressed as: R2i \u00fe R4 > R3i \u00fe \u00f0r2 \u00fe r3\u00de \u00f052\u00de Based on Eq. (52) and analysis results, it is found that as the geometric parameters of the roller drive, R2i , R4, R3i , r2 and r3, approach the relationship R2i \u00fe R4 \u00bc R3i \u00fe \u00f0r2 \u00fe r3\u00de, then there is less speed fluctuation as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003094_j.mechmachtheory.2007.12.001-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003094_j.mechmachtheory.2007.12.001-Figure3-1.png",
        "caption": "Fig. 3. RR-RR-PP Assur group.",
        "texts": [
            " This is confirmed by the following consideration: For a given position of the external joints A, D1 and F1 of the triad (Fig. 2), the internal joint E lies on the fourth order curve of the ABCD1 four-bar mechanism of the RRRP type [5,12]. Also E belongs to the straight line parallel to the sliding direction of the external prismatic joint F1. The intersection of the fourth order coupler curve with a straight line will be at four real intersection points at most. Therefore the maximum number of the assembly modes of the RR-PR-PR triad is four. The input data for the position analysis of the RR-RR-PP Assur group (Fig. 3) are the coordinates of the external joints A (0, 0), D (d, 0) and of the auxiliary point F (xF, yF), the dimensions of each link as the lengths lAB, lBC, lCD, the distances di (i = 1, 2, 3) and the angles a and h. The position of the triad links is described by a small number of parameters, such as the displacements s1 and s2. The constraint equations to be solved describe the length of links lAB and lCD and are given as x2 B \u00fe y2 B \u00bc l2 AB \u00f037\u00de \u00f0xC d\u00de2 \u00fe y2 C \u00bc l2 CD \u00f038\u00de where the coordinates of the joints B and C are evaluated in terms of the unknowns s1 and s2",
            " The system of non-linear equations (47) and (48) is solved through application of the resultant method [17,18]. The variable s2 is eliminated from Eqs. (47) and (48) yielding the second order final polynomial equation in the only unknown s1: X2 i\u00bc0 P isi 1 \u00bc 0 \u00f049\u00de where the coefficients Pi (i = 0, 1, 2) depend only on the Assur-group data. The second order of the final polynomial equation in parameter s1 is minimal. This is confirmed by the following consideration: For a given position of the external joints A, D and F1 of the triad (Fig. 3), the internal joint C lies on the second order curve (circle) of the ABEF1 four-bar mechanism of the RRPP type [5,12]. Also C belongs to the circle centered in D, of radius CD. C is the intersection point of two circles and there will be at most two real intersection points. Therefore the maximum number of the assembly modes of the triad is two. In this section the position analysis of the PR-PR-RP Assur group with one internal prismatic joint and two external prismatic joints (Fig. 4) is solved",
            " For each real value of the displacement s1, the coordinates of the internal revolute joints B, C and E are determined. The two assembly modes of the triad are presented in Fig. 7. 1 nd solutions of the RR-RP-RP Assur group d = 40, d1 = 30, d2 = 45, d3 = 35, lAB = 75.4053, xF = 103.9025, yF = 78.9332, a = 50 . s x y s1 195.2970 32.1881 68.1901 75.0733 54.3158 34.3636 67.1201 17.6599 22.3916 4.9553i \u2013 \u2013 \u2013 22.3916 + 4.9553i \u2013 \u2013 \u2013 Example 3. The geometrical data and the position of the external joint D and of the auxiliary point F of the RR-RR-PP triad (see Fig. 3) are given in the upper part of Table 3. For the specific geometry here considered, by solving the second order polynomial equation (49) two real roots are obtained. For each real value of the displacement s1, the coordinates of the internal revolute joints B and C are determined using Eqs. (39), (40) and (43), (44), respectively. The two configurations of the triad corresponding to the real solutions are presented in Fig. 8. Table 3 Data and solutions of the RR-RR-PP Assur group Data lAB = 48, lBC = 51, lCD = 58"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001806_1.2199857-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001806_1.2199857-Figure3-1.png",
        "caption": "Fig. 3 Geometrical interpretation of the ECOF",
        "texts": [
            " The position vectors are defined by: xC = CxC1 + 1 \u2212 C xC2, 0 C 1 1 xF = FxF1 + 1 \u2212 F xF2, 0 F 1 2 where xCj and xFj j=1,2 denote the position vectors at the edge of the contact segments between objects 1 and 2 and the pusher and object 2, respectively. Also, the inequalities 0 C 1 and 0 F 1 indicate that xC and xF, respectively, are included in each edge. We consider the friction force between each object and the floor acts through the effective center of friction ECOF proposed in 8 . The ECOF can be defined for general motion of the objects including rotation while the conventional COF cannot. As shown in Fig. 3, the point along the line of action nearest the COR becomes the ECOF, and the position of the ECOF is obtained in the Appendix . Note that the ECOF velocity is antiparallel to the frictional force. 4.2 Contact Forces for Maintaining Contact. As for the contact between two objects, the relative motion does not occur if the contact force is included strictly inside of the friction cone and if the line of action passes strictly inside of the contact segment. We consider extending this idea to the manipulation of two objects by pushing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001265_ias.1999.799202-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001265_ias.1999.799202-Figure3-1.png",
        "caption": "Fig. 3. Structure of the rotor.",
        "texts": [
            " 2b) with the rotor in the same position, the magnetic flux of the stator winding and rotor are at right angles to each other; this is the q-axis position. The fourth step is to perform the DC decay test in the q-axis position and obtain the q-axis impedance relating to each frequency, Z,(o), using (1) in the same way as for the d-axis position. The d- and q-axis operational impedances (per phase) at motor start-up are calculated from and xd(js) = {&(a)-2r}/(j2s) (2) x,(js) = 2(~ , (o) -3r /2) / ( j3s ) (3) where s : slip (=U/@), respectively. 00 : angular frequency of the power source, B. Equivalent circuit constunt3 Fig. 3 shows the rotor structure of the tested PM motor. Because the damper winding has a double squirrel-cage structure, the d- and q-axis equivalent circuit of the tested PM motor at standstill are expressed as Figs. 4 and 5, respectively. Here, h d and 11, are the leakage inductances caused by leakage fluxes interlinked with only the upper winding,lu and lzq those by leakage fluxes interlinked with only the lower winding, and 11u and 11% are by leakage fluxes interlinked with both upper and lower windings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003717_08ias.2008.78-Figure23-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003717_08ias.2008.78-Figure23-1.png",
        "caption": "Fig. 23. No-load flux density vector distribution with 3000 ampere-turns field excitation.",
        "texts": [
            ", and the stator core outer diameter is 10.6in. The PM properties used in the simulation are Br = 4 kG, and Hc = 16 kOe. The low Br value indicates a relatively low-cost permanent magnet. Fig. 22 shows that under the no-load condition, the airgap flux density can be changed significantly by changing the excitation ampere-turns. This indicates the field weakening and enhancement capabilities of the HSUB machine. The corresponding flux density vector distribution with 3000 ampere-turns field excitation is shown in Fig. 23. Fig. 24 shows the flux density vector distribution at maximum torque position with stator current magnitude of 200 A and field excitation of 3000 ampere-turns. Fig. 25 shows the comparison of output torque versus various excitation ampere-turn values. A torque increase over 60% can be achieved by flux enhancement. . VI CONCLUSIONS \u2022 An HSUB machine is introduced. It can be built as an axial-gap or a radial-gap machine. \u2022 The dc flux produced by an excitation coil is delivered to the rotor through an undiffused magnetic path without brushes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000287_0963-8695(91)90003-l-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000287_0963-8695(91)90003-l-Figure2-1.png",
        "caption": "Fig. 2 Transducer location",
        "texts": [
            " The tangential acceleration was then reduced to the base circles in order to compare experimental and numerical results, since torsional masses have been modelled as translating ones. 0963-8695/91/060303-04 \u00a9 1991 Butterworth-Heinemann Ltd NDT&E International Volume 24 Number 6 December 1 991 303 m v z 0 < n\" I,LI _J ILl o c.) < . J z ILl O Z < V-- tw U.I +50 -40 . . . . . . . . . . . . + 5 0 - 4 0 + 5 0 -40 0 3000 (a) (b) (c) FREQUENCY (Hz) Fig. 1 Spectrum of wheel tangential acceleration wi th undamaged teeth. Wheel speed 760 rpm, torque 1160 N m, other data as in Reference 8 and in Figure 2: (a) measured by tangential accelerometers ( after TSA) ; ( b ) recovered ( after TSA); ( c ) model result Figures la and c show a comparison in the frequency domain for the case of undamaged teeth. The resemblance can be considered very good, so the model turns out to be effective. The model was then used to predict torsional gear vibration in the presence of a cracked tooth. A fatigue crack in a tooth has been considered through stiffness weakening as the 'cracked' tooth meshes. It was found that the presence of a crack is clearly detectable in the phase modulation pattern of one of the meshing harmonics of gear vibration tsl, thus confirming that information about faults can be obtained by torsional vibration, probably more clearly than by case vibration",
            " Strictly speaking, the FRF can be defined only for a linear, time invariant system, so it cannot be defined for the system under consideration. However, since the purpose is not system identification but signal recovery, the use of H t to obtain the filtering function is allowable and the related results are reliable, as will be shown later. Experimental evaluation of this function for the gear testing machine in question was done by simultaneously picking up wheel tangential acceleration ( i e torsional vibration) and case vibration velocity in the undamaged condition ; Figure 2 shows the location of the transducers. The autopower spectra Saa, Svv and the cross power spectrum Say of the two signals were evaluated over 427 averages during a slow sweep in wheel speed, first decreasing from 770 to 250 rpm and then increasing to 770 rpm again. This procedure allows a wide frequency range to be excited, thanks to the meshing harmonics sweep. The Hv estimation tl\u00b0J of the FRF was finally evaluated, considering gear tangential acceleration as input and case velocity as output"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002315_1.2192974-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002315_1.2192974-Figure4-1.png",
        "caption": "FIG. 4. A two-wheeled system with a rod of variable length.",
        "texts": [
            " This problem stems from the fact the modeling of this example as a system subject to affine constraints does not take into account that the jump in the angular velocity of the table takes place no matter what. Therefore, after the impact, we should really regard C+ as the new set of affine constraints acting on the whole configuration manifold. With this interpretation, x would obviously be a plus-in point and hence decisive . In other words, the trajectory of the ball gets reflected back by the blow of the greater velocity +. Consider a system composed of two wheels of different radii, r1 r2, connected by a massless rod of variable length see Fig. 4 . For simplicity, assume that the two-wheeled system moves along a line, and that both the masses and the momenta of inertia of the wheels are unitary. The wheels are subject to the standard constraints of nonslipping. Assume that the length of the rod is constrained between a minimum length a and a maximum length b. Here we consider the following two situations: i when the length of the rod becomes extreme, an elastic impact occurs; ii when the length of the rod becomes extreme, an arresting device fixes it, and therefore an inelastic impact occurs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001261_1.1584477-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001261_1.1584477-Figure2-1.png",
        "caption": "Fig. 2 Free-body diagram of half of the blade section",
        "texts": [
            " It also builds on an earlier development of simple companion physical models ~Sinclair and Cormier @2#!. These models are largely analytical. Preliminary to devising an approach for reducing fatigue failures in dovetail attachments, we summarize the findings of these two papers. We begin with some results for nominal contact stresses during loading up, then we discuss results for peak contact stresses during loading up, then stresses during unloading. 1.2 Nominal Contact Stresses During Loading Up. A free-body diagram for half of the blade section of Fig. 1~a! is given in Fig. 2. The loading of this half-blade comes from the centripetal acceleration of its self mass, Fv , and that of the portion of the blade not shown, Fb . These \u2018\u2018forces\u2019\u2019 are balanced by normal and shear forces, N and T, acting on a contact region of extent 2a inclined at an angle a. By virtue of symmetry, there are no counterbalancing forces on the centerline and only a horizontal force there, H. All these forces are per unit thickness in the outof-plane direction in Fig. 2. In general there can be a moment reaction on the contact region, M ~per unit thickness!. This is balanced by an equal and opposite moment on the centerline, which also has a further moment M F to offset the moment produced by Fv and Fb about the head of N. Contributed by the International Gas Turbine Institute ~IGTI! of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Paper presented at the International Gas Turbine and Aeroengine Congress and Exhibition, New Orleans, LA, June 4\u20137, 2001; Paper 2001-GT-0550",
            " An illustration of this for the normal contact stress sc is given in Fig. 3. This is for maximum load ~rpm! and when there is no friction, the situation producing the highest sc ~cf., ~3!!. Normalization is by s0 , a stress representative of the loading and defined by 1See, e.g., @1#, Section 2, for a discussion of contact inequalities and their roles in conforming contact problems. OCTOBER 2003, Vol. 125 \u00d5 1033 003 by ASME 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F s05 Fv1Fb b , (4) where b is the half-blade width ~Fig. 2!. The sharp peaks in Fig. 3 are not equal because of the presence of bending contributions ~i.e., the presence of M!. For the higher of the two peaks, the value of sc max can be expressed by 1034 \u00d5 Vol. 125, OCTOBER 2003 rom: http://gasturbinespower.asmedigitalcollection.asme.org/ on 01/28/20 sc max56.3s\u0304c . (5) Hence, at maximum load, a stress concentration factor of 6.3 in effect (s\u0304c51.9s0 , thus the lower factor in ~5! than in Fig. 3!. Crucial to determining the peak contact stress of Fig. 3 with finite elements is to try and ensure convergence: Only then can one be reasonably sure that peak stresses are being accurately calculated",
            " Irrespective of the source, two different responses can be identified. Without friction, N and sc max during unloading take on the same values as during loading up for corresponding loads ~to within 0.5%, @1#, Section 4.2!. With friction, N and sc max during unloading increase, at least initially. This result is contrary to any onedimensional physical reasoning. However, it can be explained with two-dimensional reasoning. Consider what happens at the section through the disk at AA8 in Fig. 1~a!. With unloading, Fv1Fb in Fig. 2 is reduced. Therefore so is the radially outward pull on the disk at AA8. Consequently the material above AA8 in the disk retracts radially inward. Because the periodic symmetry line through A8 is not parallel to the central symmetry line through B ~Fig. 1~a!!, this retraction is accompanied by a tendency for the disk contact region to move laterally towards the centerline. Without friction, the blade can slip radially inwards and thereby accommodate lateral motion of the disk contact region. With friction, the blade can stick and get pinched by lateral motion of the disk contact region",
            "5, shows that indeed sticking and pinching during unloading is consistent with increases in N, hence sc max . Results from the analysis for @1# and reported in @2# confirm sticking with pinching and quantify the increases in N and sc max ~e.g., a 20% unload leads to a 13% increase in sc max when m50.4!. One consequence of this pinching is that T and tc max drop significantly on unloading. This is because there are two sources of reduction in the shear force T. The first is the expected reduction occurring because there is less load to be balanced ~i.e., because Fv1Fb in Fig. 2 is less!. The second is the less-expected reduction occurring because the normal reaction is increased and consequently is balancing a greater share of the load ~i.e., because the vertical component of N in Fig. 2 is increased!. Results from the analysis for @1# reported in @2#, Section 2.5, confirm and quantify the significant drops that can occur in T and tc max ~e.g., a 20% unload leads to a 68% decrease in tc max when m50.4!. 3There are other contributions to the sh in the dovetail attachment that are not present in the configuration in Poritsky @6#, so that precise compliance with ~9! is not to be expected. rom: http://gasturbinespower.asmedigitalcollection.asme.org/ on 01/28/20 A further consequence of this pinching is that it produces large fluctuations in the peak hoop stress, sh max ",
            " While such barreling profiles consist of curved arcs as do precision crowns, the heights involved are considerably larger. Pape and Neu @9# also employ a similar curved geometry, with a far larger height than that for precision crowning, in fretting test pieces. 5In 3D , the exacting convergence checks of ~6!, ~7! can be expected to involve two-three orders of magnitude more degrees-of-freedom than in 2D . 6As an aside here, we report that we did consider a third tactic for reducing fluctuations in sh , namely varying a of Fig. 2. We could not find an a which resulted in any real reduction. 1036 \u00d5 Vol. 125, OCTOBER 2003 rom: http://gasturbinespower.asmedigitalcollection.asme.org/ on 01/28/20 where E is the Young\u2019s modulus and n Poisson\u2019s ratio. These moduli are taken to be the same for both the blade and the disk. Further, d da 5S a aa D 2 . (11) From ~10!, ~11!, for the specifications given in @1#, we obtain a minimum d of 25.4 mm ~1/1000 in! for 87% contact when m50 and N is a maximum. That is, aa50.87a when d525.4 mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000099_icsmc.1999.812539-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000099_icsmc.1999.812539-Figure5-1.png",
        "caption": "Figure 5: Mass Distribution. The upper body and waist have three mass distributions, respectively.",
        "texts": [
            " The foot of the robot does not slide on the contact surface. IV - 956 The fifth assumption states that the friction coefficients between the foot and the contact surface are very large. 3.2 ZMP Equation and Moment Compensation During the walking, the combination motion of the upper trunk and waist compensates for the moment produced by the whole body. For simplicity, the head mass is regarded as a part of the neck mass, each arm mass as a part of the shoulder mass, and the spine mass as a part of the waist mass as shown in Figure 5. The mass of the legs is concentrated on the ankle, knee and the hip joints. According to the mass distribution of the bipedal robot, the force and moment around the contact point P on the floor surface can be obtained by using d\u2019Alembert principle. The contact point P is defined as ZMP which is the total ground reaction point [5]. The ZMP equation is written with respect to the moving coordinate frame Fo as murp x i;Tt + mT(FT - F Z M P ) x ( & - + Q + G ) + mwsrwt x Fwf -k G ) f m w ( f w - F Z M P ) X (Fw -b = - M , (1) where mu denotes the mass of the shoulder including the arms, and mT the total mass of the upper body including the arms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000121_bit.260351103-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000121_bit.260351103-Figure1-1.png",
        "caption": "Figure 1. strate gradient. Schematic representation of a biocatalyst particle and the sub-",
        "texts": [
            " This means that for each parameter, the substrate concentration should be determined via a fourth-order Runge Kutta integration routine. This demands a lot of calculation, but profit of time can be gained against derivative-free methods because the algorithm converges in 6 to 10 steps when the initial values are well chosen. In that case the sum of squares changes less than 0.001% around the minimum. Immobilized Enzyme: Kinetics and Diffusion As a model system an oxygen consuming enzyme immobilized in a carrier material was used.\u2019 The immobilization resulted in spherical biocatalyst particles. Figure 1 gives a schematic representation of the concentration gradient due to diffusion limitation and external mass transfer resistance of the rate limiting substrate. For the model describing transport and reaction of the limiting substrate the following assumptions have been made: 1. The kinetics of the enzyme can be well described by the Michaelis-Menten equation. 2. The enzyme is homogeneously distributed in the particle. 3. There is no interaction between the substrates and/or products. 4. There is no interaction between the substrates and the carrier material"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000966_0005-1098(86)90082-8-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000966_0005-1098(86)90082-8-Figure7-1.png",
        "caption": "FIG. 7. Orientation (q), angular velocity of satellite (QI and wheels (co) and control signals (u) (PIDt.",
        "texts": [
            " The PD controller is not able to compensate lot the disturbance due to the friction of the reaction wheel, so that a 1% accuracy of the start quaternion cannot be reached. Owing to the gain K , the adaptive controller can reach nearly any accuracy. TABLE I. RELATIVE ENERGY CONSUMPTION AND SLEW TIMES WITHOUT WHEEL-SPEED SATURATION Controller Energy T3 % TI % PD PID A - E AU - E A + E A U + E 103 165 - - 216 158 160 126 107 114 112 107 111 107 106 109 100 I00 100 In Fig. 6 the responses of this large-angle slew are shown with the proposed adaptive controller equipped with model updating and following the Euler axis (AU + E). In Fig. 7 the responses of the same slew, but now with a PID controller are supplied. From Figs 6 and 7 it can be concluded that the adaptive controller is able to force the satellite to follow the Euler axis as defined by the reference model. The fixed-parameter PID controller is not able to realize such a slew. It is successful in realizing the desired orientation at the expense of much more control energy, a longer slew time and an undefined trajectory, which may be highly undesirable for observation satellites such as IRAS",
            " The proposed adapt ive controller is able to deal much better with this interaction than a fixedparameter controller, for four reasons: ( 1 ) The main objective for using an adaptive controller has been to force the satellite to follow the Euler axis. By implementing this trajectory in the reference model we are able to realize this objective with the proposed adaptive controller (Figs 6 and 8). Owing to the highly nonlinear gyroscopic coupling, a fixedparameter controller is not able to realize a slew about the Euler axis (Fig. 7), instead it realizes a rather undefined slew which is undesirable for observation satellites. There is no coordination among the three axes. (2) The adaptive controller uses up to three times less energy than the fixed parameter controllers (Tables 1 and 2). (3) The three-axes slew is realized faster with the adaptive controller than with the fixed-parameter controllers (Tables 1 and 2). (4) The adaptive controller is less sensitive for parameter variations, although a fixed-parameter controller still yields an acceptable performance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003738_icelmach.2008.4800247-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003738_icelmach.2008.4800247-Figure1-1.png",
        "caption": "Figure 1. Winding connection",
        "texts": [
            " Numerical simulation based on this model is provided which clearly shows aforementioned behaviour of this machine. Moreover, numerical simulation of this type of machine, presented in this paper, clearly shows that this machine could reach double synchronous speed without need for rotor acceleration by some other means. This, till now, unknown fact is currently under study and must be proven by experimental work. The voltage equations for this winding connection one could write down simply by inspection of this connection, Fig 1. Voltage equations could be written in matrix form as follows: [ ] [ ][ ] [ ] ( )[ ][ ] [ ]i dt dLLiRu \u03b8++= 21 (1) Resistance matrix is diagonal matrix with elements which are sum of the stator and rotor phase resistances: [ ] [ ] [ ] \u23a5 \u23a5 \u23a5 \u23a6 \u23a4 \u23a2 \u23a2 \u23a2 \u23a3 \u23a1 + + + =+= bC cB aA rs RR RR RR RRR 00 00 00 (2) Matrix of inductances [L1] is matrix of constant coefficients assuming linear magnetic circuit and cylindrical geometry of induction machine. This matrix is sum of two matrices: matrix of self and mutual inductances of stator windings [Lss] and matrix of self and mutual inductances of rotor windings [Lrr]: [ ] [ ] [ ] \u23a5 \u23a5 \u23a5 \u23a6 \u23a4 \u23a2 \u23a2 \u23a2 \u23a3 \u23a1 +++ +++ +++ =+= bbCCbcCBbaCA cbBCccBBcaBA abACacABaaAA rrss LLLLLL LLLLLL LLLLLL LLL1 (3) Matrix of inductances [L2(\u03b8)] consist of elements which are rotor position dependant i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001128_38.20335-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001128_38.20335-Figure3-1.png",
        "caption": "Figure 3. Hull volumes of different objects.",
        "texts": [
            " Using this distance function, we can usually eliminate most objects. After this elimination there are only local objects to consider, which will often be only one object. To calculate the possible intersection of two objects, we can now use their geometrical models. But in the most likely case it is sufficient to use a simplified model, such as the hull volumes. Three simple geometries are useful: the convex hull, the hull sphere, and the hull cylinder. The choice of one of them depends on the geometry of each object (see Figure 3). Modifying the path If there is a collision with an environmental object, we must modify the path. Before the modification we have to analyze the collision of the path with the object. There are two important questions: 0 For what distance does it collide with the object? 0 How deep is the collision? To answer these questions, we can estimate the start, middle, and end of the collision position of the path for each segment and calculate the distance between the middle collision point and the surfaces of the object"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000462_s0263574701003691-Figure13-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000462_s0263574701003691-Figure13-1.png",
        "caption": "Fig. 13. Combination of deformations expressed in the local frame (0, , ).",
        "texts": [
            " The relation between the curvature K, the velocity and the heading is: = v2 x2 v1 x1 sin cos v1 x2 sin2 + v2 x1 cos2 || v || (20) In this section we introduce a constraint in our model in order to control the curvature of the trajectories. In this way, we guarantee that a mobile robot can follow any particle. A fluid particle which moves in a complex environment, is affected by a combination of deformations like elongation, crushing shear but no extension or compression because our assumption of fluid incompressibility (Figure 13). According to the Stokes\u2019 equations (equations 21) when a fluid particle is turning, its shape is modified (Figure 14). = p I+2 D d \u0131v= + f= 0 (21) d \u0131v= v=0 where I is the identity tensor, D the deformation rate tensor, and the viscosity coefficient. We call the perpendicular shear rate the deformation movement in the direction perpendicular to the particle motion (Figure 14). = v (22) v=v +v (23) where (0, , ) is a local normalised reference frame where = v || v || (24) There is a direct relationship between local normal shear deformation movement and the curvature of a trajectory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001283_robot.2000.846401-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001283_robot.2000.846401-Figure5-1.png",
        "caption": "Figure 5: Periodicity of a zigzag",
        "texts": [],
        "surrounding_texts": [
            "Every nontrivial time-optimal control must fall in one of the above cases. However, the converse is definitely not true-not every trajectory conforming to the cases above is optimal. For example, a robot turning in place for several revolutions is not time optimal. To keep the distinction clear, we refer to trajectories satisfying Pontryagin\u2019s Maximum Principle as extremal, and we note that the timeoptimal trajectories are a subset of the extremal trajectories. We place a coordinate system as follows. Put the robot start on the negative x axis, and the put the goal on the positive x axis, such that 5, = -2,. The y axis is then the perpendicuar bisector of the segment between x, and x,, oriented in the usual way. We define the range of 6, and 6, to be ( -T , 7 r ] . Restrictions on TCCW and TCW trajectories Theorem 3 The cost of the fastest TCW or TCCW trajectory is t = b(min( 10, I + le, I, 27r - les I - le, 1 ) ) + - x,) (43) Furthermore, optimal trajectories of type TCW or TCCW can be composed of no more than three actions. Proof: TCW or TCCW trajectories with three actions are of the form straight-turn,(2,+l)-straight or of the form turnstraight-turn. The theorem is elementary for the first case. Now consider turn-straight-turn trajectories. If we let 41 and 4 2 be the magnitudes of the first and second turns respectively, the cost of this trajectory is t = b(4l + 42) + (., - 2,) (44) Choosing turning directions to minimize equation 44, we find that l Q s l + l6,l is the magnitude of the total angle turned through by the fastest turn-*-turn trajectory, and 7r - 16, I + 7r - 16, I is the magnitude of the total angle turned through by the fastest turn-U-turn trajectory. This verifies equation 43. To complete the proof, note that any four action TCW or TCCW trajectory must turn through more than 7r, and costs no less in translation than the fastest three action tangent trajectory. 0 Applying theorem 3 and equation 42, we immediately have the following corollary: Corollary 1 For every time-optimal trajectory a(T) 5 7 r Restrictions on ZR and ZL trajectories Zigzag trajectories are composed of alternating turn or straight line actions. Successive turns or straights must be in opposite directions, but have the same magnitude. Simple geometry also gives a relationship between 4, the turning angle of the zigzag, and d, the length of each straight. We have: (45) 4 d = 2b tan( -) 2 Theorem 4 Zigzag subsections containing three turns are not optimal. Proof: Consider a zigzag subsection with three turns, and two straights. The straights are the same length, so the second turn (the via point) must fall on the y axis. Construct the circle containing the start, the goal, and the via point as in Figure 4. If we perturb the via point to a nearby point on the same circle, the turning time is unchanged, and the translation is decreased. 0 Zigzags can also be said to be periodic. Let r be the smallest positive time such that: e( t ) = e( t+ 77(4t), Y ( t ) ) = r l (4 t + T), Y ( t + r ) ) Acknowledgments The authors wish to thank Jean-Paul Laumond for encouragement and guidance throughout the project. We would also like to thank A1 Rizzi, Howie Choset, Ercan Acar, and members of the Manipulation Lab for comments and discussion. Theorem 5 A zigzag trajectory ($more than one period is not optimal. Prooj! Consider a zigzag of more than one period, beginning at time 0 and ending at time T > 7. By theorem 4, the zigzag is not optimal if n(T) > 24. If s (T) > 2d, then there are three straights. The first and last straights are parallel. If we reorder the segments to perform these consecutively, then we have a path which costs no more than the original but which is no longer a legitimate zigzag. Since it is not extremal, neither it nor the original path can be optimal. 0 Enumeration Theorems 3, 5, and 4 allow a finite enumeration of the structure of optimal trajectories. The structure must be either one of the following, or a subsection of one of the following: 7 Summary and Conclusion. This paper analyzed the bounded velocity differential drive model using Pontryagin\u2019s Maximum Principle. The Maximum Principle provides an elegant geometric program that generates all optimal trajectories. Further necessary conditions were used to generate a finite set of optimal trajectory structures. Our companion paper [I] analyzes this set to determine the cost and structure of the optimal trajectories between any start and goal configuration. References [ I ] D. J. Balkcom and M. T. Mason. Time optimal trajectories for bounded velocity differential drive robots. In IEEE Intemational Conference on Robotics and Automation, 2000. [2] J.-D. Boissonnat, A. CCrCzo, and J. Leblond: Shortest paths of bounded curvature in the plane. In Proceedings of the I992 International Conference on Robotics and Automation, pages 2315-2320, 1992. [3] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko. The Mathematical Theory of Optimal Processes. John Wiley, 1962. [4] P. Soukres and J.-D. Boissonnat. Optimal trajectories for nonholonomic mobile robots. In J.-P. Laumond, editor, Robot Motion Planning and Control, pages 93- 170. Springer, 1998. [5] P. Sougres and J.-P. Laumond. Shortest paths synthesis for a car-like robot. IEEE Transactions on Automatic Control, 41(5):672-688, May 1996. [6] H. Sussmann and G. Tang. Shortest paths for the reedsshepp car: a worked out example of the use of geometric techniques in nonlinear optimal control. SYCON 91-10, Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, 1991."
        ]
    },
    {
        "image_filename": "designv11_28_0003983_aim.2008.4601660-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003983_aim.2008.4601660-Figure10-1.png",
        "caption": "Fig. 10 The model of the pseudo-3D:(a) is the side view;(b) is the top view.",
        "texts": [
            " It shows that 2D features in most cases, have enough information to classify those three types of insufficient, horizontal and vertical displacement, but the feature of good and excess is overlapped. vertical axis Since the 2D feature vectors for some samples such as good paste and excess paste are difficult to distinguish, the 3D features are used for classifying those samples however, it needs a laser scanner and it is relatively slowly. To overcome these disadvantages, a pseudo-3D inspection approach was used in order to calculate the volume ratio by creating a simple pseudo-3D model of the solder paste depositing [15]. As shown in Fig. 10(b), there is a dark loop around the solder paste. One reason for the dark loop is that the PCB is illuminated by the coaxial illuminator of the vision system, thus the ray is perpendicular to the PCB according to the principle of reflection. If only the ray is perpendicular to the surface, the reflected ray is captured by the camera, so the image is bright; otherwise the image is dark, as shown in Fig.10 (a). As shown in Fig. 10(b), Ap is the area of a pad, As is the area of particle of a solder paste and Ad is the area of the dark loop around the solder paste. The volume ratio of the solder paste deposit can be obtained by psdpdsstav AAAhAhAAAVVR /)2/1()/())((2/1/ +=\u22c5\u22c5++== (6) where Va represents the actual volume of the solder paste and Vt is the theoretical volume of the solder paste, the h represents the virtual height of solder pastes and is neutralized in the (6). So the total feature vector X is defined as follows X=[Apad, Asolder , GH , GV , R , Rv ]T (7) In such a real-time application, an efficient algorithm for detection is always expected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001616_pime_proc_1985_199_127_02-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001616_pime_proc_1985_199_127_02-Figure1-1.png",
        "caption": "Fig. 1 Geometric parameters of slot entry journal bearing",
        "texts": [
            " When designing gas bearings it is important to specify the limits of size of dimensions which influence the operating performance. These dimensions include bearing length, diameter, axial land width, bearing diametral clearance C , and the dimensions of the 0 supply The M S wus receiwd on I3 July 1984 and was ucceptedfor publication on 26 85/85 0 IMechE 1985 0263-7154185 $2.00 + .05 Proc Instn Mech Engrs Vol 199 No C4 at UNIV CALIFORNIA SANTA BARBARA on June 26, 2015pic.sagepub.comDownloaded from Proc Instn Mech Engrs Vol 199 No C4 appropriate inlet device (Fig. 1). It is therefore useful to briefly review these dimensions, combined, as they usually are, into dimensionless design parameters, and examine the way in which they influence the operating performance of gas-lubricated bearings. 1.2 Lengthdiameter ratio LID Figure 2 presents the load deflection curves for different LID ratio bearings. It is shown that bearings with differing length-diameter ratios yield closely similar values for load parameters although the actual load capacity obtained for the bearings increase as the bearing length, L, increases for constant bearing diameter, D",
            " The test shaft was driven by an electric motor via a belt and pulley (9), and its speed was monitored by a tachogenerator. Provision was made for displaying the bearing supply pressure, bearing load, shaft speed, ex, ey , eres, and in a digital form. 1.8 Test bearings Two bearings were tested: a slot entry bearing and an orifice compensated bearing [the experimental work using the orifice bearing has been reported earlier in (3)]. The test bearings had a nominal diameter of 50 mm. The slot entry bearings had the inlet provided by shims fitted between the bearing segments and are formed as shown in Fig. 1. These segments provide the inlets at a/L = 0.25. The test bearings were manufactured from lead bronze while the test shaft was manufactured from stainless steel EN 58M. These materials have closely compatible coefficients of linear expansion, and therefore the effects of temperature on clearance are minimized. The bearing surfaces were finished, lapped and the absolute sizes measured by air gauges to obtain clearances. 1.9 Experimental results The results obtained from the slot compensated bearing are shown diagrammatically in Fig",
            " 1975, 39-52. APPENDIX 1 Notation U ; n 4 I\u2019 - Z Cd K , D K L N P P R T, U a* r P axial land width slot width radial clearance inlet slots per row dimensionless flowrate inlet slot length inlet slot thickness diametral clearance bearing diameter power ratio pressure ratio bearing length speed pressure dimensionless pressure gas constant temperature surface velocity slot factor viscosity mass density Suffixes a ambient 0 supply Proc Instn Mech Engrs Vol 199 No C4 Basis of the theoretical analysis Figure 1 presents a diagram of the geometric form of the slot entry bearing being analysed. The analysis of hybrid bearings is based on the solution of the Reynolds equation for compressible flow incorporating the appropriate terms to account for velocity-induced flow and hence velocity-induced pressure. A suitable form of the two-dimensional Reynolds equation is - - a (Ph3 E)++ a ah -)=?-(?) ap ax 1211 ax aZ 12r Z ( 1 ) Transforming equation (1) directly to the finite difference form and solving for the pressure at a point i yields the following equation for flow through parallel elements of the grid network : P I 2 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000462_s0263574701003691-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000462_s0263574701003691-Figure5-1.png",
        "caption": "Fig. 5. Streamlines with friction force.",
        "texts": [
            " Two terms are in evidence in the equation 7: The first one is the global pressure difference and the second one is the viscosity forces work. As walls and obstacles are motionless, viscosity forces slow down fluid particles and so the viscosity forces work between G and S is negative (equation 8). Wu = G S v \u2022 T ds\u22640 (8) In conclusion, the more a particle is far from obstacles, the faster it travels, i.e. in the middle of canal. Let us add an external friction force F in the model. This force has the direction opposite to the velocity vector and its value is assumed here to remain constant all over the domain (Figure 5). Now, energy is not only dissipated by viscous forces but by friction forces too. By following a particle along its streamline, we notice that the mechanical work of friction forces (L \u2022 F) depends on the length L of the particle trajectory (equations 9 and 10). G S v \u2022 T+ G S F \u2022 T= G S \u2207p \u2022 T=pG pS (9) Wu L \u2022 F=pG pS (10) As the viscous forces work Wu is negative and as the potential energy due to the difference of pressure pG pS is constant (equation 11), adding a constant friction force F modifies the flow line shapes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000266_s0301-679x(00)00141-9-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000266_s0301-679x(00)00141-9-Figure1-1.png",
        "caption": "Fig. 1. Journal bearing configuration and relevant parameters under changing load.",
        "texts": [
            " [9] and the equation of journal motion are linearized, and the steady and perturbed pressures are then solved. The lubricating film is modeled as the dynamic coefficients (stiffness and damping coefficients). Therefore, the characteristic equation of the present system is derived, and the combined effects of surface roughness and flow rheology on the instability threshold are then discussed. 2. Analysis 2.1. Geometric configuration The configuration of a generic hydrodynamic journal bearing is shown in Fig. 1. This figure presents the effect of load variation on the rotor\u2019s position and specifies the relevant parameters associated with these changes. Some notations are introduced: subscript 0 refers to the quasi steady-state position, x and z are the rotor displacements away from this position and e is the eccentricity with respect to the geometric center of the bearing. 2.2. Modified Reynolds equation A number of restrictive assumptions are introduced before starting with the present lubrication analysis of journal bearings",
            " (1) is simplified as \u2202 \u2202y hn+2fp yy \u2202p \u2202y 6nUn \u2202 \u2202x (h sfs xx) 12nUn\u22121 \u2202h \u2202t . (5) Considering a well-aligned and dynamically loaded journal bearing [11], the film thickness can be expressed as h c e cos(q ), (6) where c is the radial clearance when the rotor and bearing are concentric, q is the position of film thickness away from the inverse direction of the load vector and is the attitude angle, which is defined as the angle between the load vector and the line of centers of the bearing and rotor. From Fig. 1, we have e0 cos 0 x e cos (7) and e0 sin 0 z e sin . (8) Multiplying Eq. (7) by cos q and Eq. (8) by sin q and rearranging, we obtain e cos(q ) e0 cos(q 0) x cos q (9) z sin q . Substituting Eq. (9) into Eq. (6) yields h h0 x cos q z sin q , (10) where h0=c+e0 cos(q 0). Eq. (10) is the perturbed form of the film thickness about the equilibrium point. Consider a similar first-order expansion of the pressure: p p0 px x pz z px\u0307 x\u0307 pz\u0307 z\u0307, (11) where p0 (p)0, px \u2202p \u2202x 0 , pz \u2202p \u2202z 0 , px\u0307 \u2202p \u2202x\u0307 0 and pz\u0307 \u2202p \u2202z\u0307 0 , in which the dots indicate time derivatives"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000500_acc.2002.1024608-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000500_acc.2002.1024608-Figure2-1.png",
        "caption": "Figure 2: Characteristic values for the rear axle position estimation",
        "texts": [
            " The basic equations for dead-reckoning z ( k + 1 ) = z ( k ) + A X Y ( k + 1) = Y ( k ) +AY ( 2 ) e ( k + i ) = e ( k ) + A e simply state, that the new configuration at step k + 1 can be calculated based on the old configuration at time step k plus a change of the coordinates and the orientation. It is the basic equation for both the extension of the well known rear wheel algorithm as well as the new algorithm based on the driven path length measured at the front wheels. All following equations apply either for forward or backward driving, dependent only on the sign of the direction, i.e. positive for forward and negative for backward driving. Figure 2 shows the geometric and characteristic values which are used to calculate the vehicle's position. For sufficiently small time steps it is assumed that the steering angle is not altered. The car's motion can then be approximated by circle-arcs. The angle (Y depicts the car's change in the orientation A0 = -a and depends on the driven path length according to where br is the rear track width. The driven path length ~ R L , R R is computed on the basis of the number of measured increments inCRL,RR using where nRL,RR is the number of increments per wheel revolution and TRL,RR being the wheel radius"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002721_oceans.2004.1406351-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002721_oceans.2004.1406351-Figure3-1.png",
        "caption": "Fig. 3. Coordinate frames representation of ith W M S",
        "texts": [
            " Section Il summarizes the multiple UVMS kinematic constraint and dynamics models and its main properties. Section Ill proposes a saturated proportional-derivative (SP-D) controller with gravitational and buoyancy force compensation and provides conditions on the controller gains to ensure the system stability. Section N proposes a saturated proportional-derivative (SP-D) controller with gravity regressor. Finally, Section V concludes this paper. 11. PROBLEM FORMULATION We consider k cooperative UVMS holding a common load rigidly in a 6 degree of freedom space as illustrated in Fig. 2 and Fig. 3. Let vi E R6 denotes the ith vehicle velocity vector in body fixed frame; qi E Rn' denotes the joint position vector of the ith manipulator where ni is the number of joints and pe , E R6 denotes the position and orientation of the ith end effector in the earth fixed frame. The kinematic relations between velocities can be written in a compact form as ~11,[21,[31,~91,[191: When multiple W M S cooperate to manipulate a common load, the motions in the whole systems are coupled due to the fact that the velocities of the end effectors are related via the rigid load"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003995_memsys.2008.4443786-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003995_memsys.2008.4443786-Figure3-1.png",
        "caption": "Figure 3 : Detail configuration of an optical system for developed OET.",
        "texts": [
            " A shape and position of the projecting light patterns on the 978-1-4244-1793-3/08/$25.00 \u00a92008 IEEE MEMS 2008, Tucson, AZ, USA, January 13-17, 2008836 photoconductive film can be controlled arbitrarily. Cadmium Sulfide (CdS) is newly adopted as a photoconductive film. Since the band gap of CdS lies in the spectral range about 2.4 eV, blue light is absorbed and red light is transmitted. Thus, blue light is utilized for manipulation and red light is utilized for observation of the component manipulation for assembly steps through CdS film. Figure 3 shows the detail configuration of the developed OET system. Blue light generated by a Xenon short arc lamp with cold and dichroic filters illuminates a Digital Mirror Device (DMD). The image on the DMD is projected on a photoconductive film through a lens and a beam splitter. A pixel size of the image is 10 \u03bcm \u00d7 10 \u03bcm. Red light generated by a LED ring illuminates components and assembly sites through the photoconductive film. A microscope with a CCD camera is used to observe the reflected light image from the components and the assembly sites"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000887_304-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000887_304-Figure2-1.png",
        "caption": "Figure 2. For a given initial speed there are, in general, two firing angles to strike a target. For the maximal range Rmax there is only one firing angle \u03b81 = \u03b82 = \u03b8max.",
        "texts": [
            " The final solution for Rmax is, of course, equal to the expression (4). Brown [4] presented a complete review of the history of the problem in his article \u2018Maximizing the range of a projectile\u2019. An elegant solution can be found in the article by Inouye and Chong [5] where they used implicit differentiation. It is surprising that among the numerous different approaches we could not find one very simple and obvious solution. Namely, for a given initial speed v0 there are, in general, two firing angles to strike a target (figure 2). By increasing the distance to the target, the angles \u03b81 and \u03b82 approach each other. For the maximal range Rmax there is only one firing angle (\u03b81 = \u03b82 = \u03b8max). Therefore, the maximal range Rmax can be determined by requiring that the equation \u03b8 = f (R) has only one solution. The familiar equation describing the parabolic trajectory of the projectile is y = x tan \u03b8 \u2212 gx2 2v2 0 (1 + tan2 \u03b8). (5) At impact with the ground, y = \u2212H and x = R, it gives gR2 2v2 0 tan2 \u03b8 \u2212 R tan \u03b8 + ( gR2 2v2 0 \u2212 H ) = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000297_s0736-5845(01)00037-0-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000297_s0736-5845(01)00037-0-Figure7-1.png",
        "caption": "Fig. 7. Joint coordinates of the GMF-S400 robot.",
        "texts": [
            " xci \u00bc fx\u00f0xi; yi; zi;C\u00de b1\u00f0C\u00dexi \u00fe b2\u00f0C\u00deyi \u00fe b3\u00f0C\u00dezi \u00fe b4\u00f0C\u00de; \u00f03\u00de yci \u00bc fy\u00f0xi; yi; zi;C\u00de b5\u00f0C\u00dexi \u00fe b6\u00f0C\u00deyi \u00fe b7\u00f0C\u00dezi \u00fe b8\u00f0C\u00de; \u00f04\u00de in these two equations C is a vector that contains six view parameters C1;y;C6; and, b1\u00f0C\u00de \u00bc C2 1 \u00fe C2 2 C2 3 C2 4 ; b2\u00f0C\u00de \u00bc 2\u00f0C2C3 \u00fe C1C4\u00de; b3\u00f0C\u00de \u00bc 2\u00f0C2C4 C1C3\u00de; b4\u00f0C\u00de \u00bc C5; b5\u00f0C\u00de \u00bc 2\u00f0C2C3 C1C4\u00de; b6\u00f0C\u00de \u00bc C2 1 C2 2 \u00fe C2 3 C2 4 ; b7\u00f0C\u00de \u00bc 2\u00f0C3C4 \u00fe C1C2\u00de; b8\u00f0C\u00de \u00bc C6: \u00f05\u00de The two expressions (3) and (4) relate the camera-space location \u00f0xci; yci\u00de of a given point i; with its physical location \u00f0xi; yi; zi\u00de; referred to an arbitrary x0y0z0 coordinate system (which for practical purposes can be considered fixed to the base of the manipulator), as depicted in Fig. 7. The view parameters describe a nonlinear relationship between the internal joint-coordinates of the robot and the location of the visual features attached to a given manipulated object if the physical coordinates \u00f0xi; yi; zi\u00de are obtained using the nominal forward kinematic model of the manipulator. As explained in [12], the six view parameters can be estimated using samples of both camera-space location of visual features and the corresponding physical location of the features obtained with the robot\u2019s kinematic model, using a nonlinear estimation scheme such as the least-square differential correction described by Junkins [13]",
            " Furthermore, the approximation of Cn 5 and Cn 6 obtained as explained in Section 2.1 might also be insufficient. A solution for the determination of the initial point of the approach trajectory was found by resolving independently two partitions of the vector H \u00bc \u00bdy1;y; y6 T that contains the joint coordinates which describe the configuration of the industrial manipulator used in the experiments. The first partition HI includes only the first three joint coordinates, while the second partition HII includes the joint coordinates at the wrist of the manipulator as shown in Fig. 7. The first partition was resolved based on the inexact set of view parameters Cn \u00bc \u00bdCn 1 ;y;Cn 6 T; obtained from the measured angular displacement of the platform supporting the cameras, as described below. The second partition, containing the three joint coordinates in the wrist of the robot, were fixed during the determination of the first three joint coordinates, and adjusted later to improve the visibility of the visual features in order to facilitate their detection in the image-plane of all participating cameras",
            " This fact can be used to determine a suitable parameter that quantifies \u2018\u2018how perpendicular\u2019\u2019 the plane containing the features is with respect to each camera. In practice, this parameter, referred to as Z; was considered to be the sum of the dot products between a vector perpendicular to the plane and a vector directed along the optical axis of each camera. Consider \u00f0px; py; pz\u00de to be the components of a vector perpendicular to the plane containing the manipulated features and protruding from the wheel, which is referred to the xwywzw coordinate system on the wheel (tool reference system), as depicted in Fig. 7. The scalar parameter Z can be defined in matrix form as Z \u00bc E TK\u00f0H\u00de px py pz 0 2 6664 3 7775; \u00f018\u00de where E \u00bc Xnc i\u00bc1 2\u00f0ei 1ei 3 \u00fe ei 0ei 2\u00de Xnc i\u00bc1 2\u00f0ei 2ei 3 ei 0ei 1\u00de \" Xnc i\u00bc1 ei2 0 ei2 1 ei2 2 \u00fe ei2 3 0 # \u00f019\u00de for nc participating cameras. The Euler parameters are obtained considering the parameters Cn 1 ;y;Cn 6 using the approximation in Eq. (6). The 4 4 matrix TK\u00f0H\u00de describes the transformation between a fixed coordinate system x0y0z0 attached to the base of the robot and the tool coordinate system xwywzw (Fig. 7), and constitutes the nominal forward kinematic model of the manipulator. The minimization of Z is performed by considering experimentally found limits to the angular displacements of the joint coordinates at the wrist of the manipulator, for a variety of distant locations of the brake plate. The parameter Z was evaluated within these limits and the joint coordinates that produce a minimum value are chosen as the second partition HII: Note that once the second partition of joint coordinates is resolved, the value of the first partition can be reevaluated in order to improve the accuracy in the positioning of the single destination point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002132_s1474-6670(17)31751-2-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002132_s1474-6670(17)31751-2-Figure7-1.png",
        "caption": "Fig. 7. Two ROYs with different thruster configurations (overactuated in the horizontal plane).",
        "texts": [
            " If the desired virtual control input \" 2 = S2 lies in <I>\\<I> p' the fixed-point algorithm converges toward the exact solution T;f = ~ , which lies on the solution set 3 2 and has lower 12 norm than any other point in 3 2, The corresponding sequence in the virtual control space converges toward the desired S;f = S2' CAMS 2004 (a) If \" 2E <I>\\<I>p' then T;f =~E3 2 is the exact solution, optimal in the 12 sense. V, (b) If \" 2 E <I> \\ <l> p , then S;f = S2 ' Two ROYs (FALCON, SeaEye Marine Ltd. and URIS, University of Girona, Fig. 7.) with different thruster configurations are used to demonstrate the performance of the proposed hybrid approach. The normalised control allocation problem for motion in the horizontal plane is defined by (Omerdic and Roberts, 2004) I I FALCON: 4 4 4 4 I I I I (13) !!= 4 4 4 4 I I I 1 4 4 4 4 319 320 1 0 0 - URIS: 2 2 (14) 1 1 !!= 0 0 - - 2 2 I 1 I I - -- -- 4 4 4 4 [ IX] the virtual control input! = ~: (k = 3) (15) r y.l~ the true control input!! = : : (m = 4) Y.4 (16) r -II ry.l.l+ 11 'h\"\"\"\"'o\"o\",\"\",,, ~: r :: < :: j ( (7) The constraint control subset g is a 40 unit cube "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001840_s00216-005-3212-6-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001840_s00216-005-3212-6-Figure1-1.png",
        "caption": "Fig. 1 a Schematic representation of screen-printed carbon electrode. b Sheet of 96 screen-printed carbon electrodes",
        "texts": [
            " L-Cyste- ine (Cys), tris(hydroxymethyl)methylamine (Tris), hydrochloric acid (HCl), potassium chloride (KCl) and mercury(II) atomic absorption standard solution (1,000 mg L 1 in 1% nitric acid) were obtained from BDH (Poole, UK). The cadmium(II) atomic absorption standard stock solution (994 lg mL 1 in 1% HNO3) was from Sigma (St Louis, USA). The buffer used in the experiments was 0.025 M Tris\u2013HCl containing 0.1 M KCl (pH 7.4). Leachate solutions from extracted soil samples were supplied by Tecnicas de Proteccion Ambiental (TPA), S.A., Madrid (Spain) and Grup de Techniques de Separacio\u0301 (Universitat Autonoma Barcelona, GTS-UAB, Spain). Electrode fabrication The screen-printed electrode (SPE, Fig. 1), comprising of a working electrode (1.3-mm2 planar area), counter electrode and reference electrode, was mass fabricated inhouse by a multi-stage screen-printing process using a DEK model 248 machine (DEK, Weymouth, UK). The electrodes were printed onto 250-lm-thick Melinex ST725 polyester sheet obtained from Cadillac Plastic (Swindon, UK) using different printing inks. The basal tracks were printed first using graphite based ink E423SS obtained from Acheson Colloids (UK) and dried in an oven at 60 C for 2 h"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000319_1.1519275-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000319_1.1519275-Figure1-1.png",
        "caption": "Fig. 1 Schematic graph of pitting",
        "texts": [
            " b is a parameter determined by the gear material property and gear geometry, and is given by b5H 4L pW F12m1 2 E1 1 12m2 2 E2 GY F 1 r1 1 1 r2 G J 1/2 (2) In the absence of pitting damage on a tooth\u2019s surface, the contact width W should remain constant. However, when there is pitting damage present, the width changes at the location of the pitting because of the removal of material from the surface of the tooth. Considering that the depth of pitting is usually much larger than the local contact deflection of the tooth, it is assumed that no tooth contact occurs in the pitting area. A schematic graph of pitting is shown in Fig. 1. Pitting is modeled as a circular indentation occurring near the pitchline. W1 is the tooth width of contact for the surface without failure. W2 is the tooth width for the surface with pitting. These widths may vary with respect to each other. When a different width of contact is substituted into Eqs. 1 and 2, a different local tooth deflection will be computed. The local tooth deflection is used in the calculation of mesh stiffness. 2.2.2 Modeling a Root Crack. A tooth root crack typically results from tooth bending fatigue and most of the time it is initiated from a flaw"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000056_acc.1988.4790076-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000056_acc.1988.4790076-Figure1-1.png",
        "caption": "Figure 1. Existing methods to find swcing points",
        "texts": [],
        "surrounding_texts": [
            "ALGORITHM In this secton, we show that the poits, which we shall refer to as characteristic switching points, wh the phase plane trajectory jw meets the maximum velocity carve witout violating the actator cnstraints, can be exhaustively classified into thne possible types We call ese the zero-inertia point, the discontinuity point, and the tangent point. We describe how the characteic switchig points can be diedy obtained withoUt computing the maximum velocity airve explicitly, ad how this property can be exploited to simplify the computaion of the time optimal solution Section 3.1 finds the switcting points whr the maxnrum velocity curve is continuous but not differentiable (zero-inerda points), which coresmnds to having on of the a, chages signs. Section 3.2 coven the c,(s) = G(s) (12) (23) case where the maximum velocity curve is discontinuous (discontinity points). Section 3.3, which represents the main result of this paper, derives a simple procedure to find the switching points where the maximum velocity curve is cortinous and differendable (tangent points). The resulting algorithm is summarized in Section 3.4. point, with the tk actator saturated. Then there must be at least one other actuator torque tm which, at the tangent point, satisfies the conditions T = am(s) { k-b,(s)s 2-cfs)j /* + bl(s)s 2 + Cm(S) (25) 3.1 Case 1: The ZerIna-tia Point If, in (21) and (22), a,) =0 for some i, then a, an A, cannot be defied. In tis case the aceleraton i at the maximum velocity ; M= is not uniquely determined The dme-optimal phase-plane tajectory may include this singular pomt, which is a candidate char risi switching point, as noticed in [Pfeiffer and Johanni, 1986]. We call this case the zero-inertia point, sine a,ss) repr an iertia-ike term in the pameterzed dynamic equatio Zero-ineria points can be easily found, fom the expression of a,(s). 3.2 Case 2: Tbe Discntinnity Point Our hypothesis on the local smoodthes of the maxim velocity auve iplies that the torque t, is continuous and diffrentiable in the viciity of the tangent point Since T.n must meet the actuator consti tangntally dtm =O (26) Since, frm (25), c, can be expressed as a functio of only s and s, condition (26) is equivalent to a'. +a9T =0 aS as (27) In this sbsection and the nenxt, we shall assme that none of the axs) is zero in the vciny of the araeriswitching point coded. We can always assune that the first derivative of the parameteized path fuction namely P, of [Bobrow, et at., 1983; 1985] or f, of [Shin and Mc Kay, 1983; 1985], is coniuous. Inded, if this is not the case at a particular point, ten at this point the velocity along the path is necearily zero (sinc, physicay, the velocity vector cant be discontnous), so that the task cma be partitoned into two independent opdmal control problems. However, the second derivative p1,, (or f,), may be disconiuous. It can be easily shown, from (19) that (asming as we do that none of the as(s) is zero) the maximum velocity curve is discontinuous if and only if Pu. (or f3) is discontinuous (Figure 2). Using (24), (25), and (27), yields (28)v(s)-(<s)s 2 = O where v(s) = a + 2(akb,,-a.baXta -ck)/Iak2 (29) (30)w(s) = 2 (a,b. -a. bk) btla 2 fberefore, for each value of s, we can solve equation (28) for S * and then cbeck for the value (*,s;) wheter The corresponding discontinuy points are easy to find. One must compute the values of s, where p,1 (or f) is discontinuous, then calcula the associated maximum velocity limits. Two vaes of s are obuined for each value of s, the smaller of which is the possible point where the phase-plane trjeo ry can touch. For example, if the path is puameteried in task space, and the parameter s is the displacement along the path from the starting point, then the posit components of p., are the acceleration components normal to the path, the magnitude of which is the reciprocal of the rads of the path. In this case, the discontinuity point is where the curvature of the path changes discontinuously. 3.3 Case 3: The Tangent Point Subsection 3.1 determined the switching points where the maimum velocity acrve is condnuous but not differerniable (which corespodis to having one of the a, chages sigs). Subseccdon 3.2 covered the case where the maximum velocity curve is discontinuous. This subsection completes the analysis, by deriving a simple procedure to find the switching points where the maximum velocity crve is continous and differentiable. When the maximum velocity curve is condnous and differentiable at the switching point, as assumcd in this subsection, the time optimal phase plane trajectory must meet th maximum velocity curve tangentiazly at the switching point (or on somc finitc portion of the maximum velocity curve), as n'= ,m U( ifa. > 0 ) or 'c, =z, ((ifa,,<O) while the otber actuator torques remain within their admissible bounds. If this is the case, then (s*, ) is a possible tagent point. Note that in (29) the term a need not be computed explicy, but rater can be approximated with appropriate accuracy using e.g. a central differentiation metd, since the actuator torque is assumed to be a smooth function of s and s in the vicinity of the tangent point. Also, since, by definition, k and m cannot be equal there are only n(n-l)/2 possible combinations of joints for equation shown in Figure 3-(a). If the trajectory hits the maximum velocity curve other than tangentially, then in order for the manipulator tip to stay on the prescribed path, at least one of the actuator would have to violate its constraints, as shown in Figure 4(b). By conta, if the trjectory meets the maximum velocity curve tangentially (Figure 3-(a)), then from that point on the manipulator tip can continue folnowing the path without violating any actuor constraint, and at least one of the actuator should meet the actuator constraint boundary tangentially, as shown in Figure 3-(b). This must be true whether the manipulator tip condnues accelerating or decelerating in the vicinity of the tangent point, or switches at the tangent point from acceleration to deceleration or vice versa. Now, a necessary condition for the point (s *) in the phase plane to be a tangent point can be derived as folows. In the vicinity of the tangent point, we have, for some k s = at(s. ) = (t -bks); 2 _cS))Iags)k4) whiihd mcans tat declration contines jus befoe awl afer the tacgen (n2M. Ths combinations can be computed in a parallel and indep t fashion, so that the computaton time may only uease modesdy nith the number of the links s I Flgur 2. Maxium veloity curve with a d isc ntity point Fre 5. The procedure to get the lmit cuwve and speposition of the maximum elocity cuve Figre 6. The complete optiml trajectory with supepoition ofthe maximum veloity curve 0.5 S. (a) 'eflu tajectory mets -1,1tgeiay. S (a) Path I I5I k - - - - - - -_ (b)The torqumets tangentially. Figur 3. 'flu trajctr and the torque meet tangedntily. 1 .N5 (b) Path 2 Fgure 7. Two paths example _W ~~~~~~~~~~~~~~~~~~~~ 7 4.- t gs 243 : .2 - .6.. - - - 4- - - - - - - - - - ,2. 1o.l (a) The limti curves (b) lbeiming cre with superposition of themim -eKl curv i S. 2. ci (c) 11e complete optimaltjo 45. 3.0 I5.s 0. -IL -20. -a. (d.Tec.optma toqebltr (d) 'Ih lK iFn n optima torqe htr Fiure Simulation reslt for path 1 S.1 In the above the secticn we descd how to fid al dt possie ponts that the phas-pin trajectory can meet in the time-opimal soton. These th pes of points are uey i m the given path, tic manipulator dynms, atid the acuaor ains, a a in of the initial and finl positons aid veloduia along the pat This fact alows us to avoid t exbausive seartbes over the whole ran of s and i of the earlier methods The new algodh can be sun zd as follws; 1. Fin al the candidate st witching point, as explained in secions 3.1, 3 2, and 3.3. 2. From thse points, integrae i =ca( s,s ) backward in dime, and S' s, s) forward in time, unti the phase-plane traory hits the s axis, the i axis, or the s=s., line, or utml one of the actuator constaints is violated If, frm a candid sc wthing poit, one cannot integrate both forward and bwkward without violating the actuator constraints, then such point should be discarded Then, the admissible region for the phase-plane trajectory is under sulting limit curves. Tbe procedure is described graphically in Figure 5. The maximum velocity curve is also shown, in order to help unders how the new algorithm differs from the earlier methods. Note ta te shaded region in Figure 5 is inadmissible. 3. The switching points can be obtained as follows (Figure 6). If the final point is between 0 and sf, , then there is only one switching pont between a and b, which is the point where the deceleration trajectory, IV CL a. .I. 'I 4 :9 5. I a. C I s -1- .5 Si CL1 CIs EU Os *l; I I I I I I I e 3A Squmary (a) The limiting curves fl _ _ fl ,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ywlliL .1 -m E. 0. I 19I I. L- s I . WC integrated backward in time from the final point, meets the acleration trajetory, integrated forward in time from the asarng poit If the final point is between sf and s2, then then am thre switcbing points, namely, b, c, aid some point between c and d where the deceeation ectory from the final point hits. Simrn y, if the final point is between sp and then there ame five switching points, namely, b, c, d, e, and some point between e andf. By repeating the above rasoning, all switching points can be obtined. Note hat this implies that the number of switching points must be odd. 4. If the condition for a tangent point is satisfied over a some fiite interval, then the phase-plane trajectory coincides with the maximum velocity curve along a finite arc. 4. NUMERICAL EXAMPLES To demonstrate the efficecy of the new algithm, simulations are carried out for a planar two-link mazipulator on two types of paths. Each link has unt mass and unt length, and the actuatr torques xl and '2 are limited in ablute value to 30 and 10 NM . FIgure 7 shows the paths in task-space. The paraneterized equations for tese two paths are Path x=s+0.5 y =4(s-0.5)3 Path 2 if s <0.75 x2, then x = 0.75 { 1 +cos(s/0.75)}, y = 0.75 sin(sjU.75) if s > 0.7154x2, then y = 15 -0.75 cos(sfl.755-x12) x= 0.75 1 -sin(s/O.75-x/)2 Note hat, for path 1, the parameers is arbitrarfly chosen, while for path 2 it is the legth along the path from the starting poin The result of the algoritm for path I is shown in Figure 8. Figure 8-(a) is the limit curve which is obtined by the above method. The maxmum velocity curve frm the earier method is also drawn wth the limit curve in Figue 8-(b), in order to show the consistency between the two metbods. Figure 8-(c) represents the complete time-optimal phase plane trajectory. If sm is between 0 aid 0.737, then there is a single switching point If s. is between 0.737 and 0.944, then the a tre e switching points. If s,,x is between 0.944 and 1, then there are five switching points. Figure 8-(d) gives the conesponding actuator histories. he simulation result for path 2 is sbown in Figure 9. Note that it has a discontinuity point, due to the fiac that the parameter s is the kngth along the path, and that the path changes curvatr dscontnously. bThe corresponding actuator history is shown in Figure 9-(d) This algorithm owes it efficiecy to the fact tha it does not need to conpute the maimum veloity curve, and that all the charaisc switching points can be obtaned by searching just once over the value of s using a simple method, while earlier apprnaches need systematic searches to find a swithing point with the help of the maximum velocity cuve, and should repeat te as long as thre am more switching points ahead An exact efficiecy comparson between the earlier metxods and this new algorithm is difficult; since, for instace, the step sizes in s and i which ase used to get the maxmum velocity relarely affec the co uttion time of Bobrow's algor as do other implementation choes in a metods (such as dicbotomic searches in Bobrow's algorthm). In the imnplementation of the above numerical examples, however, we found tha for this simple two-link manipulatr case, our new algorithm is more efficient than Bobrow's method roughly by a factor of 50 or more. Furthermore, we expect the relave efficiency of our algorithm to inrease with the number of links, since the algorithm does not require iterative searches, and in adition could be impkmented in paralel, as explained in sction 3.1. S. CONCLUDING REMARKS Important fiuther research directions involve computationay efficient yapprocbcs to the global, point-to-point minimum-time problem (given initial and finl stats, possibly with obstades), and issue of robusss to model uncertainties ( particular, smoothess of the optimal solution with respect to parametric ikccuracies)."
        ]
    },
    {
        "image_filename": "designv11_28_0002167_1-4020-4611-1_8-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002167_1-4020-4611-1_8-Figure8-1.png",
        "caption": "Figure 8. Flow cell for electrochemiluminescence measurements: (a) glassy carbon electrode; (b) sensing layer; (c) reagent solution outlet; (d) Plexiglas window; (e) liquid core single optical fiber; (f) stirring bar; (g) reagent solution inlet; (h) platinum electrode.",
        "texts": [
            "01 for the luminol chemiluminescence reaction. L.J. Blum and C.A. Marquette 169 As mentioned above, an original and unusual way to obtain a high sensitive hydrogen peroxide detection is the electrogenerated chemiluminescence of luminol (ECL). Based on this electro-optical process, a flow injection analysis optical fibre H2O2 sensor has been developed 53,54 . The electrochemiluminescence was generated using glassy carbon electrode polarized vs a platinum pseudo-reference electrode and integrated in a flow injection analysis system (Figure 8). Chemiluminescence-based Sensors 170 The optimization of the reaction conditions showed that an applied potential of + 425 mV vs a platinum pseudo-reference electrode enabled the realization of a sensitive H2O2 sensor while avoiding passivation of the working electrode. An optimum pH measurement of 9 was found and moreover, the pH dependence of the ECL sensor appeared less pronounced than when using immobilized HRP as the sensing layer. Under optimum conditions, hydrogen peroxide measurements could be performed in the range 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001970_0301-679x(78)90179-2-Figure15-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001970_0301-679x(78)90179-2-Figure15-1.png",
        "caption": "Fig 15 Regions o f cavitation near a lubricated eccentrically mounted annulus. The disc rotates about its centre S,",
        "texts": [
            " 2 2 i I 0 I I 0 mm mm Film profile AA' Film profile BB' 4l b Direction of radial component Direction of radiat component a b E The total load P was 0.5 kg and the sliding speed u at the annulus was approximately 10 mm/s. Fig 14(a) shows the interferogram and deduced film profile observed at 0 = 90 \u00b0 when the disc was rotated in one direction and Fig 14(b) when it was rotated in the opposite direction. It is seen that the f'dm profile is that to be expected for a cylindrical specimen moving in a direction at right angles to its axis. There was a tendency for cavitation to occur (Fig 15) in the elastohydrodynamic film portion of the contact zone on that side of the rubber specimen that corresponded to the exit region of the contact, ie on the same side as the nip. It was found that cavitation increased with increasing speed of rotation. It is easy to calculate the parameters NI and N2 as defined earlier replacing the velocity u by the radial velocity Ur since it is this component of the velocity that is responsible for the build-up ot~ the elastohydrodynamic film. Such measurements can be carried out at any value of 0 if the appropriate value of Ur is used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002908_bf03266511-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002908_bf03266511-Figure1-1.png",
        "caption": "Figure 1 \u2013 Set-up of filler metals on base metal",
        "texts": [
            " To study the metallurgical changes, macrostructures across the welded joint were observed and the dendrite arm spacing (DAS) was measured. The base metal was a hot extruded and rapidly cooled A6N01 aluminium alloy sheet, artificially aged to T5 temper designation (age hardened between 170-180 oC for 8 hours). Its chemical composition is shown in Table 1. The chemical composition of the filler metal Al-12 %Si used is shown in Table 2. Additional alloying elements were added as explained above to this filler metal to find their effect on the weld metal strength. The base metal sheet was machined with a central groove as shown in Figure 1 to place the filler metal with a rectangular cross section prior to the bead-onplate laser welding. Two combinations of filler metal section and groove depth were used to achieve full penetration [see Figure 1 a)] with slow travel speeds of 3 to 9 m/min, and partial penetration [Figure 1 b)] with fast travel speeds of 12 to 18 m/min. The twin-beam Nd: YAG laser head with in-line configuration is shown in Figure 2. The laser beam is transmitted by an optical fibre to the head with a distance of 0.6 mm along the welding direction. The laser output from the front beam was 2 kW, and that of the rear beam was 3 kW, giving a total power of 5 kW. The defocusing distance was kept on 0 mm. Argon gas was used for shielding with a flow rate of 10 l/min. The Vickers hardness was measured with 100 gf loads across the weld bead to find the hardness distribution with an interval distance of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001055_s0304-3886(01)00096-1-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001055_s0304-3886(01)00096-1-Figure4-1.png",
        "caption": "Fig. 4. The TonerJet direct printing process in which triboelectric charged toner is transported to an electrode array that controls the deposition of toner onto paper moving over a back electrode electrically biased to attract toner gated through the apertures.",
        "texts": [
            " There have been a number of concepts proposed for electrostatically controlling the deposition of charged particles with an electroded aperture array spaced from an intermediate receiver or paper. For such systems, the imaging physics is of the Q( E) type. In this case, E is time-dependent to provide a spatially-dependent image on a moving intermediate or paper. TonerJet (www.array.se) is a charged powder direct printing technology that controls the particle deposition with an electrostatically gated aperture array as illustrated in Fig. 4 [6]. Toshiba has described a liquid ink Q( E) direct marking concept in which charged ink particles in a hydrocarbon #uid are electrostatically concentrated and ejected from an array of microfabricated electrodes [7]. OceH (www.oce.com/tech/Ccolrtec.asp) has described a full-color direct marking technology in which the imaging and charged particle deposition occur simultaneously [8]. Conductive toner is induction charged and loaded onto an imaging drum that consists of circumferential ring electrodes (400 per inch) overcoated with a dielectric layer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002166_50006-7-Figure5.22-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002166_50006-7-Figure5.22-1.png",
        "caption": "FIGURE 5.22",
        "texts": [
            " When the reformation front is aligned to be parallel to 'y*' then q~ = 0 and when the front is parallel to 'x*' then q~ = ~/2. In descriptive terms, equation (5.80) states that flow from a cavitation front which is constant and equal to the Couette flow at this front should be equal to the increased Couette flow at the reformation front minus the backwards pressure flow from the reformed oil film. This condition imposes a significant positive pressure gradient at the reformation front because of the step change from cavitated to full flow. This principle of film reformation is illustrated in Figure 5.22. Continuity principle of film reformation in a hydrodynamic journal bearing. The reformation condition may be applied to every positive pressure generated down-stream of the cavitation front as an inequality based on finite difference approximations to the pressure gradients. Positive pressures which do not satisfy this inequality are set to zero until a front is established. A similar method was developed by Dowson et al. [15]. If the reformation condition is not applied in the analysis then the extent of the non-cavitated lubricant film will be overestimated, causing an imbalance between lubricant flow from the grooves and lubricant flow out of the bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000986_1.1596241-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000986_1.1596241-Figure9-1.png",
        "caption": "Fig. 9 Arrangement of experimental gear train, DC-motor and measuring devices",
        "texts": [
            " (10) The Laplace transform notation is not suitable to develop a computer algorithm able to process a velocity profile given in the time domain. A more general manner to calculate the response of a system, knowing its transfer function, represents the Convolution Integral. A descritized version was implemented into the program to approximate the required voltage. Solving for the output voltage va(t), this expression gives: va~ t !5 v~ t ! Dt 2( n51 n g~nDt !va~ t2nDt ! g~0 ! (11) where v(t): angular velocity g(t): transfer function of the motor Dt: time step n: integer The experimental gear train is shown in Fig. 9. The system consists of a dc-motor driven gear stage with incremental encoder on the output shaft to determine the remaining time delay. Additional measuring devices include a tachometer and encoder on the driving shaft to monitor the desired motion performance. The center distance between the two shafts was adjustable so as to introduce different amounts of backlash into the system. The adjusted backlash in the gear train varied from 0.022 to 0.089 radians and the nominal velocity slope in the backlash area varied from 3p to 9p radians per square-second during the experiment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001681_robot.2004.1307975-Figure15-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001681_robot.2004.1307975-Figure15-1.png",
        "caption": "Fig. 15. Cone Where Gripping Point Can Be Placed",
        "texts": [
            " To avoid jamming, the manipulator should estimate the inclinations and revise the insertion direction. The revision method is that a,dy,,j, a,dy,,f are added to desired position of gripping point respectively. The inclinations a and a, are calculated with linear regression using the position of gripping point at the time when insertion operation is available. We illustrated the desired position of the gripping point, the base position to generate desired position, and the current position in Fig.14. Fig.15 shows the cone where gripping point can be placed, where pa is radius ofcircle where gripping point can be placed when the task begins, and ppc is radius of circle when peg is inserted. The ideal condition of peg and hole is one-point contact, because friction force of one-point contact is less than one of tw&point contact. However the positioning accuracy of manipulator is required to realize the one-point contact, because the deeper peg is inserted the smaller pc becomes. Therefore, the method to realize one-point condition and to position of gripping point and current position on the xy plane are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003740_1.2975154-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003740_1.2975154-Figure5-1.png",
        "caption": "FIG. 5. a Computation of M magnetization components along the axes X, Y, and Z for a left handed helicoidal magnet; b angle of cylindrical helix .",
        "texts": [
            " 4 the distribution of M along a generic cylindrical helix with starting and ending points A and B, respectively, is illustrated by a qualitative picture. In this drawing we denote the radius of by r and suppose that the extension of is almost equal to two revolutions. In Fig. 2 b is quantitatively defined by fixing the suitable value of the angle . Now, since the orientation of M is the same one of n we straightaway obtain the components Mx, My, and Mz of M. In fact, with reference to O X ,Y ,Z and Eqs. 11 \u2013 13 , it follows that Fig. 5 a Mx = M cos , 14 My = \u2212 M sin sin \u2212 , 15 Mz = \u2212 M sin cos \u2212 . 16 Substituting Eqs. 9 and 10 in Eqs. 11 \u2013 16 , we obtain in each point P of the magnet the volume and surface charge density M P and M P , respectively. In particular, in order to compute M P by Eq. 9 , it is convenient to write Mx, My, and Mz as a function of the Cartesian coordinates x, y, and z of P, that is the point where M is applied. Observing Fig. 3 b we find that r = y2 + z2, 17 where y and z are just the two coordinates of P in the frame of reference O X ,Y ,Z . Because cos \u2212 = \u2212 y r , 18 sin \u2212 = z r , 19 from Eq. 17 it follows that [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: 131.230.73.202 On: Thu, 18 Dec 2014 07:41:10 cos \u2212 = \u2212 y y2 + z2 20 and sin \u2212 = z y2 + z2 . 21 Moreover, if we denote by p the pitch of the cylindrical helix shown in Fig. 2 b , the relationship among the helix angle , r, and p is see Fig. 5 b = arctan p 2 r . 22 Considering again Eq. 17 , we obtain = arctan p 2 y2 + z2 . 23 Substituting Eqs. 20 , 21 , and 23 in Eqs. 14 we find the following three equations: Mx = M cos arctan p 2 y2 + z2 , 24 My = \u2212 M sin arctan p 2 y2 + z2 z y2 + z2 , 25 Mz = \u2212 M sin arctan p 2 y2 + z2 y y2 + z2 . 26 Calculating the partial derivatives Mx / x, My / y, and Mz / z by using Eqs. 24 \u2013 26 , we obtain the following expressions: Mx x = 0, 27 My y = \u2212 Mp3yz 8 3 1 + p2 4 2 y2 + z2 3/2 y2 + z2 6 + Myz y2 + z2 1 + p2 4 2 y2 + z2 , 28 Mz z = Mp3yz 8 3 1 + p2 4 2 y2 + z2 3/2 y2 + z2 6 \u2212 Myz y2 + z2 1 + p2 4 2 y2 + z2 ",
            "202 On: Thu, 18 Dec 2014 07:41:10 In this section we show that if the magnetization M of the magnet has still a helicoidal orientation, but is not the same as the normal n\u2212n that passes through the generic point P of the cylindrical helix , then the volume charge density M P is not equal to zero. As a starting point, let us consider the left handed helicoidal magnet characterized by a constant value of the magnetization magnitude M. As illustrated in the previous section, M is oriented along the normal n\u2212n. Now we rotate M so that it defines an angle S in the plane YZ with respect to n\u2212n. In Fig. 7 c , after the rotation S, M is denoted by the symbol M . The magnitude of M is M and is equal to M, M = M . 38 As illustrated in Fig. 7 c , the components My and Mz reported in Fig. 5 a become My and Mz , respectively. Moreover, observing Figs. 2 b and 7 c we see that the component Mx of M is equal to the component Mx of M. Then, an equation analogous to Eq. 14 is valid, Mx = M cos . 39 Substituting Eq. 23 in Eq. 39 , we can write the explicit expression of Mx , Mx = M cos arctan p 2 y2 + z2 . 40 Observing again Fig. 7 c , since the magnitudes of M and M are equal to M Eq. 38 , we can write the following equations: My = \u2212 M sin sin \u2212 + S , 41 Mz = \u2212 M sin cos \u2212 + S , 42 where sin \u2212 + S = sin \u2212 cos S + cos \u2212 sin S, 43 cos \u2212 + S = cos \u2212 cos S \u2212 sin \u2212 sin S",
            " If we consider again the magnetization M oriented along n and its magnitude M = M =constant, from Eq. 8 we obtain the surface charge density M1 in each point of S1, M1 = M . 85 In the same manner we compute M2 on the surface S2, M2 = \u2212 M . 86 On the contrary, on S2 n has an opposite orientation with respect to M, therefore, in Eq. 86 , M has the sign \u201cminus.\u201d In relation to the rectangular surface S3, between n and M, an angle equal to /2+ is defined in each point of S3. By applying again Eq. 8 , the corresponding surface charge density M3 is M3 = \u2212 M sin . 87 Because from Fig. 5 b it results sin = p p2 + 4 2r2 . 88 Substituting Eq. 88 in Eq. 87 we obtain M3 = \u2212 M p p2 + 4 2r2 . 89 With reference to the surface S4, the angle between n and M is equal to /2\u2212 . Then, by Eq. 8 we carry out M4 = M sin . 90 Equations 88 and 90 combine to yield M4 = M p p2 + 4 2r2 . 91 Finally, in each point of the surfaces S5 and S6 n has always a perpendicular orientation with respect to M. Consequently, on these surfaces Eq. 8 gives the surface charge densities M5 = 0, 92 M6 = 0. 93 The evaluation of the magnetic flux B around a cylindrical helicoidal magnet with the helical magnetization of the kind considered in the previous sections is based only on the surface charge density M"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001626_0094-114x(81)90040-9-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001626_0094-114x(81)90040-9-Figure1-1.png",
        "caption": "Figure 1.",
        "texts": [
            " With a double infinite set of possibilities of where this extreme normal could be located, the line connecting the robot's hand to its base cannot be expected to coincide with it. Another approach is presented here with a geometric proof. The problem of multivariable optimization is solved by a rapidly converging algorithm. Four parameters are needed to specify the geometry of each member of a general manipulator. These consist of the link ai~ and the offset S t, the angle 0j which measures the relative angular displacement of successive links, and the angle a# which measures the relative angular displacement of successive offsets (Fig. 1). The angle 0 r becomes the joint variable and must admit a 360 degree rotation for this analysis. It is usually restricted due to mechanical limitations. These parameters have been developed into loop equations[3, 4] which express the combined effect of displacement and orientation as one proceeds from the base to the hand. These equations are not derived here, but a brief listing is given in the Appendix. s3 tApplications Manager, Interactive Computer Graphics Center, Rensselaer Polytechnic Institute, Troy, NY 12181, U"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000545_rob.4620060405-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000545_rob.4620060405-Figure2-1.png",
        "caption": "Figure 2. Coordinate frame for a link.",
        "texts": [
            "^ that are based on inertial coordinates, and which require the use of finite strain beam theories capable of treating the resulting large displacements and finite deformations. In order to show the implementation aspects of the new formulation the authors will consider the application of this approach to flexible planar robots. The procedure however carries over to the three dimensional case with no further difficulties. Let us consider a planar robot formed by elastic beam members. The configuration of a link S, is defined as illustrated in Figure 2. The floating frame (Oi, x , y ) attached to St is characterized by the set of coordinates ( X , ( t ) , x(t), Oi(t)) . The elastic deformation at a given section P of S, is defined by (u,(x, t ) , u,(x, r ) , @ ( x , I)), which represent the displacements and rotations with respect to the moving frame. The kinetic energy of Si is Serna and Bayo: Forward Dynamics of Elastic Robots 37 1 where Li and m represent the length and the mass per unit length of the link S i ; 77 is the radius of gyration, v and 8 are the velocity and rotation of the section P, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002538_bf01515877-FigureI-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002538_bf01515877-FigureI-1.png",
        "caption": "Fig, I, Schematic diagram of generalized squeezingflow experiment, a = 3.75 cm",
        "texts": [
            " With both instruments there was no detectable normal force, hence v ~ - v2 is not greater than 40P a at rates of shear up to 1000s -1 and v~ is not greater than 10Pa at rates of shear up to 200 s- 1. The third and final comparison, with greases C (from rel. (1)) and E (from this work) is more I: range of peak values of vl using cone-and-plate rheogoniometer x: post overshoot values of T using cone-and-plate rheogoniometer qualitative in view of the slight difference in composition. For this comparison we refer to fig. I l of ref. (1) and fig. 16 of this paper. The shear stresses for grease C (after allowance for a small overshoot) lie a few percent lower than for grease E thus showing fair agreement. On the other hand, the values of vl for grease C are widely scattered and about three times lower than for grease E. This discrepancy is another example of the yield stress interfering with the rheogoniometer measurement. It is a severe discrepancy for greases C und E since they are relatively inelastic and have moderately high yield stresses (45 Pa for grease C)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003561_j.jsv.2007.04.017-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003561_j.jsv.2007.04.017-Figure1-1.png",
        "caption": "Fig. 1. Non-cylindrical helical springs.",
        "texts": [],
        "surrounding_texts": [
            "0022-460X/$ - s doi:10.1016/j.js\nTel.: +82 1 E-mail addr\nThe pseudospectral method is applied to the free vibration analysis of non-cylindrical helical springs. The entire domain is considered as a single element and the displacements and the rotations are approximated by the sums of Chebyshev polynomials. The internal forces and moments are substituted to give six equations of motion, which are collocated to yield the system of algebraic equations. The boundary condition is considered as the constraints, and the set of equations is condensed so that the number of degrees of freedom of the problem matches the number of the expansion coefficients. Numerical examples are provided for clamped\u2013clamped, free\u2013free, clamped\u2013free and hinged\u2013hinged boundary conditions. r 2007 Elsevier Ltd. All rights reserved.\n1. Introduction\nPrevious investigations on the free vibration of non-cylindrical helical springs [1\u20136] were based on the multielement methods such as the transfer matrix method. The set of equations was expressed as\nd\ndy fX \u00f0y\u00deg \u00bc \u00bdZ fX \u00f0y\u00deg (1)\nwith the state vector\nfX \u00f0y\u00deg \u00bc UtUnUbOtOnObF tFnF bMtMnMbf gT, (2)\nwhere the differential matrix [Z] was a function of R(y). U, O, F and M represent the displacements, the rotations, the internal forces and the internal moments, respectively. Subscripts t, n and b stand for the tangential direction, the normal direction and the binormal direction. Because the horizontal radius R(y) is not constant for non-cylindrical helical springs they had to employ relatively large number of elements to compute the natural frequencies. Busool and Eisenberger [7] set six equations of motion, where dR(y)/dy as well as R(y) was included, and computed the natural frequencies with a smaller number of elements.\nRecently, Lee [8] applied the pseudospectral method to the free vibration analysis of cylindrical helical springs. In the pseudospectral method, the entire domain is considered as a single element and the governing\nee front matter r 2007 Elsevier Ltd. All rights reserved. v.2007.04.017\n6 9321 2589; fax: +82 41 862 2664. ess: jinhlee@wow.hongik.ac.kr.",
            "equations are collocated at a number of collocation points inside the element. Since each spectral coefficient is determined by all the collocation point values the pseudospectral method can be made as spatially accurate as desired through exponential rate of convergence with grid refinement. Moreover, neither numerical differentiation nor numerical integration process is associated with the present method. The differentiations of basis functions can be performed analytically, which enhances the accuracy of the solution of the pseudospectral method.\n2. Formulations for non-cylindrical helical springs\nFigs. 1 and 2 describe typical non-cylindrical helical springs and the schematic geometry of a helical spring. R(y) is given for barrel and hyperboloidal types from\nR\u00f0y\u00de \u00bc R1 \u00fe \u00f0R2 R1\u00de 1 2y Y\n2\n(3)\nand for conical type from\nR\u00f0y\u00de \u00bc R1 \u00fe \u00f0R2 R1\u00de y Y , (4)\nwhere (0pypY \u00bc 2pnc) and nc is the number of turns of the helix. Yildirim [2] derived the equations of motion for the free vibration of a helical spring as\nF 0t CF n \u00bc o2 rAR C Ut; F 0n \u00fe CF t SF b \u00bc o2 rAR C Un, (5a,b)\nF 0b \u00fe SFn \u00bc o2 rAR\nC Ub; M 0\nt CMn \u00bc o2 rJR\nC Ot, (5c,d)\nM 0 n\nR C Fb \u00fe CMt SMb \u00bc o2 rInR C On; M 0 b \u00fe R C F n \u00fe SMn \u00bc o2 rIbR C Ob (5e,f)\nat natural frequency o in rad/s, where the notation 0 stands for the differentiation with respect to y. C and S represent cos a and sin a, where a is the pitch angle of the helix. A, In, Ib and J are the cross-sectional area, the",
            "ARTICLE IN PRESS\nJ. Lee / Journal of Sound and Vibration 305 (2007) 543\u2013551 545\nsecond moments of area with respect to the normal axis and to the binormal axis, and the torsional moment of inertia of the cross-section.\nWhen the range of the independent variable is given by (0pypY), it is convenient to use the normalized variable\nx \u00bc 2y Y\nY 2 1; 1\u00bd . (6)\nThe displacements and the rotations are expressed as sums of Chebyshev polynomials as follows:\nUt\u00f0x\u00de \u00bc PK\u00fe2 k\u00bc1 akTk 1\u00f0x\u00de; Un\u00f0x\u00de \u00bc PK\u00fe2 k\u00bc1 bkTk 1\u00f0x\u00de; Ub\u00f0x\u00de \u00bc PK\u00fe2 k\u00bc1 ckTk 1\u00f0x\u00de; Ot\u00f0x\u00de \u00bc PK\u00fe2 k\u00bc1 dkTk 1\u00f0x\u00de; On\u00f0x\u00de \u00bc PK\u00fe2 k\u00bc1 ekTk 1\u00f0x\u00de; Ob\u00f0x\u00de \u00bc PK\u00fe2 k\u00bc1 f kTk 1\u00f0x\u00de; (7)\nwhere ak, bk, ck, dk, ek and fk are the expansion coefficients. K is the number of collocation points. Tk(x) is the Chebyshev polynomial of the first kind defined as\nTk\u00f0x\u00de \u00bc Tk \u00f0cos f\u00de \u00bc cos kf \u00f0 1pxp1\u00de, (8)\nwhere f \u00bc cos 1 x. Its derivatives with respect to x are\ndTk\u00f0x\u00de=dx \u00bc k sin kf= sin f; d2Tk\u00f0x\u00de=dx 2 \u00bc k2 cos kf=sin2 f\u00fe k cos f cos kf=sin3 f \u00f0 1oxo1\u00de\n( (9)\nand\ndnTk=dx n x\u00bc 1 \u00bc \u00f0 1\u00de k\u00fen Yn 1 p\u00bc0 \u00f0k2 p2\u00de=\u00f02p\u00fe 1\u00de (10)\nat x \u00bc71."
        ]
    },
    {
        "image_filename": "designv11_28_0003538_iecon.2008.4758160-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003538_iecon.2008.4758160-Figure2-1.png",
        "caption": "Fig. 2- A 6x4 doubly salient SRM [5].",
        "texts": [
            " This paper presents a comparison between two converters that can be used both in wind powered SRG and in hydropower plants. The tests result shows that the conventional half bridge converter, largely used, is not a good choice. A reduced switches count converter emerges with some remarkable advantages that are shown. The switched reluctance machine \u2013 SRM is an unsuccessful old idea now renewed by the recent power electronics and microprocessors developments. It is a doubly salient poles arrangement as showed in Fig. 2. It works as a generator as well as a motor just depending on the firing angles [3]. The inductance of an excited winding reaches its maximum when a pole of the rotor is aligned with the stator pole corresponding to this winding. This is a position of stable equilibrium and the natural trend is the alignment of these poles in the SRM. When the rotor is moved from the aligned position by a mechanical agent, the resulting torque produces a back electromotive force (EMF) in addition to the applied voltage and then the machine generates electrical power acting as a SRG"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000449_isie.2001.931878-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000449_isie.2001.931878-Figure3-1.png",
        "caption": "Fig, 3, Rcprcscntation of position and velocity vectors at p, Fig. 4. Surface charge densities for the motion of the disk in the y direction.",
        "texts": [
            " A direct current is applied to the coil wound around the electromagnet. The conductive disk rotates a t a constant angular velocity w in the counter-clock wise (CCW) direction. All the unprimed variables are represented in the fixed frame(zy coordinate) located at the center of the air gap bctween the pole faces. All the pr;imed variables are represented in the moving frame(z y coordinate) attached to the center of the rotating disk. r and r\u2019 are the displacement vectors to the point P from the fixed frame and the moving frame centers as shown in Fig. 3, respectively. v is the velocity vector at the point P with respect to the moving frame and its magnitude is expressed as T\u2019W. From Fig. 3, by using the geometrical relations of y = r\u2018sin 4\u2019 and R + z = r\u2019 cos $\u2019, the velocity components of w, and wy in the fixed frame are respectively, (2) w, = usin$ = w r sin$ = wy zly = w cos 4\u2019 = wr\u2018 cos$\u2019 = w ( ~ + z) . (3) I ! v is represented by -w,i + w y j , where i and j are the unit vectors of z and y directions, respectively. 679 ISIE 2001, Pusan, KOREA Now, we face on the problem how we can calculate the surface charges which are forced to move to the end of the pole projection area. For the motion of the disk in the y direction, the positive charges move rightward and the negative ones move leftward as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002578_tmag.2006.871596-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002578_tmag.2006.871596-Figure3-1.png",
        "caption": "Fig. 3. Interface of magnetized materials. Each side\u2019s equivalent magnetizing current is displayed for the proposed generalized method when in contact.",
        "texts": [
            " The main idea of the proposed generalized magnetizing current method is that flux density due to the opposite material\u2019s current is added to the external flux density as in (5). This is because, even if magnetized bodies are in contact, as shown in Fig. 1(b), their equivalent surface currents are supposed to still be effective for the force calculation. This concept should be differentiated from the free charge cancellation phenomenon which occurs in the interface of conducting materials. From Fig. 3, and are the induced magnetizing current densities at the surface of material 1 and material 2, respectively, from the application of (3) at each region. These current densities are the sources of and , as in Fig. 3. In this case, the flux densities at the material 1 and 2 are expressed as, respectively (6) (7) Due to the fact that and , the external flux density is same as (4) in the conventional method. In other words, is the average of the magnetic flux density on both sides of the surface. It should be noted that the flux density due to the surface current of material 1 affects the flux density at the region of material 2, and vice versa. By upgrading (5), the new surface force and at each material are written as, respectively (8) (9) where , and and are tangential unit vectors of each material region"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000752_bf03179258-Figure13-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000752_bf03179258-Figure13-1.png",
        "caption": "Fig. 13. Cross sectional shape of a solidified shell in the flow pass of melt (200 rpm, 20% of melt).",
        "texts": [
            " Mold filling behavior [23] The melt flow and mold filling behavior under the horizontal centrifugal force field (0-30G) are examined by casting experiments, in which the amount of alloy melted and poured at 1950\u00b150 K, 0.8Pa in an electron beam furnace is adjusted to be less than that required for the complete filling of the casting tree [23]. In a typical survey of castparts, the shapes of two simple castparts in the tree consisting of two mold cavities (80\u00d780 \u00d710 mmT with a gate of 40W\u00d720L\u00d710 mmT) are almost the same. The cross-sectional view of the solidified shell at the inside walls of the gate and mold cavity shown in Fig. 13 suggests that the flow pattern of the melt is as follows: 1) Melt flows into mold cavities with increasing velocity with distance from the axis of rotation in an anti-clockwise direction, keeping contact with the vertical walls of the gates and cavities on the anti-rotation side. 2) Solidification at the vertical walls is retarded (Fig. 13) and only several ten percentages of the cross sectional area of the gate are used for the melt flow. 3) Filling of the cavities with the melt proceeds prior to that of the gates and runner under the centrifugal force field, 4) Due to these results, solidification proceeds mainly from the far end of the cavity to the gate for the mass supplied into the cavity, namely in the mode of directional solidification, and 5) Thickness of the solidified shell in the upper side of the cavity is almost the same as the lower side, suggesting that gravitational force can be neglected under the centrifugal force field"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002015_j.mechmachtheory.2004.03.003-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002015_j.mechmachtheory.2004.03.003-Figure5-1.png",
        "caption": "Fig. 5. Free-body diagram of the planet gear.",
        "texts": [
            " 4, the three scalar equations of motion that are applied to the crank body can be written as F34x \u00fe F 0 34x \u00fe F14x \u00bc m4a4x \u00f021\u00de F34y \u00fe F 0 34y \u00fe F14y \u00bc m4a4y \u00f022\u00de \u00f0R34xF34y R34yF34x\u00de \u00fe R0 34xF 0 34y R0 34yF 0 34x \u00fe t34 \u00fe t034 \u00fe t14 \u00fe Tin \u00bc I4a4 \u00f023\u00de where m4 is the mass of the crank, I4 is the moment of inertia of the crank about the center of mass, and a4x and a4y represent, respectively, the magnitudes of the X and Y components of the center of mass acceleration of the crank. Furthermore, R34x and R34y can be expressed as: R34x \u00bc R4 cos h4 Rb3 cos h34 and R34y \u00bc R4 sin h4 Rb3 sin h34, and h34 (h34 \u00bc tan 1 F34y=F34x), is measured counterclockwise from the X axis to the common normal at the contact point P34. In Fig. 5, since the constant velocity joint that behaves kinematically like an articulated parallelogram, the common normal at the contact point P5i3 of the planet gear and ith disc pin is parallel to R * 4. Assuming that an external load T * 53 acts on the planet gear, and the elastic deflection at the contact point causes the planet gear to rotate a small angle Du. Since the elastic deflection at the contact point is very small, it is also assume that the force exerted by the ith disc pin on the planet gear F * 5i3 is proportional to the deflection De along the common normal at the contact point P5i3; i",
            " Therefore, the resultant frictional force f * 53 exerted by the disc pins on the planet gear can be expressed as f * 53 \u00bc Xn5 i\u00bc1 f * 5i3 \u00bc L53xF53 i * \u00fe L53yF53 j * \u00f029\u00de where L53x \u00bc l53 Pn5 i\u00bc1 sinui Xn5 i\u00bc1 D5i3 sinui sin h4 and L53y \u00bc l53 Pn5 i\u00bc1 sinui Xn5 i\u00bc1 D5i3 sinui cos h4 The total torque acting on the planet gear caused by the two forces F * 5i3 and f * 5i3 can be determined as T * 53 \u00fe t * 53 \u00bc Xn5 i\u00bc1 R * 5i3 F * 5i3 \u00fe f * 5i3 \u00f030\u00de where R * 5i3, which represents the vector from O3 to the contact point P5i3 can be expressed as: R * 5i3 \u00bc \u00bdR3d cos\u00f0h4 \u00fe ui\u00de r3d cos h4 i * \u00fe \u00bdR3d sin\u00f0h4 \u00fe ui\u00de r3d sin h4 j * . Here R3a and r3a are the radius of the circle containing rollers in the planet gear and the radius of the disc pin, respectively. Substituting Eqs. (25) and (28) into Eq. (30), gives T * 53 \u00fe t * 53 \u00bc K53tF53k * \u00f031\u00de where K53t \u00bc R3d Pn5 i\u00bc1 sin2 ui Pn5 sinui \u00fe l53D53 R3d Pn5 i\u00bc1 sinui cosui Pn5 sinui 2 664 r3d 3 775 i\u00bc1 i\u00bc1 In addition to the force exerted by the disc pins, the ring gear rollers also exert force on the planet gear. As sown in Fig. 5, when the crank rotates counterclockwise, force F * 23 and frictional force f * 23 exerted by the ring gear roller on the planet gear, and these forces cause torque T * 23 and frictional torque t * 23 with respect to the center of the planet gear. Since the roller drive has only a single tooth meshed while it is gearing, the forces acting on the planet gear exerted by the ring gear roller can be written as F * 23 \u00bc F23 cos ha i * \u00fe F23 sin ha j * \u00f032\u00de f * 23 \u00bc l23F23D23u *t 23 \u00bc l23F23D23 sin ha i * l23F23D23 cos ha j * \u00f033\u00de where D23 \u00bc x3=jx3j. Also, u *t 23 denotes the unit vector of common tangent of the contact point P2i3 and l23 is the frictional coefficient between the planet gear roller and ring gear roller. The total torque acting on the planet gear caused by the forces F * 23 and f * 23 can be determined as T * 23 \u00fe t * 23 \u00bc R * 2i3 F * 23 \u00fe f * 23 \u00bc K23tF23k * \u00f034\u00de where K23t \u00bc R3 sin\u00f0ha h3\u00de \u00fe l23D23\u00bdr3 R3 cos\u00f0ha h3\u00de and R * 2i3 is the vector from O3 to P2i3. With reference to Fig. 5, three scalar equations of motion which apply to the planet gear can be written as F53x \u00fe f53x \u00fe F23x \u00fe f23x F34x \u00bc \u00f0m3 \u00fe m3a\u00dea3x \u00f035\u00de F53y \u00fe f53y \u00fe F23y \u00fe f23y F34y \u00bc \u00f0m3 \u00fe m3a\u00dea3y \u00f036\u00de T53 \u00fe t53 \u00fe T23 \u00fe t23 t34 \u00bc I3a3 \u00f037\u00de where a3x and a3y , which represent the magnitudes of the X and Y components of the center of mass acceleration of the planet gear, respectively, can be expressed as: a3x \u00bc a4R4 sin h4D41 x2 4R4 cos h4 and a3y \u00bc a4R4 cos h4D41 x2 4R4 sin h4, where D41 \u00bc D14 \u00bc x4=jx4j. In addition, m3, m3a and I3 denote the mass of the planet gear, the planet gear roller and the moment of inertia of the planet gear about the mass center"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001681_robot.2004.1307975-Figure12-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001681_robot.2004.1307975-Figure12-1.png",
        "caption": "Fig. 12. Task Condition",
        "texts": [],
        "surrounding_texts": [
            "center. In the process to calculate MZ,, F,, is multiplied by L,. Because the output of force sensor implies the noises and the noises are also multiplied by L,, the accuracy of Mz, is not ensured. If the gain of force feedback control for M,, is increased the vibration of the manipulator will occur. On the contrary, if the gain is decreated the force to correct the orientation of the peg will not occur. At all, a adjustment of the gain becomes difficult under the condition using a long\nC. Influence of Endem Hole\nFinally, we describe the influence of a tandem hole. The positional precision is required when the tip of a peg is inserted into the second hole as shown in Fig7. When the peg is restricted by the first hole the tip of the peg P, and the gripping point Pg are located with the central focus on the middle of the first hole Po, having radii L1 and LZ respectively. Under this condition, the deflection of P, from a central axis (a horizontal broken line) is Ll/Lz times larger than the deflection of Pg.\n111. CONTROL SYSTEM\nThe experiment i s performed with manipulator PA10 made by Mitsubishi Heavy Industries. A proportional and derivative (PD) control algorithm is used to control the manipulator\npeg.\nsystem, and the input values are desired position of a gripping point on Cartesian coordinate system (Fig.8). Where, X d is desired position on Cartesian coordinate system, qd is desired joint angle of manipulator, q is current joint angle, q is joint angular velocity, and K,,, K , are feedback gains. There is a force sensor on the wrist of the manipulator. It is not used for feedback control of manipulator, but only used to observe for the evaluation of a experiment.\n1v. PROPOSED ALGORITHM\nIn this section, The algorithm that. a manipulator finds correct posture of a peg inserted into a tandem shallow hole is detailed. We call this algorithm insertion using search trajectory generation. The algorithm is shown in Fig.9. A basic idea is that firstly a manipulator recognizes the availability of insertion operation and secondly if insertion operation is available the manipulator continues the task keeping a trajectory, otherwise the manipulator searches the correct p o s t u ~ of the Peg.\nA . Fme Wrist A peg could get four degrees of freedom of posture due to the clearance, when a manipulator inserts the peg into a shallow hole(Fig.10). Where, X h , & are positions of the peg , and W X h , W Z h are posture of the peg around the hole. Combinations of four parameters make search area so large that a manipulator will not find a correct posture. Thus we make a free wrist device to reduce number of position and posture which the manipulator must correct(Fig.11). The free wrist is attached between the tip of manipulator and a",
            "gripper, and has structuTe that float part is put to the inside of the base part with balls. With the described structuh, the free wrist has stiffness for Dosition. and zero-stiffness for Dostwe\nD. Insertion Using Search Trajectory Generation We show the generation method of trajectory as follows when the manipulator recognized that an insertion operation has been unavailable.\nYd Yc- dy, (4) dy7.f = Yd -Yref, ( 5 )\n2 0 = a,dy,,f + xrefr (6) zo = azdyref + zrefr (7) Xd = Xo+dx, (8) Zd = 20 + dz, (9)\ndx = U T , cos&, (13) dz = U ri s in&, (14)\nwhere, Xd,yd,Zd are desired position of gripping point, y, y,, z, are current position of gripping point, dy,,f is distance from base position to desired position on y axis, x,,f, yTef, zref are the base position to generate desired position. dx.du.dz are distance from current Dosition to desired . I \", position, ax,az are inclinations of insertion direction, r o is an initial radius at search action, dr is the radius increase when the trajectory makes one revolution, N is the number\naround wX,, wY, and wZ,. By virtue of the free wrist, the number of position and posture to correct can be reduced from two directions of position and two orientations of posture to two directions and zero orientation.\nE. Condition of Experiment\nof search circle division, i is the continuation number counted while the insertion operation is unavailable(See Fig.P.), 00 is initial angle of search, L,,, is the length of inserted peg, and Lt is the full length of peg.\nIn this paper, a manipulator starts the insertion operation with condition that the tip of a peg was already inserted into the shallow hole. Firstly, the manipulator inserts the peg into negative direction on y axis with force F. Secondly the manipulator changes the trajectory of gripping point according as insertion operation is available or not.\nC. Recognition of Task Condition\nThe period of the recognition of insertion availability and changing the mathod of trajectory generation T, is enough large than manipulator control period Tc. Because to take the effect of change a trajectory and to recognize the insertion availability need the enough time. In this paper, task condition is evaluated as follows\nCondition A = Ivy1 > Ivydl U a~vy > 0, (3)\nwhere, V, is insertion velocity, Vyd is required insertion velocity and ay is insertion acceleration. If condition is A the manipulator continues the operation with keeping the trajectory, otherwise the manipulator behave to find the condition in which an insertion operation is available.\ndy is set to make the insertion force F suitable. The trajectory of gripping point on the xz plane is shown in Fig.13. In this paper, we adopt Xd,Yd,Zd at the last time when the insertion is available as xr..f, yTef, zref. We consider that inclinations of insertion direction make the jamming phenomenon. To avoid jamming, the manipulator should estimate the inclinations and revise the insertion direction. The revision method is that a,dy,,j, a,dy,,f are added to desired position of gripping point respectively. The inclinations a and a, are calculated with linear regression using the position of gripping point at the time when insertion operation is available. We illustrated the desired position of the gripping point, the base position to generate desired position, and the current position in Fig.14.\nFig.15 shows the cone where gripping point can be placed, where pa is radius ofcircle where gripping point can be placed when the task begins, and ppc is radius of circle when peg is inserted. The ideal condition of peg and hole is one-point contact, because friction force of one-point contact is less than one of tw&point contact. However the positioning accuracy of manipulator is required to realize the one-point contact, because the deeper peg is inserted the smaller pc becomes. Therefore, the method to realize one-point condition and to",
            "position of gripping point and current position on the xy plane are shown in Fig.20,and The trajectories of desired position of gripping point and current position on the yz plane are shown in Fig.21. Because insertion direction is negative direction on y axis, the laspes of the time are shifted from right to left in Fig.20 and Fig.21. Finally the estimated inclinations a, and a, are shown in Fig.22.\nprogress the insertion operation even if two-point occurs are needed. Thus, firstly the search trajectoty generation is adopted to recover from jamming condition to one-point condition. In order to realize recovery, parameters of algorithm must be set adequately. The ideal parameter of T< is pa, but with consideraion of friction of joint ri must be increased. In this paper, ro equals pa, Secondly, the estimation of inclinations is adopted to avoid jamming even with two-point condition.\nNext, we show the equation to generate the trajectory as follows.\nYd = Yc-dY, (15) d y r e f = Yd - Y r e f > (16)\nS d = a,dy,,f + X , e f , (17) Zd = a&,f + zref. (18)\nThe algorithm means to change the trajectory generation method according to insertion availability in order to avoid the jamming phenomenon.\nV. EXPERIMENT To verify the validity of the proposed method, the experi-\nment is performed with the manipulator system.\nA. Condition ofExperimenta1 For the experiment, we set the value for the abovementioned parameters of insertion using search trajectory generation algorithm as follows. T,=Zms, T8=2OOms, dr=lmm, ro=lmm, and V , d = l h d S .\nB. Experimental Result The appearace of experiment is shown in Fig.16, and the trajectory of gripping point on the insertion direction is shown in Fig.17. The absolute value of the insertion velocity is shown in Fig.18, and a dotted line means Vyd.\nThe force on x and z direction measured by the force sensor on the wrist are shown in Fig.19. The trajectories of desired\n- . -\nFirstly, as shown in Fig.17, the jamming phenomenon is caused at the 1.6 seconds. Then the force on x and z direction grows respectively as shown in Fig.19. At the same time, The insertion velocity was decreased, and the'manipulator starts make trajectory to search the correct posture of the peg by recognition that insertion operation is unavailable. The jamming phenomenon is avoided by search trajectory generation at 2.8 seconds.\nSecondly, the manipulator estimates the inclinations of insertion direction as shown in Fig.22. Because the manipulator has stopped the estimation until manipulator collects enough data of trajectory, the estimated inclinations are zero from 0 seconds to 4 seconds in Fig.22. The desired position of gripping point has inclinations on the xy plane and the yz one in the area where a position on y axis is less than 620 mm. That is the effect of estimated inclinations a, and a,. We can see the difference between one-point contact and two-pint contact in Fig.18. The insertion velocity until 1.4 seconds is faster than that after 2.8 seconds. Therefore, it is expected that one-point contact occurs from start to 1.4 seconds and twopoint contact occurs from 2.8 seconds to last. When two-pint contact occurs, the estimation of insertion direction is effective for peg to move forward along inside of the hole.'\nFinally, the estimation of insertion direction functions effectively and the process which peg is inserted into the second hole is achieved without collision phenomenon.\nVI. CONCLUSION\nWe focused on the task to insert a long peg into tandem shallow hole, as one of the difficult assembly task example to which we can not apply such conservative methods like RCC device and passive force sensor feedback. Then, we proposed the method using not the force sensor feedback but the search trajectory generation to correct peg posture. We also proposed the method to estimate the inclination of insertion direction. The estimation of the inclination avoided the jamming phenomenon, while two-point contact had occured. Finally, we verified the effectiveness by the experiment."
        ]
    },
    {
        "image_filename": "designv11_28_0001806_1.2199857-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001806_1.2199857-Figure2-1.png",
        "caption": "Fig. 2 Model of the system",
        "texts": [
            "org/about-asme/terms-of-use Downloaded F chanics problems with friction, however, this condition is not sufficient to guarantee that the objects will not slide or roll relative to each other and the pusher. In this section, we will obtain some conditions for the pusher motion to push a chain of n objects stably. We first show the mathematical condition where each edge contact can support forces through the edge and inside the friction cone. By discretizing the COR space, we then show the condition for the pusher motion to stably push two objects. We further show that the proposed method can by simplified by introducing some assumptions. 4.1 Model of the System. Figure 2 shows the model used in this research where two polygonal objects are pushed by a pusher whose translational/rotational velocities are controlled. Let fC be the contact force which object 2 exerts on object 1 at the point xC rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 08/16/2017 where the line of action passes through. Also, let fF be the contact forces which the pusher exerts on object 2 at the point xF where the line of action passes through. The position vectors are defined by: xC = CxC1 + 1 \u2212 C xC2, 0 C 1 1 xF = FxF1 + 1 \u2212 F xF2, 0 F 1 2 where xCj and xFj j=1,2 denote the position vectors at the edge of the contact segments between objects 1 and 2 and the pusher and object 2, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002971_robot.2006.1642273-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002971_robot.2006.1642273-Figure4-1.png",
        "caption": "Fig. 4. Notation for the docking configuration computation in the case of two sensors. On the left image, the couples landmark-perception are represented. For each sensor i, landmark lji and perception pj i match together. Landmarks are carrier line of segments. The current robot configuration is q. Current sensors positions are respectively x1(q) and x2(q). The sensors positions at the end of the trajectory are x1(qend ) and x2(qend ) and they are not solutions of observation function (2) for any couple (lji ,pj i ). On the right image, sensors docking positions xdock",
        "texts": [
            " We define an observation function f that maps a sensor position x and a landmark from L with a perception from P as : f : R nl \u00d7 SE(3) \u2192 R np (l,x) \u2192 p = f(l,x) (2) What is important to notice here is that the sensor position xdock when the robot is at docking configuration is solution of equation (2). Then, given a sensor docking position xdock, the set of nm couples m = (lj ,pk) that satisfy equation (2) is noted M. It is the set of matches landmark-perception. We can define a batch observation function F that map all the elements of M from a given sensor position x. Let L and P be such that: P = F (L,x)\u239b \u239c\u239d p1 ... pnm \u239e \u239f\u23a0 = \u239b \u239c\u239d f(l1,x) ... f(ln m ,x) \u239e \u239f\u23a0 (3) Figure 4 presents these notations in a docking task scene with two sensors. The robot being at a current configuration q, it must compute the docking configuration qdock (right image). At this docking configuration, the observation function (2) is satisfied for all matched couples landmark-perception:(lji ,p j i ), for each sensor i. That is: \u2200i, j pj i = f(xdock i , lji ) 3) Probabilistic framework: Because we do not measure the true values of any of the preceding variables, we model them as real random variables",
            " Because the real values of the variables are unknown we can use only the estimated values. Thus equation (2) is never exactly satisfied and we are bound to find the couples that \u201cbest\u201d match. The criterion we use to evaluate the likelihood of a match is the Mahalanobis distance between the expected perception and the actual perception. The expected perception p\u0302j of the landmark l\u0302j from the sensor position x\u0302 is given by equation (5). At this time, x\u0302 = x(q\u0302 ) = x(qend) is the sensor position at the last configuration on the planned trajectory (see figure 4). For a given perception pk, the Mahalanobis distance (Djk)2 is then defined as: (Djk)2 = (pk \u2212 p\u0302j)Vp(pk \u2212 p\u0302j)T (8) This distance follows a \u03c72 np distribution, with np the dimension of the observation vector p. Algorithm 1 Matching algorithm for each sensor i do \u03c72 95 \u2190 p(\u03c72 np = 95%) x\u0302i \u2190 xi(q\u0302 ) Mi \u2190 \u2205 for each observation pk i in Pi do D2 \u2190 \u221e lbest \u2190 \u2205 for each landmark lji in Li do p\u0302j i \u2190 equation (2), lji and x\u0302i (Djk)2 \u2190 equation (8), p\u0302j i and pk i if ((Djk)2 < \u03c72 95 \u2227 (Djk)2 < D2 ) then lbest \u2190 lji D2 \u2190 (Djk)2 end if end for if lbest = \u2205 then insert {pk i , lbest} in Mi end if end for end for Algorithm 1 describes the matching"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002957_tmag.2006.871448-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002957_tmag.2006.871448-Figure6-1.png",
        "caption": "Fig. 6. Flux distribution for d-axis inductance calculation of the SM.",
        "texts": [
            " The inductances are calculated at 100 Hz for both the SM and DRM, and the calculated results are shown in Table I (the rows \u201cPM has no magnetism\u201d). Then both saliency and saturation are considered, i.e., the influence of the flux produced by the permanent magnets is considered. The calculated results are also shown in Table I (the rows \u201cPM has magnetism\u201d). For the d-axis inductance calculations of the SM, the flux distribution with the magnetism of the permanent magnets considered is shown in Fig. 6. It can be seen that the d-axis magnetic path is much more saturated than the q-axis for both the SM and DRM, and the d-axis magnetic path of the DRM is more saturated than that of the SM. As can be seen from Table I, when only the saliency is considered, for the DRM, the inductances obtained from the phase voltage and line voltage are almost the same, and the d- and q-axis inductances are almost the same as well; for the SM, they are different from both the two aspects. This means that saliency (only the SM has obvious saliency) is one reason for the two kinds of inductance differences. When the magnetism of the permanent magnets is also considered, for the DRM, both the d- and q-axis inductances and the inductances obtained from the phase and line voltage are different. This is because of the d-axis magnetic-path saturation. It can be seen from Fig. 6 that the d- and q-axis magnetic path have quite different saturation levels, which will lead to different permeances and different inductances. Of course the d-axis saturation also has influence on the SM inductances, which can be seen from Table I. The SM inductances are influenced by both the saturation and saliency, and the DRM inductances are only influenced by the saturation, but the two kinds of inductance differences are more serious for the DRM. This is because of the higher level of d-axis saturation of the DRM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001278_robot.1998.680976-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001278_robot.1998.680976-Figure1-1.png",
        "caption": "Fig. 1. Human-robot coordination",
        "texts": [
            " To overcome these restrictions, a totally new and attractive concept, human-robot coordination, was studied in [l] and [2], etc. The advantages of the humanrobot coordination are well stated in [l] and will not be further addressed here. Other related work including manipulator extender ([3]) and teleoperation ([9]) which also include force interaction between human arm and robot. However, only in the human-robot coordination both human hand and robot manipulator have contact with the object (Fig. 1). In order to implement the human-robot coordination, compliant motion control ([l]), and reflexive motion control ( [ a ] ) were used. In both mechanisms, a wrist force sensor is installed on the end-effector of the robot. When the human operator moves the object, a force (including moment) is exerted on the endeffector. The force sensor interprets the desired motion of the human and directs the robot to make proper motions. Unfortunately, rotational motion of the object has never been seriously addressed in the previ- ous studies"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002372_1.2167651-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002372_1.2167651-Figure1-1.png",
        "caption": "Fig. 1 The planar and the spherical SBL",
        "texts": [
            " Using the change of variables x= cos and y= sin in Eqs. 5 and 8 , and then solving for with respect to , the polar equation of the path is as follows: = a \u2212 b3 cos + b1 2 \u2212 b3 2 sin2 18 The important point about Eq. 18 is that this equation is valid rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/201 for all cases of type 2. Equation 18 is more appropriate than Eqs. 5 and 8 in the applications. 4.1 The Parametric Equation. Let again consider the spheri- cal SBL depicted in Fig. 1 b . Point C lies on the geodesic arc AB , so as the mechanism moves, the location of point C is changed on the surface of the sphere. To derive the parametric equation of the coupler curve for point C, according to Fig. 11, axis x1 passing through O should coincide with axis x6 passing through C. Let us assume the coordinate system x1y1z1 such that axis x1 will coin- cide with QO and axis y1 will coincide with the plane of QO and QB . Axis x1 can be transformed to the axis x3 when the coordinate system x1y1z1 transforms under the Eulerian orthogonal transformations as a rotation about x1 through and obtaining x2y2z2 and b rotation about z2 through 1 and obtaining x3y3z3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000152_ma000110q-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000152_ma000110q-Figure8-1.png",
        "caption": "Figure 8. Unit cell in (a) the original BB-5 fiber and (b) the elongated one depicted from the variation in the X-ray patterns under elongation shown in Figure 7. The tilt direction of the unit cell coincides with c-director of the SmCA structure. The fiber axis is in a vertical direction.",
        "texts": [
            " On the other hand, the reflections on the (01l) line in Figure 7 do not shift so much by the elongation (compare Figure 7a with Figure 7b-d). Especially, the (010) reflection is not affected at all. In contrast, the reflections on the (10l) line shift significantly. These simply indicate that the tilting arises along the (010) planes. As a reason for this particularly preferred direction of tilt, this direction may agree with a c-director (or tilt direction) of the mesogenic groups in the SmCA phase. Figure 8 illustrates the tilting of unit cell in a real space. The diffraction patterns derived from the tilting of unit cell can be obtained by using the equation reported by Bunn et al.14 They are compared with the observed ones in Figure 9. All the predicted reflections given in a right-hand side section of the figure showed a good agreement with those of the actually observed patterns (left-hand side) in every elongated fiber. We thus reach the conclusion that the elongated fibers form the same crystal as the original fiber but the crystal layer is tilted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000603_2001-01-1007-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000603_2001-01-1007-Figure9-1.png",
        "caption": "Fig. 9. Vector interpretation of the k-th order harmonic component of the cylinder torque",
        "texts": [
            "3 0.4 0.5 0.6 0.7 0.8 0.9 IMEP [MPa] Cycle Number Cylinder Number Fig.7. Variation of the IMEP of individual cylinders for 10 successive cycles. Uniform cylinder operation, 1187\u00b12 rpm. A harmonic component of the gas pressure torque may be represented by the projection of a rotating vector on the crankshaft axis [5]. For a given harmonic order k the vector has a phase \u03d5k with respect to the top dead center (TDC) position of the corresponding crank and rotates k-times faster than the crankshaft (Fig. 9). If the crank of cylinder \u201ci\u201d has a position defined by the crank angle \u03b8, the corresponding vector will take a position defined by the angle ikk \u03d5\u03b8 + . Thus, for the half harmonic order (k=1/2), the vectors will have the same phase angle diagram as in Fig. 2, but rotated with the angle k\u03d5 . Because of the random character of the vectors interpreting a harmonic component of the cylinder torque, their magnitude and phase will be randomly distributed. Assuming a normal distribution, the tip of the vector interpreting the harmonic component of order k for cylinder \u201ci\u201d will be situated inside the ellipse of dispersion having as half axes the values ikT\u03c33 and iikT \u03d5\u03c33 (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003930_robot.2008.4543509-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003930_robot.2008.4543509-Figure2-1.png",
        "caption": "Fig. 2. View of arm curl machine showing the linear actuator connected to lever and belt drive.",
        "texts": [
            " Isolation of muscle groups will facilitate clinical evaluation of the machine. To accelerate the development process, a commercial exercise machine was retrofitted with an active drive system rather than building a new device from scratch. This strategy allowed the development to focus on controls and software rather than the hardware. The commercial version of the Keiser Arm Curl 250 machine using a pneumatic piston to push on a lever which then pulls on the arm curl bar using a rubber belt attached at the other end of the lever as shown in Figure 2. To achieve the high control bandwidths required for this application, the piston assembly was replaced with an UltraMotion actuator, which consisted of a lead screw with 0.125 in (0.3175 cm) pitch driven by an electric motor. The lead screw had a 20 cm stroke (greater than the original piston) and was capable of moving approximately 45 cm/sec unloaded, and 20 cm/sec with a 445 N load. Because of the complexity of the cam, lever, and drive belt assembly and absence of mechanical drawings, the mapping between the lead screw displacement and the elbow flexion angle was determined experimentally"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000584_5326.868444-Figure14-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000584_5326.868444-Figure14-1.png",
        "caption": "Fig. 14. Operational space errors in discussing robustness to the coefficient",
        "texts": [
            " By testing the workspace errors we noticed that the distortion of the constant term has the greatest influence to the performance. In fact, the results are distinguished between the three cases: no distortion of the constant term, increase of 20% of the constant term value, and its decrease of 20%. This leads to a conclusion that SA-based procedure is the most sensitive to the variation of constant term coefficient. Workspace errors with distorted coefficients of higher indices, one at a time, are depicted in Fig. 14. Each trace depicts the error due to % change of only one of coefficients. The largest error corresponds to the variation of the coefficients of quadratic terms , and decreases with distortion of coefficients with larger indices . Therefore, we conclude that the influence of higher coefficients can be neglected if the maximum accuracy of RR is not of primary importance. In that case, the workspace errors that correspond to the neglected coefficients behave similarly to the case of distorted coefficients but the errors are twice larger"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000865_s0389-4304(03)00084-5-Figure17-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000865_s0389-4304(03)00084-5-Figure17-1.png",
        "caption": "Fig. 17. Interior spaciousness comparison between 2WD model and 4WD model with motor-assisted 4WD system.",
        "texts": [
            " The motor-assisted 4WD system is 15% lighter in weight than existing mechanical 4WD systems. That weight reduction was achieved by adopting a simple system configuration consisting only of a generator and a rear-wheel drive unit, without using any dedicated batteries or AC motor, and discontinuing the mechanical means of power transmission required in conventional mechanical 4WD systems. In addition, interior spaciousness comparable to that of a 2WD vehicle is also achieved with this system because it does not have a propeller shaft or a transfer case. Fig. 17 compares the interior spaciousness of 2WD and 4WD models when the motor-assisted 4WD system is applied to a small front-wheel-drive car. The motorassisted 4WD system allows the same vehicle layout as that of the 2WD model, except for the rear floor. The difference in the rear floor height between the 2WD and 4WD models is kept to around 90mm. To minimize deterioration of fuel economy relative to the 2WD base vehicle, a clutch provided in the reduction gear can be disengaged to reduce friction torque in driving situations where drive torque is not needed at the rear wheels"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000327_01445150310501208-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000327_01445150310501208-Figure4-1.png",
        "caption": "Figure 4 Laminate orientation considerations in tool design",
        "texts": [
            " For successful tool manufacture, it is vital to orientate the laminations in a direction that is conducive to obtain good integrity bonds between the laminates, and to minimise the occurrence of poorly supported laminates during the brazing/bolting process. The orientation must also be chosen that suites geometrical features of the tool. For example, a tool built with horizontal laminations may Rapid laminated die-cast tooling Gregory John Gibbons et al. Assembly Automation Volume 23 \u00b7 Number 4 \u00b7 2003 \u00b7 372\u2013381 D ow nl oa de d by K un gl ig a T ek ni sk a H \u00f6g sk ol an A t 1 1: 30 3 0 Ja nu ar y 20 16 ( PT ) have \u201cislands\u201d that require fixing in position prior to bonding; dowels or temporary supports are suitable methods to achieve this (Figure 4). For component manufacture, the anisotropic thermal conductivity of the tool becomes important, with high cooling rate applications requiring the higher thermal conductivity offered by the vertical lamination orientation. It has been found, both through laboratory evaluation and casting trials, that horizontal lamination is unsuitable for die-casting applications due to the tendency for lamination debonding to occur. Unlike conventional CNC tool manufacture, laminated tooling requires the generation of NC code for the cutting of the tool laminations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001616_pime_proc_1985_199_127_02-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001616_pime_proc_1985_199_127_02-Figure7-1.png",
        "caption": "Fig. 7 Schematic diagram of test rig",
        "texts": [
            " In an attempt to reduce the variation between theory and experiment it has been found necessary to greatly improve on the experimental technique and also to obtain very accurate information relating to the sizing and envelope tolerances of the manufactured components under test. This section of the paper outlines the experimental method and is followed by a description of the evaluation of the effects of departure from their design size. 1.7 The test apparatus The test rig conforms to the general design indicated in Fig. 7. The test shaft (1) and close-fitting sleeves (2) were supported in hydrostatic slave bearings (3) which took the form of combined journal and thrust bearings. The test bearing (4) positioned between the slave bearings was loaded upwards by a pneumatic load cylinder (5) which housed a piston supported in aerostatic bearings to minimize friction. The adjusting mechanism (6) permitted the test bearing to be loaded with parallel motion in the bearing clearance. The test bearing was restrained to prevent rotation without influencing the radial loading. Proc lnstn Mech Engrs Val 199 No C4 The load cylinder pressure was monitored by a pressure transducer (7). Adjusting the pressure in the load cylinder by a precision controller enabled the load to be applied to the test bearing with relative ease and in a continuously variable manner. Wayne Kerr capacitance probes (8) were mounted in line with the load as shown in Fig. 7 to record the vertical movement. Two other probes were orthogonal to the load line to record horizontal deflections. The test shaft was driven by an electric motor via a belt and pulley (9), and its speed was monitored by a tachogenerator. Provision was made for displaying the bearing supply pressure, bearing load, shaft speed, ex, ey , eres, and in a digital form. 1.8 Test bearings Two bearings were tested: a slot entry bearing and an orifice compensated bearing [the experimental work using the orifice bearing has been reported earlier in (3)]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002971_robot.2006.1642273-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002971_robot.2006.1642273-Figure2-1.png",
        "caption": "Fig. 2. Docking pattern. It consists in a set of landmarks defined relatively to a sensor. On the left image, the docking pattern defines a parking lot for a CyCab car. On the right image the docking pattern is defined relatively to the laser sensor mounted on the trailer of a robot.",
        "texts": [
            " Moreover, the end of the trajectory may also need to be adapted at the parking stage, for several reasons: \u2022 the parking process can require a precision that the localization is not able to provide, \u2022 the map used for planning may be too imprecise to be employed to park in. \u2022 the parking position may have changed. All these elements converge towards the same idea: defining the parking configuration in the global frame does not allow for parking in practical applications. The parking configuration must be defined relatively to the environment. For instance, one can define a car parking lot as: \u201cthree white lines on the ground. One on each side of the car and one in front of it\u201d (see figure 2). That is, a parking configuration can be defined indirectly through a set of landmarks to be perceived from this configuration. We call this set of landmarks a docking pattern. In this paper we address the problem of precise motion of nonholonomic systems during the parking stage. Our approach takes advantage of a nonholonomic path deformation method [6] to reach a final configuration defined relatively to the environment. The idea of defining a position as a desired sensor perception is the basis of sensor-based control",
            " As explained in the introduction, this technique does not allow precise parking, since it does not adapt the parking configuration to the environment. The concept of docking task addresses this issue. A docking task is a mission given to a robot that consists in following a planned trajectory and reaching a docking configuration. The docking configuration is not defined beforehand as a known robot location. On the contrary it is specified as a set of sensor perceptions from this configuration. The set of landmarks to be perceived when the robot is at the docking configuration is called a docking pattern. Figure 2 presents such docking patterns. On each image, the docking configuration is represented relatively to the docking pattern. Thus a docking task takes as input: - a collision free trajectory planned within a model of the environment - a set of landmarks relative to the docking configuration: the docking patterns. Figure 3 illustrates the principle of a docking task. The robot is following the trajectory planned from qinit to qend. Arriving at the end, it detects the docking pattern in the environment using its sensor",
            " Following the notation of section III-A.2, we define the docking pattern as a set of landmarks L relative to this sensor. In this experiment the landmarks are segments. The docking pattern L can be composed of any number of segments li. In order to be robust to occlusions, the matching algorithm of section IIIB treat segments as straight lines. In this experiment, the docking pattern represents the shape of the unloading platform as perceived by the sensor when the trailer is parked. It is represented in figure 2. Thus the inputs of the docking task are: \u2022 a planned trajectory for the robot towards a goal config- uration \u2022 the docking pattern L. Figure 5 illustrates the case where the unloading platform has been moved and the map has not been updated. Moreover, the shape of the unloading platform has changed: it is larger than the docking pattern. The matching between the perception and the docking pattern is robust to these perturbations and the docking configuration is still defined relatively to the unloading platform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001326_6.2002-3793-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001326_6.2002-3793-Figure1-1.png",
        "caption": "Figure 1.\u2014Finger seal design.",
        "texts": [
            " All other rights are reserved by the copyright owner. American Institute of Aeronautics and Astronautics NASA/TM\u20142002-211589 American Institute of Aeronautics and Astronautics NASA/TM\u20142002-211589 The finger seal is similar in general configuration to a brush seal, but functions in a different manner. Instead of a random array of fine wires, the finger seal uses a stack of tight-tolerance sheet stock elements. Each element is machined to create a series of slender curved beams or fingers around the inner diameter (fig. 1). Each of these fingers (7) has an elongated contact pad (6) at its free end. Each element (1) also has a series of assembly hole pairs (8) near its outer diameter. These holes are for the rivets (5) that assemble the seal. The holes are spaced such that when the elements are alternately indexed to the two holes, the spaces between the fingers of one element are covered by the fingers of the adjacent element. Usually a seal is assembled with multiple finger elements (1), forward and aft spacers (2) and forward (3) and aft (4) cover plates"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001669_03093247v204217-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001669_03093247v204217-Figure5-1.png",
        "caption": "Fig. 5. Nodal load distribution acting on bore surface at 16000 Ibf total pin load",
        "texts": [
            " The equations for the conditions that prevail when the load is further incremented past this point where node 2 just touches the pin are as follows cos a3 a 1 3 a 3 3 a43 a5 3 0 0 1 0 0 cos a4 a14 a24 a34 a44 a54 0 0 0 1 0 cos a5 0 a15 -cos a1 a25 -cos a2 a35 -cos a3 a45 -cos a4 a55 -cos a5 0 0 0 0 0 0 0 0 1 0 loads and clearances are then factored back-up again to make the next event occur and the process carried on until the highest required total pin load is exceeded. 4 RESULTS The procedure described above was incorporated into a finite element program. To illustrate the validity of the method, the stresses in a typical lug end of a link were calculated using the load distribution which was obtained from the program and shown in Fig. 5. These calculated stresses were compared with results obtained from a photoelastic study (Figs 6 and 7). 0 -1 0 - 0 0 0 1 0 0 0 0 0 0 - 1 0 - 0 0 0 1 0 0 0 0 0 0 -1 0 - 0 0 0 0 0 0 0 0 0 0 - 1 0 - 0 0 0 0 0 As before the non trivial equations can be portioned off and solved separately as follows cos a1 cos a2 0 0 0 0 a1 1 a1 2 0 0 0 -cosal 0 2 1 a 2 2 0 0 0 -cos a2 a3 1 a 3 2 -1 0 0 -cos a3 a41 a 4 2 0 -1 0 -cos a4 a5 a, , 0 0 - -cos a5 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 0 0 -1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 cos a3 cos a4 cos a5 a 1 3 a14 5 a 2 3 a24 a2 5 a3 3 a34 a3 5 a43 a44 a4 5 a 5 3 a54 a5 5 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 The six equations shown boxed would be solved and new percentage changes of nodal loads and clearances are calculated by dividing the changes in nodal loads and clearances by the values of the nodal loads and clearances that existed when node 2 was just touching the pin (i",
            " Figure 7 indicates the stress distribution across the critical section of the lug. It was clear from the photoelastic results that the stress distribution in the lug is complicated and a simple analysis is likely to yield unreliable results. For that reason it was decided that a finite element analysis, which took account of the complex load distribution, would have to be used if the complicated stress distribution was to be calculated with adequate accuracy. The load distribution which was obtained for a total pin load of 16000 lbf is shown in Fig. 5. Using that distribution, with the assumption of a rigid pin and negligible friction between the surface of the pin and the lug, the stresses in the lug at its bore and outer surface were calculated using the finite element model shown in Fig. 4 and using the boundary conditions described earlier. When these calculated results are compared with the values obtained from the photoelastic study, good agreement, as shown in Fig. 6, was found. The photoelastic results in Fig. 7 show a fairly non-linear stress distribution across the critical section, and although only four elements were used across the section, the photoelastic and finite element results match closely"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003740_1.2975154-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003740_1.2975154-Figure9-1.png",
        "caption": "FIG. 9. a Conchospiral referred to a right handed orthogonal cartesian system O X ,Y ,Z ; b height h of the circular cones family whose generatrix is gc\u2212gc.",
        "texts": [
            " Then, there is a correspondent infinite number of conchospiral helices that are associated with the relative infinitesimal helicoids that have an infinitesimal rectangular section. These helices are joined one after the other. Therefore the shape of the helicoid illustrated in Fig. 8 can be completely described by using a set of infinite coaxial circular cones whose axis, common vertex, and height are a\u2212a, O, and OT, respectively. Then, the generic point P of the mass of this helicoid is geometrically identifiable as a point of the correspondent conchospiral that passes through all the helicoidal body. Figure 9 a shows a part of with reference to a right handed orthogonal Cartesian system O X ,Y ,Z whose origin corresponds to the vertex of the cone on which is defined. In this figure the point P of is geometrically identified by the generatrix gc\u2212gc, the radius r that has the starting point A, and the oriented angle that has been measured from the plane XY. The angle is a function of the angles and , = \u2212 . 58 In order to describe the generic angular position of the conchospiral around the axis X that corresponds to the axis indicated in Fig. 8 by a\u2212a, the angle has been considered. Observing Fig. 8 we also verify that enables us to specify the angular rotation around X of the whole helicoid. Moreover, as soon as we fix the value of , it is possible to identify the position of P that belongs to by defining the value of the angle Fig. 9 a . Then, we can define the whole curve by changing . Now, to identify the position of P for successively computing the volume magnetic charge M, it can be useful to consider a spherical coordinate system. The origin of this coordinate system is the vertex O, that corresponds to the origin of the orthogonal Cartesian system previously defined. Therefore, the position of P is defined by the following spherical coordinates: the length g straight line from P to O measured on the generatrix gc\u2212gc, the angle , and the angle of inclination of gc\u2212gc with respect to the axis X",
            " Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 131.230.73.202 On: Thu, 18 Dec 2014 07:41:10 n = n sin c, 60 n = 0. 61 From the equations of the hand righted conchospiral written by the cylindric coordinates see Figs. 9 a and 10 , r = Re sin cot c, 62 x = r cot , 63 considering the Neperian logarithm of the members of Eq. 62 , ln r = ln Re sin cot c , 64 we obtain the c expression as function of and , c = arctan sin ln r R . 65 From Fig. 9 b , having denoted by h the height OT of the generic circular cone whose generatrix is gc\u2212gc, it follows that r R = g cos h , 66 and obtaining from Eq. 58 = \u2212 , 67 Equation 65 gives c as a function of the spherical coordinate associated with the generic angular rotation of around the axis X, c = arctan \u2212 sin ln g cos h . 68 Here also represents the rotation of the whole conchospiral helicoid characterized by a finite rectangular section with sides re\u2212ri and b. Finally, by Eq. 68 , the components ng, n , and n of the unit vector n can be explicitly expressed versus the spherical coordinates g, , and , ng = \u2212 n cos arctan \u2212 sin ln g cos h , 69 n = n sin arctan \u2212 sin ln g cos h , 70 n = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002301_105994905x75484-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002301_105994905x75484-Figure6-1.png",
        "caption": "Fig. 6 Schematic diagram of TIMETAL 15-3 bleed air system on the Airbus A380 (Ref 11)",
        "texts": [
            " 5 and 6, TIMETAL 15-3 strip is now used Journal of Materials Engineering and Performance Volume 14(6) December 2005\u2014705 in the environmental control system ducting of several aircraft models, including the Boeing 777 and Airbus A380. TIMETAL 15-3 ducting has been used in the Boeing 777 since 1992 (Ref 1). Using TIMETAL 15-3 instead of commercially pure titanium saves approximately 64 kg (140 lb) per Boeing 777 aircraft (Ref 10). Tubing wall thicknesses are typically 0.5 mm (0.020 in.) or 0.8 mm (0.032 in.). The ducts carry air at temperatures of up to 232 \u00b0C (450 \u00b0F) (Ref 1). More recently, TIMETAL 15-3 has been considered for use in portions of the ducting system of the Airbus A380 (Fig. 6) (Ref 11). For plug-and-nozzle and other types of exhaust systems, TIMETAL 21S is now used in lieu of much heavier nickel alloy systems on several aircraft models. Examples for the Boeing and Airbus aircraft are provided in Fig. 7 and 8, respectively. Using TIMETAL 21S instead of nickel-base alloys saves approximately 82 kg (180 lb) on each Rolls Royce Trent engine (or 164 kg [360 lb] total) on the Boeing 777 aircraft (Ref 3). TIMETAL 21S is also used in the exhaust systems of several military aircraft programs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000478_tec.2003.816601-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000478_tec.2003.816601-Figure8-1.png",
        "caption": "Fig. 8. Focal axis for two values of in linear conditions.",
        "texts": [
            " These are the points, which are the nearest to the origin. They are bound to each other by the curve . Saturation acts on the constant torque curve shape so that the curve is not exactly hyperbolic. On the other hand, the hyperbola position is modified [i.e., the angle is modified (Fig. 7)]. In linear conditions, as we saw in Section III for an angle , we find a bundle of hyperbolas of focal axis located by the angle , which is independent of the torque value. For an angle , we find a bundle of hyperbolas of focal axis located by the angle (Fig. 8). In saturation condition, the experimental angle is then modified compared to the linear case. It now depends on the electromagnetic torque, we note . Consequently, for a saturated machine, the optimum point is shifted with respect to the optimum point determined in the linear case (Fig. 7). The transformation matrix is dependent on the position and on the electromagnetic torque . We define then (23) Thus, for a given value of the electromagnetic torque, there is a single transformation. We define a transformation table which is parameterized according to the electromagnetic torque"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003477_icit.2008.4608494-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003477_icit.2008.4608494-Figure4-1.png",
        "caption": "Fig. 4 Flux linkage vector in DTC",
        "texts": [
            " Substitute (11) in (12), we can get 5 1 2 M S Uh U (13) The other equations besides (11) used to describe the HE-SVPWM arithmetic can be written as follows: ( 1) ( 1)s Lk Mk L k M kT T T T TLk Mkref L(k+1) M(k+1)U U U U U (14) ( 1) ( 1)s zLk Mk L k M kT T T T T T (15) 1kL MhT T 1k (16) Where ( 1) 5 kj LU eLkU , ( 1) 5 kj MM U ekU , j refU erefU Solutions of the equations above are sin( ) sin / 5 5 ref s Mk L M U T kT hU U (17) 1 1sin( ) sin / 5 5 ref s M k L M U T kT hU U (18) ( 1) ( 1)( )z s Lk Mk L k M kT T T T T T (19) Based on the HE-SVPWM proposed above the DTC system of the five-phase PMSM is constructed as shown in Fig. 3. The operation principle of the system can be explained by virtue of Fig. 4. In Fig. 4, * s is the given reference value of stator flux-linkage, and s is the actual stator flux linkage. The difference of them is denoted as s, which can reflect the change of the stator flux linkage. L is defined as torque angle which is the angle between the rotor flux-linkage and stator flux-linkage, and it is got by the PI adjuster of the torque loop. The value of L reflects the change of electromagnetic torque. According to Fig. 4 the increment of stator flux-linkage in frame can be expressed as follows: * 1 * 1 cos( ) cos( ) sin( ) sin( ) s L s s L s (20) Where is the angle between -axis and M-axis (that is the axis of stator flux-linkage). Combined the voltage equations in (4), the reference voltage used in the next control period for HE-SVPWM can be deduced that: * 1 1 * 1 1 / / s s s s u T u T 1 1 R i R i (21) Equations (20) and (21) constitute the reference vector builder in Fig.3. The torque and flux-linkage observer is established with the motor model, that is 1 1 1 1 1 1 s s u R i d u R i d t t (22) 2 2 1s 1 (23) For the task of suppressing harmonic current is completed by HE-SVPWM arithmetic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002785_1.3438180-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002785_1.3438180-Figure4-1.png",
        "caption": "Fig. 4 The RCCC mechanism geometry",
        "texts": [
            " 3 for a series of closely separated positions of the input crank, assuming constant value for the input angular speed (j = 1 rad/sec. Identical results were obtained for the relative coupler rotation a accurate to 8 significant digits using Newton's Method for the singular non linear equation (18). The iterative method took about 5 times as much computation time as the explicit method on a CDC 6400 computer using single-precision arithmetic. Kinematics of the RCCC Mechanism The RCCC mechanism may be identified as shown in Fig. 4 by the vector Z as IX = (b - bo)t(a 2 [T(u)] - 2a[P(u)])(b - a) - IIbl1 2 - (b -- bo)'(2V,,(b' - iI) + b') .(b - bo)'[P(u)](b - a) (23) 01', (b - bo)tbli:i~o + IIbl12 (b - bo)'[P(u)](b - a) The instantaneous velocity and acceleration of any coupler Point X(x) can now be determined as Journal of Engineering for Industry (25) Though not a prerequisite for kinematic analysis, the number of components of Z may be reduced by choosing uo = (cos /3, 0, sin (3)', ao' = (0, 1', 0)' MAY 1973 / 483 Downloaded From: http://manufacturingscience"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000652_0470867906-Figure8.19-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000652_0470867906-Figure8.19-1.png",
        "caption": "Figure 8.19 Deflection of a micromirror (a), structure of the FE model (b)",
        "texts": [
            " The finite element method is particularly suited to answering the questions of structural mechanics in such cases. Certain questions are essential to the consideration of the interaction between electronics 184 8 MICROMECHATRONICS and mechanics. Initially the relationship between the voltage applied and the resulting deflection should of course be investigated. Furthermore, the feedback of the mirror capacitance on the electronics and the possible excitation of resonances of the mirror is also of interest. Figure 8.19 shows the typical deflection of a micromirror and the structure of the associated FE model. This is based upon plate elements, which are particularly well suited for the layer structure of micromechanics. The following representation deals with rectangular plate elements, which are treated in detail in Gasch and Knothe et al. [113]. The description of modelling is dealt with more briefly here in comparison with the previous demonstrator because \u2014 like the beams introduced in Chapter 6 \u2014 small deflections result in constant mass and stiffness matrices for the rectangular plate elements used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002516_cdc.2006.377020-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002516_cdc.2006.377020-Figure3-1.png",
        "caption": "Fig. 3. Important region of the Nyquist plot of P where the number of encirclements of- 1 , Ai :A 0, change as function of eAi",
        "texts": [
            "5 Z(Z -1) The Lapacian when the link is active is given in (5), and when the link is inactive only the last row changes. The mean Laplacian, Lrv is the same as L but with the last row replaced by 1[2 1- e 0 0 0 11. and the other components of the Mean Network are L, = [-2 20 0 0 0],Lwr= [ 0 0 0 0 1]',and Lzw = 0. We have picked the node dynamics so that, the closed loop is (marginally) stable when the link is active and unstable when the link fails. This implies that when e -> 0 the mean closed loop system M is marginally stable, and it becomes unstable as e -> 1. Figure 3 shows the root locus of -1 where Ai is a nonzero eigenvalue of Lrv as e variesAi form 0 to 1. We see that the Nyquist plot of P crosses the root locus. This provides a graphical test for checking the (relative) stability (in the Mean) of the nominal closed loop M for different values of e. Figure 4 shows the Log-Log histograms of the absolute difference between the output of node 1 and that on node 6, E = IYl-Y6 Table I reports the values Of p(u2M) (which must be less than one for MS stability) as function of e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002649_1464419jmbd12-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002649_1464419jmbd12-Figure4-1.png",
        "caption": "Fig. 4 Geometrical arrangement of bearing",
        "texts": [
            " For taper-roller bearings, the summation of all the roller contributions is made as follows. An axial set displacement, r, which would be the normal method of achieving the preload results in an axial preload displacement for each bearing of r/2. If the inclination of the roller axis to the shaft axis is b then the radial displacement applied to each roller is (r sin b)/2. The Hertzian stiffnesses corresponding to various set displacements may thus be obtained and the method of summation may be illustrated by considering a geometrically perfect bearing, as shown in Fig. 4. If the shaft is displaced a distance do with respect to the housing then the deflection across the apex roller is also do. The deflection across the nth roller is given by dn \u00bc do cos nl where l is the angle between adjacent rollers. (dP/dd) is the same for each roller as each suffers the same preload, so a force Pn is induced in the nth roller where Pn \u00bc dP/dd)dn . t The radial component, Pn cos b, is summed in the principal direction PTot \u00bc Xnr n\u00bc0 dP dd cos bdo cos nl cos nl Dividing by do gives the Hertzian stiffness for one bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000570_095440802760075021-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000570_095440802760075021-Figure3-1.png",
        "caption": "Fig. 3 Kinematic scheme of spatial gear pair with linear contact between toothed surfaces S1 and S2 synthesized using a mesh region (MR)",
        "texts": [
            " This is obtained by a suitable choice of a pitch contact point location in space, so that the synthesized gear pair has some optimal quality characteristics: strength and durability of the gear pair, accuracy of the realization of the desired angular velocity ratio, conditions for an effective driving energy, etc. The mathematical model given here is widely used in spatial gear synthesis. It is also necessary to formulate criteria to provide the quality characteristics in the vicinity of the contact point. When synthesizing skew axes gears with linear contact, it is clear that their quality should be controlled in the whole mesh region. Such approaches require an adequate mathematical model. Its kinematic scheme is shown in Fig. 3. A mathematical model based on a mesh region is not universal. The reason is that the speci c geometrical and kinematic characteristics of the mesh region depend on its position in space and geometrical characteristics of the generating anks Si \u2026i \u02c6 1; 2\u2020 of the tool surface Sj. Proc Instn Mech Engrs Vol 216 Part E: J Process Mechanical Engineering E0101 # IMechE 2002 at MICHIGAN STATE UNIV LIBRARIES on June 14, 2015pie.sagepub.comDownloaded from This mathematical model is suitable when: 1. Pitch circles cannot be de ned"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003188_1.2919780-Figure13-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003188_1.2919780-Figure13-1.png",
        "caption": "Fig. 13 Schematic of the experimental apparatus",
        "texts": [],
        "surrounding_texts": [
            "Many simulations are necessary to analyze the general behavior of the cavity length. Preliminary simulations have shown that the set of the well known dimensionless Moes parameter M and L is very convenient. M = W E \u00b7 R2 0 \u00b7 us E \u00b7 R 3/4 7 L = E \u00b7 \u00b7 0 \u00b7 us E \u00b7 R 1/4 8 Some accuracy considerations need to be taken into account. In many simulations focused on the film thickness and shape, the domain is usually chosen as small as possible to optimize the ratio JULY 2008, Vol. 130 / 031502-3 of Use: http://www.asme.org/about-asme/terms-of-use b s r a c c A fi o 1 w T e 2 c w o e t e ca F a p 0 Downloaded Fr etween the number of nodes necessary and the resulting mesh ize. The fewer points, the faster the calculation. However, this esults in a larger mesh size, which in turn reduces the numerical ccuracy. Here, a large domain is necessary in order to simulate for the avity length. By having some drawbacks with regard to the calulation speed, a large amount of 1025 1025 nodes was chosen. s a comparison, a domain of 2 X 2 and 2 Y 2, by using a nest grid with 129 129 nodes, leads to a grid size X and Y f 0.03125. The large domain of 16 X 16 and 16 Y 16 with 025 1025 nodes will have the same grid size. A more elegant ay is to use the adaptive grid method, as reported in Ref. 17 . his feature will be addressed in future works. Simulations have been conducted for an oil similar to a minral bright stock BS having a pressure viscosity index of 6.3 GPa\u22121 and a viscosity 0 of 1.375 Pa s at 20\u00b0C. No reference values exist for cavity length. However, the calulated film thicknesses, even when using a large domain, agree ith standard EHL film thickness formulas. Figure 8 shows lines f central film thickness calculated by the Hamrock and Dowson quation, as found in Hamrock 21 for the piezoviscous elastic PE lubrication regime, and simulation points. Simulated film hicknesses show good agreement with the EHL theory. A curve fitting of the points shown in Fig. 8 results in the quation ig. 5 Dimensionless midplane pressure P, film thickness H, nd amount of oil H in X-direction, 25.4 mm steel ball/glass late, 5 N, 20 mm/s, BS oil, pcav=\u22120.1013 MPa 31502-4 / Vol. 130, JULY 2008 om: http://tribology.asmedigitalcollection.asme.org/ on 01/30/2016 Terms Hcen = 1.1 \u00b7 M\u22120.7L0.56 9 The equation was obtained for a limited simulation range and nterferogram \u201eright\u2026 25.4 mm steel v=\u22120.1013 MPa \u2026, i p cavity Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use t H l l p c T p 1 t p t n v l t r = a c circles for better differentiation only\u2026 J Downloaded Fr herefore predicts only for Moes parameters around 10 M 1000 and 2.5 L 20 central film thickness values similar to amrock and Dowson equation 21 . In Figs. 9 and 10, the dependences of the dimensionless cavity ength Xc /a on the parameters M and L are shown. For clarity, ines fitted to the simulation points are also shown in the figures. The results are obtained from the simulation made by assuming cav= pvacuum. However, in thin oil films, the exact value of the avity pressure is not exactly known and very difficult to measure. herefore, the dependence of the dimensionless cavity length on cav must be considered by introducing a correction factor. In Fig. 1, it can be seen that by reducing pcav from vacuum pressure owards zero gauge pressure the cavity length increases by the ower of about 0.32. As presented later, experimental observations have revealed hat a pressure viscosity index correction factor is necessary. A umber of simulations have been repeated for different pressure iscosity indices. In Fig. 12, it is shown that the simulated cavity ength increases for lower pressure viscosity indices compared to he previously found cavity length dependencies on the Moes paameter M and L with a pressure viscosity index of 26.3 GPa\u22121 see Figs. 9 and 10 . Combining all the dependences of the cavity length described bove and focusing on the simulation results around the PE lubriation regime, the following equation was obtained. ournal of Tribology om: http://tribology.asmedigitalcollection.asme.org/ on 01/30/2016 Terms Fig. 10 Cavity length over L for different M \u201eempty and filled circles for better differentiation only\u2026 \u201ee.g., M=100, L=10, =26.3 GPa , 0=1.375 Pa s\u2026 JULY 2008, Vol. 130 / 031502-5 of Use: http://www.asme.org/about-asme/terms-of-use H s i f c p v a p n 5 1 g m s d d u T o m d c 0 Downloaded Fr Xc a = 9.2 \u00b7 M\u22120.27L0.3 pvacuum pcav 0.32 sim 0.3 10 ere, pvacuum=\u22120.1013 MPa cavity gauge pressure used in the imulation and sim=26.3 GPa\u22121 pressure viscosity index used n the simulation . The last two terms in parentheses of Eq. 10 are the correction actors for cavity pressures and pressure viscosity index. The most ritical term in Eq. 10 is the correction factor for the cavity ressure. In this work, the cavity pressure is assumed to have a alue around 60\u2013100% of the vacuum pressure. For a cavity type, s shown in Fig. 1 b , where the cavity pressure is that of ambient ressure, the cavity length would be infinity and the equation will ot be valid. Experimental Investigation Some details of the experimental apparatus are shown in Fig. 3 11 . A precision steel ball with a diameter of 25.4 mm and a lass disk of 15 mm thickness is used. The equivalent elastic odulus E is 120 GPa. The steel ball is loaded by a spring and upported by back-up rollers against the underside of the glass isk coated with a semireflecting chromium layer at the track iameter of 63.5 mm. Loads of 5 N, 10 N, 20 N, and 50 N are sed. The rolling speeds were 0.02 m /s, 0.05 m /s, and 0.1 m /s. his results, depending on the oil used, in a Moes parameter range f 1.5 L 13.5 and 20 M 2000. Therefore, not all experiental results exactly lie in the PE lubrication regime. The experiments have been carried out under fully flooded conitions and in such a way that the length of the cavity type as ommon in reciprocating contacts see Fig. 1 a could be mea- 31502-6 / Vol. 130, JULY 2008 om: http://tribology.asmedigitalcollection.asme.org/ on 01/30/2016 Terms sured under steady state conditions. The velocity pattern is shown as an example in Fig. 14. Black dots indicate the measurements at constant speed. This type of velocity pattern always generates new cavities. In real reciprocating motion, due to very short cycle times, the cavity inside the oil meniscus has no time to accumulate dissolved air. To minimize, on the one hand, the accumulation of dissolved air and to assure, on the other hand, that the cavity length is measured under steady state conditions, a trapezoid velocity pattern was chosen. In Fig. 15, it can be seen that, for the maximum rolling speed used, the cavity length remains constant during the period of constant speed and transient effects such as time-delayed big fluctua- Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use w c r t l c d b 6 r s l o p a v c v u F r o J Downloaded Fr After setting the test conditions, both the specimen and disk ere reciprocated 100 cycles in 40 s or 80 s and a high speed amera recorded at the frame rate of 500 fps for 8 s during the eciprocation. Thus, running-in effects are negligible. Afterwards, he recorded interferograms selected at constant speed are anayzed by means of measuring the cavity length. For every test onditions, at least three measurements at different cycles were one and averaged. Ten different types of oil at a room temperature of 20\u00b0C have een tested. The properties of the oils are listed in Table 1. Results and Discussion First, by using Eq. 10 and taking into account only the corection for the cavity pressure having 70% of the vacuum presure, some differences between measured and estimated cavity ength values occur. As shown in Fig. 16, the cavity length values f oils silicone, turbine, and polyalphaolefin PAO having a ressure viscosity index lower than that of the reference oil BS re usually longer than the estimated values. The cavity length alues of the traction oil KY0707 , having a high pressure visosity index, are slightly shorter than the estimated values. In Fig. 17 below, after including the last term with the pressure iscosity index of Eq. 10 , the correlation between measured vales and estimated values is good. ig. 16 Correlation of estimated cavity length without corection and experimental measured cavity length for different ils ournal of Tribology om: http://tribology.asmedigitalcollection.asme.org/ on 01/30/2016 Terms As mentioned in Sec. 4, the correction for the pressure viscosity index is more a cancellation of inside the Moes parameter L. Thus, the physical influence of the pressure viscosity index seems to be small and the cavity length depends more on the geometry Hertzian contact parameter a and hydrodynamic conditions outside the contact region. In other words, the pressure around the cavity is low and thus the piezoviscosity has little effect. However, to be exact, for higher film thicknesses e.g., at high velocities, etc. , the influence of the pressure viscosity index could increase, because affects the pressure distribution and therefore the deformation of film thickness in EHL contacts. The cavity length seems to depend also on the film thickness e.g., central film thickness , because it indirectly defines the geometry or shape of the contact. Figure 18 shows some relation between the cavity lengths and the film thickness geometry . Therefore, the change in film thickness will, in turn, also affect the cavitation region. The simulated curves close together are around the PE regime. Similar curves will be also obtained by using Eq. 9 as the x-axis and Eq. 10 without correction factors as the y-axis. A relation can be found, which is shown as a curve in Fig. 18. JULY 2008, Vol. 130 / 031502-7 of Use: http://www.asme.org/about-asme/terms-of-use 7 s c t t p f M i t 0 Downloaded Fr Conclusion Based on experimental observations and a numerical parametric tudy, an equation for the cavity length in an EHL rolling point ontact was developed. The equation is only valid for enclosed ype cavities enclosed in the oil meniscus . For the time being, he usage of the equation is mainly limited to rolling motion in the iezoviscous elastic EHL regime. In rolling contacts, thermal efects due to sliding are relatively small. The cavity length could be described by the dimensionless oes parameters, assumed cavity pressure, and pressure viscosity ndex. In other words, the dimensionless cavity length is propor\u2212a b ional to the product of M and L plus a correction factor for the 31502-8 / Vol. 130, JULY 2008 om: http://tribology.asmedigitalcollection.asme.org/ on 01/30/2016 Terms cavity pressure and the pressure viscosity index. Rearranging Eq. 10 to Eq. 11 shows that the cavity length is dominated by the viscosity, sum velocity, cavity pressure, and geometry of the contact. In practice, the estimated cavity length can be a parameter to define the degree of starvation in a reciprocating EHL contact."
        ]
    },
    {
        "image_filename": "designv11_28_0002022_s10973-005-0803-6-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002022_s10973-005-0803-6-Figure1-1.png",
        "caption": "Fig. 1 Exploded view of the immersion calorimeter",
        "texts": [
            " adsorption isotherms or adsorption isotheres) \u2022 calorimetric methods: these are usually classified as adiabatic, isothermic, Tian\u2013Calvet and immersion calorimeters [18\u201322] This study is the result of the work of our re- search groups during the past 18 years, combining different developments in the area of calorimetric instrumentation. We have adapted ideas reported in literature to design a new adsorption calorimeter. This new immersion calorimeter was connected to a computational measuring unit, resulting in a novel workstation that measures immersion heat. Description of the newly built calorimeter Figure 1 shows a complete exploded view of the immersion calorimeter. Its design is not very common and it was not reported previously in the literature. A detailed view from the inner of the equipment to the exterior of the calorimeter is shown in Fig. 1. In the diagram, part number 13 corresponds to the calo- 1388\u20136150/$20.00 Akad\u00e9miai Kiad\u00f3, Budapest, Hungary \u00a9 2005 Akad\u00e9miai Kiad\u00f3, Budapest Springer, Dordrecht, The Netherlands Journal of Thermal Analysis and Calorimetry, Vol. 81 (2005) 435\u2013440 Y. Ladino-Ospina1, L. Giraldo-Gutierr\u00e9z2 and J. C. Moreno-Piraj\u00e1n3* 1Chemistry Department Professor, Universidad Pedag\u00f3gica Nacional de Colombia, Calle 72 No.12-09, Bogot\u00e1, Colombia 2Chemistry Department Professor, Calorimetry Laboratory, Universidad Nacional de Colombia, Ciudad Universitaria, Bogot\u00e1, Colombia 3Chemistry Department Professor, Universidad de Los Andes, Research Group on Porous Solids and Calorimetry, Carrera 1 No"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000736_apec.2001.912467-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000736_apec.2001.912467-Figure7-1.png",
        "caption": "Fig. 7. Experimental System",
        "texts": [
            " In FOC, the measured currents are firstly transformed into the d\u201d - and q\u201c -axes and the high frequency components of the transformed currents are extracted through the band pass filter. Finally, the estimated rotor position, e,, and the estimated rotor speed, , is calculated via the \u2018PreProcessor\u2019 and the \u2018Correction Controller\u2019 block. In this process, the estimated rotor position is compensated with from the compensator. ~ 1 PWM VSI PI Position and Speed Controller t , LPF I 6 Fig. 5. Block diagram ofthe total system. IV. EXPERIMENTAL RESULTS V. CONCLUSION The experiments to verify the proposed sensorless algorithm are performed. Fig. 7. shows the experimental system. For the experiments, PWM Voltage Source Inverter controlled by the DSP TMS320C3 1 has been used and its switching frequency is 5 kHz. The parameters of the SMPMM are' listed in TABLE I. The experimental results of proposed sensorless speed control algorithm are shown in Fig. 8 and Fig. 9. In Fig. 8 and Fig. 9, the measured rotor speed, the estimated rotor speed, the measured rotor position and the q-axis current relating the load torque are represented, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000603_2001-01-1007-Figure24-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000603_2001-01-1007-Figure24-1.png",
        "caption": "Fig. 24. Position of the ellipse of dispersion for the half order component of the crankshaft\u2019s speed, corresponding to different degrees of non-uniformity of cylinder #4",
        "texts": [
            " Similar calculations may be performed, assuming that other cylinders are not contributing to the total engine torque. Each individual cylinder that is a lesser contributor will determine a specific phase domain for the half order component of the crankshaft\u2019s speed. This situation is presented in Fig. 23. If all cylinders are operating uniformly, with a reasonable scatter of the IMEP, the measured amplitude of the half order component of the crankshaft\u2019s speed is small and its phase is arbitrarily scattered over a 360\u00b0 domain (Fig. 24, a). If a cylinder starts to contribute less to the total engine torque, the amplitude of the half order component of the measured speed starts to increase and the angular domain of its phase starts to decrease and to have a preferential direction (Fig. 24, b, c). When a cylinder ceases to contribute to the total engine torque, the amplitude of the half order component of the crankshaft\u2019s speed becomes very large and its phase varies very little from a preferential direction that indicates the deficient cylinder (Fig. 24, d). The possibility to detect a non-uniformity in the cylinder operation and to identify the deficient cylinder by analyzing the crankshaft\u2019s speed variation is exemplified in Fig. 25. This figure shows the average amplitude and the phase domain of the half order component of the crankshaft\u2019s speed during 10 successive cycles and different operating conditions. The measurements have been made on the six cylinder diesel engine operated at about 1200 rpm and an average IMEP \u2245 0 82\u00b10.02 MPa. When a cylinder was completely disconnected (the case for cylinders #1 and #3 in Fig",
            " A similar situation was obtained with a cylinder almost disconnected (the case of cylinder #4 and #5 in Fig. 25). In this later case, the amplitude was a little bit smaller and the phase domain larger. For less dramatic non-uniformities, the amplitudes were significantly smaller and the phase domain larger, but also in these situations the phase domain was located around the value predicted by the statistical model. For uniform cylinder operation, the experimental results were looking similar to the ones presented in Fig. 24, b, indicating that cylinder #6 contributed systematically about 10% less than the other cylinders. The average amplitude of the half order component of the crankshaft\u2019s speed was in this case very low (0.115\u00b10.05 rad/s) indicating a fairly uniform operation of all cylinders. \u2022 The Variation of the crankshaft\u2019s speed is determined by the variation of the external torque and the dynamic response of the crankshaft structure. For steady state operation conditions, the lower harmonic components of the gas pressure torque do not excite torsional vibrations and the crankshaft behaves as a rigid body"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002963_icar.2005.1507465-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002963_icar.2005.1507465-Figure2-1.png",
        "caption": "Fig. 2. Frame assignment and parameter definition of the mobile base.",
        "texts": [
            " Using experimental results carried out on the actual robot, the effectiveness of dynamic compensation is demonstrated by achieving a more even joint torque distribution and minimized amount of slip between wheels. These results improve wheel-floor traction, hence decrease the chances of wheel-floor slippage. This in turn produces a more accurate odometry of the base. The strategies described were implemented on the omnidirectional mobile robot and real time experimental results are presented in this paper. The frame assignment and parameter definition of a mobile base with N PCWs are shown in Fig. 2. Frame B is defined as the frame attached to the center of the mobile base and moves with the base. The location of the wheel with respect to Frame B is defined by vector hi, of length hi, forming an angle \u03b2i with the x axis of Frame B. The contact point between the wheel i and the ground is defined as point Ci and its position with respect to Frame B is defined as pCi. A Frame Ci is defined with its origin at 5670-7803-9177-2/05/$20.00/\u00a92005 IEEE point Ci, with axis yCi defined along the translational motion of the wheel and the axis xCi perpendicular to yCi so that it results in axis zCi pointing vertically upwards",
            " The kinematics of the mobile base can be derived by equating the velocities of the wheel-floor contact points Ci as generated by the task space velocity at the center of the base (x\u0307 = [v,\u03c9]T ) and those generated by the joint space velocities (q\u0307 = [\u03c6\u03071, \u03c1\u03071, \u03c6\u03072, \u03c1\u03072, ...\u03c6\u0307N , \u03c1\u0307N ]T ). When expressed in Frame B, it is described by the following equation: Bv +B \u03c9 \u00d7 BpCi = b\u03c6\u0307i BxCi + r\u03c1\u0307i ByCi (1) where BxCi and ByCi (expressed in Frame B) are BxCi = [ \u2212sin(\u03b2i \u2212 \u03c6i) cos(\u03b2i \u2212 \u03c6i) ] ByCi = [ \u2212cos(\u03b2i \u2212 \u03c6i) \u2212sin(\u03b2i \u2212 \u03c6i) ] (2) Vector BtCi is obtained by rotating pCi by 90o keeping the same magnitude. The result of the cross product B\u03c9 \u00d7B pCi is simplified as: \u03c9BtCi, where \u03c9 is the scalar value of the rotation of the base around the vertical z axis (Fig. 2). Equation (1) is rearranged into: [ I2\u00d72 BtCi ] [ Bv \u03c9 ] = [ b BxCi r ByCi ] [ \u03c6\u0307i \u03c1\u0307i ] (3) For convenience, (3) can be expressed with respect to individual Frame Ci to reveal the individual contribution of the steer and drive joint motions of each wheel i. This is done by pre-multiplying both sides of the equation with rotation matrix CRB = [BxCi ByCi]T . The resulting equation of motion for the mobile base, taking into account all the available joints, is expressed as A x\u0307 = B q\u0307 (4) where A =   BxT C1 BxT C1 BtC1 ByT C1 ByT C1 BtC1 BxT C2 BxT C2 BtC2 ByT C2 ByT C2 BtC2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002439_0015-0568(80)90002-0-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002439_0015-0568(80)90002-0-Figure1-1.png",
        "caption": "Fig. 1.",
        "texts": [
            " (vi) A double centre of compression-dilation acting at (0, 0, - c ) . For further information, the reader is referred to the original paper by Mindlin. 5 3. REPLACEMENT OF THE FIBRE BY A LINE OF MINDL1N-STATE The basic idea behind the slender-body theory is that the disturbance displacement field due to the presence of the fibre embedded in the matrix is approximately the same as that due to a suitably chosen line distribution of Mindlin-state. Distance along the fibre in the :-direction (see Fig. 1) is denoted by c, ce[0, l], where I is the effective embedded length of the fibre. The cross-sectional shape of the fibre is not necessarily independent of =. A representative radius of the fibre is denoted by R o. We require that Ro/I ~ 1. If Mindlin-states of strength P(c) are distributed over the interval [0, l] on the zaxis, then the resulting displacement field in cylindrical co-ordinates is given by r { f t \u00b0 P(c)(z - c) fi(3-4v)P(c)(z-c) ur - 16rtr/(i - v) [(z 7 @ _]_ r213/2dc \"+\" [(2-q----C~ + ~ 2 dc f l 4(1 - v)(l - 2 v)P(c) -- [(a + C) 2 + r2 ] t /2 [ ( (z + C) 2 + r2) 1/2 + z + C] dc (\" 6cz(z + c)P(c) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003826_s1064230708020019-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003826_s1064230708020019-Figure1-1.png",
        "caption": "Fig. 1. A pendulum.",
        "texts": [
            "63 INTRODUCTION A pendulum (Fig. 1) is a well-known example of a nonlinear mechanical system, which is frequently used for testing control algorithms. In numerous publications, various methods for feedback control have been proposed that steer the pendulum in the lower stable equilibrium position under constraints on the modulus of the control torque. In some of them (see, e.g., [4, 5]), the problem of optimal synthesis was considered for sufficiently large admissible control torques, but the solution was not complete. Namely, the threshold constraint on the modulus of the control torque for which trajectories with more than one control switch arise in the pattern of optimal synthesis was not specified or was not found correctly",
            " In the specified works, with accuracy up to several one hundredths, two bifurcation values of the control torque were found. In the first of them, optimal trajectories with two switches arise, and, in the second one, optimal trajectories with three switches arise. To detect the bifurcations, it is sufficient to analyze visually the patterns of optimal synthesis. Consider a pendulum that can revolve about the horizontal axis O and is controlled by a torque M applied to it. Let us introduce the following notation: \u03d5 is the angle between the pendulum and the vertical axis (Fig. 1), m is the mass of the pendulum, J is the moment of inertia relative to the axis O , l is the distance from the axis O to the center of mass of the pendulum, and g is the grav- 166 JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL Vol. 47 No. 2 2008 RESHMIN itational acceleration. The motion equation of the pendulum has the form (1.1) where the dot means the derivative with respect to the time. Assume that the constraint \u2264 M 0 (1.2) is imposed on the control torque, where M 0 is a given constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001795_00368790510575950-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001795_00368790510575950-Figure1-1.png",
        "caption": "Figure 1 Physical configuration of the cross section for a long journal bearing",
        "texts": [
            " Based on the technique of linear stability analysis, bearing characteristics including equilibrium points (i.e. the steady eccentricity ratio and the steady attitude angle), stiffness and damping coefficients, and stability threshold speed are evaluated. Comparing with the classical Newtonianlubricant case, bearing results are presented for various values of couple stress parameter and eccentricity ratio. Consider the physical configuration of the cross section for a rigid rotor supported on long bearings shown in Figure 1. The journal rotor of radius R is rotating with angular velocity v within the bearing shell. The lubricant in the system is taken to be an incompressible Stokes couple stress fluid. Under the usual assumptions of thin-film lubrication theory, the continuity equation and the Stokes motion equations in the absence of body forces and body moments are: \u203au \u203ax \u00fe \u203av \u203ay \u00bc 0 \u00f01\u00de \u203ap \u203ax \u00bc m \u203a2u \u203ay 2 2 h \u203a4u \u203ay 4 \u00f02\u00de \u203ap \u203ay \u00bc 0: \u00f03\u00de In these equations u and v denote the velocity components in the x and y directions, respectively, p the pressure, m the shear viscosity, and h represents the new material constant with the dimension of momentum and is responsible for the couple stress property"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000316_00207720119654-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000316_00207720119654-Figure3-1.png",
        "caption": "Figure 3. The inverted pendulum system.",
        "texts": [],
        "surrounding_texts": [
            "In this section, the proposed controller architecture developed in the preceding section is applied to control the inverted pendulum system, as shown in \u00ae gure 3. The dynamic equations of the inverted pendulum system are given as (Wang 1994) _x1 \u02c6 x2; _x2 \u02c6 g sin x1 \u00a1 \u2026mlx2 2 cos x1 sin x1\u2020=\u2026mc \u2021 m\u2020 l\u20304 3 \u00a1 \u2026m cos2 x1\u2020=\u2026mc \u2021 m\u2020\u0160 \u2021 \u2026cos x1\u2020=\u2026mc \u2021 m\u2020 l\u20304 3 \u00a1 \u2026m cos2 x1\u2020=\u2026mc \u2021 m\u2020\u0160 ; \u202644\u2020 where x1 represents \u00b3, x2 represents _\u00b3, g \u02c6 9:8 m s\u00a12 is the acceleration due to gravity, mc is the mass of the car, m is the mass of the pole, l is the half-length of the pole and u is the applied force. In the simulation, the true values of the parameters are chosen as mc \u02c6 1 kg, m \u02c6 0:1 kg and l \u02c6 0:5 m, and the initial states of the plant are set as \u2030x1\u20260\u2020; x2\u20260\u2020\u0160T \u02c6 \u20300; 0\u0160T. The aim of control is to derive the system output y \u02c6 x1 to track the reference command yd \u02c6 \u2026\u00ba=6\u2020 sin \u2026t\u2020: As the design procedure described in last section, we can de\u00ae ne the vectors and variables as follows: x \u02c6 \u2030x1; x2\u0160T, xd \u02c6 \u2030yd; _yd\u0160T, ~x \u02c6 x \u00a1 xd \u02c6 \u2030~x1; ~x\u0160T, e \u02c6 \u2030\u00b6 1\u0160~x, \u00b8 \u02c6 \u00a1 xd \u2021 \u20300 \u00b6\u0160~x and z \u02c6 \u2030x1; x2; e; \u00b8\u0160T. The adaptive RBF NN system with the proposed enhanced control algorithm is then u \u02c6 \u00a1kse \u2021 W\u0302TR\u2026Y\u0302T\u00b7z\u2020 \u2021 us; \u202645\u2020 us \u02c6 \u00a1K\u0302\u00bf sgn \u2026e\u2020; if jej > \u2019; \u00a1K\u0302\u00bf e \u2019 ; if jej 4 \u2019; 8 >< >: \u202646\u2020 where ks is the convergent factor for Lyapunov stability; \u00b7z \u02c6 \u2030\u00b7z1; \u00b7z2; . . . ; \u00b7z`\u0160T with \u00b7z1 7 kz \u00a1 cik, in which ci is the \u00ae xed and predetermined centres of the hidden units; \u00bf is from the parametrization vector for the error bound as derived in (22). The estimated parameters of the RBF NN system for on-line reconstructing the ideal controller are W\u0302 , Y\u0302 and K\u0302 according to the adaptation mechanism formulated in (27) with the modi\u00ae cation (43). D ow nl oa de d by [ D U T L ib ra ry ] at 2 0: 19 0 7 O ct ob er 2 01 4 D ow nl oa de d by [ D U T L ib ra ry ] at 2 0: 19 0 7 O ct ob er 2 01 4 By inspecting the transient performance de\u00ae ned in (34) and (41), large L will perform a faster transient response, but with larger transient error; conversely, large ks can reduce the bound F. Through the practical evaluation for some trade-o\u0152, in the following simulation, we choose ks \u02c6 25 and L \u02c6 20. Meantime, the parameters in (43) and the adaptation scheme (27) are set as Gw \u02c6 diag \u20260:8\u2020, G\u00b3 \u02c6 diag \u20260:3\u2020, Gk \u02c6 diag \u20260:8\u2020, \u00bc \u02c6 0:2 and \u2019 \u02c6 0:05. Since jxij 4 p=6, jej 4 p=3 and j\u00b8j 4 4p under the selection of ks and L, centres of the multidimension Gaussian functions are chosen as c1 \u02c6 \u2030\u00a1p=6, \u00a1p=6, \u00a1p=3, \u00a14p], c2 \u02c6 \u2030\u00a1p=9, \u00a1p=9, \u00a12p=9, \u00a18p=3\u0160, c3 \u02c6 \u2030\u00a1p=18, \u00a1p=18, \u00a1p=9, \u00a14p=3\u0160, c4 \u02c6 \u20300; 0; 0; 0\u0160, c5 \u02c6 \u2030p=18; p=18; p=9; 4p=3\u0160, c6 \u02c6 \u2030p=9; p=9; 2p=9; 8p=3\u0160, c7 \u02c6 \u2030p=6; p=6; p=3; 4p\u0160 for the seven hidden nodes. The initial conditions W\u0302\u20260\u2020, Y\u0302\u20260\u2020 and K\u0302\u20260\u2020 of the controller are taken randomly in the intervals \u2030\u00a11; 1\u0160, \u20300; 0:01\u0160 and \u20300; 2\u0160 respectively. Simulation results of the tracking control are shown in \u00ae gure 4. Figure 4(a) shows that the controller can successfully control the pendulum angle y \u02c6 x1 \u02c6 \u00b3 to follow the speci\u00ae ed command trajectory yd. Figure 4(c) further indicates that the tracking error y \u00a1 yd converges rapidly to a small region around zero in 1 s. The control Figure 5. Simulation results of the tracking control for the inverted pendulum system (Pole length is time-varying). D ow nl oa de d by [ D U T L ib ra ry ] at 2 0: 19 0 7 O ct ob er 2 01 4 e\u0152ort shown in \u00ae gures 4(b) and (d) represents good reconstruction of the control input using our proposed adaptive RBF NN controller. Finally, all the signals are bounded and the global stability of the overall system is guaranteed, as shown in \u00ae gures 4(e)\u00b1 (h). Furthermore, to verify the capability of the proposed controller to control the time-varying plants, the length of the pendulum pole is considered to be a time function: 2l\u2026t\u2020 \u02c6 1 \u2021 0:5 sin \u20266t\u2020. From the simulation results illustrated in \u00ae gure 5, good system performance of controlling a time-varying plant is obtained and the stability of the whole system is still ensured. To compare with NN control in the use of a conventional RFB NN, we simulate the same example under the same conditions as \u00ae gure 4 but \u00ae x Y\u0302 \u02c6 diag \u2026p=24\u2020 without adaptation (Sanner and Slotine 1992). The comparison results of the tracking error for the inverted pendulum system on adopting di\u0152erent NN schemes are illustrated in \u00ae gure 6, in which the simulation result obtained using an MLP-type NN structure is also involved (Ge et al. 1998). Figure 6 obviously reveals that our proposed scheme indeed signi\u00ae cantly upgrade the on-line re-construction ability of the ideal controller, thereby exhibiting excellent tracking performance for the inverted pendulum system. Also, the number of adaptation laws can also be reduced by utilizing the proposed enhanced scheme as shown in table 1, thereby saving the computational e\u0152ort."
        ]
    },
    {
        "image_filename": "designv11_28_0001322_20020721-6-es-1901.00087-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001322_20020721-6-es-1901.00087-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the Furuta pendulum",
        "texts": [
            " The LPV synthesis technique provides a framework to incorporate gain scheduling strategies in the controller (Kajiwara et al., 1999). Simulation results show that with this gain scheduling strategy, the swing up and balancing behaviour of the pendulum is less sensitive to the changes in the parameters of the swing up law. In this section, we will show how an LPV model can be obtained from the nonlinear model of the Furuta pendulum. The LPV model will then form the basis for the robust predictive control strategy described in Section 4. Fig. 1 shows a schematic and the co-ordinate system used for the derivation of the dynamic model for the Furuta pendulum. The pendulum system consists of two sections, namely the rotating arm and the pendulum whose angular positions are denoted respectively by \u03b1 and \u03c8 = \u03b8\u2212\u03c0 (\u03c8 = 0 in the upward position). Using the method of Lagrange, the nonlinear model of the Furuta pendulum is J(\u03c8) [ \u03b1\u0308 \u03c8\u0308 ] +C(\u03c8, \u00fa\u03c8, \u00fa\u03b1) [ \u00fa\u03b1 \u00fa\u03c8 ] = [ t3v t6 sin\u03c8 ] (1) where J(\u03c8) = [ 1+ t7 sin2 \u03c8 \u2212t1 cos\u03c8 \u2212t4 cos\u03c8 1 ] (2) C(\u03c8, \u00fa\u03c8, \u00fa\u03b1) =   t2 + 1 2 t7 \u00fa\u03c8sin2\u03c8 t1 \u00fa\u03c8sin\u03c8+ 1 2 t7 \u00fa\u03b1sin2\u03c8 \u22121 2 t8 \u00fa\u03b1sin2\u03c8 t5   (3) ti, 1 \u2264 i \u2264 8, are suitable coef\u00decients depending on the physical parameters of the system and v is the motor voltage input"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000489_robot.1994.350998-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000489_robot.1994.350998-Figure3-1.png",
        "caption": "Figure 3: (a) The robot on a flat surface. (b)The robot on a slope keeping the same joint positions leads to an unbalanced condition.",
        "texts": [
            " These two steps effectively multiply the distal error by an estimate of the transpose Jacobian matrix (aF/du). By using the three terms just described, the algorithm for training the inverse model is based on the following estimated gradient: 111. Distal Supervised Learning Applied to Biped Robots We assume that the robot currently possesses a stable flat floor walking gait. On the flat surface, the center of gravity will be directly between the supporting feet. When placed on the slope, the center of gravity will shift away from the center of the supporting area, see Fig. 3. The learning algorithm needs to adjust the robot\u2019s joint positions so as to regain stability. A . Walking Gait/Problem Description Since only the joint motions in the sagittal plane will affect the stability of the biped walking on the slope, our study will concentrate on the sagittal plane. In the sagittal plane, the robot is equivalent to have five links and four joints as shown in Fig. 1. When the biped makes one step forward (puts one foot forward) it goes through four phases. The four phases are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000462_s0263574701003691-Figure16-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000462_s0263574701003691-Figure16-1.png",
        "caption": "Fig. 16. Example of particle shapes with different values of k.",
        "texts": [
            " Gx1,x2 = v cos sin v cos2 v sin2 v cos sin (26) The stress produced by the constraint tensor G on a particle frontier is by definition equal to F= G \u2022 n (27) where n is the normal vector at the surface of a fluid particle n=a +b F= G \u2022 n= a sin v a cos v xi,x2 = 0 a v (28) v and n, F \u2022 v=0 The G tensor produces a force F opposite to the deformation (Figure 15). We define a new tensor by adding a term to the Stokes\u2019 equation: = p I+2 D+k( x) G (29) where I is the identity tensor, D the deformation rate tensor, the viscosity coefficient, and k the curve coefficient depending on the local position. By using local internal constraints opposite to shear, we can control local fluid particle deformations and consequently the global fluid direction (Figure 16). To influence the particle direction, a different value of the stress coefficient k is used. New global equations are then defined: div + F= 0 (30) div v=0 (31) With the following additional constraint: v || v || < max where Kmax is the upper bound of the curvature. By this method, roads with a bounded curvature radius are obtained (Figure 18), to be compared with the classical simplest Stokes\u2019 equation (Figure 17). http://journals.cambridge.org Downloaded: 03 Jun 2014 IP address: 150.216.68.200 A non-holonomic robot is only able to start in a limited range of directions (Figure 19)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002533_17488840610653397-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002533_17488840610653397-Figure1-1.png",
        "caption": "Figure 1 The micro aerial vehicle configuration (MicroHawk)",
        "texts": [
            " Within this area of interest, a research activity was started at Politecnico di Torino (Fantinutto et al., 2005). In the present paper, a control design application for the MicroHawk micro aerial vehicle is discussed. The MicroHawk (Pralio et al., 2003) concept was designed within a European Union funded project (Micro Aerial Vehicles for Multi Purpose Remote Monitoring and Sensing Project), by a research group at Politecnico di Torino. It consists of a fixed wing, tailless integrated wingbody configuration, powered by a DC motor and tractor propeller (Figure 1). Three versions have been developed and tested, Flight control system for a micro aerial vehicle Giorgio Guglieri, Barbara Pralio and Fulvia Quagliotti Volume 78 \u00b7 Number 2 \u00b7 2006 \u00b7 87\u201397 characterized by different size and weight. A 150mm wingspan platform \u2013 named MicroHawk150 \u2013 has been designed and developed for very short range, remotely piloted missions, characterized by low flight duration and narrow operating scenario. It has been equipped with basic on-board systems (DC motor, propeller, battery pack, controller, receiver and servos), for a total weight of approximately 35 g"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003996_j.ijmultiphaseflow.2009.02.005-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003996_j.ijmultiphaseflow.2009.02.005-Figure1-1.png",
        "caption": "Fig. 1. Definition sketch for two drops covered with incompressible surfactant interacting due to an applied temperature gradient rT.",
        "texts": [
            " (2003) on two contaminated drops in shear flow confirmed the usefulness of the theoretical results of Blawzdziewicz et al. (1999), probed the limits of the incompressible model, and made modifications for the more general surfactantcoverage case. Herein, we investigate the limit of nearly uniform surfactant coverage in the case of two spherical drops in thermocapillary motion. The assumptions behind the model, problem formulation and method of solution are the subject of Section 2. Results and discussion are found in Section 3, and concluding remarks in Section 4. Fig. 1 depicts schematically the interaction due to a constant applied temperature gradient rT1 of two drops of one liquid immersed in a second immiscible liquid under conditions such that inertia and convective transport of energy are negligible, i.e., when the Reynolds number Re \u00bc qeV \u00f00\u00de2 a2=le and Marangoni number Ma \u00bc a2V \u00f00\u00de2 =DT for the larger drop are small. The quantities qe and le are the surrounding liquid density and viscosity, respectively, while qd and ld are the drop density and viscosity",
            " (2000), and Zinchenko (1980): Bispherical coordinates are employed for LA along the line of centers and multipole techniques for MA perpendicular to the line of centers. Relevant details can be found in Appendices A and B. The mobility functions GA and HA were previously determined for bubbles by Blawzdziewicz et al. (1999) and arbitrary viscosity ratio by Rother and Davis (2004). Once the mobility functions are known, it is possible to calculate the collision efficiency E12 via a trajectory analysis for thermocapillary motion. For an arbitrary trajectory in an applied temperature gradient, as in Fig. 1, the drops have an initial horizontal offset d1 when well separated. As the larger drop catches up to the smaller one, the drops will either collide and coalesce, or eventually separate. The collision efficiency E12 is determined through the critical horizontal offset d 1 demarcating trajectories which lead to coalescence and separation. In thermocapillary motion without attractive forces (Zhang and Davis, 1992), E12 \u00bc d 1 a1 \u00fe a2 2 \u00bc exp 2 Z 1 2 MA LA sLA ds : \u00f011\u00de When molecular forces are included in Marangoni-induced motion, there is no longer a closed-form solution for E12"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002307_1.2406105-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002307_1.2406105-Figure9-1.png",
        "caption": "Fig. 9 Hob-setting angle h of an involute hob",
        "texts": [
            " For computation f the actual value of the angle , the following expression can be sed tan = db.h 4 \u00b7 R2 \u2212 db.h 2 14 Then, consider three unity vectors A, B, and C. These vectors ield the following analytical representation A = cos h 0 sin h 1 T 15 B = sin n sin h \u2212 cos n \u2212 sin n cos h 1 T 16 C = \u2212 cos r tan \u2212 cos r \u2212 sin r cos 1 T 17 Here h designates the hob-setting angle of the involute hob. he angle h is measured in the auxiliary rack R pitch plane. It is he angle that is a perpendicular to the rack R tooth and axis of otation of the hob Fig. 9 8,14 . For further computations of the required hob-setting angle h an be chosen by a designer of the gear hob. Usually, it is recom- ended to assign the actual value of the hob-setting angle h ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ash equal to the pitch helix angle h of the hob. As was proved in our earlier work 14 , in order to satisfy the equality h= h this conditions is the best possible the actual value of the hob-setting angle is required to be computed from the equation tan h = m \u00b7 Nh do",
            "ash more equation of two unknowns, namely of r and . Further, consider the set of two equations, say of Eqs. 19 and 22 of the two unknowns r and . The solution to the set of the above equations can be represented in the form tan = cos h \u00b7 tan tan n + sin h \u00b7 tan 23 tan r = tan sin 24 The hob-setting angle h specifies inclination of the gear hob axis of rotation Oh with respect to the auxiliary rack R. It is necessary to point our here that the angle h is a parameter of the gear hob design, and is not a parameter of gear hobbing operation. Figure 9 reveals that it could be either positive + h 0 deg , or negative \u2212 h 0 deg , as well as it could be of zero value h =0 deg . Under special conditions, the hob-setting angle could be equal to the gear hob pitch helix angle R i.e., the equality h = R could be observed . Equations 23 and 24 are necessary for computation of the required values of the angles r and . These angles are necessary and have been indicated in the involute hob blueprint. The involute hob of novel design 15 with the angle computed from Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002462_s00466-006-0120-3-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002462_s00466-006-0120-3-Figure10-1.png",
        "caption": "Fig. 10 The resultant force and moment on the joint",
        "texts": [
            " The resultant force on element i at point A, located at a distance x from the midpoint M of the contacting side (see Fig. 9) is d F = d Fs + d Fd (6) The total force acting on the contacting side of element i is then found by integrating the normal and tangential forces in each of the connecting fibers. It is given by F = \u239b \u239d L\u222b \u2212L ( Kndn + Cn dn d\u03c4 ) dx \u239e \u23a0 n\u0302 + \u239b \u239d L\u222b \u2212L ( Ktdt + Ct dt d\u03c4 ) dx \u239e \u23a0 t\u0302 (7) where 2L is the length of the contacting side. The resultant force is assumed to act through the midpoint M of the side. Note that this is accompanied by a moment about M as shown in Fig. 10, given by MM = L\u222b \u2212L ( Kndn + Cn dn d\u03c4 ) xdx (8) The force F has normal and tangential components Fn and Ft, respectively. The normal and tangential stresses on the joint are approximated by dividing the corresponding force components by the contact length: \u03c3n = Fn 2L (9) \u03c3t = Ft 2L (10) This assumption is valid only if the moment MM is small and if the force distribution along the joint is uniform. In order to compute the orthogonal stresses (\u03c3xx, \u03c3yy and \u03c4xy) at the element centroid G, the stress retrieval algorithm proposed by Bolander et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003682_optim.2008.4602380-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003682_optim.2008.4602380-Figure1-1.png",
        "caption": "Figure 1. Stator-field- oriented space-phasor diagram of the synchronous motor with adjustable exciting field and controlled stator flux operating at unity PF for different values of the load torque",
        "texts": [
            " the direct and quadrature axis components of the stator flux ( sd\u03b8\u03a8 and sq\u03b8\u03a8 ) and of the damper winding flux ( Ad\u03a8 and Aq\u03a8 ), the excitation flux ( e\u03a8 ) and the rotor electrical angular speed (\u03c9 ), resulting the following equations: \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a9 \u23aa\u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a8 \u23a7 \u23a5\u23a6 \u23a4 \u23a2\u23a3 \u23a1 \u2212\u22c5\u03a8\u2212\u22c5\u03a8\u22c5= \u22c5\u2212= \u03a8 \u22c5\u2212= \u03a8 \u22c5\u2212= \u03a8 \u03a8\u22c5\u2212\u22c5\u2212= \u03a8 \u03a8\u22c5+\u22c5\u2212= \u03a8 ,)( 2 3 ; ; ; Lsdsqsqsdp tot p AAA A AAA A eee e sd \u03b8sq \u03b8ssq \u03b8 sq \u03b8 sq \u03b8sd \u03b8ssd \u03b8 sd \u03b8 miiz J z dt d ;iRu dt d ;iRu dt d iRu dt d \u03c9iRu dt d \u03c9iRu dt d qqq q ddd d \u03b8\u03b8\u03b8\u03b8 \u03c9 (1) The exciting and damper windings will be referred to the armature number of turns and number of phases: in the armature there are three ones, contrary to the single-phase exciting winding; the proper two-phases of the damping bars are also transformed into another two-phase equivalent one, corresponding to a fictitious three-phase winding, like that of the stator [2]. The above presented mathematical model is used both for simulation and implementation purposes, because the computation of the control variables are made based on them. III. STATOR-FIELD-ORIENTED VECTOR CONTROL The stator-field orientation ensures the most suitable procedure for the control of the power factor and the resultant stator flux. The power factor is maximum, when the stator voltage and stator current are in phase, as is shown in Fig. 1. Consequently, the stator-flux vector \u03a8s results perpendicular onto the current space phasors is1,2,3. each corresponding to another load torque. In order to achieve the unity power factor the top of the stator resultant flux \u03a8s must be situated on the semi-circle, which diameter is the space phasor of the exciting flux \u03a8me. given by the exciting current in the air gap. This statement results from the stator-voltage equation, written with space phasors, if the derivative of this flux (it is controlled or the machine is in steady state) is zero. In rotor-oriented diagram, if the top of \u03a8s is inside the circle, the synchronous motor will operate with capacitive current [2]. The diagram from Fig. 1 also shows, that not only the stator voltage, but also the exciting current must be adjusted according to the load torque in order to keep constant both the resultant stator field (ims the corresponding magnetizing current, too) and the power factor at unity value [2]. The perpendicularity between the resultant stator-flux and the armature current space phasor can be achieved if the resultant stator-field-oriented longitudinal armature reaction is cancelled. The structure of the vector control system based on the above presented principle is presented in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001234_ias.1989.96727-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001234_ias.1989.96727-Figure2-1.png",
        "caption": "Figure 2 . Construction of the flywheel energy storage unit.",
        "texts": [
            " [ 2 ) , [3] To get the unity input power factor and high efficiency, the power converter with the simple half bridge configuration is presented. To get sinusoidal input current and output voltage waveforms, the converter and the inverter are controlled with high response current and voltage follow-up methods,respectively. This paper presents about the process of the development of the new UPS using the flywheel energy storage unit and its energy conversion systems. 2. Flywheel Energy Storage Unit Figure 2 shows the construction of the flywheel 89CH2792-0/89/0000-0711$01.00 0 1989 IEEE where m(r), h(r) and w are mass, density and height and angular velocity of the flywheel material, respectively. J and E calculated from above equations are 0.167 (Kgm2) and 0.23(KWh), respec t ively . The unit which exchanges between mechanical and electrical energies is adopted an induction machine, because of cost, life time, efficiency and high speed construction. The outer rotor construction having cage windings inside of the flywheel is employed as shown in Figure 2. The inside of this bessel is vacuumized about 0.05 (Torr) by 60 (W) vacuum pump to decrease windage losses. Windage losses obtained from the system may be only 1 (W). The pump is operated about ten minutes every week when the pressure rises above 0.1 (Torr),so the mean energy consumed by the pump is very small. This bessel is tighten with 0 ring to protect a leak of the air. To support the high speed rotor, it is employed three types of bearings, (1) Magnetic bearing made of the rare earth metal lifts up 90 ( X ) of the rotor weight",
            " These influences on the flywheel energy storage unit can be ignored but it is very dangerous when the earthquake or some vibration is occurred. But this unit have a high ability of earthquake-proof till the earthquake shock factor 5 which corresponds to a severe shock. For protection in this case, at first, the inside of the bessel is filled by air using a electro-magnetic value, and the rotor is quickly decreased its speed under 10000 (rpm) by windage losses. Even if the flywheel rotor is destroyed, the rotor can be decreased the speed by friction with the protecting ring shown in Figure 2 . 712 mtor current im I Figure 7. Experimental result of the transient phenomena. Figure 5 shows experimental results of the flywheel free run characteristics. The windage loss is increased according to the inside pressure rise. It becomes almost zero (under 1W) at 0.02 (Torr) where the deceleration characteristic is almost linear. A s shown before, the moment of inertia of the flywheel is 0.167 (kgm'). So, mechanical losses of the flywheel unit is evaluated about 37 (W). The loss is mainly generated by viscosity resista'nce of the spherical spiral pivot bearing oil"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000078_0076-6879(88)58059-x-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000078_0076-6879(88)58059-x-Figure2-1.png",
        "caption": "FIG. 2. Rotating disk electrode (a) side and (b) bottom views. A, brass spindle; B, Teflon insulator; C, electrical contact; D, electrode material. Arrows show direction of rotation of electrode and of fluid flow about the rotating electrode.",
        "texts": [
            " They also measure the current flowing through the indicator electrode (and through a counter electrode which completes the circuit). The output is values of potential and current which can be displayed during the experiment. The plot of current versus potential is called a voltammogram. Here we discuss rotating disk voltammetry, normal and differential pulse voltammetry, staircase and square wave voltammetry, and linear scan voltammetry. Potential programs for these techniques are shown in Fig. 1 together with typical voltammetric response. Several views of a rotating disk indicator electrode are shown in Fig. 2. It consists of a conducting disk sealed into an insulator, the whole assembly having the form of a cylinder. When this is rotated about the cylindrical axis in solution, steady-state convection to the disk is established, which in turn gives rise to a steady-state current. The resulting voltammogram for an uncomplicated reversible reaction is S-shaped, described exactly by the equation i/iL = 1/(1 + C0) (1) where i is the current, iL the limiting (or plateau) current, ~ the quantity ( D o ~ D R ) 2/3 where Do and DR are the diffusion coefficients of the oxidized and reduced forms, respectively, and 0 = e \"F(E-~')mT (2) where F is the value of the Faraday, R the gas constant, T the absolute temperature, E \u00b0' the formal potential, and n the stoichiometric number of electrons for the reaction 0 + n e - = R (3) The value of F / R T at 25 \u00b0 is 38"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002307_1.2406105-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002307_1.2406105-Figure5-1.png",
        "caption": "Fig. 5 Cylindrical generating surface T of an involute hob",
        "texts": [
            "2 The DG/K Approach of Generation of the Surface T of n Involute Hob. Equation of the generating surface T of an invoute gear hob can be derived using elements of theory of envelopng surfaces, which is a part of the DG/K approach of surface eneration. In order to derive equation of the surface T, it is convenient to onsider the relative motion that the auxiliary rack R is performng with respect to the coordinate system XhYhZh embedded to the ob. The coordinate system XhYhZh is the left-handed Cartesian oordinate system Fig. 5 . Similarly to Eq. 2 , the operator Rs R T of the resultant oordinate system transformation could be composed Rs R T = Rt ,Zh \u00b7 Tr 0.5dh,Yh \u00b7 Tr l,Xh 9 In Eq. 9 , the hob angle of rotation is equal to = h \u00b7 t, and ranslation of the auxiliary rack R can be computed from the equaion l= VR \u00b7 t. The hob pitch diameter is designated as dh. The derived Eq. 5 together with Eq. 9 could be employed or analytical description of the auxiliary rack R, which is perorming screw motion with respect to the hob axis of rotation Oh"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002624_1-4020-3393-1_7-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002624_1-4020-3393-1_7-Figure7-1.png",
        "caption": "Fig. 7. Describing more complex muscle actuators.",
        "texts": [
            " In order to obtain muscle forces or muscle activations, these multipliers must be multiplied by proper scalar factors, which are closely related with the type of muscle model adopted. Muscle actuators defined with more than two points are introduced in the Jacobian matrix of the constraints as a sum of several two-point muscle actuators. Consider, for example, the muscle tensor fasciae latea presented in Figure 5. This muscle is described using three two-point muscle actuators, labeled respectively m1, m2 and m3 in Figure 7. The Lagrange multipliers m1, m2 and m3 are associated to muscle actuators m1, m2 and m3, respectively. With the information presented before, the term q T of Equation (4) is assem- bled for muscle actuators m1, m2 and m3, and written as: 1 2 3 1 3 3 1 2 4 14 4 2 3 5 25 5 6 3 3 7 5 m m m m m m m m m m m m q q 0 0 q q q 0 q 0 q q q 0 0 0 q 0 0 q (8) where q3 to q7 indicate the rows of the Jacobian matrix and represent the set of natural coordinates defining the rigid bodies interconnected by the muscle, and \u2022 mi/\u2022qj are the partial derivatives of muscle actuator equation mi with respect to the natural coordinate qj"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003195_s11071-007-9275-5-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003195_s11071-007-9275-5-Figure2-1.png",
        "caption": "Fig. 2 Position vectors of the plane body centers S, S1 and S2 with respect to a fixed point O",
        "texts": [
            " If external forces and moments act on the system, the differential equations (21) are extended to M dv dt = FS + , I d\u03a9 dt = MF S + +M\u03a6 S + dI dt (\u03a92a \u2212 \u03a9). (22) Comparing the relations (22) with those in [15], the total compatibility of the systems is evident. Consider the body which moves in-plane before and after body separation. The absolute velocity of the whole body, remainder and separated body are defined by (3) and (10), with projections vSb = vSbx i + vSbyj, vS1 = vS1x i + vS1yj, u = ux i + uyj, (23) where i and j are unit vectors in the plane of motion (Fig. 2). For the in-plane motion the angular moments of the whole body, separated body, and remainder body are LS1 = IS1\u03a91ak, LSb = IS\u03a9bk, LS2 = IS2\u03a92ak, (24) where k is the unit vector orthogonal to the plane of motion. Substituting (24) into (17) we obtain the angular velocity of the remainder body as a function of the angular velocity of the separated body IS1\u03a91ak = IS\u03a9bk \u2212 IS2\u03a92ak + SS2 \u00d7 (vS1 \u2212 u)m, (25) where SS2 = SS2x i + SS2yj. (26) In relation (25) the absolute angular velocity of the remainder body is the function of the absolute angular velocity of the separated body"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003236_proc-1038-o05-09-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003236_proc-1038-o05-09-Figure3-1.png",
        "caption": "Figure 3: Two design modifications to the crystal growth system are considered in the computations presented here. The first, depicted on the left, is a change to the ampoule support system meant to increase the axial flow of heat. The second, shown on the right, is a change to the shape and composition of the ampoule.",
        "texts": [
            " Then the thermal environment is changed in a time-dependent manner to effectively translate the melting point upward along the charge, as indicated by the right-hand side of Figure 2. Moving the melting point induces directional solidification of the charge and enables crystal growth. The EDG system employs computer control of individual heating zones to impose a specific temperature setpoint schedule for growth. In the computations presented here, we consider the outcome from two design changes to the growth system, as depicted in Figure 3. The first change (shown on the left side of the figure) involves a modification of the ampoule support system meant to increase the axial flow of heat through the bottom center of the ampoule. The silicon carbide (SiC) support rod is extended completely through the refractory material plugging the bottom of the furnace bore. This change allows for a heat path through the relatively high thermal conductivity SiC rod out of the hightemperature region of the furnace to the cooler ambient. The other modification adds a graphite disk under the tip of the ampoule to maintain intimate thermal contact between the ampoule and the support system. The next design change is more substantial and indicated on the right of Figure 3. Here, we wish to predict the impact on growth conditions by replacing the existing graphite ampoule with one fabricated from pyrolitic boron nitride (PBN). Profiles of the temperature field along the system centerline, through the molten charge, are shown in Figure 4 for both ampoule types for the original furnace design (old) and the new ampoule support configuration (as indicated on the left-hand side of Figure 3). Note that the temperature field is plotted on the abscissa while vertical position (normalized so that the origin corresponds to the bottom, interior tip of the ampoule) is plotted on the ordinate. The temperature curves correspond to furnace conditions (by vertical translation of the set points) that place the melting point of CZT at the bottom tip of the original graphite ampoule. These furnace set points are then employed for all of the other design configurations shown in Figure 4. It is instructive to compare these profiles case by case",
            " In this system, the new support clearly increases the axial flow of heat out of the ampoule tip and produces much lower temperatures and increased axial temperature gradients. (Note that a steeper axial temperature profile appears flatter in the plots shown here, with temperature on the abscissa and position on the ordinate.) This is a generally desirable outcome which will be discussed further in the conclusions section. A more significant effect in the crystal growth system is achieved by changing the ampoule design (as indicated by the right pane of Figure 3). Figure 5 depicts both systems, with temperature contours shown on the left-side and streamfunction contours for flow within the melt shown on the right. The velocity of the melt is everywhere tangent to the streamfunction contours (also known as streamlines), and the volumetric flow is proportional to the differences between the streamfunction values. For equally spaced streamfunction contours, as are shown here, the flow is stronger where the streamlines are more closely spaced. All other features of the system are unchanged for these two computations, and we consider the design of the new support system indicated by the left pane of Figure 3. In particular, both of these systems employ the same furnace set-point profiles. Each state corresponds with a shifted furnace setpoint profile that yields the freezing point of CZT at the bottom interior of the ampoule. In these unseeded systems, this point corresponds to just prior to the nucleation of solid material and growth. For the system with the graphite ampoule, the temperature profile through the melt is nearly linear in the axial direction, as indicted by the nearly constant vertical spacing of the temperature contours; however, the gradient increases slightly as the cone region is approached"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001757_acc.1994.735044-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001757_acc.1994.735044-Figure2-1.png",
        "caption": "Figure 2: Initial values",
        "texts": [
            " Supose that 0 is the selected point, then the equation which is to be solved is 20 = I v + RU while a priori setting v = X O - R ~ U = 6. Linear programming then starts with checking the signs of the components of U. For comparison, we use the example given in [RaHa75]. The system under consideration is Iul 5 1, t 2 0. With a sampling period of 0.1 s, we get the discrete-time model 0.9324 0 0 0.9704 i.0951 1 \" zt+l = To initialize the linear programming algorithm, a feasible solution is necessary, thus the vector N , , ~ cannot be used. Instead, the following points can be chosen as starting points (see fig. 2): o The point where ups intersects the boundary of the box, A, can be computed as ~ p s / I I u p s / ~ c o r I I , , The nearest point B on the boundary has the values of ups, if they are feasible, or the values of ucor otherwise, 0 the nearest point C from ucor on the hyperplane given by ucor - ups(ttLjtlcor/Ukjups - I) , 2vector division : elementwise. l U , , t l S l , Z = l , 2 , t = 0 , 1 , ...) k - 1 Solutions of t,he above problem for different initial conditions have been calculated without and with the acceleratmion method"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003868_s10015-008-0557-x-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003868_s10015-008-0557-x-Figure2-1.png",
        "caption": "Fig. 2. Proposed manipulator. a Manipulator, b Duplex mechanism",
        "texts": [
            " So, it is diffi cult for conventional robots to go through in its space. Second is electric power supply. We cannot supply enough electric power, because of blackout in disaster site. On the other hand, an industrial endoscope is used in such situation. An industrial endoscope does not have the above problems because the size is small enough, and we do not require power supply for moving it. However, the industrial 3 Proposed mechanism 3.1 Structure In this paper, to solve the problem written in section II, we propose new manipulator that has duplication system Fig. 2 shows mechanism of the proposed manipulator. The manipulator has many passive joints that have lock mechanism. Two wires are installed around both sides of the manipulator, and a hose is installed in its center (Fig. 2a). A rail is installed on a side of the manipulator. Two manipulators are connected by the rail. They can be moved along the rail each other (Fig. 2b). 3.2 Mechanism of changing direction Wire is fi xed on top rink and tube is fi xed on the end rink. By pulling the wire, we can change head direction, and then lock the joints at the state (Fig. 3). 3.3 Lock mechanism Figure 4 shows structure of each joint. Each joint have two frictional materials.And, hose passed through the center. By putting water into the hose, the hose expands, and the expanded hose pushes inside friction materials, then, inside friction materials engages with outside friction materials"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000877_bf00384690-Figure5.1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000877_bf00384690-Figure5.1-1.png",
        "caption": "Fig. 5.1. A thick-walled model of the tube. The undeformed configuration is referred to the cylindrical coordinates R, 0, Z, and the deformed configuration to the cylindrical coordinates r, 0, z. The pitch angles are \u2022 and q~, respectively.",
        "texts": [
            " Therefore in this section we consider a model in which the two rubber cylinders have a finite thickness, whereas the steel braid is an infinitely thin membrane. Fur ther we assume the rubber of the two cylinders to be a Mooney material [7, 8], and we take the steel wires as being inextensible. As in the previous section we use one cylindrical coordinate system for the undeformed hose, as well as for the deformed one. The Langrangian coordinates are X ~ ( X 1 = R, X 2 = O, X 3 = Z ) , and the Eulerian coordinates are x~(x I = r, x 2 = 0, x 3 = z), as depicted in Fig. 5.1. In the usual way we define the natural base vectors G~, pertaining to the Lagrangian coordinates, and in the current state the natural base vectors gi, which belong to the Eulerian coordinates. F rom these we derive the set of reciprocal base vectors G ~ and gi. The metric tensors G~, G ~, gij and giJ are calculated as usual. In the following the notat ion of the various kinds of components will follow from the text, however, in view of the simplicity of the analysis we shall pass to the use of physical components as soon as possible hereafter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002839_1.15015-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002839_1.15015-Figure1-1.png",
        "caption": "Fig. 1 Typical wing-flap section.",
        "texts": [
            " In this context, the linear-quadratic-Gaussian (LQG) control strategy using SMO will be implemented, and some of its performances will be put into evidence. These will be compared with conventional LQG with Kalman filter. For the purpose of control, in general, not all of the states are available online because of either initial configuration or malfunctions, and the feedback control should be implemented via the estimated states. In this connection, we consider two cases; for one it is possible to measure only the plunging displacement h, whereas in the other case, the measurement of the pitching displacement \u03b1 is available, only. Figure 1 presents the typical wing-flap system that is considered in the present aeroelastic analysis.7,8 The three degrees of freedom associated with the airfoil appear clearly from Fig. 1. The pitching and plunging displacements are restrained by a pair of springs attached to the elastic axis with spring constants K\u03b1 and Kh , respectively. The control flap is located at the trailing edge. A torsional flap spring of constant K\u03b2 is also attached at the hinge axis; h denotes the plunge displacement (positive downward), \u03b1 the pitch angle (measured from the horizontal at the elastic axis of the airfoil, positive nose up), and \u03b2 is the flap deflection (measured from the axis created by the airfoil at the control flap hinge)",
            " In the presence of external time-dependent excitations, the determination of the time history of the quantities [h\u0303(\u2261 h/b), \u03b1, \u03b2], at any flight speed lower than the flutter speed, requires the solution of a boundary-value problem.10 In the absence of the control input, the open-loop aeroelastic response is obtained, whereas in the presence of the control, the closed-loop aeroelastic response is derived. Figure 3 shows that for the case of the only plunging measurement available as a sensor output the Kalman filter finally produces stable pitching state estimates based on the measurement of plunging displacement only and, consequently, makes the system stable after more than 10 s (Fig. 1 is shown up to 7 s), the obtained data being simulated with the initial conditions h\u0303 = 0.01 and \u03b1 = 0.1 rad and at the flight speed V f = 430 ft/s (131 m/s). Figure 4 reveals that for the case of only pitching measurement available, stable pitching state estimation is achieved in about 3 s through sliding-mode observer with the same initial conditions h\u0303 = 0.01 and \u03b1 = 0.1 rad and V f = 430 ft/s (131 m/s). The same conclusion as in Fig. 4 is reached D ow nl oa de d by U N IV E R SI T Y O F SH E FF IE L D o n Ju ne 4 , 2 01 4 | h ttp :// ar c"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000500_acc.2002.1024608-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000500_acc.2002.1024608-Figure1-1.png",
        "caption": "Figure 1: Geometric dependencies used to calculate the position of the vehicle",
        "texts": [
            " The paper concludes with Section 5 . The motion of the vehicle is described by the well known non-holonomic equations for a rear wheel driven tricycle [6]: i = cos(e).vR $ = sin(0) ' v ~ (1) e = +tan(bFM).vR where V R is the velocity of the rear wheels, 1 the wheel base and ~ F M the steering angle of the virtual middle front wheel, respectively. The equations describe the position of the car's coordinate-system, attached to the midpoint of the rear axle, with respect to the world coordinate system as depicted in figure 1. The figure shows a car with the so called Ackermann-steering, which means that no lateral forces occur at the front wheels during driving, which is not true for real cars for driving dynamic reasons. Thus, a so called virtual wheel, comprising the effective steering angles of each front wheel simplifying the real car to a tricycle model or the so called single track model, can be introduced. It can be further assumed that the no slip condition applies for the wheels. This model is the basis for path planning purposes as well as for the model based position estimation which will be described in detail in the next section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002032_j.jbiomech.2005.06.015-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002032_j.jbiomech.2005.06.015-Figure2-1.png",
        "caption": "Fig. 2. Illustration of the optical apparatus.",
        "texts": [
            " The specimens were shaken gently in recipients with 20ml of phosphate-buffered saline before the experiment, in order to eliminate the excess of synovial fluid on the articular surface. As the experiments were carried out in the physiologic saline solution, the presence of synovial fluid, which assists the lubrication, in amounts that cannot be controlled in each specimen could increase the standard deviations of the results. The schematic illustration of the optical apparatus is presented in Fig. 2. The images were captured from a laser light reflected at the interface between a prism and the specimens of AC using a CCD camera (CCD 2 in Fig. 2). The wavelength of laser light used in this experiment was 632.8 nm and power was 0.25mW (Melles Griot Co.). The refractive indices of the prism (glass BK7) and the bath solution, physiological saline, were 1.51 (n1) and 1.34 (n2), respectively. For the occurrence of TIR, the angle of incidence was set at 64.81. The experiments were realized in a dark room, in order to avoid the capture of undesired lights. According to the mentioned parameters, the effect of the evanescent waves is limited to about 200 nm from the interface. For the calculation of the reflectance (ratio between the reflected and incident light intensities), images of incident laser light were also captured (CCD 1 in Fig. 2). The attenuation of reflectance was evaluated through the comparison of the images that were acquired during the friction tests with the reference image. The reference image represents the situation when only saline is placed on the prism surface (without specimens loaded against the prism surface). All images were acquired in 8-bits pattern, which provides a resolution in the arbitrary range from 0 to 255 (28) for the light intensity. In Fig. 3, a schematic illustration of the device that was utilized in the friction tests is shown"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002671_tsmcb.2006.870636-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002671_tsmcb.2006.870636-Figure4-1.png",
        "caption": "Fig. 4. Transformation of point Pc(xc, yc, zc) \u2208 R3 with respect to {C} into point Pb(xb, yb, zb) \u2208 R3 with respect to {B}.",
        "texts": [
            " The wavelength of the laser beam ranges from 645 to 665 nm, and the optical output power is 25 mW. The CMOS web camera, the ZECA MV402 of Mtekvision Co., Ltd., is used to detect the laser-line segment. The inclinometer, the 3DM of MicroStrain, Inc., is used to measure the absolute angles from 0\u25e6 to 360\u25e6 on both the yaw and pitch axes, and from \u221270\u25e6 to 70\u25e6 on the roll axis with respect to the universal frame {U}. The data of the inclinometer is obtained via the RS232 serial interface. The relation between the base frame {B} and the camera frame {C} is depicted in Fig. 4, where the Yc axis is defined parallel with the Yb axis. Thus, point Pc(xc, yc, zc)with respect to {C} can be transformed into point Pb(xb, yb, zb) \u2208 R3 with respect to {B} as follows:   xb yb zb 1   =   cos \u03b8bc 0 sin \u03b8bc \u2206xbc 0 1 0 0 \u2212 sin \u03b8bc 0 cos \u03b8bc \u2206zbc 0 0 0 1     xc yc zc 1   (5) where \u2206xbc and \u2206zbc are the translational distances between origins of {B} and {C} about the Xb and Zb axes, respec- tively, and \u03b8bc is the angle between {B} and {C} about the Yb axis. In Fig. 5, point Pc(xc, yc, zc) \u2208 R3 on the laser line is obtained from point Pimg(u1, u2) \u2208 R2 on the image plane by comparing the similar triangles \u2206PcMC and \u2206PimgM \u2032C as follows: [xc yc zc] = b\u2032 f cot \u03b8lp + u2 [f u1 u2] (6) where f is the focal length of the camera, \u03b8lp is the projection angle of the laser line on the image plane, and b\u2032 is the distance between the center C of the camera lens and the intersection L\u2032 of the Zc axis and the laser beam"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003404_acc.2007.4283138-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003404_acc.2007.4283138-Figure6-1.png",
        "caption": "Fig. 6. Composition of the feasible region for the phantom given its next-step speed limits (annulus) and angle limits (sector) and those for two ECAVs.",
        "texts": [
            " Therefore, a relaxation is made for \u03c5max in (4): \u03c5max \u2192 s\u03c5\u03c5min + (1 \u2212 s\u03c5)\u03c5max =: \u03c5s, 0 \u2264 s\u03c5 \u2264 1 2 (5) Given \u03b8min, \u03b8max, and \u03b3 for each ECAV, the feasible region for the phantom is determined by intersecting the ECAV sectors, the phantom\u2019s annulus defined by its nextstep speed limits (from speed rate constraints), the phantom\u2019s sector defined by its next-step angle limits (from turn rate constraints), and any sectors coming from restrictive \u03b3\u2019s. The phantom\u2019s turn rate and speed rate limits are required to be less than or equal to those for each ECAV so that the phantom cannot outmaneuver the ECAVs. Figure 6 illustrates how the feasible region for the phantom is composed, without considering \u03b3. Although the basic idea comes from [2]-[3], the authors did not consider incremental speed limits as a way to incorporate speed rate constraints. In addition, we use \u03b8min, \u03b8max, \u03b3 to obtain the entire feasible region for the phantom instead of just \u03b3, which gives a conservative one. Given the feasible region for the phantom, its heading is chosen as close as possible to \u03d5\u2217 T , which points toward the desired waypoint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000663_tia.2002.800779-Figure11-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000663_tia.2002.800779-Figure11-1.png",
        "caption": "Fig. 11. Vector diagram illustrating the estimation of the stator resistance; S marks stationary reference frame ( ; ) and C marks the current reference frame (x; y).",
        "texts": [
            " The proposed algorithm relies on the orthogonal relationship in steady state between the stator flux vector and the induced voltage. The inner product of these two vectors is (13) This expression depends on the stator resistance. To reduce the online computation time for its estimation, (13) is transformed to a reference frame that aligns with the current vector. This current reference frame ( frame) rotates in synchronism and is displaced with respect to stationary coordinates by the phase angle of the stator current, as shown in Fig. 11. We have and, consequently, and . Of the superscripts, refers to stator coordinates and refers to current coordinates. The estimated value of the stator resistance is obtained as the solution of (13) in current coordinates (14) using the relationships (15) and (16) which can be taken from the vector diagram Fig. 10. Furthermore, we have in a steady state (17) where is an estimated stator flux value defined by (20). The signal flow diagram of the stator resistance adaptation scheme is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003193_s0034-4877(07)80102-9-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003193_s0034-4877(07)80102-9-Figure1-1.png",
        "caption": "Fig. 1. A sleigh with a knife blade installed rigidly at the center of mass.",
        "texts": [
            " We refer to the constraints for which both (23) and (12) are simultaneously satisfied as Chetaevian type, and call the requirements imposed on the virtual displacements like Eq. (23) the Chetaev condition. For a Chetaevian system, we obtain a new set of equations of motion from Eqs. (4), (12), and (23) (instead of Eq. (3)), namely d OT k Ofj ~ ~r/ -- Fi +/~__1Xj~r/, i = 1 . . . . . N, (24) or in generalized coordinates: d OT OT k Ofj dt Ogl~ Oq~ = Q~ + ~ ~'j Ogle' ot = 1 . . . . . n. (25) j = l Now we apply the methodology discussed above to a few classical examples. We consider a sleigh with a knife blade installed rigidly at its center of mass, as depicted in Fig. 1. The generalized coordinates are the x, y coordinates of the center of mass and the angle ~ which the knife blade makes with the x-axis. The knife blade is assumed to be in contact with the ice surface whereas the sleigh may move freely in the direction along the blade; the motion in the directions normal to the blade is however prohibited. Thus, the constraint equation reads The corresponding virtual displacement equation is sin cp~x - cos ~p3y = 0, (28) which suggests that the virtual displacement has no component normal to the trajectory of the center of mass"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003935_s0263574709990506-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003935_s0263574709990506-Figure3-1.png",
        "caption": "Fig. 3. Position of the connecting points to the base and payload platforms.",
        "texts": [
            " Each chain comprises two links: the first link (linear actuator) is always normal to the base and has a variable length li with one of its ends fixed to the base and the other one attached, by a universal joint, to the second link; the second link (fixed-length link) has a fixed length L and is attached to the payload platform by a spherical joint. Points Bi and Pi are the connecting points to the base and payload platforms. They are located at the vertices of two semi-regular hexagons, inscribed in circumferences of radius rB and rP , that are coplanar with the base and payload platforms (Fig. 3). Regarding kinematic modelling, a right-handed reference frame {B} is attached to the base. Its origin is located at point B, the centroid of the base. Axis xB is normal to the line connecting points B1 and B6 and axis zB is normal to the base, pointing towards the payload platform. The angles between points B1 and B3 and points B3 and B5 are set to 120\u25e6. The separation angles between points B1 and B6, B2 and B3, and B4 and B5 are denoted by 2\u03c6B (Fig. 3). In a similar way, a right-handed frame {P} is assigned to the payload platform. Its origin is located at point P, the centroid of the payload platform. Axis xP is normal to the line connecting points P1 and P6 and axis zP is normal to the payload platform, pointing in a direction opposite to the base. The angles between points P1 and P3 and points P3 and P5 are set to 120\u25e6. The separation angles between points P1 and P2, P3 and P4, and P5 and P6 are denoted by 2\u03c6P (Fig. 3). The main kinematic RCID parameters were adjusted in order to maximize the manipulator dexterity31 inside a prescribed workspace: the payload platform may be positioned anywhere inside a sphere of radius 10 mm (centred at a point of the line containing axis zB) and rotate \u00b115\u25e6 around any axis containing the payload platform centre. This requires the actuators displacement of li = 70 mm, approximately. The main kinematic parameters values are shown in Table I. Table I. RCID main kinematic parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000966_0005-1098(86)90082-8-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000966_0005-1098(86)90082-8-Figure8-1.png",
        "caption": "FIG. 8. Orientation (q), angular velocity of satellite (fl) and wheels (aJ) and control signals (u) with wheel-speed saturation (AU + E).",
        "texts": [
            " It is successful in realizing the desired orientation at the expense of much more control energy, a longer slew time and an undefined trajectory, which may be highly undesirable for observation satellites such as IRAS. When a reaction wheel reaches its maximum wheel speed during a slew the satellite starts coasting, provided that the rderence model follows the Euier axis. Such a slew requires less energy; it is tabulated in Table 2. The same data is used, except that the initial wheel-speed vector is now changed to co(0)= ( -70, -100, - 10) r. This slew is illustrated in Fig. 8 with the proposed adaptive controller (AU + E). Both tables clearly illustrate the importance of the Euler axis trajectory for low energy consumption. It should be noted that due to model updating the reference model moves away from its Euler axis trajectory. However, only small deviations are found. The size ofthedifferencesbetwcenthetrajectoriesoftheupdated(AU + E) and the non-updated (A + E) reference model has about the same size as the differences between the trajectories of the satellite and the referencemodel (AU + E and A + E)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002664_icar.2005.1507503-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002664_icar.2005.1507503-Figure9-1.png",
        "caption": "Fig. 9. Target grasping and joint transportation home.",
        "texts": [
            " This chain reaction process allows to spread the warning throughout the entire swarm which is then enabled to achieve self-assembly without any explicit message passing (Figure 7). Each time a new unit approaches the vicinity of a target, it position itself around it on the side of one peer. A robot perceives that it has closed the loop around a target when it detects that there are peers on both its sides. This situation is acknowledged with the issue of a red light signal (Figure 8). The whole group (swarm-bot) can at this point move to grasp the target and then re-orient itself towards a light beacon located at the initial base of the swarm (Figure 9). The tight group motion, whose result is the transportation of the target, can be viewed as a constant trade-off between achieving the common goal of maximizing the gradient of light detected and adapting to the constraints enacted by the environment. This means that the motion home of the swarm can be occasionally subsumed by a distributed obstacle avoidance behavior which allows the swarm-bot and its load to get around the hindrance as if it were a single robot entity. To test the implementation of fetching and retrieval presented earlier, we used swarmbot3D, our highly ductile software developing environment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001411_a:1015685325992-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001411_a:1015685325992-Figure1-1.png",
        "caption": "Figure 1. The simplest walker: coordinate system.",
        "texts": [
            " The main procedural advantage of this reverse asymptotic approach, as predicted already by physical reasoning above, is that all quantities of interest at a particular order are determined at that same order. The results obtained are summarized in Table 2. Note that the results for \u03c41 and \u03c42, for example, differ from the corresponding values obtained using the forward asymptotic approach. This is because the expansion parameters are different by a multiplying factor: \u03b4\u0302 = \u03b4 2/3 \u2248 \u03b4 2/3 0 . Retaining the lowest-order expression for above, we find that we should compare, e.g., the figure 1.579129 (Table 1, row 2, column 3) with the figure (from Table 2, row 2, columns 3 and 5) 1.675014/1.0924492/3 = 1.579129 (comparisons between the higher order terms are a little more complicated). Thus, on accounting for the differences in the two expansion parameters, the two sets of results are equivalent. The stability calculation proceeds as before, and the two approaches are identical. The matrices B, D and E are not reproduced here. However, the final stability results are given in the Appendix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003230_14644193jmbd103-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003230_14644193jmbd103-Figure1-1.png",
        "caption": "Fig. 1 Schematic representation of two bodies in contact",
        "texts": [
            " In this section, some definitions and basic results obtained in previous investigations that will be used in this study are briefly reviewed. In particular, the geometric description of the wheel and rail and the basic methods used to formulate the constrained equations of motion of multi-body railroad vehicle systems are discussed. In order to determine the location of the point of contact between two bodies, a complete parameterization of the surfaces can be used [6\u20138]. In general, a set of four surface parameters is used to describe the geometry of the two surfaces in contact, as shown in Fig. 1. The surface parameters can be written in a vector form as s = [si 1 si 2 sj 1 sj 2]T (1) where superscripts i and j denote body i and body j, respectively. Using these parameters, the location of the contact point P can be defined in the body coordinate systems as u\u0304i P = u\u0304i P(si 1, si 2) and JMBD103 \u00a9 IMechE 2007 Proc. IMechE Vol. 221 Part K: J. Multi-body Dynamics at UNIV CALIFORNIA SANTA BARBARA on June 24, 2015pik.sagepub.comDownloaded from u\u0304j P = u\u0304j P(sj 1, sj 2). Using these vectors, the tangents t\u0304i 1 and t\u0304i 2, and the normal n\u0304i to the surface at the contact point are defined, respectively, in the body coordinate system as t\u0304i 1 = \u2202u\u0304i P \u2202si 1 , t\u0304i 2 = \u2202u\u0304i P \u2202si 2 , n\u0304i = t\u0304i 1 \u00d7 t\u0304i 2 (2) This parameterization can be used to describe the wheel and rail surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001259_robot.1986.1087707-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001259_robot.1986.1087707-Figure2-1.png",
        "caption": "Figure 2. Possible configurations for 7 joint serial chains following the arguments",
        "texts": [
            " T h i s l e a d s t o t h two conf igu ra t ions shown in F igu re 2. The conf igu ra t ion shown i n F i g u r e 2a would not be e f fec t ive in removing e i ther the \"shoulder\" o r \"wrist\" s i n g u l a r p o s i t i o n s r71, since the screw a x i s of j o i n t 4 always l i e s w i t h i n t h e s c r e w system defjned by axes 2 , 3 and 5 except when axes 2 , 3 and 5 a re cop lana r ( the \"elbow\" s i n g u l a r i t y ) . Hence t h i s c o n f i g u r a t i o n would not be s a t i s f a c t o r y . The conf igu ra t ion of Figure 2b removes t h e w r i s t and elbow s i n g u l a r i t i e s . I t does not , however, remove the shou lde r s ingu la r i ty . Th i s i s because thscrew system defined by j o i n t s 2 , 3 , 5 , 6 , 7 c o n t a i n s a l l z e r o p i t c h s c r e w s p a r a l l e l t o a x i s 2 . Thus , the screw ax is o fjo in t 4 belongs to th i s sys tem and the sys tem def ined by i o i n t s 2 through 7 has o rde r 5 r a t h e r t h a n 6. Consequent ly , any s ingular i ty which involves joint 1, s p e c i f l c a l l y t h e s h o u l d e r s f n g u l a r i t y , i s not removed",
            " Note tha t t he e lbow s ingu la r i ty shou ld no t be ignored s ince , fo r t he r ea l i s t i c ca se o f non-ze ro hand l eng th , i t i s e n t i r e l y p o s s i b l e ? f o r t h i s t y p e L of singularity to occur without the reference point being on the workspace boundary [6]. Also, as will be seen in the next section, its kinematic equations are manageable and, in fact, it lends itself to exceedingly simple, and operationally useful, coordination strategies. DEVELOPMENT OF JACOBIAN The Jacobian matrix for the configuration of Figure 2b will be developed using the notation of reference [13]. The geometric parameters of the links and the joint angles are defined as shown in Figure 3. For the chosen configuration, the parameters are listed in Table I. A s was noted in reference [131, the form of the Jacobian is greatly simplified by transforming to a new fixed frame which is instantaneously coincident with one of the intermediate link reference frames. We choose to work in a frame coincident with frame 5 since, although the expressions for the positions of the inboard ioints will be relatively complex, this choice will produce a quadrant of zeros in the Jacobian matrix",
            " , \"Connected Differential Mechanism and its Applications,\" Proceedings of '85 International Conference on Advanced Robotics, Tokyo, September 1985. [13] Waldron, K. J., Wang, S.I.. , and Bolin, S. J. , \"A Study of the Jacobian Matrix of Serial Table 1 1 0 0 7112 variable 0 0 variable 2 '6 0 TI2 variable 0 variable 5 0 r vi2 variable 6 0 O5 7112 variable 7 O r 0 variable 7 Q [14] Klein, C.A. and Huang, C.H., \"Review of the Pseudoinverse for Control of Kinematically Redundant Manipulators,\" IEEE Transactions on Systems, Man and Cybernetics, March, 1983. in this paper. Figure 2a is rejected because it is always geometrically singular. Figure 2b is the configuration analyzed in detail in this paper."
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003230_14644193jmbd103-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003230_14644193jmbd103-Figure4-1.png",
        "caption": "Fig. 4 Wheel geometry",
        "texts": [],
        "surrounding_texts": [
            "In this section, some definitions and basic results obtained in previous investigations that will be used in this study are briefly reviewed. In particular, the geometric description of the wheel and rail and the basic methods used to formulate the constrained equations of motion of multi-body railroad vehicle systems are discussed."
        ]
    },
    {
        "image_filename": "designv11_28_0001297_iros.1991.174423-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001297_iros.1991.174423-Figure8-1.png",
        "caption": "Fig. 8: Passible motions for a rectangular parallelepiped in a hole.",
        "texts": [
            " Figure 5 shows an example of the contact between the vertices and between a vert,ex and an edge. At least one of four conditions must hold a t the contact point between the vertices, and a t least one of two ones must hold at t h e point between the vertex and the edge. Though such a Figure 7 shows three differential motions of the triangular prism that correspond t o V I E l , VIE, , VIE , in the equation (17) respectively. A n arbitrary motion that breaks the con- tact can be represented by a nonnegahe linear combination of them. Figure 8 illustrates three differential motions of the rectangular parallelepiped shown in Fig.4. They corresponds to V1E1. VxEa, VIES respectively, and there is no motion that does not change the contact state in this example. 5 Conclusion The results are summarized as follows: Acknowledgement The authors would like t o thank Dr.Toshitsugu Yuba, Dr.Hideo Tsukune, Dr.Tomomasa Sato, Dr.Gordon I.Dodds and the robotics research group at Electrotechnical Laboratory for their advice and encouragement. They also thank Prof"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002222_acs.929-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002222_acs.929-Figure3-1.png",
        "caption": "Figure 3. Membership function and boundaries of Rk:",
        "texts": [
            " Each of these variables constitutes a gene of the chromosomes for the GAs. Boundaries of chromosomes are required for the creation of chromosomes in the right limits so that the GAs are not misled to some other area of search space. The technique adopted in this paper is to define the boundaries of the output membership functions according to the furthest points and the crossover points of two adjacent membership functions. In other words, the boundaries of FKF consist of three real-valued chromosomes (Chs), as in Figure 3. Copyright # 2006 John Wiley & Sons, Ltd. Int. J. Adapt. Control Signal Process. 2007; 21:205\u2013236 DOI: 10.1002/acs The trapezoidal membership functions\u2019 two furthest points, 0:135 \u00f0D1\u00de; 0:135 \u00f0D2\u00de and 0.135 \u00f0I3\u00de; 0.135 \u00f0I4\u00de of FKF, remain the same in the GAs\u2019 description to allow a similar representation as the fuzzy system\u2019s definition. This section discusses the implementation of the FKF optimized using GAs discussed earlier for fusing heading data acquired during a real-time experiment. The Hammerhead AUV second order model used herein was derived using system identification techniques [19]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003694_jst.104-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003694_jst.104-Figure10-1.png",
        "caption": "Figure 10. 3D vector diagrams (straight shot, beginner); the coordinate system indicated corresponds to the ball coordinate system (c.f. Figure 3). The Force Vectors of back and forward swing are represented as single vectors; the scale bar corresponds to 20 cm (ball dimensions) and 40 N (force vectors); the force vectors applied by the ball to the hand are displayed on the ball and the finger tubes (where the forces originate from); the first three rows show the entire vector diagram; the 4th row shows selected force vectors; Th 5 thumb, Mi 5 middle finger, Ri 5 ring finger. The Moment Vectors of the forward swing are represented as a regular surface; the scale bar corresponds to 1 m (ball dimensions) and 1 Nm (moment vectors) in the right view, and to 5 m and 5 Nm in the top and front views; the origin of the moment vectors is set to the centre of the ball. In the right column, the force and moment vector diagrams are shown with respect to the bowler immediately before release of a straight ball (the scale bars do not apply to the right views in the right column).",
        "texts": [
            " The peak moment of Mxball and Mzball occurs after the Myball moment peak in better bowlers (Figure 9e), whereas in beginners, the three peaks occur approximately at the same time (Figure 9f). Additionally, Mzball shows a negative moment spike before release (Figure 9e,f) with an angular impulse of approximately one fifth of Myball in better bowlers. Immediately before release, the negative z-axis is pointing rightwards as the ball has been rotated by 180 degrees. The moment peaks and spikes show a strong correlation with the average score (Table 2). Better bowlers impart larger moments to the ball. The principles of 3D vector diagrams are explained in Figure 10. The diagrams can be displayed as single subsequent vectors, one per time step (force vectors; Figures 10 and 11), or as regular surfaces (moment vectors; Figures 10 and 12). With the time colour coded, the vector diagrams become four dimensional (4D). This allows distinguishing between peaks and terminal spikes of forces and moments. In the 4D force vector diagrams, weaker bowlers show smaller forces, which do not fan out as much as in better bowlers (Figures 11 and 13). The force peaks of back and forward swing can be distinguished from the colour of the force vectors: between green and cyan in the back swing, and www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000524_nafips.2000.877478-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000524_nafips.2000.877478-Figure2-1.png",
        "caption": "Fig 2. The fuzzification of switching function S for a Fuzzy Sliding Mode Controller",
        "texts": [
            " The resulting Fuzzy Sliding Mode Controller (FSMC) is actually a Single-InputSingle-Output fuzzy logic controller. The input to the controller is the switching function S. The output from the controller is the control command U . The number of rules in the rule base depends on the fuzzification level of S and U however it is generally much fewer than a typical fuzzy logic controller for the same system [6][8]. A typical rule of a FSMC has the following format: If S is PB (and S is PB), then U is PB or a constant. How the switching function S is fuzzified is illustrated in Fig 2. This kind of rule format effectively adds a boundary layer to the system. This boundary layer is illustrated in Fig 3. The main drawback of a FSMC is that before the fuzzification, the coefficients of the sliding surface have to be pre-defined by expert carefully. That is, the value of 2 in equation (2) has to be determined first. The only advantage of a FSMC compared with a typical SMC is that in the former case, the boundary layer is nonlinear whereas in the latter case the boundary layer is linear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001154_0097-8493(90)90038-y-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001154_0097-8493(90)90038-y-Figure3-1.png",
        "caption": "Fig. 3. A 3 \u00d7 4 rational B~zier patch.",
        "texts": [
            " (22) By the use of(21 ) we are able to compute a and get the tenuous result 2\u00a24 1 + 2 cos ~b) - 2 sin if(2 + cos ~k) a = (23) sin \u00a24sin ff - if) Using this constant, all free parameters of our B~zier interpolant are determined and so the axial motion, too. As mentioned above, we use this motion to generate kinematic rational B6zier patches again, which interpolate given helical surface patches. There is no use to draw a figure showing a helix and 280 S. MICK and O. ROSCHEL its quartic interpolant, because the eye cannot perceive any difference between the two curves. Fig. 3 shows a 3 X 4 rational Brzier patch which is generated by the algorithm given above. There are further possibilities to interpolate such a helical mot ion by an axial one. The authors have tried to give another quartic interpolation, where the interpolant b and the helix (3) have the same tangents and osculating planes at v = 0 and v = 1. But we recognized that in this case the difference between helix and interpolant is greater than that o f Section 6. REFERENCES 1. W. Boehm. G. Farin, andJ. Kahmann, A su~eyofcu~e and surface methodsin CAGD"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003007_6.2006-6147-Figure14-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003007_6.2006-6147-Figure14-1.png",
        "caption": "Figure 14. Tandem-rotor longitudinal forces and moments.",
        "texts": [
            " Also, notice how the longitudinal differential collective pitch terms have cancelled out\u2014 leaving only the quasi-steady longitudinal control derivative as expected. LON Z\u03b4 The effects of dynamic inflow are also observed in the longitudinal COLxa \u03b4/ frequency response (Figure 19); and although the coherence was poor, the effect was also noticeable in the COL\u03b4\u03b8 / frequency response. A general arrangement of the rotor forces and moments acting upon the helicopter in the longitudinal axis is presented in Figure 14. Recall that the summation of moments in the longitudinal axis is given by: 0:0 ===\u2211 qIIM yyyy &&&\u03b8 (24) American Institute of Aeronautics and Astronautics 17 Therefore, by multiplying the thrust coefficient perturbation by the moment arm and dividing by the mass moment of inertia, we achieve a simple approximation for the thrust coefficient contribution to pitching moment given by: yy TCT yy I T CMC I RR T ll \u0394 ==\u239f \u239f \u23a0 \u239e \u239c \u239c \u239d \u239b \u03a9 ~~)( 22\u03c0\u03c1 (25) LON M\u03b4 In the hybrid model structure, the thrust coefficient contribution replaces the and control derivatives as shown in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002197_1.1867270-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002197_1.1867270-Figure2-1.png",
        "caption": "FIGURE 2. Slepian Concept Schematics.",
        "texts": [
            " (4) as applied to the EM momentum carriers in polar dielectrics coincides with that obtained by using a modified EM force density formalism (Brito, 2004). The latter was found to be equivalent either to Minkowski\u2019s plus the forces on Roentgen currents, or Abraham\u2019s minus the Kelvin forces contribution. The time-averaged thrust is accordingly given by 2 0 sin 2 r nIV dT c \u03b5 \u03c9 \u03d5= . (5) Corum\u2019s works are based on Slepian\u2019s EM space-drive which consists of a solenoid and a parallel-plate capacitor electrically wired in series and driven by an RF source, as shown in Figure 2 (Slepian, 1949). According to Corum, in this arrangement Heaviside force densities acting even on empty space will develop on the space between the plates as given by the following equation . ( )H t \u2202= \u00d7 \u2202 f D B . (6) Slepian concludes that since the momentum density D\u00d7B in the space between the plates is caused to vary at a rapid rate, by the law of conservation of momentum there will be an equally large but opposite rate of change in the momentum of the material system. This will correspond to an unbalanced instant-by-instant force on the material system whose magnitude will equal \u2013 f H of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002852_iros.2006.281799-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002852_iros.2006.281799-Figure9-1.png",
        "caption": "Fig. 9 Sudden change in joint velocity at optimal initial posture",
        "texts": [
            " It means that for this case the velocity fluctuation of surviving joints is smaller and the manipulators operate more stably. Thus, we can conclude that reducing the sudden change in joint velocity can obviously raise the stability of fault tolerant operations for two coordinating manipulators. Using the fault tolerant planning algorithm proposed in this paper, we can obtain the optimal initial posture with minimum sum of the sudden change in joint velocity, (1.148,0,0.815)m , 041 -194.8 042 -1410 .The magnitude of this sum is 45rad/s, which is much smaller than that at the arbitrary initial posture. Fig. 9 indicates that, in the case of this optimal initial posture, when joint 3 of master and slave manipulators fails and is locked at t=2.45 s, the sudden change of surviving joint 3 for the two manipulators reaches maximum value, i.e. 0.22rad/s and 0.24rad/s respectively, which are also smaller than these at the arbitrary initial posture. When the failed joints are locked at this moment, the simulation results of the fault tolerant operations for the optimal initial posture are shown as Fig. 10. In comparison with Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000697_305-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000697_305-Figure1-1.png",
        "caption": "Figure 1. Several members of a family of projectile trajectories corresponding to one firing speed (solid curves) and the envelope of the family (dashed curve). Two horizontal target planes are shown and maximal projectile ranges are indicated.",
        "texts": [
            " This has motivated several authors to present alternative solution methods [1\u20136], some of which require simpler mathematics. Revisiting this classical problem and following a simple line of reasoning, we have found yet another elegant solution. Moreover, the solution that we have found can be applied to solve more demanding problems. Let us consider a \u2018gedanken experiment\u2019 where we fire the projectiles at a certain speed and gradually change the firing angle to obtain the maximal range on a given target surface. Figure 1 shows the projectile trajectories in one such procedure with the firing point at height H above and at depth D below the target plane. The equation of the trajectory of a projectile fired at speed v0 from the origin of the coordinate system at an angle \u03b8 with the x axis is y = x tan \u03b8 \u2212 gx2 2v2 0 (1 + tan2 \u03b8). (1) 3 Author to whom any correspondence should be addressed. 0143-0807/02/060637+06$30.00 \u00a9 2002 IOP Publishing Ltd Printed in the UK 637 The above equation can be viewed as representing a family of trajectories of projectiles all fired at the same speed v0, but at different angles. The equation of the family can more conveniently be written as F(x, y, u) = xu \u2212 gx2 2v2 0 (1 + u2) \u2212 y = 0, (2) where the parameter u is u = tan \u03b8. (3) All trajectories in figure 1 are, therefore, members of one such family. Note that the trajectories with u > 0 correspond to upward shots towards x > 0 while the trajectories with u < 0 correspond to upward shots towards x < 0. The downward shots are not considered in the context of maximizing the projectile range since their range is in all circumstances inferior to the range of the horizontal shot (u = 0). In addition to the trajectories in figure 1 there is the dashed curve that \u2018encloses\u2019 all trajectories touching each at its \u2018most protruding point\u2019. We recognize the dashed curve as the envelope of the family of the trajectories. It is evident that no trajectory on any target plane reaches a range greater than the \u2018range\u2019 of the envelope and there is only one trajectory reaching each point on the envelope. It follows that the intersection of the envelope and the target plane gives the maximal range and that it can be reached by only one trajectory from the family (2). In section 2 we derive the equation of the envelope in three different ways. In section 3 we use the equation of the envelope to solve several problems in addition to the one originally posed. Calculus defines the envelope of a family of curves as the curve that, if it exists, fulfils the two conditions: (i) at each of its points the envelope is at a tangent to some member of the family and (ii) each member of the family is at a tangent to the envelope [7]. Figure 1 shows that the dashed curve meets these conditions. Postponing the mathematically complete derivation of the equation of the envelope of the family (2), we first take the opportunity do derive it by guesswork. We start by observing that the maximum of the envelope occurs at x = 0 (intersection with the y axis) and that it represents the maximal height reached by the projectile fired vertically upward (\u03b8 = \u03c0/2): y(x = 0) = v2 0 2g . (4) Next we consider the opposite extreme. It is plausible from figure 1 that when H \u2192 \u221e the maximal range is obtained with \u03b8 \u2192 0, i.e. with the close-to horizontal shot. However, the envelope must enclose the trajectory of the horizontal shot at all x , so we write y(x) > \u2212 gx2 2v2 0 . (5) We now combine the two results into the \u2018guessed\u2019 equation of the envelope: y(x) = v2 0 2g \u2212 gx2 2v2 0 (6) and continue to show that this is indeed the envelope of the family of curves (2). The common point of a member of the family (2) and the curve (6) can be found by equating their y coordinates",
            " (9) By eliminating u we obtain the equation of the envelope E(x, y) = v2 0 2g \u2212 gx2 2v2 0 \u2212 y = 0 (10) which is, however, equivalent to (6). Interestingly, due to the simple form of the curves (2), the equation of the envelope can be derived by means of a simple argument without using the standard procedure. Let us consider two neighbouring trajectories, both members of the family (2), one displaced from the other by an increment \u03b4 in the parameter u. They intersect at the origin (firing point) and at one additional point. It can be deduced from figure 1 that the latter intersection point approaches the envelope as \u03b4 goes to zero. The coordinates of the intersection of the two trajectories can be found by solving the system of two equations: F(x, y, u) = 0 and F(x, y, u + \u03b4) = 0. (11) Eliminating u (this is most easily accomplished by subtracting one equation from the other) and solving for y one gets y = v2 0 2g \u2212 gx2 2v2 0 (1 + \u03b42/4). (12) Letting \u03b4 \u2192 0 we once more obtain the equation of the envelope (10). The useful property of the envelope (10) of the family of the projectile trajectories (2) is that it indicates the maximal range reachable by the projectile with firing speed v0",
            " (14) The procedure is applied in the examples that follow. Let us first solve the original problem. The equation specifying a horizontal target plane at height c above the firing point is y = c. For the x coordinate of the intersection with the envelope (10) we obtain x1,2 = \u00b1v2 0 g ( 1 \u2212 2gc v2 0 )1/2 . (15) As we are considering only the shots towards x > 0 we take Rmax = x1. Note that for c > v0/(2g) there is no intersection (no real solution) because the firing speed is insufficient for the projectile to reach the target plane. Referring back to figure 1 for the two maximal ranges we have RH = v2 0 g ( 1 + 2gH v2 0 )1/2 and RD = v2 0 g ( 1 \u2212 2gD v2 0 )1/2 . (16) In both cases the optimal firing angle is obtained through (14). As a more complicated example we find the intersections of the envelope and the parabolic target surface given by y = ax2 + bx + c. For the x coordinates of the intersection we get x1,2 = v2 0 g + 2av2 0 ( \u2212b \u00b1 ( 1 \u2212 2gc v2 0 + b2 + 2a ( v2 0 g \u2212 2c ))1/2) . (17) In a simple situation, such as in figure 2, the two solutions are real and such that x2 < 0 < x1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000986_1.1596241-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000986_1.1596241-Figure7-1.png",
        "caption": "Fig. 7 Modified velocity and displacement",
        "texts": [
            " Knowing this velocity, the straight line within the interval Dt2 can be determined by varying the slope m2 . The most direct way to choose a proper gear train performance in order to meet the needs of a particular application is to consider the required displacement. However, the limits on displacement performance can be obtained by integrating the maximum possible velocity function, which is the step response. In practice, it is common to use a velocity profile of trapezoidal shape to achieve a fast motion performance. Figure 7 shows a trajectory profile including reversals of direction with implemented compensation triangles to improve the backlash behavior. The performed displacement function in this case is a compound parabolic-straight line course. In the enlarged view of the backlash zone ~Fig. 8!, the displacement signal, obtained from the modified velocity profile, is compared with the theoretical required step known from Fig. 3. The arrows indicate the amount of error remaining through the loss of contact while traversing the backlash gap in a real system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000297_s0736-5845(01)00037-0-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000297_s0736-5845(01)00037-0-Figure2-1.png",
        "caption": "Fig. 2. Computer-controlled platform.",
        "texts": [
            " This approximation, as explained in [11], is given by ei 1E Ci jjCjj ; jjCjj \u00bc C2 1 \u00fe C2 2 \u00fe C2 3 \u00fe C2 4 1=2 i \u00bc 1;y; 4: \u00f06\u00de The relative nominal orientation between the XYZ coordinate system attached to the camera and the xyz robot-fixed coordinate system is described by the following 3 3 direction cosine matrix (see [14]); R \u00bc e2 0 \u00fee2 1 e2 2 e2 3 2\u00f0e1e2 \u00fee0e3\u00de 2\u00f0e1e3 e0e2\u00de 2\u00f0e1e2 e0e3\u00de e2 0 e2 1 \u00fee2 2 e2 3 2\u00f0e0e1 \u00fee2e3\u00de 2\u00f0e1e3 \u00fee0e2\u00de 2\u00f0e2e3 e0e1\u00de e2 0 e2 1 e2 2 \u00fee2 3 2 64 3 75: \u00f07\u00de When the camera is panned or tilted, the change in orientation of the coordinate system attached to the camera can be quantified depending on the amount of angular rotation and depending on the geometry of the computer-controlled platform used. A number of different configurations of pan/tilt units are reported in the literature (see, for example, [15,16]). For our experiments, the computer-controlled platform depicted in Fig. 2 was used. This device is mounted on a vertical shaft with axis v\u2013v which is fixed to the wall. The tilt-axis t\u2013t is fixed and the pan-axis p\u2013p rotates when a tilt rotation takes place. It is important to note that the geometrical configuration depicted in Fig. 2 corresponds to a position in which the pan and tilt angles can be considered as zero. Assuming that the camera is initially panned and tilted an angle a0 and b0; respectively, from the orientation shown in Fig. 2, when the cameras are panned through an angle a and tilted an angle b; the transformation between the original and the new coordinate system attached to the camera is described by the following transformation matrix P: P \u00bc cbs\u00f0a\u00fe a0\u00desa0 \u00fe c\u00f0a\u00fe a0\u00deca0 s\u00f0a\u00fe a0\u00desb sbsa0 cb s\u00f0a\u00fe a0\u00deca0 c\u00f0a\u00fe a0\u00decbsa0 c\u00f0a\u00fe a0\u00desb 2 64 c\u00f0a\u00fe a0\u00desa0 s\u00f0a\u00fe a0\u00decbca0 sbca0 s\u00f0a\u00fe a0\u00desa0 \u00fe c\u00f0a\u00fe a0\u00decbca0 3 775; \u00f08\u00de where s* \u00bc sin\u00f0* \u00de and c* \u00bc cos\u00f0* \u00de: Note that the sequence in which the rotation takes place is immaterial as far as the transformation matrix P is concerned",
            " For this experiment, the receiving brake plate was placed at different, distant locationsFas much as 1:5 mFso that the cameras must be reoriented in order to include it within their fields of view. Every new location of the brake plate was defined in such a way that the visual features attached to it were visible to all the participating cameras following appropriate pan/tilt, but it was otherwise arbitrary. The experiment was aimed at achieving the same level of precision as obtained for the case where the cameras were fixed and the manipulator\u2019s workspace was limited [19]. The cameras were mounted on the platform depicted in Fig. 2. The unit has a CCTV-1410 Panasonic camera and is equipped with two optical encoders BEI MX2212-25-1000 used to measure the pan and tilt angular rotations. Such optical encoders are capable of measuring angles as small as 0:091; which is a typical resolution of this type of measuring device. In order to drive the unit, a gearmotor Pittman GM14604 with planetary gearhead ratio of 24:1 was used to control the pan-rotation and a gearmotor Pittman GM8712 with a gearhead ratio of 1804:1 was used to drive the tiltrotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000319_1.1519275-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000319_1.1519275-Figure2-1.png",
        "caption": "Fig. 2 Model of tooth root crack; \u201ea\u2026 Idealized tooth root crack; \u201eb\u2026 Modeling of crack",
        "texts": [
            " A tooth root crack typically results from tooth bending fatigue and most of the time it is initiated from a flaw. The effect of a crack on a tooth is to reduce the CEMBER 2002 esign.asmedigitalcollection.asme.org/ on 09/09/20 bending stiffness. Previous studies indicate that crack propagation paths are smooth, continuous, and rather straight with only a slight curvature @15#. To simplify the modeling of this type of damage, the shape of the crack is approximated as a straight line. This is displayed in Fig. 2~a!. The modeling of a crack is shown in Fig. 2~b!. In Fig. 2~b!, t1 , t2 , t3 , etc., define the thickness of a tooth in the region of a crack. To model the crack, the tooth under mesh is divided into many segments. The bending stiffness of the tooth is calculated from the deflection of a tooth computed from a summation expression as shown in Eq. ~3! @20# below: yB5 L cos2 fL8 E ( i51 n d iF l i 22l id i1d i 2/3 I\u0304 i 1 2.4~11m!1tg2fL8 A\u0304 i G (3) Transactions of the ASME 13 Terms of Use: http://asme.org/terms Downloaded F where yB is the bending deflection of the tooth pair under mesh. i is the segment index. All the nomenclature used in Eq. ~3! is displayed in Fig. 3. In Eq. ~3! the terms 1/I\u0304 i and 1/A\u0304 i are given by: 1/I\u0304 i5~1/I i11/I i11!/2 (4) 1/A\u0304 i5~1/Ai11/Ai11!/2 (5) Where I is the moment of inertia and A is the area of the tooth cross section. Both of these two parameters are related to the thickness of the tooth. From Fig. 2~b!, it is apparent that the thickness of the tooth has a significant effect on the crack area. When substituting the thickness of the tooth with a crack into Eq. ~3!, the crack will affect the deflection and bending stiffness of the tooth. 2.2.3 Modeling Wear. Wear is modeled as the removal of material across the entire width of a tooth. A pictorial of this damage type is displayed in Fig. 4~a!. Because wear typically involves the loss of material over the entire width of a tooth, the profile of a tooth is different from the perfect involute profile"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002584_robot.1987.1087740-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002584_robot.1987.1087740-Figure1-1.png",
        "caption": "Figure 1: Simplified representation o f two manipulators.",
        "texts": [
            " It is always possible to f ind a ( n l x k ) matrix Jo(Y) called the pseudo-inverse of J so that : is a ( n l x l ) a rb i t r a ry vec to r , which can be used t o s e t some c r i t e r i o n : for example, i f F(YJ is a pos i t ive sca la r func t ion of y, the choice x= - grad F makes F to decrease during the motion. The term ( I - J o J ) z is an optimisation term which doesn ' t a f fec t the main term J o (x)&> - b) Relative_ ?asks. 2. Let Robl and Rob2 be two robots w i t h respect ively n l and n2 independant joints, R 1 and R2 two frames l inked to the terminal devices of the robots (Figure 1) . The re la t ive task cons is t s in loca t ing the frame R 2 w i t h r e spec t t o R 1 . The f i r s t way to solve t h i s problem is to express each displacement of R 1 and R2 w i t h respect to the reference frame RO. I f \"kk\" is the number of independant components of t h i s t a sk , w e know tha t so lv ing t h i s geometric Droblem throuqh the reference frame RO L - needs a t l e a s t k independant j o i n t s for -- each r & o t m secondly, to plan the absolute task i n the common pa r t of the workspace of each robot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000040_robot.2001.933027-Figure13-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000040_robot.2001.933027-Figure13-1.png",
        "caption": "Fig. 13 Experimental result (Rotation about X - , Y - , Z- axis)",
        "texts": [
            " Kazamura, \"Control of Robot Handling the robot transport the object cooperatively to the target an Object in Cooperation with a Human,\" IEEE. Int. position from the initial position. The initial and target Workshop on Robot and Human Communication, positions of the robot a 'e (x,y,z,8,,8,,8,) = PP.142-147, 1997. (-0.47,-0.47,0.37,0,0, O), (0.35,0.2,0.63,0,0, k / 2 ) in the L71 R. Ikeura and H. Inooka? 'Variable Impedance IEEE Int Conf. on Robotics and Automation, experimental result with the rotation about Y - , Z-axes and pp,3097-3i02, 1995, Fig.13 shows the experimental result with the rotation [8] 0. M Al-Jarrah and y, F. Zheng, ttArm - Manipulator about X - , Y - , Z-axes. Fig.14 shows the rotational angle Coordination for b a d sharing using ~ ~ f l ~ ~ i ~ ~ Motion about X-axis in each experiment. The rotation about Y - Control,\" Proc. 1997 IEEE Int. Conf. on Robotics and and Z-axes results in the rotation about X-axis during the Automation, pp.2326-2331, 1997. transportation to the target position. The operator cannot [9] R. M. Murray, Z"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000773_jmaa.2001.7531-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000773_jmaa.2001.7531-Figure1-1.png",
        "caption": "FIG. 1. The guided missile along the guideline to the target of an attack.",
        "texts": [
            "uncertain dynamical system 5.1 described by differential inclusions is \u017d .traced by an observation function H , where y is the state of the guided missile and x is the state of the infrared laser beam transmitted by the \u017d .guided plane or satellite. Here, let the curve Z x x be a guideline of x \u017d . \u017d . \u017d .in the infrared laser guidance system. Note if H x x and Z x H x , then the guided missile y and the laser guided beam x touch each other, \u017d .that is, the missile y can be guided to the guideline see Fig. 1 . The goal is \u017d . \u017d .to find a pair of generalized feedback control inputs u x, y and u x, y1 2 such that the missile y can be guided by the infrared laser beam x to the guideline after a finite time T , and the guided missile y is asymptotically \u017d .stable along the guideline y Z x x to the target z 3 of an attack,0 \u017d .and so take J x x 3. This implies that the nonlinear uncertain \u017d .dynamical systems 5.1 enjoy the complete tracking control property with \u017d \u017d ..exponential asymptotic stability along J x t after a finite time T"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000652_0470867906-Figure7.1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000652_0470867906-Figure7.1-1.png",
        "caption": "Figure 7.1 Semi-active suspension",
        "texts": [
            " [137] or [138], Duttlinger and Filsinger [89] or Roppenecker [352] for the technical fundamentals. The idea of semi-active wheel suspension is that the system adapts the parameters of shock absorbers or body springs to the current road conditions and the corresponding driving situation. This is achieved by an embedded processor, which means that electronics, mechanics and software have to be considered at the same time here. The system described in what follows reflects the concept of BMW\u2019s \u2018electronic damper control\u2019, see [137] and [138] and Figure 7.1. A similar system is also offered by Mercedes-Benz, see [89]. The difference between semi-active and active wheel suspension is that, in the latter case, forces can be applied by hydraulics, for example, in order to improve driving safety and comfort. Put simply, the vehicle lifts one or more wheels up in order to minimise the vertical movement of the body. This approach has, however, not yet become prevalent for reasons of cost and energy. 7.2 DEMONSTRATOR 1: SEMI-ACTIVE WHEEL SUSPENSION 137 The motivation for the use of semi-active wheel suspension is that driving safety and comfort represent competing goals in the context of suspension systems",
            " In addition, driving manoeuvres that also require increased stability are recognised, for example, sharp braking, fast driving through bends or quick accelerator pedal movements in automatics. The resulting pitching and rolling movements of the vehicle should be limited by higher damping. After the identification of the road condition and the driving state, the next step is to determine the correct damping level and to set this at the shock absorber. The implementation is based upon a digital controller that processes embedded software, see Figure 7.1. This carries out the actual control algorithm and takes on a whole range of additional functions such as, for example, the plausibility testing of the sensor values to be processed, the safety concept, or the provision of data to other components of the vehicle. In addition, there are electronics for the signal processing, such as D/A and A/D converters, which provide the connection between the digital and analogue worlds. The actual conversion between the physical quantities is taken care of by the acceleration sensor and the adjustable shock absorbers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003977_s12213-008-0010-1-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003977_s12213-008-0010-1-Figure1-1.png",
        "caption": "Fig. 1 Flexible micromanipulation using versatile robots under microscopy",
        "texts": [
            " In situ microprocessing under microscopes is an interesting application although the costs of installing fine mechanisms to microscopic instruments is expensive [11]. There are many reports about a micromanipulation supported by precise microrobots to study industrial applications where such precise microrobots provide effective benefits [12\u201315]. Over the last several years, we have developed versatile microrobots for microscopic manipulations [16]. We have also developed flexible micromanipulation organized by three versatile microrobots under microscopes as shown in Fig. 1 [17]. Here, a spherical micromanipulator is used as a microscopic manipulator. In experiments, we have demonstrated precise and flexible handling of a miniscule pipe under the good collaboration of these small robots. This manipulation device has 11 DOF with less than 100 nm resolution. We confirmed the efficiency of the microrobots. However, O. Fuchiwaki (*) : C. Kanamori :H. Aoyama Department of Mechanical Engineering and Intelligent Systems, University of Electro-Communications (UEC), 1-5-1 Chofugaoka, Chofu, Tokyo, Japan e-mail: fuchiwaki@sys"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003094_j.mechmachtheory.2007.12.001-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003094_j.mechmachtheory.2007.12.001-Figure6-1.png",
        "caption": "Fig. 6. Assembly modes of the RR-RP-RP Assur group.",
        "texts": [
            " The geometrical data and the position of external joints A, D and F are given in the upper part of Table 1. For the specific geometry here considered, by solving the fourth order polynomial equation (17), two real roots and two complex roots for the displacement s are obtained (see Table 1). For each real value of the displacement s, the coordinates of the internal joint B and the displacement s1 are calculated. The two configurations of the triad corresponding to the real solutions are presented in Fig. 6. Example 2. The geometrical data and the position of the auxiliary points D and F of the RR-PR-PR triad (see Fig. 2) are given in the upper part of Table 2. For the specific geometry here considered, solving the fourth order polynomial equation (36) two real roots and two complex roots are obtained. For each real value of the displacement s1, the coordinates of the internal revolute joints B, C and E are determined. The two assembly modes of the triad are presented in Fig. 7. 1 nd solutions of the RR-RP-RP Assur group d = 40, d1 = 30, d2 = 45, d3 = 35, lAB = 75"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000545_rob.4620060405-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000545_rob.4620060405-Figure1-1.png",
        "caption": "Figure 1. Inertial and floating frame.",
        "texts": [
            " The constraint conditions are not appended to the resulting Lagrange\u2019s equations in the form of algebraic constraints, but inserted in them by means of a penalty formulation, and therefore the number of unknowns of the system does not increase as is the case when using the Lagrange\u2019s multipliers technique. The,final result is a set of ordinary differential equations, that can be solved using standard numerical algorithms. Serna and Bayo: Forward Dynamics of Elastic Robots 365 The authors consider a robot composed of elastic links. Let Si be a link of the robot whose origin is defined by the vector Ri, and let P be a generic material particle on Si, as shown in Figure 1. The position vector R of the point P with respect to an inertial coordinate frame (0, X) is given by: where r is the position vector of the point P with respect to the floating frame (Oi,x) that moves with the link Si. The orientation of the coordinate frame (Oi, x) with respect to the inertial system may be defined by means of three angular parameters 0; ( j = 1,2,3), which determine an orthogonal transformation E(&) such that: with [X,] and [XI representing the components of the same vector X with respect to the floating and inertial frame, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003174_ichr.2008.4755942-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003174_ichr.2008.4755942-Figure4-1.png",
        "caption": "Fig. 4 Single inverted pendulum",
        "texts": [
            " Anyway, these solutions come into great algorithm complexities, which makes their use in real situations very difficult. II. THE CONTROL ARCHITECTURE The novel control scheme proposed in this paper is the one shown in Fig. 3, where two different control loops are considered: a) humanoid's body posture stability and b) collaborative controlloop.r-- -----. To find the equilibrium points, we set XI = X2 = 0 and solve for Xl and X2: In a very simplified way, the dynamic model of the humanoid robot RH-1 can be considered similar to that of the inverted pendulum in Fig. 4. . g. k X = --SIDX --x 2 I 1 m 2 (2) The equilibrium points are located at (n, Jr) for n =0, \u00b11, \u00b12, ... From the physical description of the pendulum, it is clear that the pendulum has only two equilibrium positions corresponding to the equilibrium points (0,0) and (Jr ,0). Other equilibrium points are repetitions of these two positions, which correspond to the number of full swings the pendulum would make before it rests at one of the two equilibrium positions. Physically, we can see that these two positions are quite distinct from each other"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000151_bc015509d-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000151_bc015509d-Figure1-1.png",
        "caption": "Figure 1. Schematic process of the fusion enzyme formation.",
        "texts": [
            " GA is a monomer with a molecular weight of 99-112 kDa (21), and GOD is a dimeric flavoprotein with a molecular weight ranging from 150 to 186 kDa (22). The fusion enzyme constructed through gene fusion consists of two molecules of GA and one molecule of GOD. Since little information is available for predicting the structure and function change of a fusion enzyme, there is high risk in construction of such a complex hybrid protein. To avoid failure, a flexible linker peptide [-(SerGly)5-] was inserted between GA and GOD. This was thought to aid the independent folding of the two components (23). Figure 1 shows the schematic formation of GLG. Theoretically, GA and GOD would be adjacently immobilized with constant ratio by the proposed method if the fusion enzyme were successfully expressed. Reaction kinetics and reproducibility of the sequence biosensor should be accordingly improved. Details are reported herein. Materials. Restriction enzymes, DNA polymerase, and T4 DNA ligase were obtained from Takara and Promega. Lyticase, bovine serum albumin (BSA), O-dianisidine, soluble starch, PEG3350, glucose oxidase, and glucoamylase were purchased from Sigma"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000449_isie.2001.931878-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000449_isie.2001.931878-Figure2-1.png",
        "caption": "Fig. 2. Configuration of the rotating conductive disk and the extended array of the electromagnets.",
        "texts": [
            " This will lead to a separation of the charges, the positive ones rnovirig to the bottom of the rod and the negative ones to the top. But these separated charges will produce an electric field E pointing upward that will tend to decrease the total force on a given charge in the interior. Finally, enough charges will be separated so that the electric field E produced by them will lead to an opposite force that just balances the magnetic force.\u201d Unlikely with the above idealized problem, in our case E # -v x B since there is current in the pole projection area as shown in Fig. 2, which was revealed by a lot of studies [1]-[4]. So, we are to derive E from the surface charges by using Coulomb\u2019s law. Figure 2 shows a rotating conductive disk to which magnetic field from the electromagnet is applied. a and b are the width and radial length of the rectangular pole of the electromagnet. r d , R, and d are the radius of the disk, distance to the pole center from the center of the disk, and thickness of the disk, respectively. A direct current is applied to the coil wound around the electromagnet. The conductive disk rotates a t a constant angular velocity w in the counter-clock wise (CCW) direction. All the unprimed variables are represented in the fixed frame(zy coordinate) located at the center of the air gap bctween the pole faces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002462_s00466-006-0120-3-Figure14-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002462_s00466-006-0120-3-Figure14-1.png",
        "caption": "Fig. 14 The semi-infinite domain formed by square elements",
        "texts": [
            " Accordingly, the element velocities at the next time step are given by x\u0307t+1 = x\u0307t + t \u00b7 x\u0308t (21) y\u0307t+1 = y\u0307t + t \u00b7 y\u0308t (22) \u03b8\u0307t+1 = \u03b8\u0307t + t \u00b7 \u03b8\u0308t (23) and the element positions at the next time step are xt+1 = xt + t \u00b7 x\u0307t (24) yt+1 = yt + t \u00b7 y\u0307t (25) \u03b8t+1 = \u03b8t + t \u00b7 \u03b8\u0308t (26) After determining the new element positions, the compression (elongation) in the connecting fibers is computed by considering the relative displacement between contacting elements. The process is repeated for each element of the body. Figure 14 shows the semi-infinite domain formed by square elements which is used to simulate the elastic half-space. Note that the elements are all aligned along the coordinate frame x-y . Theoretically, a semi-infinite domain extends infinitely in the plane of paper and has a finite thickness perpendicular to this plane. However, for practical purposes, the domain used here extends to a depth of 10b and 5b on either sides of the contact, where 2b is the width over which the pressure profile is applied. This is based on the fact that the stresses beyond this distance are practically unaffected by the contact loading. The thickness of the domain is taken as unity. Figure 15 depicts the corresponding domain formed using Voronoi elements. A Hertzian pressure load, corresponding to a maximum pressure of pmax is applied to the central elements on the top surface of the domain, as shown in Fig. 14. Since the elements are of unit thickness, the corresponding forces acting on the center of gravity of the boundary elements are found by multiplying the pressure by the length of the side of the element on which the pressure is applied. Also, since the model is dynamic in nature, an instantaneous application of external loading creates instabilities in the system, mainly due to the finite inertias of the elements. For this reason, the load is applied gradually with time. An exponential loading function of the form p(x, t) = pmax [ 1 \u2212 ( x b )2 ]1/2 e\u2212\u03b1/t, \u2212b < x < b, (27) is used, where \u03b1 is a constant which defines the rate of loading",
            " However, note that the non-dimensional, in plane stresses for a semi-infinite domain subjected to a line loading are independent of the elastic properties of the body. Therefore, the values of Kn and Kt that can be used in the model are arbitrary as long as their ratio is appropriately selected in regard to the element type. There are other factors that restrict the spring stiffness values. For example, large values of Kn reduce the time step required for stability and increase the computation time. For the analysis using square elements, a semi-infinite domain with b = 100 \u00b5m is created. Figure 14 illustrates the domain used for analysis. Elements of size 2L = 10 \u00b5m are used to give a resolution of a hundred elements in the x and y directions. The density of the material is 7,800 kg/m3. The damping coefficients \u03ben and \u03bet are 0.1 each. The spring stiffnesses Kn and Kt are assumed to be 200 GPa each (note that E for steel is 200 GPa). A time step of t = 5 \u00d7 10\u22129 s is employed. This is sufficiently small to satisfy the stability criterion in Eq. 20. Note that the objective of the current study is to obtain sub-surface stresses in a crack free medium that allows a comparison with available results"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003363_isorc.2007.32-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003363_isorc.2007.32-Figure1-1.png",
        "caption": "Figure 1. Collision areas of nodes.",
        "texts": [
            " One actuator node a and multiple sensor nodes s1, \u00b7 \u00b7 \u00b7 , sn (n \u2265 1) in an event area W are interconnected in one wireless broadcast channel. 2. Every sensor node si can receive a message m if an actuator node a sends m and no message collision occurs in the collision area C(si), i.e. C(a) = W . 3. A message sent by a sensor node si can be received by only a limited number of nodes if there is no message collision, i.e. C(si) \u2286 W . An actuator node a sends a message with a stronger radio channel than sensor nodes and can deliver a message to every node in an event area as shown in Figure 1. On the other hand, a sensor node si can deliver a message to only nodes in the collision area C(si) of the sensor node si due to weaker radio. Typically, a sensor node can deliver messages to nodes in at longest 15 [m] while an actuator can deliver to node is 100 [m]. Every sensor node may not directly deliver a message to an actuator node a. A sensor node forwards a message to other nodes in multi-hop communication while actuator-sensor communication is a one-hop type. If a pair of different nodes c1 and c2 simultaneously send messages, nodes in a common collision area C(c1)\u2229C(c2) of cannot receive both the messages due to collision in a wireless channel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003014_ba-1975-0142.ch016-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003014_ba-1975-0142.ch016-Figure5-1.png",
        "caption": "Figure 5. Log of the shear modulus vs. the elas tomer phase content",
        "texts": [
            " T W were linear over the range T w = (1-40) \u03a7 10 5 dyne/cm 2 , which agreed with the findings of Rosen and Rodriguez for a different heterophase system (6) . (b) Temperature d id not effect extrudate expansion over the experi mental range of 180-240\u00b0 C , shear stresses being equal. (c) The molecular weight of the S A N (distribution being equal) had no noticeable effect on the extrudate expansion of the resins and of the blends at the same elastomer phase content. (d) As expected, \u0392 of the broader distribution sample was higher; the shear modulus, G , (see Table II and Figure 5) was not dependent on tempera ture, shear stress, or S A N molecular weight over the experimental ranges. (e) Progressive addition of elastomer phase definitely decreased the ex pansion, which agreed with previous reports on A B S resins (5) and high impact polystyrene (2). H a n (5) , on the basis of his previous data on blends of polystyrene and polypropylene, suggested that melt elasticity goes through a maximum at a certain blending ratio. W e , however, have observed that the diameter of the elastomer phase extrudate was almost equal to the capillary diameter, even if it was difficult to collect precise data because of the poor consistency",
            "0 \u00b7 R (15) However, experimentally it was calculated that the value of constant \u03b7 would be changed 10% by increasing the elastomer phase content from 0 % to 4 0 % . This variation was considered reasonably acceptable, considering the com plexity of the elaboration. The hypothesis of the rubber effect on the change in M6o of the pure resin can be confirmed by the extrudate expansion data. According to the rubber elasticity theory: \u03a1 RT M7 (16) From Equations 14 and 16, we obtain log GR = log - nR = log G\u20aco - nR (17) W i t h our graft polymer, log G \u0397 = log Gen + 2.0 R (18) Experimental findings (see Figure 5) indicated that GR can be expressed by the equation: log GR = log Get) + 2.05 R (19) GR is then independent of S A N molecular weight (which agrees with theory), and it is exponentially dependent on rubber content as predicted by Equa tion 17. The agreement between the experimental and predicted values of the constant of the exponents was very good. The \u039c \u0393 ( ) of the S A N copolymer, as calculated by the extrudate expansion data, was 64,000. This value was higher than that for the polystyrene homopolymer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002268_epepemc.2006.4778544-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002268_epepemc.2006.4778544-Figure1-1.png",
        "caption": "Fig. 1. Stator winding ofan IPMSM with a turn fault",
        "texts": [
            " MODELING OF A STATOR TURN FAULT IN AN IPMSM In spite of their simple forms and fast simulation speeds, the qd-variable machine models, which are based on the assumption that the machines are perfectly symmetric, are inappropriate to represent a fault that breaks the symmetry, like stator turn faults. An approach in modeling an IM with stator turn faults was proposed in [2]. Although Tallam considered only the case of IMs, the proposed approach is also applicable to the case of IPMSMs with modification to the rotor-related parts. A schematic of the stator winding of an IPMSM with a stator turn fault on the a-phase winding is shown in Fig. 1. In the figure, as, and as2 represent the healthy turns and the shorted turns, respectively; ,u denotes the fraction of shorted turns, i.e., the ratio of the number of shorted turns to the number of turns per phase winding; and if represents the circulating current in the shorted turns. For the henceforth analysis, it is assumed that the leakage inductance of the shorted turns isuLs , where Lls is the per-phase stator leakage inductance and the possible external impedance between the shorted turns is resistive (Rf ), and referred to as the \"fault impedance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003133_j.autcon.2007.02.002-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003133_j.autcon.2007.02.002-Figure4-1.png",
        "caption": "Fig. 4. Notations for straight-line tracking control in a 3-D space.",
        "texts": [
            " (5) can be more simplified by: p p V \u00bc g p V v \u00f07\u00de where, g p V=R T pgV=(cos\u03b7\u03c8, sin\u03b7\u03c8) T, gV=(cos\u03c8, sin\u03c8) T. From Eqs. (5), (6), and (7), the error dynamics for straightline tracking control on a horizontal plane is obtained from: \u03b7x \u03b7y \u03b7\u03c8 0 @ 1 A \u00bc cos\u03b7\u03c8 0 sin\u03b7\u03c8 0 0 1 0 @ 1 A v xzV : \u00f08\u00de This equation represents the motion of the vehicle with respect to the path frame and assumes a relatively simple form by introducing a fixed path frame. The 3-D error dynamics can be also formulated in the same way. Fig. 4 shows the notations for straight-line tracking control in a 3-D space. The vectors pp, pp+1, pV and pV p denote the positions of Op (the origin of the path frame or the first way point) and Op+1 (the second way point) and the positions of the vehicle on the fixed frame, O\u2212XY, and the path frame, Op\u2212XpYp, respectively. Let pV p=(\u03b7x, \u03b7y, \u03b7z) T and \u03b7V p=(\u03b7\u03d5, \u03b7\u03b8, \u03b7\u03c8) T be the position and orientation errors of the vehicle with respect to the path frame, respectively, and l=(lx, ly, lz) T=pp+1\u2212pp is a vector indicating a straight line path"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001221_aim.2001.936456-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001221_aim.2001.936456-Figure1-1.png",
        "caption": "Figure 1. Frictional point contact model",
        "texts": [
            " In the case of frictionless grasp, the robotic finger can only apply the contact force in the normal direction inward to the object. Hence, the wrench (forcehorque) that can be generated by the grasp has the following representation where .(pi) and ai 20 represent the unit inward normal vector and the amplitude of the contact force at point p i , respectively. For frictional grasps, the Coulomb frictional model is employed, the friction cone at each contact point is approximated by a polyhedral cone with m facets (see figure 1). Denote the edge vectors of the polyhedral cone at p i by fq; j = l , . . . , m . In order to avoid the breakage of the point contact, the contact force is required to lie in the friction cone. Hence, the wrench that can be generated by the grasp has the following form (3) Both (2) and (3) can be written as N w = c a i w i (4) f = I where {w1,w2,.-.,w,,,} is called the set of primitive wrenches of the grasp. For frictionless and frictional grasps, we have N = n and N = n m , respectively. A grasp is said ta achieve force-closure if the primitive wrenches positively span the whole wrench space"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003331_ls.42-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003331_ls.42-Figure6-1.png",
        "caption": "Figure 6. (Inlets on the left). (a) Concentration at z = 40 \u00b5m, U = 0.3 ms\u22121, \u03b7 = 0.5 Pa, h0 = 10 \u00b5m. (b) Partially starved elastohydrodynamic lubrication (EHL) contact.13 (c) Starved EHL contact.13",
        "texts": [
            " In the conjunction entry region, a disturbance starts near the ball surface, as in Figure 5a and 5b. This comes from the oil piling up there and widening as the free surface is approached, before passing round the sides of the ball, eventually to form the track ridges. The widening air region in between (blue) lies above the track floor. Tiny oil wavelet sections on the track floor are seen in Figure 5a. A closer look at the track ridges shows regions of varying concentration on either side, made clearer in Figure 6a. This shows a plan section of the exiting wavelets seen as complete in Figure 2. Another view of the wake formation is the interference fringe picture in Figure 6b, from Wedeven.13 He used a three-ball and plate machine where the wake remaining on the plate from a ball can influence the lubricant inlet geometry of the adjacent ball. Here is an example of an EHL contact where the top half of the inlet region is more starved than the bottom half. There has been no distinctive carry-over of an exit wake into the inlet region, only an uneven oil distribution. The more starved region is beginning to form an exit ramp wall covered in air\u2013oil fingers leading to a ridge, just as in Figure 6a. The lower half has sufficient oil passing round its side to allow the outboard ramp oil\u2013air wavelets to fan out into an adequate oil supply, as illustrated in Yin et al.8 (similar to a Kelvin wake in boat hydrodynamics). When starvation becomes more severe, Figure 6c results. The two-track ridges seen leaving the exit, also appear in the inlet to the contact on the left. They are similar to those in Figure 6a. Figure 7 shows transverse cross sections of the flow across the same film. It is worth noting here that the scales are the same in all three dimensions. The sections show the flow geometry right through the contact. At entry is shown the approaching wavy oil surface. The second picture down shows the start of the oil piling up prior to entering the Copyright \u00a9 2007 John Wiley & Sons, Ltd. Lubrication Science 2007; 19: 197\u2013212 DOI: 10.1002/ls conjunction further downstream. Observe that, except within the pressurised region, the oil is invariably capped with vapour"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003391_coase.2008.4626479-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003391_coase.2008.4626479-Figure5-1.png",
        "caption": "Fig. 5 Dexelisation and voxelisation of a slice [16]",
        "texts": [
            " So the shrinkage model in X direction for a laser power of 36 W (Fig. 3) is given below A. Single direction dexel model of SLS process The concept of dexel was first proposed by Tim Van Hook [13] in 1986. It is a single direction dexel model. The dexel and voxel models have been utilized in visualization of the RP process [14-15]. The single direction dexel model of the SLS process is given in Fig. 4. A single dexel can represent the big voxel. The scan length corresponds to the dexel length. Fig. 5 shows the dexelisation and voxelisation for a typical 2D slice. Here the single direction hatch vectors represent the 3D voxel for a slice. Compensating dexel along single direction dexel space is nearly equal to compensating the voxel. When the shrinkage scaling factors are constant, shrinkage compensation is relatively easy. The scaling transformation can be used to offset the vertices of the triangles of the STL file to the single scaling factor value in each X, Y and Z direction. However if the shrinkage scaling factors varies with scan length, compensation requires offsetting each scan line of the part"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001376_robot.1995.525506-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001376_robot.1995.525506-Figure8-1.png",
        "caption": "Fig. 8 A passage segment",
        "texts": [],
        "surrounding_texts": [
            "2 . Basic Operating Primitives Two operating primitives related to distributed resource sharing in DRS is specified. Detailed descriptions for these primitives are given in [7] , [9] and [ lo] .\n2.1 1 out of N In this problem, up to N (N 2 1) agents compete for a resource of capacity 1 (Fig. 3) . The primitive is abstracted as a function call: where ret := l-oLit-of_N(inst, agt, res, cad, act, para)\ninst: instance upon which the primitive is called ng t : id of agent running this algorithm r-es: id of the resource cad: set of potential competitors acl: a routine to be executed upon taking the resource para: list of parameters invoked by routine nct ret: value returned by routine act\nIn this paper, a robot always competes for a resource (e.g., an intersection) as the a g e n t of the passage segment i t is occupying. Argument i n s t is introduced to allow nested/concurrent invocation of this operating primitive. A routine (acl) is invoked with pre-specified parameters (para) once exclusive access to the resource is obtained.\nA fully distributed, provable algorithm for the \u201c1 out of N\u201d problem is presented in [ lo]. It guarantees mutual exclusive access to the resource, deadlock free and lockout free. This implies that an agent, once starts to compete for a resource, will eventually get it, provided no robots use the resource for infinite time.\n2.2 Deadlock Detection In [ l o ] , a fully distributed algorithm for deadlock detection i n a traffic network composed of passage segments and intersections is presented, where all passage segments are assumed unidirectional and of capacity 1 (Fig. 5 ) .\nIn the distributed traffic control problem, a robot will reserve and release passage segments (as resources) in an order not known a priori. Moreover, a robot must reserve (obtain the right of entering) its next destirzatiorz passage\nsegment while occupying another. As the sequence of these reservations is not controlled, a deadlock may occur. Until the deadlock is resolved, all robots involved are blocked indefinitely. In Fig. 5 , the desired next destinations for robots a. 6, c , d, e andfform a closed chain. Since the capacity of each passage segment is 1, nobody in this chain can move, constituting the kernel of the deadlock. In addition, robots g , h , and i cannot move, even though they are not in the deadlock kernel.\nThe distributed deadlock detection algorithm presented in [IO] guarantees that (i) if there is a deadlock, it i s initially realized by exactly one robot: and (ii) no deadlock is declared if there is no deadlock. The primitive is abstracted as a function call: where ret := deadlock(cps, dps)\ncps: id of passage segment the robot is residing dps: robot\u2019s desired next destination passage segment ref: one in {INITIATOR, FOLLOWER, NONE}\nThe function is called upon by a robot resideing in passage segment cps, and has found that its next destination dps is occupied by another robot. It returns INITIATOR if the robot invoking the function was the one first realized the deadlock: i t returns FOLLOWER if the robot is in the deadlock kernel, but is not the INITIATOR: NONE is returned if dps becomes available (i.e., no deadlock). During deadlock detection and resolution, a robot always operates on behalf of its current passage segment.\n2.3 Deadlock Resolution The system is said to have made a positive progress if at least one robot has advanced to its next destination, while the rest staying in their respective current passage segments. A number of deadlock resolution strategies have been proposed in [9], none of which guarantees positive progress.\nThe deadlock resolution strategy proposed in this paper requires a reserved logical OufSeering area at each intersection (Fig. 6). Physical implementation of this buffering area depends on application. It can he shown that positive progress is impossible unless buffering areas specially reserved for deadlock resolution are introduced.\nIn Fig. 5 , assume robot c at P5 is the INITIATOR, which\nThe news about the deadlock is first announced by the INITIATOR, and then propagated along the deadlock kernel. This is part of deadlock detection algorithm. The INITIATOR (robot c) moves into the buffering area of the intersection in front of it. The FOLLOWERS move successively (first robot b, then u , f , e , and d) into their respective next destinations along the deadlock kernel (Fig. 5 and Fig. 7).\n(2) The INITIATOR (robot c ) moves into its next designation ( P 7 ) from the buffering area. For those robots blocked by, but not in the deadlock kernel (such as robots g , h and i, the deadlock detection algorithm does not make them aware of the deadlock (although this is certainly possible). In fact, they may still be running deadlock detection even after the deadlock has been\nleads the resolution process proceeded as follows: (0)\n(1)\n1620 -",
            "announced and/or resolved. These robots will, however, quit the deadlock detection as soon as they are no longer blocked, which will eventually happen as the deadlock kernel has been resolved.\n3 . Distributed Traffic Regulation and Control\n3.1 Assuinntions\nl\u2019ossage Srgnzenls Without losing generality, we assume that all passage segments are uizidirectinizal, and have a width allowing just onc robot to move along. Thus a passage segment has exact one entrance and one ex i t , each of which is exposed to an intersection or a terminal. The capacity of any passage segment is greater than or equal to one.\nOiicc having entered a passage segment, a robot must move towards its exit, and arrive at its exit within finite amount of timc. Sensors are equipped on each robot, and are triggered upon arrival at the exit of a passage segment.\nTeiminnls A terminal is a physically enclosed area capable of holding a fixed number of robots. A robot may stay at a terminal for a unspecified, but finite amount of time. Each terminal must have one or more entrances, and exactly one cxit. (This single exit limitation is imposed due to current deadlock detection algorithm). All terminal entrances and exits are connected to passage segments.\nA terminal of capacity M is depicted as having M logical \u201cseats\u201d labeled I , ..., M . An extra seat (labeled 0) is rcserved for dcadlock rcsolution. I t is assumed that a robot has the capability of moving from an entrance into the interior of a terminal, slaying inside, and eventually moving out of the it through its only exit. Robot motion within the terminal is not the concern of this paper.\nIntersections\nIncident to two or more passage segments (with at least one incoming, and one outgoing), an intersection must be passed by robots one at a time. A robot is capable of guiding itself through an empty intersection by consulting Lhe field map. A buffering area with a capacity of holding one robot is reserved at each intersection for the purpose of deadlock\nField Map\nThe 2-D operating space can be represented as a static directed graph, in which terminals and intcrsections are vertices, and passage segment are edges. The attributes associated with a vertex indicates its finite capacity. An edge in this graph is identified with an ordered pair of vertices </lzs, rlzsi, whcre llzs is the intersection or terminal incident to the entranc\u2019e of the passage segment, and r h s is that incident to its exit (Fig. 12). This field map is consulted from time to time bv the robot to keeu track of its current locatioii in the operating field.\nThis is clearly a \u201c1 out of N\u201d problem, with the resource being the inter\u2018\\ection Robots are competing on behalf of a finite, small number of passage segments leading to the intersection, over which inter-robot communication is required Since no robot can stay at the middle of an intersection forever, a robot eventually gets its turn to enter For robot at passage segment a going into passage q e g i n e n t p , as shown in Fig. 13, it needs to invoke\nl_out_of_iV(INTERSECT, a , eizd-of(a), pred(p) , move-Liz-pass, <a, p > )\n1621",
            "where INTERSECT is a constant instance; pred@) returns set [ a , b } ; end-o f (a ) returns intersection I ; and routine nznve-iri-pass(<a, p > ) guides the robot from a to p via intersection 1.\nEntering a PaJsage Segment To entorce the finite capacity constrain of a passage segment, the traffic at its entrance must be regulated Thus a iobot must compete with (potentially) others for the right to enter its next destination passage segment.\nwhere PASS-IN is a constant instance, and pred(p) again returns set [ a , b } Routine pass-in(<a, p>) is called upon when the robot has obtained exclusive right of entering p This routine functions as tollows:\nI-oiit-of-N(PASS-IN, a, p , pred(p),pass-zn, <a, p>)\nI f p is available, (i.e., there is sufficient room at the entrance of p ) , compete for the right of passing through the intersection, and then move into p via the intersection. Stop. If p is blocked, (i.e., there is not sufficient room at the entrance of p ) , run deadlock detection. If deadlock detection results in NONE, (i.e., p is now available), compete for the right of passing through the intersection, and move into p via the intersection.\nEntering in a Terminal To enforce the finite capacity constrain of a terminal, robots must be admitted one at a time. Thus robots at various entrances of the terminal must compete for this logic right (order) to enter. This is again a \u201c1 out of N\u201d problem. In Fig. 16, robot at entrance a must invoke\nI-out-of-N(TERM-IN, a , end-ofla), pred(end-of(a)), term-in, <a, end-ofla)>)\nwhere TERM-IN is a constant instance; end-ofla) returns the id of the terminal: pred(end-of(a)) returns the set of passage segments that are also entrances of the terminal. Routine term-in is called upon once a robot has obtained the exclusive right of entering the terminal (before others) It is designated to do the following:\nIf there is a seat available in the terminal, move into that seat. Stop. If no seat is available, run deadlock detection using the exit as the desired next designation. If there is no deadlock, (i.e., the exit of the terminal is available), wait until one of the seats becomes vacated. Move into that seat. Stop.\nExiting from a Terminal Having finished its work within the terminal, a robot competes with others (inside the terminal) for the right of going through its only exit (Fig. 18). If the exit is not immediately available, the robot simply waits, since if there is no deadlock, the exit will eventually become available: and if there is indeed a deadlock, the exit will be available after deadlock resolution. This is again a \u201c 1 out of N\u201d problem with the exit of terminal being the resource. In Fig. 18, robot occupying Seat 1 invokes:\nI-out-of-N(TERM-OUT, 1 , p , term-seat(T), term-out, <T, I , p>)\nwhere TERM-OUT is a constant instance: p is the passage segment connected to the exit of the terminal: and term-seat returns the set of seats of the terminal. Routine term-out is called upon once robot has seized the right of exiting the terminal (before others). It drives the robot from its seat into the terminal\u2019s exit as soon as the exit passage segment becomes available.\nDeadlock occurs if a loop is formed along a series of passage segments/terminals that have all reached their respective finite capacity (Fig. 19). Since only those robots who are at the end (exit) of their respective passage segments may invoke deadlock detection, each passage segment is represented by at most one robot, and terminals can be treated as intersections. As far as deadlock detection is concerned, the situation can be reduced to that described in Section 2.\nDeadlock Resolution\nDeadlock resolution involves both passage segments and terminals are essentially the same as that described in Section 2 . Special consideration has been made for robots being blocked at entrances of a terminal:\n- 1622 -"
        ]
    },
    {
        "image_filename": "designv11_28_0000752_bf03179258-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000752_bf03179258-Figure7-1.png",
        "caption": "Fig. 7. Diagram of electron beam furnace for continuous casting.",
        "texts": [
            " Electron beam melting Electron beam (EB) furnaces are attractive for remelting scrap into ingots and slabs. Clean, granular, blended feedstock is introduced to EB furnaces through a vacuum system to a water cooled hearth for melting. The metal is degassed thoroughly; the high density contaminants sink and are trapped in the semi-solid skull, and the liquid metal is continuously cast into a water cooled mold. Electron beams sweep the melt area on the hearth and the cast metal in the crucible to provide good melting and sound ingots as they are slowly retracted (Fig. 7). The distinct advantages of EB furnaces are that it provides a good means for using and refining large quantities of turnings, it can use granular feed stocks and only a single melt is required for some products such an unalloyed Ti. The disadvantages of the process are the high equipment costs and the loss of alloying elements at the low operating pressures required. The most powerful guns deliver up to 1.2 MW and their reliability has made the construction of large furnaces possible. In 1983 two hearth furnaces were built in the United States for melting Ti scrap"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000418_095440603767764426-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000418_095440603767764426-Figure5-1.png",
        "caption": "Fig. 5 Zero-pitch reciprocal screw con guration at y1 \u02c6 908 and y1 \u02c6 2708",
        "texts": [
            " Similarly, the screw matrix S of joint axes at the con guration of y1\u02c6 908 or 2708 becomes 0 0 1 0 0 0 +1 0 0 0 +d 0 0 +1 0 +\u2026d \u2021 a\u2020 0 0 +1=2 0 + 3 p =2 0 +\u2026d \u00a1 a\u2020=2 0 0 +1 0 +d 0 + 3 p a 0 0 1 0 3 p a 0 2 6666666666664 3 7777777777775 \u202627\u2020 Their reciprocal screw axis of pure force constraint yields $r \u02c6 \u20301, 0, 1= 3 p ; 0, d \u2021 a, 0\u0160T or \u2030 3 p =2, 0, 1=2; 0, 3 p \u2026d \u2021 a\u2020=2, 0\u0160T \u202628\u2020 This is also a transversal one intersecting all revolute joint axes. This gives two corresponding constraint con gurations in Fig. 5. From the previous section, the reciprocal screw that belongs to one of these four special con gurations is reciprocal to itself and therefore is a subspace of the vesystem, which is de ned by the six revolute joint axis. This further illustrates that the zero-pitch reciprocal screw becomes the intersection and the total number of linearly independent screws in the union of these two screw systems is ve. The relationship between them is said not to be disjoint during the zero-pitch con gurations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002624_1-4020-3393-1_7-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002624_1-4020-3393-1_7-Figure1-1.png",
        "caption": "Fig. 1. General multibody system.",
        "texts": [
            " There are other types of kinematic constraints, such as the linear combination constraint or the cross product constraints that are also used when modeling with natural coordinates [2]. All kinematic constraints mentioned have a quadratic or a linear dependency on the coordinates. Their contribution to the Jacobian matrix of the constraints is either linear or constant. The equations of motion of a constrained multibody system acted upon by external applied forces, such as the one presented in Figure 1, are given by: T qMq g (4) where M is the global mass matrix of the system, q the Jacobian matrix of the constraints, q the vector of natural accelerations, g the generalized force vector and the vector of Lagrange multipliers [2,13,14]. Due to the presence of redundant constraints, multiple solutions of Equation (4) can be found. In order to calculate a single solution, the minimum norm condition is applied [2], assuring that the vector of Lagrange multipliers is orthogonal to the null space of q T"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003725_s10409-009-0258-2-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003725_s10409-009-0258-2-Figure1-1.png",
        "caption": "Fig. 1 Schematic diagram of a pendulum\u2013cart system",
        "texts": [
            " However, as the LQ controller designed from reductions (3) or (4) is delay dependent, the online update of the controller is needed for the time-varying delay. This process involves the online computation of a Riccati equation. Such a computation can hardly be done in realtime and will introduce a new time delay into the controlled system. 5.2 A case study To study the feasibility of the new control method to the dynamic system with a slowly time-varying delay more concretely, this subsection deals with the control problem of a pendulum\u2013cart system, as shown in Fig. 1, governed by [ M + m \u2212(ml cos \u03b8)/2 \u2212(ml cos \u03b8)/2 J0 ] [ x\u0308 \u03b8\u0308 ] + [ (ml \u03b8\u03072 sin \u03b8)/2 + \u00b5x\u0307 mgl sin \u03b8 ] = [ F 0 ] , (49) with the system parameters listed in Table 1. By linearizing Eq. (49) around the rest position [ x \u03b8 x\u0307 \u03b8\u0307 ]T = [0, 0, 0, 0]T and rewriting it in the state space, one obtains x\u0307 (t) = Ax (t) + B F(t), (50) where x = [ x \u03b8 x\u0307 \u03b8\u0307 ]T , A = \u23a1 \u23a2\u23a2\u23a3 0 0 1 0 0 0 0 1 0 \u22121.305 \u22121.581 0 0 \u221270.98 \u22125.367 0 \u23a4 \u23a5\u23a5\u23a6 , B = \u23a1 \u23a2\u23a2\u23a3 0 0 0.6079 2.064 \u23a4 \u23a5\u23a5\u23a6 . Suppose that the control process has a slowly time-varying input delay described by \u03c4 = \u03c40 + \u03b5 sin(\u03c9t)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002733_cefc-06.2006.1632900-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002733_cefc-06.2006.1632900-Figure1-1.png",
        "caption": "Fig. 1 shows the analyzed model of the EMI drive mechanism. It mainly consists of the rotor and inserted ring magnet. The rotor has two sets of 4-thin conductors, and inner and outer cores. The ring magnet has 8-ploes, and is inserted into the gap between two sets of conductors with the torque meter using the linear guide. Fig. 2 shows the EMI torque measurement system. The rotor and ring magnet are connected to the motor and torque meter, respectively. The EMI torque is produced from the eddy current flowing through the conductor when the ring magnet is suddenly inserted into the gap between conductors rotating at rotation speed of 2000 rpm by the motor. In this calculation, initial potentials of all edge elements are set to be zero in order to suppose the sudden insert of the ring magnet.",
        "texts": [],
        "surrounding_texts": [
            "I. INTRODUCTION\nConventional impact drive mechanism has been used for an electric screwdriver, however, it generates large noise due to the impact between two metal bodies. Then, authors are studying low noise EMI drive mechanism using the eddy current. In this paper, the dynamic response analysis method of EMI drive mechanism is proposed employing 3-D FEM [1].\nFig. 3 shows the distributions of eddy current and Lorenz force density vectors. It is found that the eddy current greatly flows through the conductor around the boundary of ring magnet where the gradient of flux density is the maximum. Fig. 4 shows the calculated time variations of EMI torque of eddy current. The peak value of EMI torque is about 0.8 N\u00b7m. The large EMI torque is produced because the interlinkage flux of conductor is rapidly changed when the ring magnet is suddenly inserted into the gap.\nThe dynamic response analysis method for computing the EMI torque was proposed using 3-D FEM. The validity of this\nmethod will be given by comparing with the measurement in the full paper.\n(a) Overview\nFig.3 Distributions of eddy current and Lorenz force density vectors.\nFig.4 Calculated results of time variations of EMI torque.\nV. REFERENCES\n[1] S. Ito and Y. Kawase, \u201cCAE of Electric and Electronic Apparatus Using Finite Element Method, Morikita Publishing Co., Tokyo, Japan, 2000.\nring magnet\nrotor core\nconductor\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n0 0.5 1 1.5Time (ms)\nEM I t\nor qu\ne (N \u30fbm\n)\n1-4244-0320-0/06/$20.00 \u00a92006 IEEE 108"
        ]
    },
    {
        "image_filename": "designv11_28_0002325_j.triboint.2006.09.003-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002325_j.triboint.2006.09.003-Figure1-1.png",
        "caption": "Fig. 1. Sketch of a wire race ball bearing.",
        "texts": [
            " The two critical conditions of no-load and shear-failure cases will be Nomenclature R01, R001 principal radii of curvature of a wire race in the rolling and lateral directions, m R01o, R001o principal radii of curvature of the outer wire race in the rolling and lateral directions, m R01i, R001i principal radii of curvature of the inner wire race in the rolling and lateral directions, m R02, R002 principal radii of curvature of a ball in the rolling and lateral directions, m R002o, R002o principal radii of curvature of a ball in the rolling and lateral directions along outer races, m R02i, R002i principal radii of curvature of a ball in the rolling and lateral directions along inner races, m R0, R00 equivalent principal radii of curvature, m Re equivalent curvature radius, m Reo, Rei equivalent curvature radii of the outer and inner race contact, m e ellipse of eccentricity E1, E2 Young\u2019s modulus of wires and rolling ele- ments, Pa v1, v2 Poisson\u2019s ratios of wires and rolling elements E* equivalent Young\u2019s modulus, Pa d, d1, d2, d3, d4 contact deformation of contact points, m do, di contact deformation of outer race and inner race, m dz total contact deformation of the bearing in the vertical direction, m F, Fo, Fi, F1, F2, F3, F4 normal contact forces, N P, P0 maximum contact pressure, Pa F1(e), F2(e) correction factors Fa bearing axial load, N a, b semi-major and semi-minor axes, m K(e), E(e) complete elliptic integrals of the first and second kind Gi, Gou gravity of the inner and outer frameworks, N Gb gravity of a ball, N Z number of balls a contact angle, rad tmax maximum shearing stress, Pa [t] allowable shearing stress, Pa applied in a mathematical model in order to determine the total preload magnitude of a wire race ball bearing. Fig. 1 illustrates a wire race ball bearing in cross-section used in a certain type of aircraft simulating rotary table. The wire race ball bearing, which belongs to a four point angular contact ball bearing, can support both radial and axial loads, offer very low friction and can operate well even when the load is somewhat misaligned. It consists of four elements: four wire races, some balls, a cage and two frameworks. Moreover, the pitch circle diameters of this kind of bearings are available from 150 to 3000mm [2]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001681_robot.2004.1307975-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001681_robot.2004.1307975-Figure7-1.png",
        "caption": "Fig. 7. Deflection on Second Hale",
        "texts": [
            " Because the output of force sensor implies the noises and the noises are also multiplied by L,, the accuracy of Mz, is not ensured. If the gain of force feedback control for M,, is increased the vibration of the manipulator will occur. On the contrary, if the gain is decreated the force to correct the orientation of the peg will not occur. At all, a adjustment of the gain becomes difficult under the condition using a long C. Influence of Endem Hole Finally, we describe the influence of a tandem hole. The positional precision is required when the tip of a peg is inserted into the second hole as shown in Fig7. When the peg is restricted by the first hole the tip of the peg P, and the gripping point Pg are located with the central focus on the middle of the first hole Po, having radii L1 and LZ respectively. Under this condition, the deflection of P, from a central axis (a horizontal broken line) is Ll/Lz times larger than the deflection of Pg. 111. CONTROL SYSTEM The experiment i s performed with manipulator PA10 made by Mitsubishi Heavy Industries. A proportional and derivative (PD) control algorithm is used to control the manipulator peg"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000414_bf02321411-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000414_bf02321411-Figure4-1.png",
        "caption": "Fig. 4 - -L igh t pass inclined normal to surface of the plate",
        "texts": [
            " From the good agreement of the coefficients c~ and c~, it is concluded that the greased loading parts did not disturb the plane stress state as well as the unconstraint of the longitudinal strains. Even if the beam is cut out in an arbitrary crystallographic direction, the beam will be in the plane stress state. The principal axis of the indicatrix in the deformed beams D and E does not coincide with the x3' axis. Consequently, the ray is refracted in the beam. Here, we assume a uniform stress field as shown in Fig. 4. The incident ray normal to the crystal surface is refracted in the beam. Nevertheless, the wave-normal is perpendicular to the crystal surface. The maximum angle between the ray direction and the wave-normal direction depends on the ratio of long and short semiaxes of the ellipse which was formed by cutting the indicatrix by the plane of vibration of a plane polarization. T h e maximum angle is given by 0 . ~ = + a r c t a n l ( b - b ) (28) where a and b are semiaxes of the ellipse. From eq (1), we have the change of the indicatrix from a sphere for the cubic crystal as no - n, 1 [~] - T n~ [Tr,j] [oj] (29) 298 * September 1989 Assuming that the absolute maximum value of 7rij is 10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000773_jmaa.2001.7531-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000773_jmaa.2001.7531-Figure2-1.png",
        "caption": "FIG. 2. Typical phase trajectories of the uncontrolled system.",
        "texts": [
            "2 2 2 where f x , y x y cos xy 2, g x , y y x sin xy 2,\u017d . \u017d . \u017d . \u017d . 2 2P x , y 1 sin x cos y ,\u017d . \u017d . \u017d . 2 2Q x , y 1 sin xy cos x ,\u017d . \u017d . \u017d .\u017d . F x , y a 1 x cos y y sin x a SIGN xy a 1, 1 , 4\u017d . \u017d . \u017d . 1, xy 0, 1, 1 , xy 0,SIGN xy \u017d . 1, xy 0, F x , y b x y cos x 4 b 1, 1 , 4\u017d . \u017d . F u cu sin u c 0.5, 0.5 . 4\u017d . \u017d . 2 2 2 \u017d . \u017d .From A2 A3 , we have k x , y 2 x y , k x , y 4 x y , 0.5.\u017d . \u017d . For example, for a 1, b 1, and c 0.5, by the modified Runge Kutta method, some typical phase trajectories of the uncontrolled system are depicted in Fig. 2. \u017d .If we choose A 1 and L 2, then, by 3.6 , we have M 1. \u017d . \u017d .Furthermore, let H x x, J x x 3, 1, 1, and 0.5. \u017d . \u017d .Then we can calculate the explicit form of the controllers u t and u t1 2 \u017d . \u017d . \u017d .given by 3.1 with 3.2 3.7 . They are shown as u t u x t , y t u x t , y t ,\u017d . \u017d . \u017d . \u017d . \u017d .\u017d . \u017d .1 1n 1c u t u x t , y t u x t , y t ,\u017d . \u017d . \u017d . \u017d . \u017d .\u017d . \u017d .2 2 n 2 c u x , y\u017d .1n 2f x , y P x , y x 3 x 3\u017d . \u017d . \u017d . \u017d . P x , y\u017d . 22 2x y cos xy 2 x 3 1 sin x cos y 1\u017d . \u017d . \u017d . \u017d .\u017d . ,2 21 sin x cos y\u017d "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000264_s0022-460x(02)01392-5-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000264_s0022-460x(02)01392-5-Figure4-1.png",
        "caption": "Fig. 4. Connection between shaft and support structure: K, calculation grid point; x, physical grid point.",
        "texts": [
            " (14) yields hr \u00bc c \u00bdA1\u00f0z\u00de A2\u00f0z\u00de A3\u00f0z\u00de cosj ex1 ex2 ex3 8>< >: 9>= >; \u00bdA1\u00f0z\u00de A2\u00f0z\u00de A3\u00f0z\u00de sin j ey1 ey2 ey3 8>< >: 9>= >; \u00bc c \u00bdTc fxcg; \u00f016\u00de where exi and eyi ; i \u00bc 1; 2; 3 are the shaft deformations at node i in the x and y directions, respectively (see Fig. 3). The transformation matrix \u00bdTc in Eq. (16) is \u00bdTc \u00bc \u00bdA1\u00f0z\u00decosj A1\u00f0z\u00desinj A2\u00f0z\u00decosj A2\u00f0z\u00desin j A3\u00f0z\u00decosj A3\u00f0z\u00desin j \u00f017\u00de and fxcg \u00bc f ex1 ey1 ex2 ey2 ex3 ey3 g T: \u00f018\u00de The above vector fxcg is a part of the retained d.o.f. vector fxc rg of the shaft (see Eq. (6)). A large number of non-linear spring elements are used in the circumferential direction (Fig. 4). Each non-linear spring element connects a node on the axis of the shaft with a point on the inner surface of the support. The force\u2013displacement relationship of the spring element depends on the clearance between the inner surface of the support and the outer surface of the shaft. Since the cross-section of the shaft retains its circular shape during the flexible deformation, the force\u2013 displacement relationship depends on the distance between the grid point on the shaft centerline and the inner surface of the support",
            " (3), the deformation \u00f0dx; dy\u00de of a physical grid point on the inner surface of the support in the x and y directions, respectively, is given by dx dy ( ) \u00bc \u00bdX b Y b ab xb r ( ) ; \u00f019\u00de where f ab xb r g T are the generalized co-ordinates of the support structure. Note that any grid point on the inner surface of the support belongs to the vector of internal d.o.f. fxb i g: Any point on the inner surface of the support, which belongs to the finite element mesh of the support structure, is considered as a physical grid point (see Fig. 4). The number of physical grid points at any cross-section of the support that are needed to capture the structural deformation of the support structure, is usually much smaller than the number of non-linear spring elements required to provide proper support for the rotating shaft. Therefore, a set of calculation grid points is used as shown in Fig. 4. The calculation grid points are placed at the locations of the non-linear spring elements and are utilized only for calculating the clearance between the shaft and the support. The deformation of a calculation grid point in the x and y directions, respectively, is given by dx dy ( ) \u00bc Xm Ym ab xb r ( ) ; \u00f020\u00de where the transformation matrix \u00bdXm Ym is obtained through a cubic spline interpolation from the transformation matrix \u00bdX b Y b : The radial deformation d of the support is d \u00bc dx cosc\u00fe dy sin c \u00bc \u00bd cosc sin c dx dy ( ) ; \u00f021a\u00de where c \u00bc tan 1 dy dx : \u00f021b\u00de Substitution of Eq",
            " (24) is utilized for determining the interaction forces that are created by the non-linear springs between the flexible support structure and the flexible rotating shaft. The interaction forces provide the coupling mechanism between the two components. The equations for the flexible dynamic response of the support structure and the coupled rigid and flexible dynamic response of the shaft have been presented in Sections 2 and 3, respectively. The dynamic equations for the combined shaft and support structure system are derived in this section. The interaction between the shaft and the support structure is modelled by non-linear spring elements (Fig. 4). Combining Eqs. (1) and (7) results in Mc yy Mc yf 0 Mc f y Mc ff 0 0 0 Mb ff 2 664 3 775 .y .xc .xb 8>< >: 9>= >;\u00fe 0 0 0 0 Cc ff 0 0 0 Cb ff 2 64 3 75 \u2019y \u2019xc \u2019xb 8>< >: 9>= >;\u00fe 0 0 0 0 Kc ff 0 0 0 Kb ff 2 64 3 75 y xc xb 8>< >: 9>= >; \u00bc fQeg \u00fe fQvg \u00fe fQg; \u00f025\u00de where fQg is the vector of the physical non-linear spring forces applied both on the shaft and on the support structure. The vector fQg is a function of the clearance h between the shaft and the support. Superscripts c and b denote the shaft and support structure, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002786_004051757504501201-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002786_004051757504501201-Figure6-1.png",
        "caption": "FIG. 6. the viscoelastic and frictional limits to recovery Ryi(1) and R\u2019L(t) for a hypothetical fabric with the characteriatics of Figure 2 (a) held bent for 10 min before recovery.",
        "texts": [
            " (b): Residual deformation with time for a nylon fabric following instantaneous crease-and-recovery cycles applied at times marked by points. ~. covery which would be observed in the absence of friction (Equation 2). R,.L is an interaction between the frictional moment and the viscoelastic behavior of the fibers and represents the limit imposed to recovery because of the presence of friction. Since for any time 4 RVL % 1 and RPL < 1, then the recovery of the fabric can be no better than either one of these, and they therefore represent true limits to the recovery. As an example we have plotted in Figure 6 the three R functions of Equation 4 against total time t for the relaxation function and frictional factor of Figure 2 (a). RVL, and hence R, have been calculated for a creasing time of ia - 10 min..The recovery at any time t is obtained merely by multiplying the two limits. together, and it will be seen how R(t) is bounded by both these functions. R (i) exhibits a maximum value at around 100 min, and it is at this point that the fabric ceases recovery [1], because the viscoelastic recovery moment provided by the fibers falls below the"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001970_0301-679x(78)90179-2-Figure13-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001970_0301-679x(78)90179-2-Figure13-1.png",
        "caption": "Fig 13 S represents centre o f rotation o f disc, 0 the centre o f the annulus. I f the disc velocity at point Q on the annulus is u the radial velocity o f the annulus at this point is Ur --- (ux sin O)/R",
        "texts": [
            " On the other hand, radial misalignment, where the centre of the seal does not coincide with the centre of the rotating face plate, produced stationary interference patterns which it was possible to study in detail. The first observation is that when there is a high degree of concentricity the film formed between the surfaces is virtually non-existent; as the eccentricity is increased a stable film builds up quickly and increases in thickness with increasing eccentricity. The most marked effect is observed at a position at right angles to the direction of the misalignment (Fig 13). The reason for this is simple. I fx is the radial misalignment and u is the velocity at Q due to the rotation of the disc, there is a component of velocity Ur along the direction of the radius of the seal given approximately by: u x sin 0 U r - - R At 0 = 0 this component is zero, but at 0 = 90 \u00b0 it has its maximum value U X (Ur) max R Thus when 0 = 90 \u00b0, the portion of the annulus is virtually travelling at right angles to its length with a velocity that is (x/R) times the velocity of the disc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001657_tmag.2004.824772-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001657_tmag.2004.824772-Figure1-1.png",
        "caption": "Fig. 1. E-M finite-element model of the motor with associated conditions.",
        "texts": [
            " In Section IV of the paper, we use a boundary-element model of the motor with which to demonstrate how the discontinuities can act to enhance the sound radiation caused by excitation. If two flux density waves in the air gap are represented as and , then their product (proportional to the air-gap stress wave) becomes where and are the wave amplitudes, and denote wavenumber harmonics, and are the wave circular frequencies, and and denote the phases. A stress wave with zero mode number results any time the cross product of two flux density waves yields or . The E-M finite-element model, shown in Fig. 1, represents a single pole of a 12-pole, Y-connected, three-phase 240 V induction motor. The supply frequency is 60 Hz. Ideal conditions are assumed, i.e., pure sinusoidal and fully balanced phase voltages and no rotor eccentricity, and the effects of skew are ignored for purposes of this analysis. After the startup transient settled out, a one-cycle simulation was conducted with time steps every 1/6000 second to capture forcing function variations up to 3 kHz. There were 1000 points along the arc in the air gap at which the flux densities were calculated for each time step"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003094_j.mechmachtheory.2007.12.001-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003094_j.mechmachtheory.2007.12.001-Figure9-1.png",
        "caption": "Fig. 9. Assembly modes of the PR-PR-RP Assur group.",
        "texts": [
            " The geometrical data and the coordinates of the points A, D and F of the PR-PR-RP triad (see Fig. 4) are inserted in the upper part of Table 4. The solving of the final fourth order polynomial equation (65) leads to two real roots and two complex roots (see Table 4) for the input data here considered. For each real value of the displacement s1, using back substitution, the displacement s2, s3 and the coordinates of the internal revolute joints B, C and E are calculated. The corresponding two assembly modes of the PR-PR-RP triad are illustrated in Fig. 9. Example 5. The geometrical data and the coordinates of the points A, D and F of the RR-PR-PP triad (see Fig. 5) are inserted in the upper part of Table 5. The solving of the final second order polynomial leads to two real roots (see Table 5) for the input data here considered. For each real value of the displacement s3, using back substitution, the coordinates of the internal revolute joint B and the displacements s1 and s2 are calculated. The corresponding two assembly modes of the RR-PR-PP triad are illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002371_tieci.1976.351356-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002371_tieci.1976.351356-Figure2-1.png",
        "caption": "Fig. 2. Mathematical representation of magnetization characteristic. The line from point 1 to 4 may form one section.",
        "texts": [
            " [17], after a detailed study of the above mentioned methods, have suggested that the only satisfactory way is by linear interpolation between a set of coordinate points. In the present work, the magnetization characteristics have been approximated by a suitable number of straight lines using a new approach [21]. In this approach the maximum error between the line approximation and the measured points on actual curve is kept within the certain prescribed limit. The logic is as follows: Obtain the suitably distributed points on the magnetization characteristic experimentally. Start with the nearest point to the origin (Fig. 2), say 1. Calculate equation of the line passing through points 1 and 2 and then through points 1 and 3 and see whether point 2 lies on the line through points 1 and 3 within allowable accuracy limit. If it does, then calculate the constants for the line through points 1 and 4. If any of the previous points does not lie in the allowable accuracy limit on this line then take the line calculated just previously as forming one section. Proceed in this manner until all the points are exhausted. A flow-chart of computer program for finding the number of sections and the equations of the lines in their respective sections is given in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002006_05698197708982834-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002006_05698197708982834-Figure3-1.png",
        "caption": "Fig. 3-Mechanical loading on a seal ring",
        "texts": [
            " Also, if the second ring itself is clamped, the slightest distortion would be transmitted directly to the seal ring. Thus, some types of rigid seal ring mounting could lead to distortion in actual operation. It can be shown that the first of these sources, mechanical loading, is a major source of waviness in contacting face seals. The remainder of this paper considers this source in detail. MECHANICAL LOADING In a contacting mechanical face seal, the seal rings are in general subjected to a variety of mechanical loads. With reference to Fig. 3, drive forces can act to produce several different types of loads. In general, a single drive force can act to produce a system of three components of moment and two components of force as shown. The drive may be accomplished by a single force or by a system of equally spaced but sometimes unequal forces. In addition, if not uniform, spring loading on a seal ring can act to produce a single concentrated axial load or a distribution of such loads. The secondary seal on the floating ring may produce a nonuniform radial load if the ring is pushed off center. Also, there is a nonuniform pressure distribution on the face of the ring. Finally, fluid pressure acts in the radial and axial directions, but because these pressure distributions are uniform, they produce no face waviness and are not included. All of the loads shown in Fig. 3 and discussed above can produce waviness in some instances. Before specific cases are studied, general equations for deflection are derived. GENERAL DEFLECTION EQUATIONS FOR A CIRCULAR RING Since a typical seal ring cross section has comparable dimensions in both the axial and radial directions, de- of M'aviness in Mechanical Face Seals flections can be determined by assuming that the ring behaves like a curved beam. A segment of a circular ring is shown in Fig. 4. The ring is assumed to be loaded by distributed loads p, and p, acting through the shear center and pe acting through the centroid and by distributed moments m,, mu, m,",
            " [ I l l , [12], and [13] into [14], [15], 1:16], and [17] and simplifying, the resulting stress resultant-displacement equations are Equations [27], [28], and [29] can be used to solve for the out of plane displacement v or waviness. where V = u/R, etc., and where The homogeneous solution to Eq. [30] is v = B, + Bz6 + B, sin 8 + B, cos 6 + B56 sin 6 +B66cos6 [3l] WAVINESS CAUSED BY MECHANICAL LOADING I Using the equations derived, it is possible to determine deflection for a most general case of loading such as represented in Fig. 3. However, the general character of waviness produced by drive forces can best be deter- , mined by studying some simple and specific cases that are generally applicable. Therefore, in this investigation the type of loading is restricted to cases involving either one or two drive force components or moments corre- For rings where the depth is small relative to the radius I?, the terms J,, Jx, Jxu may be found approximately by using I,, I,, Ixu, that is, by using the section properties for a straight beam"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002312_j.ijsolstr.2005.03.064-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002312_j.ijsolstr.2005.03.064-Figure2-1.png",
        "caption": "Fig. 2. There are four displacements describing the deformation of the ith node from the initial position to the deformed position: displacement in the horizontal direction, ui; displacement in the vertical direction, vi; rotation (or slope) of the substrate, /i; and rotation of the column relative to the substrate rotation, bi.",
        "texts": [
            " Based on this description of a columnar thin film, a discrete model has been constructed from a variety of components: a substrate, inextensible rods that model the columns, and springs that model the interaction between the model s components. Fig. 1 shows a particular configuration of a central portion (excluding the boundaries) of such a discrete model. The model shown in Fig. 1 is similar to a classical beam model in that it is defined over one dimension (horizontal in the figure) and is allowed to deform into two dimensions (horizontal and vertical). Before proceeding with a discussion of the components of the discrete model, it is necessary to present the kinematics of the model, which have been shown in Fig. 2. At each node i, there will be four independent displacement terms: ui, vi, /i, and bi. Note that bi is a relative rotation, since it is the rotation of the column relative to the rotation (or slope) of the substrate. For bi = 0, the ith column is perpendicular to the substrate. In the initial configuration, as shown in Fig. 1, ui = vi = 0 and /i = bi = 0. Keeping in mind the earlier physical description of a columnar thin film, it is now possible to associate an energy and deformation mechanisms with each of the components"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001231_robot.1986.1087722-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001231_robot.1986.1087722-Figure7-1.png",
        "caption": "Figure 7 . The Parameters o f a General E l e w n t",
        "texts": [
            ", \"Dynamics Motion Analysis of Planar Mechanisms ViaJoint Force Analysis,\" Proceeding of the Third Applied Mechanism Conference, November 1973, 0. s . u., Stillwater, Oklahoma pp. 17. 1-17. 20. Amin, A. U. \"Automatic Formulation and Solution Technique in Dynamics of Machinery, \"Ph. D, Dissertation. University of Pennsylvania, 1979. APPENDIX The line elements used to model the links of the manipulator have constant cross-sectional properties. The elements are connected by joints. Each joint experiences three freedoms consisting of two linear freedoms and one rotational freedom. Figure 7 shows an element with its initial and terminal joints and their freedoms. There are two types of freedoms, active freedoms and inactive freedoms. The active The properties and orientation of the elements relates the displacement in the direction of the freedoms and the loads applied at the two ends of the element. This relation is summarized in the following equation: Ipe16x1 = [ke16x6 {'e16xl where {Pel is the vector containing the six loads applied in the direction of the six freedoms of the element, Eke] is the element-stiffness matrix, and {Xe) is the vector containing the six displacements in the direction of the six freedoms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003977_s12213-008-0010-1-Figure18-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003977_s12213-008-0010-1-Figure18-1.png",
        "caption": "Fig. 18 Dish positioning robot with manual Z stage",
        "texts": [
            " However, we could not control the discharge rate Displacement of the pump when the inner diameter of injection pipette is smaller than 10 \u03bcm. Generally, inner diameter of the injection pipette should be less than a few micrometers at the artificial insemination and nuclear cell transfer. We plan to improve the sensitivity of this small pump. 4.2 Collaboration of three two-axial orthogonal microrobots We attach small manual stages to two-axial microrobots for positioning pipettes and a dish in Z direction as shown in Fig. 18. We positioned pipettes and the dish in focal height by manual Z stage in experiments. Fig. 19 is the photograph of the experimental set up and the working area for a cell processing organized by the three two-axial orthogonal microrobots on an inverted microscope. We put the holding pipette on the left robot for sample capturing. We also put the injection pipette on the right robot. Between these robots, we arrange another microrobot that moves the dish. The whole cell-processing device is very small, 200 mm in length, 150 mm in width and 60 mm in height, so we can easily arrange the device to the microprocessing instruments even if the working area is very small"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003193_s0034-4877(07)80102-9-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003193_s0034-4877(07)80102-9-Figure2-1.png",
        "caption": "Fig. 2. The Appell-Hamel dynamical system.",
        "texts": [
            " Only when the sleigh is subject to a centripetal force the trajectory deviates from a straight line. The prediction in textbooks is just a limit case when the blade has a vanishing length or when the reaction torque vanishes. If the sleigh moves along a straight line in the direction of the edge of the blade (i.e. cp = const, without rotation) the constraint (27) becomes holonomic and the virtual displacement condition (28) leads in this case to the correct equations of motion. The Appell-Hamel problem, schematically depicted in Fig. 2 consists of a block of mass m that is confined in a vertical smooth tube [40] and is attached to the end of a thread that passes over two small massless pulleys, and is wound around a drum of radius b. The latter is rigidly attached to a wheel of radius a. The wheel rolls on a horizontal xy-plane at a point of contact P. The legs of the frame supporting the pulleys and keeping the wheel vertical slide on the xy-plane without friction. The masses of the pulleys and the frame are negligible. Let x, y, z be the coordinates of the mass m, and xp, yp be the coordinates of point P, whereas 0 is the angle between the plane of the wheel and the x-axis. The angle ~b describes the rotation of the wheel in its own plane. The distance between the centers of both pulleys is p, and the initial distance of the mass m from the horizontal plane is h. As seen from Fig. 2, the various transformations are related by x = xp + p cos 0, (29) y = y p + p sin 0, (30) z = h - bq~. (31) The constraints at the contact point P in the directions tangential and normal to the wheel are respectively kp cos 0 + ~p sin 0 = aq~, (32) 2p sin 0 - ~p cos 0 = 0. (33) The sum of the squares of Eq. (32) and (33) is thus 22 + ~2 = a2q~2. (34) Inserting the time derivative of Eqs. (29)-(31) into (34) yields a 2 (2 + p0 sin0) 2 + (~ - p0 cos0) 2 = ~ 2 . (35) 22 _~_ ~2 = a 2 . ~-~Z 2. (36) This is a nonholonomic constraint which is nonlinear in the velocity components of the block"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001370_s0167-8922(08)71076-9-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001370_s0167-8922(08)71076-9-Figure2-1.png",
        "caption": "Figure 2. Wedged Spacer Layer on Disc.",
        "texts": [
            " One disadvantage of Westlake and Cameron\u2018s approach i s tha t a given spacer layer can only measure one s p e c i f i c o i l f i lm thickness below A / Q i e . ( A / Q - hS) . To measure a range of thicknesses a range of spacer layered d iscs are needed. (Beam ( 1 ) passes t w i c e through b o t h t h e spacer l a y e r and o i l fi lm. ) This paper describes the appl ica t ion of a var iab le th ickness , wedged-shaped, spacer layer method. An alumina layer has been sput te red on a chromium-plated g l a s s d i sc SO that its thickness var ies from approximately 0.05pm a t one edge t o 0 . 2 ~ a t the o t h e r , a s shown schematically i n Figure 2. The d i sc i s used i n a conventional, o p t i c a l EHD r i g a s shown i n Figure 3. As the d i s c r o t a t e s , a cyc l i ca l ly varying f i l m thickness of spacer ( T h i c k n e s s great ly exaggerated) l ayer passes through the contact. This produces a corresponding, varying interference f r inge pattern, a s the separa t ing film th ickness , which cons is t s of a constant o i l f i l m thickness p l u s a varying spacer layer , changes. I t i s a simple matter t o map the f r inges seen a t d i f f e ren t times a t the microscope posit ion t o t h e i r corresponding posit ions on t h e moving t r ack "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002589_annals.1370.014-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002589_annals.1370.014-Figure4-1.png",
        "caption": "FIGURE 4. Example of relative motion in circular orbits.",
        "texts": [
            " Two different methods have been developed for parameterizing relative trajectories as a function of geometric components. The first method applies to circular orbits, the second to eccentric orbits. In both cases, the in-plane (x\u2013y) and out-of-plane (z) motions are decoupled. In the case of circular orbits, the geometry of the relative motion is easily expressed as a superposition of along-track offset, in-plane elliptic motion, and cross-track oscillation. The five parameters shown in TABLE 1 are used to fully define the geometry of any type of relative trajectory: an example trajectory is shown in FIGURE 4 on the following page, illustrating the separate in-plane and out-of-plane motions. The relative ellipse is a 2\u00d71 elliptic shape in the x\u2013y plane that is achieved by a small eccentricity difference. The phase angle \u03b20 defines the location of the x v( ) y v( ) x\u2032 v( ) y\u2032 v( ) z v( ) z\u2032 v( ) r1 v( ) r2 v( ) r3 v( ) r4 v( ) r5 v( ) r6 v( ) d1 d2 d3 d4 d5 d6 R v( )D,\u2261= D R v0( ) 1\u2013 X v0( )= X v( ) R v( )D= satellite on this ellipse at the moment when the absolute orbit crosses the equator. The center of this ellipse is located at the along-track offset, y0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000880_ijcat.2002.000288-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000880_ijcat.2002.000288-Figure7-1.png",
        "caption": "Figure 7 Spline free body diagram.",
        "texts": [
            " The literature survey provided values for m ranging between 0.03 and 0.33 for splined couplings depending upon surface roughness and lubricant quality [4]. In this study, the magnitude of the friction coef\u00aecient was assumed to be 0.15. With misalignment moments present in the splines, the misaligned coupling requires reacting forces at the two ends (splines) to maintain its equilibrium as a free body. These unbalanced forces can be generated through a redistribution of the spline tooth loads, whereby a net force (P) is produced, Figure 7. Thus far, the misaligned tooth loads have been assumed, symmetrical about the plane of misalignment, i.e. all teeth on one side of the plane of misalignment carry identical loads as their counterparts on the other side. With re-distribution, an uneven tooth load distribution such as that shown in Figure 7 would be present, and the net reactions generated are approximately given by: P1 P M1 L P2 P M2 L 15 which will result in the additional reacting forces at the shaft bearings R as shown previously in Figure 1. Up to now, the misalignment moments calculated have been based on a \u00aexed angle of misalignment, i.e. the angle of misalignment is assumed unchanged throughout the spline coupling and is equal to the angle of misalignment between the shafts connected to the coupling. However, under the misalignment moments generated at the splines, the coupling will undergo elastic deformation as a simply supported beam subjected to externally applied moments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003347_j.sna.2007.10.018-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003347_j.sna.2007.10.018-Figure9-1.png",
        "caption": "Fig. 9. Dimensional view of the front-view pattern.",
        "texts": [
            " he pattern of the vibration mode still holds on both sides of he piezoelectric buzzer due to positive and negative charges aused by a residual electric field Er, as shown in Fig. 7(b), after lectrically turning off. Moreover, patterns of the vibration mode t both sides of the piezoelectric buzzer are depicted in Fig. 8(a) nd (b) if the piezoelectric buzzer is electrically energized by n electrical sine source, involving the amplitude of 5 V and he frequency of 73.25 kHz. In the patterns, dark areas indicate odes of the vibration mode, and bright areas indicate loops of he vibration mode. From Fig. 9, the diameter of the first nodal t t o e V; (b) Vdc = 4, 5, 6 V; (c) Vdc = 7, 8, 9 V; (d) Vdc = 10, 11, 12 V. ircle, \u03c6n1, is approximately 5.9 mm, the diameter of the second odal circle, \u03c6n2, is approximately 14.0 mm, and the diameter f the third nodal circle, \u03c6n3, is approximately 21.2 mm. Next, a two-dimensional (2D) wave equation of a thin-disk iezoelectric element such as a thin-disk piezoelectric buzzer is efined as follows 2u(r, \u03b8, t) = 1 c2 \u22022 \u2202t2 u(r, \u03b8, t) (2) where = \u221a T \u03c1 ere, u is the vibration amplitude, r is the radius, and \u03b8 is the eometrical angle; c is the sound velocity, T is the horizontal ension, and \u03c1 is the mass density"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002462_s00466-006-0120-3-Figure16-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002462_s00466-006-0120-3-Figure16-1.png",
        "caption": "Fig. 16 The equivalent spring stiffnesses and the beam element",
        "texts": [
            " Specifically, for plain strain conditions, the elastic property relations using Voronoi elements are E = 0.25KnL ( 5 \u2212 Kt Kn )( Kt Kn + 1 ) (29) \u03bd = 0.25 ( 1 \u2212 Kt Kn ) (30) To evaluate similar relationships for square elements, the method proposed by Griffith and Mustoe [6] is employed. The method is based on the stiffness matrix and strain energy formulations and was originally applied to a closed packed arrangement of uniform circular elements. Contacts between elements are replaced by single equivalent normal and tangential springs with stiffnesses Kneq and Kteq, as shown in Fig. 16. These stiffnesses are related to the fiber stiffnesses Kn and Kt by Kneq = 2KnL (31) Kteq = 2KtL (32) These springs are assumed to connect the mid-points of the two contacting sides. Next, the centers of all elements forming the macro body are connected by beam like one-dimensional structural elements. These beam elements have three degrees of freedom at each of their ends, namely, the two translational components in the plane and a rotation about an axis perpendicular to the plane. These correspond to the three degrees of freedom available at the centers of the elements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003230_14644193jmbd103-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003230_14644193jmbd103-Figure5-1.png",
        "caption": "Fig. 5 Vehicle model",
        "texts": [],
        "surrounding_texts": [
            "In order to examine the accuracy of the planar contact model in predicting the vehicle critical speed, a numerical experiment is carried out in which the constant forward velocity of the vehicle is varied from 20 to 50 m/s. Two analytical lateral bumps of height 0.35 in are included on the left rail at the start, as shown in Fig. 7, in order to initiate the hunting motion. The lateral displacement and the yaw angle along the Proc. IMechE Vol. 221 Part K: J. Multi-body Dynamics JMBD103 \u00a9 IMechE 2007 at UNIV CALIFORNIA SANTA BARBARA on June 24, 2015pik.sagepub.comDownloaded from track are as shown in Figs 8 to 10. The results obtained show that at 35 m/s, the oscillations in the lateral displacement and yaw angle die out slowly over time. At 45 m/s, it takes a little longer for the oscillations to damp over time, and at 45.5 m/s the oscillations grow with time. This behavior of the model was examined, and the obtained results indicate that the model becomes unstable at velocity of 45.5 m/s. To validate the results obtained using the planar contact formulation, these results are compared with those of the three-dimensional contact model. The comparison shows that the critical speeds predicted using the planar and spatial contact models are the same, which is an indication that the use of the planar model does not affect the accuracy of predicting the critical speed [14]. Therefore, differences between the critical speeds predicted using different computer codes JMBD103 \u00a9 IMechE 2007 Proc. IMechE Vol. 221 Part K: J. Multi-body Dynamics at UNIV CALIFORNIA SANTA BARBARA on June 24, 2015pik.sagepub.comDownloaded from are not likely to be attributed to the use of a planar contact model."
        ]
    },
    {
        "image_filename": "designv11_28_0000515_robot.2001.933195-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000515_robot.2001.933195-Figure2-1.png",
        "caption": "Figure 2: Micro5 suspension",
        "texts": [
            "13[m] Mobility System I Velocity : 1.5[cm/s] Mobility Performance Climable Step : 15[cm] I Climable Slope : 40[degl Power Actuator : less than 5[W] (MAX) Pay oad 8 cameras, Man pualor Sunsensor. Inc.,nometers etc. 371 1 2.2 Mobility System A small long-range rover is required to have both a simple and light weight mechanism like 4-wheel drive system and a high degree of mobility like rocker-bogie suspension system. In order to achieve these opposed requirements, the authors propose a new suspension systeni[l8] as shown in Fig.2. The proposed suspension system PEGASUS consists of a conservative fourwheel drive system and a fifth active wheel connected by a link. The fifth wheel which is attached to the end of the link, and the other end of the link is attached to the body with a passive rotary joint. The proposed system is designed to distribute the load of weight equally t o all five wheels whenever the rover climb up or down. I t means that the fifth wheel supports the load taken to the front wheels when the front wheels climb up rocks, and it also supports tha t taken to the rear wheels when the rear wheels climb up the rocks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003154_1.2540572-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003154_1.2540572-Figure3-1.png",
        "caption": "Fig. 3 Schematic illustration of cam-roller contact",
        "texts": [
            " Using the esult, micrometer-scale analysis is performed, using the Surface istress Analysis Toolkit SDAT module, base on the method escribed in 3\u20135 , to predict roughness induced surface and near urface stresses and surface fatigue life of the cam. The analyses focus on the effect of surface preparation and reatment of the roller only to remedy the surface failure of the am. Initially SDAT is employed along with dynamic simulation f the cam-rocker-roller system to obtain the induced contact orces. These forces were used along with topography measureent of the cam and roller surfaces Fig. 3 and analyses were erformed using the SDAT. Table 1 summarizes the geometric and mechanical properties of he cam and roller. A macro-dynamic analysis involving the cam nd roller system led to the determination of maximum contact orce. A Hertz contact analysis on the smooth cam and roller urface yields a maximum contact pressure of 1880 MPa. The rocess is depicted schematically in Fig. 3. In a micrometer-scale nalysis, it is necessary to first measure the surface topography for subsequent analysis of the contact with inclusion of surface oughness. Shown schematically in Figs. 3 and 4 are the steps eeded in this regard. Surface of the cam corresponding to the ccurrence of maximum force Fig. 3 is measured using a stylus urface profilometry Fig. 4 . It is important to note that the mea- Fig. 1 Camshaft and rocker arm assembly 22 / Vol. 129, APRIL 2007 om: http://tribology.asmedigitalcollection.asme.org/ on 01/27/2016 Terms sured region of the contact is geometrically different from the contact patch. Thus, the input force needed in the simulation of contact with roughness is important to establish the corresponding force for the sampled region. This force is obtained through an iterative process in which the simulation software SDAT is used with the assumption of elastic contact between smooth surfaces so as to obtain the same maximum contact pressure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003661_icit.2009.4939663-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003661_icit.2009.4939663-Figure1-1.png",
        "caption": "Fig. 1. Eagle helicopter",
        "texts": [
            " Owing to their adaptability, universal approximation capability and hardware implementability, NN is a suitable solution for modeling and control of many real life problems [11, 12, 13]. But the prediction accuracy of NN is a function of the available training time and the size of the training data used for capturing the dynamics. The present work deals with the implementation of Neural Network based black box Identification (NNID) technique for modeling the dynamics of the Eagle helicopter. The Eagle autonomous helicopter platform shown in Fig. 1 is under development at UNSW@ADFA with an objective to develop AFCS for fully autonomous flight. The platform is equipped with avionics built in-house and instrumented with different sensors for measurement, processing and control. This Eagle platform is the test bed for implementing the NNID algorithm. The flight data from sensors are inherently noisy due to the vibration in the platform. The availability of limited processing power for NN training introduces additional constraint in the NNID process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003245_acc.2008.4586956-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003245_acc.2008.4586956-Figure2-1.png",
        "caption": "Figure 2: Configuration of the Active disk.",
        "texts": [
            " Due to rotor imbalance the mass center is not located at the geometric center of the disk S but at the point G (center of mass of the unbalanced disk), the distance u between these points is known as disk eccentricity or static unbalance (see Vance [12]; Dimarogonas [13]). In our analysis the rotor-bearing system has an active disk mounted on the shaft and near the main disk (see Fig. 1). The active disk is designed in order to move a mass m1 in all angular and radial positions inside the disk, which are given by \u03b1 and r1, respectively. In fact, these movements can be got with some mechanical elements such as bevel gears and ball screw (see Fig. 2). The mass m1 and the radial distance r1 are designed in order to compensate the residual unbalance of the rotor bearing system. An end view of the whirling rotor is also shown in Fig. 3, with coordinates that describe its motion. The coordinate system (\u03b7, \u03be, \u03c8) of this figure is fixed to the active disk, and the coordinate system (X,Y,Z ) is an inertial frame with Z the nominal axis of rotation. The mathematical model of the five degree-of-freedom rotor-bearing system with active disk was obtained using Euler-Lagrange equations, which is given by (M +m1) x\u0308+ cx\u0307+ kx = px (t) (M +m1) y\u0308 + cy\u0307 + ky = py (t) Je\u03d5\u0308+ c\u03d5\u03d5\u0307 = \u03c41 + p\u03d5 (t) m1r 2 1\u03b1\u0308+ 2m1r1r\u03071\u03b1\u0307+m1gr1 cos\u03b1 = \u03c42 m1r\u03081 \u2212m1r1\u03b1\u0307 2 +m1g sin\u03b1 = F (1) with px (t) = Mu \u00a3 \u03d5\u0308 sin (\u03d5+ \u03b2) + \u03d5\u03072 cos (\u03d5+ \u03b2) \u00a4 +m1r1 \u00a3 \u03d5\u0308 sin (\u03d5+ \u03b1) + \u03d5\u03072 cos (\u03d5+ \u03b1) \u00a4 py (t) = Mu \u00a3 \u03d5\u03072 sin (\u03d5+ \u03b2)\u2212 \u03d5\u0308 cos (\u03d5+ \u03b2) \u00a4 +m1r1 \u00a3 \u03d5\u03072 sin (\u03d5+ \u03b1)\u2212 \u03d5\u0308 cos (\u03d5+ \u03b1) \u00a4 p\u03d5 (t) = \u2212My\u0308u cos (\u03d5+ \u03b2)\u2212m1y\u0308r1 cos (\u03d5+ \u03b1) +Mx\u0308u sin (\u03d5+ \u03b2) +m1x\u0308r1 sin (\u03d5+ \u03b1) Here J and c\u03d5 are the inertia polar moment and the viscous damping of the totor, \u03c41(t) is the applied torque (control input) for rotor speed regulation, x and y are the orthogonal coordinates that describe the disk position, r1 and \u03b1 denote the radial and angular position of the balancing mass, which are controlled by means of the control force F (t) and control torque \u03c42 (t) (servomechanism)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000593_irds.2002.1041497-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000593_irds.2002.1041497-Figure3-1.png",
        "caption": "Figure 3: The accumcy (in %) us k and n on the parameter E, (a) and on the parameter K, (b) estimated by the observable ObsD. with the straight trajectory thmugh equation ( I O ) . The total traveled distance is L T ~ ~ = n x 2 kl = 100 m.",
        "texts": [],
        "surrounding_texts": [
            "on the estimation of some quantities, called observables, whose mean values depend on the robot trajectory and on Eo, Eo, KO and KO. In order to make easier the experimental estimation of the ohservables, robot trajectories whose final configuration is very close to the initial one are chosen. The analysis carried out in 1111, 1121 and [13] showed that the hest observables to evaluate the model parameters are Obss, Obssz, Obsg and O b s p . They are defined as follows. Let consider a given robot m@ tion and let suppose to repeat this motion n times. The robot motion is always the same in the world coordinate frame of the odometry system.\n(9)\nwhere 4, is the angular difference between the initial and the final configuration, y2 is the position change along the fj-axis between the initial and the final configuration, D, is the distance between the initial and the final position related to the ith robot motion. Because of the non-systematic errors, the observables are random variables whose statistics is completely defined by the hypothesis introduced in Section 2. In particular, on the basis of those hypothesis, it is possible to compute the mean value and the variance of each observable. We want to discuss the accuracy on the parameter estimation reachable by adopting previous ohservahles. We define the accuracy on the estimation of a given model parameter K as the relative error (in %) on its estimated value (%loo%). The error sources on the estimation of K are:\n1. measurement errors on the difference in angle and distance between the initial and the final robot configuration;\n2. resolution of the odometry system;\n3. when the mean value of the adopted observable depends on parameters (previously estimated) different from K , the estimation error on these parameters propagate into the estimation error A K\n4. statistical variance of the observable.\nWhen the length p of the chosen trajectory is large enough the effect of the first two error sources becomes negligible (the minimum ?depends on the values of the non-systematic parameters and on the device adopted to measure the angle displacement and the distance between the initial and final configuration). Since now on we assume that this is the case. Let consider for a moment the case when also the 3d error source disappears (i.e. the adopted observable only depends on one parameter). In this case the error on the model parameter K estimated by adopting the observable Obs, is 4 K =\nTherefore, the accuracy is:\n100% (10) 1 UOba, acc (K, Obsi) = - K I W I\nTo proceed we have to express the observable mean values and variances in terms of the model parameters and the robot trajectory.\nConcerning Obss and O b s p we have (see 114)):\nSince the mean values < Ohss > and < Obsp > only depend respectively on the model parameters ER and KO, for the estimation of these parameters through these observables, the accuracy definition given in (10) is correct. We obtain:\nacc (Es,Obsg) = LplOO% (13) Eo L T ~ ~\nwhere LT,,~ = n x p is the total distance traveled by the robot. From equation (12) we obtain:\nCLcC (Ks,Ob882) = -100% (14) K Concerning Obsp the computation of its mean value and variance can be found in [13] and Ill] obtaining:\n< Obs) >= (1 +E,,) sin(g(s)) e-%& (15)\nwhere g(s) = O(S)+ERS and O(s) is the robot orientation as measured by the encoder sensor as a function of the curve length s always measured by encoder.\nLT",
            "In a similar way the mean value and the variance of the observable O b s p can be computed. We obtain for the mean value:\n< Obsjy >= Kpp + 2(1 + E,)* X\n3 K p p + 2 ( l + E p ) 2 F [ $ ] (16)\nwhere F [g] is just defined from the previous equation and it is a functional dependent on the robot trajectory and on the parameters En and K O . We obtain from equation (15)\n(17) < ObQ >\n( l+E, )= - J,\u201d sin(&s)) e - y d s\nTherefore. the relative error on E. is the sum of .,\u201c(e(s)) e- W d s the two terms I \u201c,\u2018,\u201cbfy; I and 1 The former corresponds to the accuracy defined in \u2019 ~ o \u2019 8 i n [ ~ s ) ) e-?ds ( lo) , the latter depends on the accuracy on En and Ke . The only observable whose mean value depends on K, is ObsD. and therefore is used for its estimation. The mean value in (16) is the sum of two terms. Therefore, the absolute error A K , is the sum of the error on the.observable evaluation (A < o b s p >E nobsDl) and the error on the quantity 2(1+E,) 2F [-] 8 due to the uncertainty on the param-\neters En, KO and E,. When 2(1+E,)*F [F] >> Kpp the relative error on K p becomes very large. In order to achieve high accuracy on K p estimation a trajectory satisfying the relation 2(1 + EP)*F [g] < K,p\nmust be chosen. In particular, when F [i] is negligible the accuracy on K O is given by (10) (in other words we can say that in this case < ObsDz > only depends on the model parameter K p ) .\n4 Results\nIn this section we consider two trajectories (straight and circular) and we explicitly compute the accuracy on the model parameters through the previous obsevables with the two trajectories. Finally, concerning the observable O b s p , we analytically investigate in order to find the conditions under which the requirement Z(I i E,) 2F [-] 8 < Kpp is verified.\nClearly, the same analysis could be done for other robot trajectories by explicitly computing the integrals in Sect. 3. However, in the case of circular and\nstraight trajectories here considered (8(s) linear in s), the computation can be carried out analytically.\n4.1 Straight \u2018Ikajectory\nIn order to estimate the model parameters in 1111, 1121 and (131 the following simple robot trajectory was considered. The robot moves straight forth and back k times in order to cover the distance p = 2kl in the odometry reference frame ( 2 is the length of each segment). Observe that the mean d u e s < Obss > and < Obsi > only depend on the length p of the robot motion while < Obsp > and < O b s p > depend also on the shape. In particular for the previous trajectory we obtain (see Ill] and [13])\n< Obsg >= - ( 1 + Ep)l Im { f ( z ) } (18)\n-11 and z is a complex quantity completely defined by the rotational error model parameters:\n,-2e-\u2019+P-2\u2019)\nwhere f ( z ) = f ( e - 2 Z - l )\n(19) Ke 2 z = -1 + iEnl\nRom previous equations we obtain:\nwhere we neglect since we assumed that the 2d error source previously remarked is negligible. When t is small in absolute value we can expand the function f(t) obtaining f (z ) k z . In this case from equation (20) we have acc (E,,Obsg) Y (\\&I + w ) x 100%. (i.e., with respect to the accuracy given in equation (10) appears the effect of the uncertainty on the parameter En).",
            "In a similar way it is possible to compute the mean value < O b s p > for the considered robot trajectory, obtaining:\n< ObsDs >= 2Kpkl+ 2(1 + EP)\u2019l2Re { F ( z ) } (21)\nIn figures 3a and 3b we plot the accuracy (in %) respectively on E, and on K p estimated by the observable ObsDz vs k and n for the fixed L T ~ ~ = lOOm and for the following values of the model parameters: Ee = - 0 . 2 9 , Ks = 0.04$$, (1 + E p ) = 0.98\nmated with the mobile robot Nomad150 in an indoor environment ( [I l l , [13])) . The accuracy is computed without considering the error on the other model parameters (i.e. is computed directly from equation (10)). Observe that by changing the values of the model parameters the qualitative behaviour does not change. Concerning Ep the accuracy becomes very rough by increasing both k and n (i.e. for a fixed L T ~ ~ = 2knl by decreasing I ) . Regarding K p we have the opposite behaviour. This opposite behaviour is crucial because it means that, when 1 is small, the error on the parameter Ep (previously estimated for example with ObsG or with O b s p with large I ) does not influence the accuracy on the estimation of the parameter Kp. This behaviour can be explained by expanding the function F ( z ) (indeed when l is small also z is small). We obtain F ( z ) 2 i k z - $ k 2 z 2 . Therefore,\nand K , = 4 10- P ,m (these are about the values esti-\n< ObSDz 2\u201d 2K0kl+2(1+Ep)212 [ ~ k l + KS ?(k1)\u2019]\n(22)\nThe requirement 2(1+ EP)* F p] < K,P is then verified by considering the limit 1 -+ 0, k -+ CO for a fixed value of 2kI = p . In this way < ObSp > only depends on K p . However, the value of p = 2kl must be large enough so that the quantity KO? can be appreciated by the device adopted to measure the angle displacement and the distance between the initial and final configuration (in other words the first two error sources previously remarked can he neglected, as assumed).\n4.2 Circular Trajectory\nThis trajectory has the advantage to be smooth without abrupt change in direction. The motion will consist of k revolution along a circumference of radius R. Actually, because of the systematic rotational error, the effective radius of the circumference will be Reff = &i.\nWe introduce a new complex quantity in order to investigate the observable statistics:\nFollowing computation similar to the straight trajectory we obtain:\n< Obsg >= -(1 +E,)? I m { ~ R ( z R ) } (24)\n< O b s p >= K,p+2(1 +Ep)*p2Re {FR(zR)} (25)\nwhere ~ R ( Z R ) = I--e-\u2018R and FR(ZR) = zs-l?zn IT( z i In figures 4a and 4b we plot the accuracy (in %) respectively on E, and on K p estimated by the observable ObsD. vs k and n for the fixed LrOt = lOOm and for the values of the model parameters considered in the straight trajectory. The results are very similar to those obtained with the straight motion. Also in this case the opposite behaviour of the accuracy on the estimation of Ep and Kp can be explained by expanding the function FR(zR). We obtain:\n< O b s p >\u201cKO?+ 2(1+ E p ) 2 K e ~ R 2 (26)\nTherefore, in this case the requirement 2(1 + EP) \u2018 F [I 0 < K p p is verified by considering the limit R -+ 0, k -i m for a fixed value of 27rkR.fj = p. As for the straight trajectory, in this limit < ObsD, > only depends on K,.\n5 Conclusions and Future Research\nIn this paper the uncertainty in odometry of a mobile robot was modeled by a four parameter statistical"
        ]
    },
    {
        "image_filename": "designv11_28_0000570_095440802760075021-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000570_095440802760075021-Figure9-1.png",
        "caption": "Fig. 9 Kinematic scheme of Spiroid gear pair",
        "texts": [
            " A basis of the modelling of skew axes gears of Spiroid and Helicon types, by using the mesh region, is the design of the kinematic model of action surfaces. The optimization process consists in determining the optimal borders of the mesh region. Proc Instn Mech Engrs Vol 216 Part E: J Process Mechanical Engineering E0101 # IMechE 2002 at MICHIGAN STATE UNIV LIBRARIES on June 14, 2015pie.sagepub.comDownloaded from A kinematic scheme of a Spiroid gear pair related to the considered mathematical model is shown in Fig. 9. It has already been noted that the technology of the considered gear manufacture is based on Olivier\u2019s second principle. The surface of action and of the mesh region depend on the Spiroid pinion anks S1. Following reference [7], the S1 are linear conical helicoids with constant axial parameter ps \u02c6 constant. The synthesis of a Spiroid pinion with right-hand threads will be examined without restricting the generality of the problem. The generation of S1 is shown in Fig. 7. In the most common case S1 is a convolute conical helicoid of which the generatix, L, is a straight line and executes complex motion consisting of the following [7]: (a) helical motion along the axis Opzp with parameter ps \u02c6 constant; (b) translation perpendicular to the axis Opzp with parameter pt and in a plane which is a tangent to the cylinder with radius r0",
            " The last of equations (20) is an analytical expression of the basic equation of meshing [equation (19)] and can be written in the form f \u2026u; y; j1\u2020 \u02c6 0 \u202622\u2020 Proc Instn Mech Engrs Vol 216 Part E: J Process Mechanical Engineering E0101 # IMechE 2002 at MICHIGAN STATE UNIV LIBRARIES on June 14, 2015pie.sagepub.comDownloaded from Thus, the analytical conditions de ning the line of the points of undercutting in the surface of action and the mesh region are r \u02c6 x\u2026u; y; j1\u2020i \u2021 y\u2026u; y; j1\u2020j \u2021 z\u2026u; y; j1\u2020k f \u2026u; y; j1\u2020 \u02c6 0 @f @u du dt \u2021 @f @y dy dt \u2021 @f @j1 dj1 dt \u02c6 0 V12;x Vr1;x \u02c6 V12;y Vr1;y \u02c6 V12;z Vr1;z \u02c6 \u00a11 \u202623\u2020 All of equations (23) are written in the coordinate system S(O, x; y; z); see Fig. 9. In the case of the non-orthogonal Spiroid gear pair shown in Fig. 9, the coordinates of the sliding velocity vector V 12 and the equations of S1 written in S(O, x; y; z) are V12;x \u02c6 \u00a1awi12 cos d \u2021 \u20261 \u00a1 i12 cos d\u2020y V12;y \u02c6 i12 sin dz \u00a1 \u20261 \u00a1 i12 cos d\u2020x V12;z \u02c6 \u00a1i12 sin d\u2026aw \u2021 y\u2020 \u202624\u2020 x \u02c6 r0 cos F \u00a7 R0 sin x sin F y \u02c6 r0 sin F \u00a8 R0 sin x cos F z \u02c6 py \u00a7 R0 cos x \u00a1 ap \u202625\u2020 As already mentioned, one point belonging to the mesh region of a spatial gear pair is a singular point of the rst order if the following conditions are satis ed: V r;1 \u02c6 @r1 @u du dt \u2021 @r1 @y dy dt \u02c6 0; j1 \u02c6 constant n1 \u02c6 @r @u 3 @r @y 6\u02c6 0 \u202626\u2020 Taking into account equations (26) as well as the third of equations (23), it is not dif cult to prove that @f @j1 6\u02c6 0 \u202627\u2020 Formula (27) is a condition for the non-existence of singular points of rst order in the mesh region of the synthesized gear set"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002107_1.1611500-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002107_1.1611500-Figure6-1.png",
        "caption": "Fig. 6 Temperature measurement around the periphery of the HDB spindle motor",
        "texts": [
            " 126, APR Downloaded From: http://tribology.asm Heat generation of the coil winding can be determined by measuring the input current and the phase resistance of a HDB spindle motor as follows @7#. q\u0307coil5i rms 2 \u2022R\u0303 (5) Table 3 shows the resistance, current and heat generation rate of the coil winding of the HDB spindle motor considering the variation of the surrounding temperature and speed. Boundary temperature of the finite element model in Fig. 5 is linearly interpolated from the measured edge temperature of the HDB spindle motor. Figure 6 shows the measurement points around the periphery of an HDB spindle motor by using thermocouple sensors, and they are measured at the room temperature of 28.7\u00b0C as well as the elevated surrounding temperature of 58.7\u00b0C in a thermo-chamber. Temperature inside the thermo-chamber is controlled by a hot air blower. Table 4 shows the measured temperature at the measurement points with the HDB spindle motor at different surrounding temperature and speeds. 2.2 Analysis of Thermal Deformation. The HDB spindle motor is composed of several components with different thermal expansion coefficients"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002056_iros.1992.594512-Figure14-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002056_iros.1992.594512-Figure14-1.png",
        "caption": "Figure 14: Manipulator End Point Trajectory in Cartesian Space",
        "texts": [
            " Figure 13(b) shows an almost 2/3 reduction in position error compared with the conventional PD-control case. Figure 13(c) shows a further 2/3 reduction in error compared with Figure 13(b). The dynamic control scheme demonstrated here is not a perfect computed torque method, however, it does lead to the achievement of a significant dynamic compensation effect. It also should be noted that motions resembling the required motions for manipulation tasks may be desirable for parameter identification, when the manipulation space is relatively limited for certain tasks. Figure 14 shows the experimental results reviewed in Cartesian space. It is clearly shown that performance is improved by introducing the dynamics compensation based on the identified parameters, compared with the PD-control case. 5 Conclusion Dynamic parameter identification for PUMA260 was experimentally investigated. The identification was validated by trajectory control experiments using dynamic control based on identified parameters. Suitable m e tion conditions were clarified for the identification effects of manipulator configuration, joint angular velocity and joint angular acceleration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003195_s11071-007-9275-5-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003195_s11071-007-9275-5-Figure4-1.png",
        "caption": "Fig. 4 Velocity distribution during separation: (a) The position of mass center is such that \u2220ASS2 = \u03b1, (b) SS2 and AS are collinear",
        "texts": [
            " By introducing the complex deflection zS = x + iy where x, y are the coordinates of the mass center S, i = \u221a\u22121 is the imaginary unit and \u03c9w = \u221a c/M is the frequency of vibration, the differential equation of motion of mass center is z\u0308S + \u03c92 wzS = 0. (37) For the initial conditions x(0) = xS0, y(0) = yS0, x\u0307S(0) = vSx0, y\u0307(0) = vSy0, (38) the deflection of mass center yields zS = (A0 + iB0) exp(i\u03c9wt) + (C0 + iD0) exp(\u2212i\u03c9wt), (39) where A0 = 1 2 ( xS0 + vSy0 \u03c9w ) , B0 = 1 2 ( yS0 \u2212 vSx0 \u03c9w ) , C0 = 1 2 ( xS0 \u2212 vSy0 \u03c9w ) , D0 = 1 2 ( yS0 + vSx0 \u03c9w ) . (40) The rotor center oscillates around the initial position of mass center. If the rotor struck the fixed part of a stator in A (Fig. 4(a)) at a moment t1, a part of the rotor is separated. The mass of the separated part is m, with mass center S2 and the moment of inertia IS2 related to the axis in S2. The velocity of S2 of the separated part is the sum of the dragging velocity vS2d and the relative velocity vr vS2 = vS2d + vr , where vS2d = \u221a v2 Sb + ( vS S2 )2 + 2vSbv S S2 sin\u03b1, sin\u03b3 = vS S2 vS2d cos\u03b1, (41) with vS S2 = \u03a9b(SS2), and according to (39) vSb = \u221a x\u03072 + y\u03072 = \u03c9w [ (C0 \u2212 A0) 2 + (B0 \u2212 D0) 2 \u2212 2(C0 \u2212 A0)(B0 \u2212 D0) sin(2\u03c9wt1) ]1/2 , \u03b1 is the angle between SS2 and SA",
            " (46) Using the relations (10), (32) and (46) the relative velocity of the mass center of the remainder body and the relative angular velocity are calculated vr1 = m M \u2212 m vS2dT , IS1\u03a9r1k = \u2212IS2 vS2dT AS2 k + m M \u2212 m SS2 \u00d7 vS2dT . (47) The absolute velocity and angular velocity of the remainder rotor are vS1 = vSb + \u03a9b \u00d7 SS1 + m M \u2212 m vS2dT , IS1\u03a91ak = IS\u03a9bk \u2212 IS2\u03a92ak + m M \u2212 m SS2 2\u03a9bk + m M \u2212 m SS2 \u00d7 vS2dT . (48) For the special case when \u03b1 = 0 and \u03b2 = 0, i.e., the mass center of the separated body is in the SA direction (Fig. 4(b)) and also the velocity vSb , the angle \u03b3 are determined sin\u03b3 = \u03a9b SS2 vS2d , (49) where vS2d = \u221a v2 b + (SS2)2\u03a92 b . (50) The separation of the body is with the relative velocity vr = \u03a9b \u00d7 SS2, (51) and the relative angular velocity \u03a9r = SS2 AS2 \u03a9b. (52) The absolute velocity and the angular velocity of the remainder body are vS1 = vSb, \u03a91a = IS IS1 \u03a9b \u2212 IS2 IS1 \u03a9b R R \u2212 SS2 = \u03a9b ( 1 \u2212 IS2 IS1 SS2 R \u2212 SS2 ) , (53) where R is the radius of the rotor. The angular velocity of the remainder body jumps to a lower value during separation: if the moment of inertia of the separated body is larger, the decrease of the angular velocity is higher"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003112_j.triboint.2008.01.007-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003112_j.triboint.2008.01.007-Figure1-1.png",
        "caption": "Fig. 1. The schematic diagram",
        "texts": [
            " In order to obtain a significant amount of tribopolymer and thus confirm the concept of wear reduction by tribopolymerization, neat n-butyl acrylate (BA) was employed in this work as the lubricant medium instead of as the additive of a lubricant, and compared with parallel procedures using other fluids. The obtained tribopolymer was subjected to various characterizations to deduce the mechanism of tribopolymerization. The rubbing experiments were conducted on a homemade pin-on-disk device. It consists of a steel disk attached to a milling machine spindle and a beam that loads a ball (the pin) against the rotating disk. A lubricant cup held the fluid to completely cover the ball and the disk surface, and the temperature of the lubricant fluid was controlled by circulating water. Fig. 1 shows a sketch of the device (Fig. 2). The ball (diameter 10mm) was made of GCr15 (AISI52100) bearing steel. The disk was made of AISI1015 steel, with a diameter of 60mm and a thickness of 5mm. BA and styrene were purified via vacuum distillation over CaH2 at a N2 atmosphere. n-Butyl alcohol, hexadecane, acetone, methanol, hydroquinone, and calcium hydroxide are all analytical reagent (AR) grade reagents used without further purification. All the reagents were purchased from Beijing Yili Chemical Reagent Co"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002984_icma.2006.257789-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002984_icma.2006.257789-Figure2-1.png",
        "caption": "Fig. 2 Locating the orientation",
        "texts": [
            " INTRODUCTION A complete robot motion includes a 3D position transition and a 3D rotation. Because the position transition can be clearly represented by a transition vector, we are more concerned with the problems related to the rotation. Typically, a rotation is represented by a rotation matrix [1]. As shown in Fig. 1, a coordinate system {b}={XbYbZb} has been attached to the robot relative to the another coordinate system {a}={XaYaZa}. If we want to deal with the rotation only, we can assume {a} and {b} have the same origin, as shown in Fig. 2. Assume that a spatial point is represented in the coordinate vector aP with respect to the frame {a}, and Pb with respect to the frame {b}, then we have PRP ba , where R is the rotation matrix, a 3 by 3 matrix, which satisfies 1TT RRRR . The rotation matrix gives the general and resultant information of the robot rotation. It does not provide the message how this rotation is progressed, and there could be different representations for the process of the rotation. In some applications, e.g., the cases of the capsule endoscope, the underwater vehicle, and the outdoor moving robot, we are interested to know the information about what the direction (or main axis) the robot faces and how the robot rotates with respected to the robot main axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002008_j.ics.2004.03.176-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002008_j.ics.2004.03.176-Figure4-1.png",
        "caption": "Fig. 4. A signal diagram (this figure) of the force feedback system illustrates that the operators advancement of the remote needle results in (a) resistance of that insertion due to tissues sensed at the medical needle and (b) an update of the virtual and imaged needles. The six-degree-of-freedom robot (Fig. 2) holds the needle in its forcesensing, pneumatic gripper (in alignment with the pre-planned trajectory).",
        "texts": [
            " 2), seamlessly integrated with the CT scanner\u2019s (Philips IDT 16 Slice Scanner) 3-D coordinate system [7,8]. The robot was equipped with a pneumatic gripper (Fig. 3) customized to align the surgical needle and to sense resistance force associated with insertion through tissue. A remote needle insertion controller provided variable resistance during the remote simulated insertion of a vicarious needle\u2014based on force feedback from the gripper\u2014while simultaneously commanding the robot to drive the surgical needle along a straight path. The tactile feedback loop is illustrated in Fig. 4. Initial alignment to a planned trajectory was performed in the treatment planning phase. An interactive planning screen enabled the interventionalist to specify a 3-D virtual needle path within a prior CT volume data set. The virtual needle included a specific percutaneous insertion point, angulation and depth-to-target superimposed on transverse axial slices, with cross-referenced multi-planar reformatted views correlating with the interventional field. After sending the virtual needle\u2019s coordinates to the robot\u2019s controller, the robot semi-autonomously moved its needle gripper from a pre-programmed home position to a position congruent with the planned puncture path while maintaining a safe clearance from the phantom, CT table and CT gantry"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001144_10402008808981807-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001144_10402008808981807-Figure2-1.png",
        "caption": "Fig. 2-Simulated Journal Bearing",
        "texts": [
            " Rather than resorting to the optical filtering methods of Winer and coworkers (4) or our own spectroscopic techniques (3, we ran two fluids whose EHD contact temperatures had been determined previously by those techniques, viz. a traction fluid and a synthetic paraffin (Lubricant G), for calibration. Since the apparatus was essentially the same as before, we believe that the EHD temperatures reported below are precise to +- 2.0\u00b0C, which is very adequate for comparisons between the samples. Polarized Infrared Spectra from a Simulated Journal Bearing This setup, illustrated in Fig. 2, made it possible to obtain infrared emission spectra from a sheared lubricant at different predetermined temperatures. A half-inch diameter stainless steel shaft of highly polished surface finish was rotated about a horizontal axis at known small distances from the bottom of a conforming groove of the same curvature, which was ground in an infrared-transparent window. The width of the groove was about 8 mm at the top surface of the window. A micrometer screw on the window assembly indicated the shaft-to-window (\"gap\") distance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003391_coase.2008.4626479-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003391_coase.2008.4626479-Figure6-1.png",
        "caption": "Fig. 6. Dexelisation (a) single direction dexel space (b) Dexelisation of a sphere (c) Comparison of compensated and uncompensated contours of a slice",
        "texts": [
            " Compensating on sliced data has been proven successful by Tong et al. [17] for compensating machine errors for SLA and FDM processes. However due to the popularity of the STL file in RP fabrication, a slicing algorithm is integrated into the compensation system to convert STL to CLI file. B. Dexelisation of STL file The dexelisation process begins with a STL file. The bounding box dimensions of the STL file are calculated. Then a single direction dexel space is created for the bounding box dimensions (Fig. 6a). STL file is sliced into layers and is stored in a layered file format called CLI file. In order to generate dexels, entire scan path of the laser has to be calculated. The contour information is extracted and all the co-ordinate points of the contour are sorted based on whether the contour is internal or external contour. After reading the contour information dexels and its lengths are found using intersection of hatch lines with the contours (Fig. 6b). Then compensation value for every dexel is calculated using the shrinkage model. After offsetting each dexel at its end points, the contour is rebuilt with its new vertices and a new compensated CLI file is written (Fig. 6c). Then this file is used for part building. Unlike the conventional compensation techniques, the compensation length varies non-linearly with the dexel length. Since percentage shrinkage is a function of dexel length and during compensation it is again multiplied by the dexel length, the amount of compensated length varies non-linearly with dexel length. C. Software development for automating compensation Software is developed to automate the compensation procedure. A graphic user interface (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001283_robot.2000.846401-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001283_robot.2000.846401-Figure1-1.png",
        "caption": "Figure 1: Two extremals: zigzag right and tangent CW. Other extremal types are zigzag left, tangent CCW, and turning in place: CW and CCW. Straight lines are special cases of zigzags or tangents.",
        "texts": [
            " By velocity bounds, we mean that the wheel velocities are bounded, but there are no bounds on wheel acceleration. In fact, discontinuities in wheel velocity are allowed. Pontryagin\u2019s Maximum Principle yields conditions that are necessary but not sufficient for time optimal trajectories. Hence the trajectories that satisfy the Maximum Principle are called extremal trajectories, and are a superset of the time optimal trajectories. The Maximum Principle provides a compact geometrical description of the extremal trajectories, and thus gives us a tool for enumerating and exploring time optimal trajectories. Figure 1 shows two of the six different extremal types. 1.1 Previous Work We know of no previous work on time-optimal control of the bounded velocity diff drive robot, but the techniques employed here draw extensively on the techniques devel- oped for steered vehicles [6, 2, 5, 41. Interested readers should see our companion paper [ I ] for a broader discussion. 2 Assumptions, definitions, notation The state of the robot is q = (x,y,8), where the robot reference point (z , y) is centered between the wheels, and the robot direction 8 is 0 when the robot is facing along the z-axis, and increases in the counterclockwise direction (Figure 2)",
            " The maximum principle does not give the location of the line; it merely says that if we have an optimal control then the line exists and the optimal control must conform to the equations above. The question that naturally arises is how to locate the line properly, given the start and goal configurations of the robot. There seems to be no direct way of doing so. Rather, we must use other means to identify the extrema1 trajectory. The behavior of the robot falls into one of the following cases (Figure 1): CCW and CW: If the robot is in the left half plane and out of reach of the 7-line, it tums in the counterclockwise direction (CCW). CW is similar. TCCW and TCW (Tangent CCW and Tangent CW). If the robot is in the left half plane, but close enough that a circumscribed circle is tangent to the 7-line, then the robot may either roll straight along the line, or it may tum through any positive multiple of 7r. TCW is similar. ZR and ZL: If the circumscribed circle crosses the 7-line, then a zigzag behavior occurs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001081_elps.200305533-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001081_elps.200305533-Figure1-1.png",
        "caption": "Figure 1. Schematic presentations of (A) the ring-disc electrode, (B) of the microseparation system. a, counter electrode; b, reference electrode; c, microcell; d, ringdisk electrode.",
        "texts": [
            " Samples were delivered from gas-impermeable syringes (Hamilton, Reno, NE, USA), which had been modified with silicon glass sleeves to be metal-free, and pumped through a syringe selector (CMA111, Stockholm, Sweden) by a microperfusion pump (CMA 100, Stockholm, Sweden) to the microseparation system at a perfusion rate of 2.0 L/min and determined by the on-line sensors. The on-line sensors were poised at 50 mV (vs. Ag/AgCl). Microdialysis probe (MAB 6; Microbiotech, Sweden) was used to implant into the medial frontal cortex of a moving rat to get the perfusate sample. Two ring-disc Au electrodes were used in this work. Figure 1 is the schematic presentation of the ring-disc electrode and the microseparation system. At the first one, the disc electrode was modified with 1.0 L ascorbate oxidase solution (AO) (2 U/ L) to preoxidize ascorbic acid (AA) and thus suppress interference via direct oxidation. Then 1.0 L Os-gel-HRP and 1.0 L glutamate oxidase (GlutaOD) solution (2 U/ L) were fabricated on the  2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim M in ia tu ri za ti o n surface of the ring electrode, respectively. At the second ring-disc electrode, first both ring and disc electrodes were modified by 1",
            "0 L Os-gel-HRP, then 1.0 L glucose oxidase solution (2 U/ L) and 1.0 L choline oxidase solution (ChOD; 0.5 U/ L) were fabricated on the surface of Os-gel-HRP of disc and ring electrodes, respectively. To stable the sensors, 0.2% polyethyleneimide (PEI) was also mixed with the enzymes. Finally, the prepared two ring-disc electrodes were cross-linked by placing the electrodes in a closed vessel contained 25% glutaraldehyde and water vapor for 20 min, dried at room temperature for 1 h, and stored at 4 C until use. Figure 1B presents the microseparation system used in this work. As can be seen, the solution flows from the first ring-disc electrode to the second electrode of the micro- separation system by microdialysis pump. In the microseparation system, (a) is the counter electrode (stainless) and (b) is the reference electrode (Ag/AgCl). Two microcells are covered on the two ring-disc electrodes; the microseparation system has a total internal volume about 5 L. All measurements were performed in Ringer\u2019s solution (pH 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001395_10402009008981956-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001395_10402009008981956-Figure7-1.png",
        "caption": "Fig. 7-A kinematically equivalent system of the bearing.",
        "texts": [
            " Load-approach relations developed by Dowson ancl Higginson (I I ) and quoted by Gupta (3) are also plottccl in this figure. T h e radii of the cylinders are 0.01 m and 0. I m, and the cylinder lengths are taken as 1.0 m. The results compare quite well, and the load-approach relation is not very sensitive to the c values chosen. This relative insensitivity is due to the logarithmic function which governs thc surface deflection of two elastic cylinders in contact. The contact entraining velocity in Eq. [2] can be calculatecl by looking at a kinematically equivalent system sketched in Fig. 7 wlicre the observer moves with the center of the roller. At the roller-outer-race and the roller-inner-race contacts, these velocities are given, respectively, by ZL; = [(mi - w,) 4 2 - w, d,J2]/2 [ 141 where a clockwise rotation is considered positive. The pressure clistribi~tions in the roller-raceway contacts are obtained by sim~~ltaneously satisfying Eq. [2] and Eq. [7] or [8], the pressure boundary conditions, and the pressure positivity constraint. T h e contact pressure forces in Eq. [ l ] are then obtaiiiecl via numerical integration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003340_bf00705581-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003340_bf00705581-Figure9-1.png",
        "caption": "Fig. 9. The foliot, pallets and verge arrangement in pre-pendulum clocks.",
        "texts": [
            " At its ends they hang two leaden weights and when the clock runs too slowly, they can render its vibrations more frequently merely by moving these weights somewhat closer to the center of the rod. To slow the clock down, it suffices to draw those same weights toward the ends because in this way the vibrations are rendered fewer and in consequence the hour intervals longer. Here the motive virtue is the same; that is, the counterpoise, the moving weights are the same weights, but their vibrations are more frequent when they are closer to the center; that is, when they move along smaller circles (Fig. 9). n This passage comes immediately after GALILEO'S s ta tement of the first law of astronomy. I t is als \u00b0 immediately followed by a passage on the pendulum, namely, the experiment in which the string of a pendulum is continuously shortened. This juxtaposition of the law of astronomy, of the foliot and of the pendulum is significant. GALILEO means tha t both the foliot with its weights and the pendulum are examples of the first law of astronomy. Now the foliot, as pointed out, is a regulatory device applied to mechanical clocks to improve their performance, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002273_14.12.692-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002273_14.12.692-Figure4-1.png",
        "caption": "FIG 4 Ca2+ dependence of [ E P ] Ieveh frotn WK Y (0) and SHR ( 0) hearts. Reactions were carried out at 0\u00b0C for 30 s in the presence of 0.3 t n g m r J protein, 50 mmol.litre-l tris-maleate buffer (pH 6.8), 0.1 niol.litre-' KCI, 1 tnniol.litre-' MgCI,, 5 tnmol.litre-' NaN,, 25",
        "texts": [
            "litre-' EGTA to achieve the desired Cap+ concentration: for [Cup+ I higher than I&\" nrol~litrc', only CuCI, was added. Results are expressed as a fraction of niaxinial [EP] levels (n= 7). higher in WKYs (0.97 , 0.1 vs 0.67 1 0.08 nniol.rng-' in S H R s , P - 0.01). The rate of Pi liberation from [y \"'P] ATP was linear with time and significantly more rapid with S H R microsomes. Both [EP] levels and Ca'+ uptake were higher in WKYs compared to untreated S H R s , but the homogenate/SR ratio was similar in both groups (table 3) . Steady-state [EP] levels depended on CaZ+ concentration in the incubation medium (fig 4). The ionised Cay+ concentration which gave half-maximal [EP] levels was 4.3 -10.1 yniol.litre-' in WKYs and 4.2 4-0.1 pniol.litre-' in S H R s . In both groups, low concentrations of ATP stimulated enzymatic activity (fig 5 ) but to a greater extent in WKYs. Antihypertensive therapy had variable effects on CaZt uptake by cardiac sarcoplasniic reticulum (table 3 ) ; increased capacity for CaZt uptake was found in u-methyldopa-treated S H R s but not following hydralazine therapy (which resulted in a small decrease in CaZt uptake)",
            " resides within the Ca2+-ATPase,17 2 6 the elementary Both may be aggravated by the superimposition of steps in the hydrolysis of ATP by the cardiac enzyme increased functional demands during the developof SHRs and WKYs were compared. It was found ment of hypertension. Amelioration of function (fig 3) that the [EP] levels were significantly lower in following antihypertensive therapy appears to be SHRs; in view of the unaltered dependency on Ca2+ mainly dependent on regression of cardiac hyper(fig 4) and ATP (fig 5), and equivalent Ca2+ uptake/ trophy rather than normalisation of blood pressure [EP] ratios in untreated SHRs and WKYs (table 31, alone. this probably reflects a decreased density of functioning pumping units in the SR preparation from Supported in part by a grant (HL 21850) from the SHRs. Interestingly, Ca2+-ATPase activity per se National Heart, Lung, and Blood Institute, National was higher in SHRs resulting in a marked reduction Institutes of Health, Bethesda, Maryland. of the stoichiometric ratio between calcium uptake and ATP hydrolysis (table 4)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003497_biorob.2008.4762844-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003497_biorob.2008.4762844-Figure5-1.png",
        "caption": "Fig. 5. Approximate model (1-particle), and definition of coordinate system and vectors.",
        "texts": [
            " 3 acts, the force is divided to two parts; one is an external force under a predetermined threshold value, and the other is an external force over the threshold value (Fig. 4). A reference ZMP trajectory is changed to compensate for an external force under the threshold value. In this research, we set the threshold value as 40 N, because the robot\u2019s feet began to leave the ground when we push WL-16RV with 70 N or more force due to mechanical deflection and so on. To compute a reference ZMP variation, we use a one particle model for the waist as shown in Fig. 5. Then, the mass of the legs are assumed to be 0. The moment balance around a varied reference ZMP can be expressed as follows: ( ) ( ) ( ){ } 0 w w zmp w s zmp ex ex m \u2212 \u00d7 + \u2212 \u2212 \u00d7 + + = x x x G x x F M T 0 (2) where wm is the mass of a robot\u2019s waist, [ ], , T w w w wx y z=x is the position vector of a robot\u2019s waist, , , T zmp zmp zmp zmpx y z\u23a1 \u23a4= \u23a3 \u23a6x is the position vector of reference ZMP, [ ]0,0, T zg=G is the gravitational acceleration, [ ], , T s s s sx y z=x is the position vector of a force/torque sensor, , , T ex x y zF F F\u23a1 \u23a4= \u23a3 \u23a6F is the external force caused by a passenger\u2019s motion, , , T ex x y zM M M\u23a1 \u23a4= \u23a3 \u23a6M is the external moment caused by a passenger\u2019s motion, and [ ]0 0,0, T zT=T is the total torque acts on a reference ZMP"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003026_978-1-59745-053-9_33-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003026_978-1-59745-053-9_33-Figure4-1.png",
        "caption": "Fig. 4. Photobioreactor used for marennin production. (From ref. 32 with permission.)",
        "texts": [
            " As compared with this the immobilized cyanobacteria (Anabaena variabilis and Anacystis nidulans) with poor catalase activity depicted a productivity of 150 and 60 \u03bcmol H2O2/mg Chl./h, respectively (29,30). Rossignol et al. (31) entrapped the benthic diatom, Haslea ostrearia in agar as well as alginate beads, and studied it for marennine production. With identical conditions, the specific productivity of marennine was higher using a photobioreactor with immobilized cells rather than free cells. Based on this study a new photobioreactor has been designed by Lebeau et al. (32) for marennine production (see Fig. 4). Most recently, whole-cell immobilization of the microalgae Botryococcus braunii and B. protuberans in alginate beads under airlift batch culture resulted in significant increase in hydrocarbon production at the resting phase of growth (33). A large number of reports are published on the use of immobilized microalgae for wastewater N and P removal (i.e., for the tertiary treatment of wastewater). In general, immobilized cells are found more efficient in removing N and P as compared to their free-living counterparts, and removal of phosphate is a much slower process than that observed for nitrogen (15)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002530_epepemc.2006.4778540-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002530_epepemc.2006.4778540-Figure4-1.png",
        "caption": "Fig. 4. Stator flux tubes.",
        "texts": [
            " Flux line models According to previous works [1][2], we propose the flux line models shown in Fig.3. They are made by line segments and arc segments in order to make flux lines always normal to the air-ferromagnetic interface. The flux density is assumed to be uniform along a flux line. These simple models permit us to define an airgap length function e( 0). This function is assumed to be separable D. Stator Reluctance Network Flux tube models in ferromagnetic parts of the stator and leakage flux tubes between two teeth are shown on Fig.4. Fig.5 shows the stator reluctance network model. The thick nodes show the interconnection nodes. Reluctances R and R are nonexistent when facing the rotor poles. fep fe into two independent parts e (0 ) and e (0 ) respectively s s r s attached to the stator and the rotor. The total airgap length function is then given by: e(0)= e (0 )+e (0 ). s s s r s (3) generally too low to cause saturation. Only the d-axis flux path is saturated. The thickness of the ferromagnetic segments was chosen so that both motors have the same direct inductance L of l2mH"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003505_robot.2007.363143-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003505_robot.2007.363143-Figure1-1.png",
        "caption": "Fig. 1. A planar vehicle model",
        "texts": [
            " This is similar to the classical problem in grasping, where given a rigid body with multiple contact points, one determines the range of net forces that may act upon the object and its accelerations without violating its contact and friction constraints. The two are similar since the net force acting on the object is related to the tangential speed and acceleration of the object\u2019s center of mass. The force constraints are computed using a simple terramechanics model that accounts for terrain surface properties. The method is developed for a longitudinal planar vehicle with two wheels. The vehicle is modeled as the planar two-wheel all-wheel drive vehicle shown in Figure 1. For simplicity, we assume that ground forces are applied on the massless wheels of radius r at the tangency points between the wheels and the terrain surface. The position vectors from the c.g. to the back and front contact points, r1 and r2, respectively, are expressed in the vehicle\u2019s x\u2212 y frame shown in Figure 1. The vehicle\u2019s orientation \u03b8 is measured relative to the inertial frame X \u2212Y . The orientation of the vehicle at any point is computed by modeling the vehicle and its contact points as a closed 1-4244-0602-1/07/$20.00 \u00a92007 IEEE. 1170 kinematic chain. The terrain profile is assumed known, so for a given back wheel contact point x1, we can compute the contact point x2 of the front wheel. Denoting d as the distance between the two wheel axles and r as the wheel radius, x2 is found numerically by solving: \u2016\u2212 rn1 +x2 \u2212x1 + rn2\u2016 = d (1) where \u2016\u2212\u2016 denotes the Euclidean norm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003133_j.autcon.2007.02.002-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003133_j.autcon.2007.02.002-Figure3-1.png",
        "caption": "Fig. 3. Straight-line tracking control on a horizontal plane: the control objective is to make \u03b7y and \u03b7\u03a8 zeros.",
        "texts": [
            " (2) is not involutive, span\u00f0g1; g2; g3; g4; \u00bd g1 g3 ; \u00bd g1 g4 \u00de \u00bc R6, and rank (g1, g2, g3, g4, [g1 g3], [g1 g4])=6, where, gi is the i-th column of the matrix and [gi gj] is the Lie bracket of gi and gj. In addition, the linear model of Eq. (2) is uncontrollable. The singular points \u03b8=\u00b1\u03c0 /2 are not a critical problem because such points at which the vehicle is facing exactly upward or downward (parallel with the z-axis of the fixed frame) are unlikely to occur in actual operation and can be avoided by dynamic motion control and coordinates transformation if necessary. In what follows, we formulate the error dynamics for straightline tracking control on a horizontal plane and in a 3-D space. Fig. 3 shows the notations for path-following control on a horizontal plane. LetO\u2212XY be the fixed frame andOp\u2212XpYp be a local frame (denoted by a path frame) of which Xp-axis is a straight line to follow. The path frame is defined by two way points Op=(wxi, wyi) and Op+1= (wxi+1, wyi+1). When a straight line is given as a path on the Xp-axis, path-following control is simply achieved by making the distance between the vehicle position and the Xp-axis and the vehicle orientation error with respect to the path frame all equal to zero, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003743_physreve.78.021704-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003743_physreve.78.021704-Figure1-1.png",
        "caption": "FIG. 1. Overview of different shear geometries: a shear with compression, b shear with compression but smaller translation the screws in the middle fix the apparatus to a back plate , c simple shear.",
        "texts": [
            " For the experiments, we used the well-known side-chain networks, which show a broad smectic-A phase and a hightemperature nematic phase, as described in the literature a couple of years ago 1 . The sample was sheared at room temperature perpendicular to the layer normal k z direction in steps of approximately five degrees and allowed to relax for one hour. The applied shear angle was measured by a digital camera. The sample size was 7.4 mm 5.0 mm 0.45 mm. We used three different shear geometries. By using an apparatus presented in Fig. 1 a or Fig. 1 b , the applied shear is accompanied by a compression, while the slider shown in Fig. 1 c provides simple shear. X-ray diffraction measurements were performed with a rotating anode system and a graphite monochromator Stoe , using Cu K radiation with =1.5418 \u00c5. The scattered intensity was detected by a two-dimensional image-plate system 700 700 pixels, 250 m, Schneider . The accuracy of the measured angle between small- and wide-angle reflections was estimated as 1\u00b0. Shearing a smectic-A elastomer is more difficult than for smectic-C networks. Applying a shear strain with the same setup used to induce a macroscopic orientation in smectic-C elastomers Fig. 1 a 12,14 causes a smectic-A sample to buckle strongly. Even if the shear were applied stepwise with a relaxation time of one hour, no homogeneous deformation could be achieved. These experimental problems may be connected with the special shear geometry. Especially at *heino.finkelmann@makro.uni-freiburg.de \u2020URL: http://www.chemie.uni-freiburg.de/makro/finkelmann 1539-3755/2008/78 2 /021704 3 \u00a92008 The American Physical Society021704-1 higher angles, an additional compression of the sample occurs. Figure 1 b shows a slightly improved apparatus. It still produces shear accompanied by a compression, but the translation is smaller. The buckling is weaker and the sample can be sheared up to angles of =13\u00b0 before it ruptures. However, the measured tilt angle between small-angle and wideangle reflections is =2\u00b0 and therefore near the experimental error. In Fig. 1 c , a third apparatus is shown, which produces simple shear and shows the best experimental performance. There is no significant buckling and the sample can be sheared more than =20\u00b0. The corresponding x-ray patterns show a small induced tilt for high shear angles Figs. 2 and 3 . The experimental results are summarized in Table I. The director follows the applied shear field, while the orientation of the smectic layers is uninfluenced. The resulting tilt increases continuously up to =6\u00b0. This is clarified by the azimuthal intensity distributions of the wide-angle and smallangle reflections Figs",
            " Obviously the applied strain component leads to a more effective coupling of the director. X-ray experiments under shear strain of a macroscopically oriented smectic-A elastomer are presented. With an increasing shear angle, a small tilt of the molecular axis is observed. Upon a maximum applied shear angle of =21\u00b0, the induced tilt is =6\u00b0 and thus in the range of the electroclinic effect in chiral smectic-A* phases. This result provides TABLE I. Results of the x-ray experiment under shear strain, using the experimental setup shown in Fig. 1 c . Shear angle deg Tilt angle deg S d \u00c5 0 0 0.81 0.03 29.3 0.5 11 1 3 1 0.81 0.03 29.2 0.5 21 1 6 1 0.82 0.03 29.5 0.5 021704-2 evidence to unlock the director and the smectic layer normal, as theoretically predicted by Stenull and Lubensky 11 . In chiral smectics, the effect induced by an electric field is particularly pronounced near the smectic-A*-to-C* transition. It would be interesting if an analogy exists for the mechanical effect, making even larger tilt angles possible. In the future, high-resolution x-ray measurements have to be performed to reveal more detailed information"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000570_095440802760075021-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000570_095440802760075021-Figure10-1.png",
        "caption": "Fig. 10 Archimedean Helicon gear pair: 1, Helicon pinion; 2, Helicon gear; number of threads of the pinion z1 \u02c6 1; number of teeth of the gear z2 \u02c6 40; centre distance (offset) aw \u02c6 50 mm",
        "texts": [
            " Thus the contact line is obtained in this interval of y. In addition, those points that are points of undercutting or ordinary nodes are obtained. As a result, the number of contact lines, the coordinates of the contact points on an existing contact line, the ordinary nodes and points of undercutting if such points exist for a given input value of j1 are obtained. The computer program is written in Turbo C and works under MS-DOS for PCs. The input data in this computer program version are initiated in the dialogue regime. Figure 10 shows an Archimedean Helicon gear pair which is designed on the basis of the mesh region mathematical model of synthesis. Thus, a Helicon gearbox of this type is manufactured. 1. This study presents a continuous systematic analysis of spatial gear transmissions. It proves the ef ciency of the kinematic approach to gear technological synthesis and design. When designing the subsequent mathematical models, a number of characteristics should be considered. These are the overall gear loading force including bearing loading and teeth strength and durability, hydrodynamic loading, gear pair ef ciency and technological restrictions of the gear cutting process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001765_0010-4361(77)90012-x-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001765_0010-4361(77)90012-x-Figure1-1.png",
        "caption": "Fig. 1 Tensile stress/strain curves of the seven epoxy resins listed",
        "texts": [
            "1) 160\u00b0C Dow DER-332/Jefferson Jeffamine 24 h at 60\u00b0C T-403 (100/39) Union Carbide E R L-2256/Uniroyal Tonox 6040 (100/29.5) 16 h at 50\u00b0C, plus 2 h at 120\u00b0C Shell EPON 826/Ciba-Geigy RD-2/Uniroyal Tonox 6040 (100/25/28.3) 3 h at 60\u00b0C, plus 2 h at 120\u00b0C Ciba XB-2793/Uniroyal Tonox 6040 (100/25.6) 2 h at 90\u00b0C, plus 2 h at 160 \u00b0 C Dow XD-7818/Dow XD-7575.02/ Dow XD-7114/Uniroyal Tonox 6040/Reilly Tar & Chemical DAP (50/50/45/14.1/14.1 ) 5 h at 80\u00b0C, plus 3 h at 120\u00b0C Dow XD-7818/Dow XD-7114/ Uniroyal Tonox LC (100/45/50.3) 5 h at 60\u00b0C plus 3 h at 120\u00b0C Seven epoxy resins were used in this study (Tables 1 and 2). Fig. 1 shows the tensile stress/strain curves of the cured r e s ins . 6,7 Specimen preparation Specimens were produced by winding flat laminates on flat mandrels with a f'dament winding machine. The fibres were impregnated with an epoxy resin during winding. Eight layers of laminates were wound with alternate layers at 90 \u00b0 to each other, thereby achieving midplane symmetry. After winding, flat plates were placed on each side of the mandrel, shimmed to the desired thickness, and cured in a heated press with just enough pressure to force out excess resin and press the plates down to the shims"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001807_nme.1620151012-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001807_nme.1620151012-Figure2-1.png",
        "caption": "Figure 2. New four-node stress membrane with 12 degrees-of-freedom",
        "texts": [
            " In the eight-node stress membrane, the number of independent force variables is 9, the number of rigid body modes is 3, and the number of element degrees-of-freedom in the local system is 12 (9 + 3). This element passes the standard set of tests as laid down in Reference 7. Having developed this element, it was realized that a new element could be derived from it using the same stress field (equation (1)) but with a different set of 12 degrees-of-freedom. The alternative freedoms are shown in Figure 2 and consist of two discrete translational forces and a discrete moment about an axis perpendicular to the membrane surface at each node. For the new element, the equivalent discrete generalized forces are obtained by using a cubic normal displacement distiibution (the standard beam function with rotations) when applying the principle of virtual displacements to the normal loading on each boundary. A linear tangential displacement distribution is used when applying the principle of virtual displacements to the tangential loading on each boundary"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003991_cimsa.2008.4595843-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003991_cimsa.2008.4595843-Figure2-1.png",
        "caption": "Fig. 2. Angle between the robot\u2019s current and desired directions.",
        "texts": [
            " The reason why an FLC is chosen in this specific application is the convenient framework it provides to incorporate human knowledge in operating machines in an intuitive manner. This controller acts as an inference engine to decide on the robot\u2019s next orientation given the current angle between the robot and the desired target location. Once the position of the robot is estimated using the PSO technique described earlier, the angle \u03c6 between its current position and its immediate desired point is determined by (5), \u03c6 = \u03c61 \u2212 \u03c62. (5) where \u03c61 and \u03c62 are the robot\u2019s current orientation and the angle of the current target point, respectively. This is illustrated in Fig 2. In the current work, we use a single-input single-output Mamdani-type FLC to decide on the amount of tuneup \u2206\u03b8 that the robot has to apply to its current direction \u03c61 to converge to its target position. The FLC\u2019s input is the angle \u03c6 derived from (5). The robot then uses this information to update its direction following update rule (6). \u03c6 (new) 1 = \u03c6 (old) 1 + \u2206\u03b8 (6) More information about this FLC can be sought in [13]. Algorithm 1: Pseudo code of the PSO algorithm Inputs: N : Population size, M : Dimension Output: Estimated robot\u2019s position, (x, y) // Variable declaration X [ ], V [ ]: Particle, Velocity array XLbest[ ], XGbest: Local and global best positions FitnessX [ ], FitnessLbest[ ], FitnessGbest: Particles\u2019 fitnesses L, U : Lower and Upper dimensions of the search space begin // Initialize the particle positions and their velocities for i = 1 to N do X [i] = L + (U \u2212 L)\u00d7 Rand() V [i] = 0 // Initialize the global and local fitness to the worst possible FitnessGbest = \u221e for i = 1 to N do FitnessLbest[i] =\u221e // Loop until convergence (a finite number of iteration is chosen) for k = 1 to max",
            " Step 2: The next destination point is determined from the set of destination points to start the next tracking phase. Step 3: Once the immediate target point is known, the robot receives the TRPs and computes the line-of-sight distances between itself and the tags in its operating range using the model defined in (1). Step 4: The robot then approximates its actual position in the world coordinate system using the algorithm 1. Step 5: Once the position is estimated, the angle \u03c6 between the robot and the current destination point is computed as depicted in Fig. 2. The angle \u03c6 is then passed to the FLC in order to compute the orientation tuneup \u2206\u03b8. The robot\u2019s current orientation is then updated by \u2206\u03b8. Step 6: The robot checks if the current tracking phase\u2019s destination point is reached. If so, the robot proceeds to Step 7; otherwise, the control simply passed back to the beginning of this inner loop (Step 3). Step 7: If the current tracking phase\u2019s destination point is the last point of the desired trajectory, then the robot simply stops navigation. If not, the algorithm restarts the outer loop starting from Step 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000095_mmb.2002.1002318-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000095_mmb.2002.1002318-Figure3-1.png",
        "caption": "Fig. 3. Various electrodes design of the biosensors: Parameters that determine sensor performance, which include area of electrode, edge length, and cathode shape.",
        "texts": [
            " Using (l), the detection current can be calculated for different experiment conditions. Such parameters include membrane material, thickness of membrane and solid electrolyte layer, area of electrodes, distance between electrodes and the shape of electrodes. 224 2\"d Annual International IEEE-EMBS Special Topic Conference on Microtechnologies in Medicine & Biology May24 2002, Madison, Wisconsin USA - 0-7803-7480-0/02/$17.00 02002 IEEE. Based on electrochemistry theory, many parameters are directly related to sensor performance. The various design structures are illustrated in Fig. 3. By changing these geometric parameters, the sensor performance are tested, recorded and compared. Interdigitated patterns for straight line design and circle shape design were also tested. All effects of these parameters are discussed and compared. Results have been used for calibration of computer based simulation software design. 111. FABRICATION 1) Materials: Polyacrylamide and Polyurethane, purchased from Aldrich, were used as enzyme entrapping matrix and glucose semi-permeable membrane respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001297_iros.1991.174423-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001297_iros.1991.174423-Figure4-1.png",
        "caption": "Fig. 4: Constraints on a rectangular parallelepiped in a hole.",
        "texts": [
            " At least one of four conditions must hold a t the contact point between the vertices, and a t least one of two ones must hold at t h e point between the vertex and the edge. Though such a Figure 7 shows three differential motions of the triangular prism that correspond t o V I E l , VIE, , VIE , in the equation (17) respectively. A n arbitrary motion that breaks the con- tact can be represented by a nonnegahe linear combination of them. Figure 8 illustrates three differential motions of the rectangular parallelepiped shown in Fig.4. They corresponds to V1E1. VxEa, VIES respectively, and there is no motion that does not change the contact state in this example. 5 Conclusion The results are summarized as follows: Acknowledgement The authors would like t o thank Dr.Toshitsugu Yuba, Dr.Hideo Tsukune, Dr.Tomomasa Sato, Dr.Gordon I.Dodds and the robotics research group at Electrotechnical Laboratory for their advice and encouragement. They also thank Prof.Kokichi Sugihara, University of Tokyo, for his valuable comments. References [l] Koutsou,A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001906_iros.2005.1545237-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001906_iros.2005.1545237-Figure4-1.png",
        "caption": "Fig. 4. Overviews of the experimental setup.",
        "texts": [
            " In order to apply force to the environment, there are various way such as: 1) fixing the joints of the legs, force is produced by the movement of the arms, 2) fixing the joints of the arms, force is produced by the movement of the legs, 3) force is produced by all of the joints. Theoretically, it seems that there is no difference in the results of the above three methods. However, probably due to the friction at the gear box of the joints, slight differences are seen in the experimentation results of the above methods. The differences are also presented and discussed. The overview of the experimental setup is presented in Fig. 4. A torque transducer 9E05-T1-100N manufactured by NEC san-ei Instruments is attached to the valve to measure the turning torque. The rated measurement torque of the transducer is 100 (Nm). A compact data logger NR-2000 manufactured by KEYENCE COOPERATION is used to save the torque data. The torque signal measured by the torque transducer is magnified by a strain amplifier. A butterworth low pass filter is used to remove noises. The cutoff frequency is 30 [Hz]. In order to synchronize data with the movement of the humanoid robot, the data is transfered to the PC embedded in the humanoid robot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001059_s0161-813x(03)00087-1-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001059_s0161-813x(03)00087-1-Figure3-1.png",
        "caption": "Fig. 3. Schemes of MAO A (A) and MAO B (B) active-site structures and possible positions of pirlindole-analogue inhibitors with \u2018\u2018flexible\u2019\u2019 (left) and \u2018\u2018rigid\u2019\u2019 (right) substituents. Arrows show that serotonin (5-HT) cannot displace both types of molecule, whereas 2-phenylethylamine (PEA) can displace the inhibitors with \u2018\u2018rigid\u2019\u2019 but not with \u2018\u2018flexible\u2019\u2019 substituents.",
        "texts": [
            " For example, the insertion of a bridge between the phenyl and tetrahydropyridine moieties of 1-methyl-4phenyl-1,2,3,6-tetrahydropyridine (MPTP), yielding more flexible molecule N-methyl-4-benzyl-1,2,3,6-tetrahydropyridine, greatly enhanced the reactivity with MAO B, but not that with MAO A (Krueger et al., 1992). Long but flexible oxodiazalones were also found to be much more potent MAO B inhibitors than their shorter rigid analogues (Krueger et al., 1995). 3D-QSAR with CoMFA of pirlindole analogues provided additional information on spatial properties of the active sites of MAO A and MAO B (Medvedev et al., 1998). On the basis of such analyses, we proposed the schemes of the MAO A and B substratebinding regions shown in Fig. 3. The substrate/inhibitor binding region of the active site of MAO A has the narrow slot corresponding to the C-8 substituents of pirlindole analogues where long, flexible (Fig. 3A, left) or rigid (Fig. 3A, right), substituents may bind to it, so that substrates, such as serotonin, cannot readily displace them. The corresponding site of MAO B in this region is shorter (Fig. 3B). This leads to non-complementary accommodation of rigid analogues that allows their displacement by substrates. Flexible analogues in compact conformation can fit into the substrate/inhibitor binding region quite tightly, thus preventing their displacement by substrates. This model can satisfactory explain why flexible molecules are more potent MAO B inhibitors than the rigid ones. However, although 3D-QSAR and CoMFA analysis provided valuable information on the important differences of MAO A and MAO B, this approach does not clarify structural differences between substratebinding regions of these two enzymes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002768_9780470116883.ch2-Figure2.20-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002768_9780470116883.ch2-Figure2.20-1.png",
        "caption": "Figure 2.20 Center-fed wire antenna representation of an EMI source.",
        "texts": [
            " A more rigorous approach to this problem is to obtain the current distribution by solving the corresponding integral equation that is discussed in details in Chapters 8 and 9. This section deals with the approximate current distributions. 2.19.4.1 Center-Fed Straight Wire Antenna One of the simplest antennas most commonly used in practice and also as an EMC model is the center-fed dipole antenna. This antenna as a device is shown in Figure 2.19, whereas the antenna as an undesired source of radiation in EMC is shown in Figure 2.20. The entire length of the wire is L. At high frequencies the reasonable and traditionally widely used approximation for the antenna current is the sinusoidal distribution defined as I\u00f0z\u00de \u00bc I0 sin k L 2 jzj \u00f02:350\u00de At sufficiently low frequencies where l > L 2 , that is, k L 2 jzj 1, eqn (2.350) becomes I\u00f0z\u00de \u00bc I0 1 2jzj L \u00f02:351\u00de The magnetic vector potential (2.319) for the case of sinusoidal current distribution becomes Az\u00f0z\u00de \u00bc Z L mI\u00f0z0\u00dee jkR 4pR dz0 \u00bc mI0 4pr e jkr ZL=2 L=2 sin k L 2 jz0j e jkz0 cos ydz0 \u00bc mI0 2pr e jkr cos k L 2 cos y cos k L 2 sin y \u00f02:352\u00de Note that the distance from the source to the observation point is approximated as R \u00bc r z0 cos y \u00f02:353\u00de For the special case of half-wave dipole, eqn (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002671_tsmcb.2006.870636-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002671_tsmcb.2006.870636-Figure9-1.png",
        "caption": "Fig. 9. Estimation of the pitch angle \u2206\u03b8Pitch(k + \u2206k1) of the agent at time k + \u2206k1 relative to the pitch angle at time k using points PbF(k) and PbF(k \u2212 \u2206k2) on the laser line detected at time k and k \u2212 \u2206k2, respectively.",
        "texts": [
            " Thus, min{xbR(k), xbL(k)} stored in the memory at time k is updated/reduced by the moving distance of the agent for each time instant and used for the index of predicted terrain data instead of \u2206k1. The estimated roll angle \u2206\u03b8Roll(k + \u2206k1) with respect to {B} is transformed into the angle with respect to {U} as follows: \u03b8\u0302Roll(k + \u2206k1) = \u03b83DM\u2212Roll(k) + \u2206\u03b8Roll(k + \u2206k1) (21) where \u03b83DM\u2212Roll(k) is the roll angle of the agent with respect to {U} obtained by the inclinometer at time k. As shown in Fig. 9, the pitch angle of the agent at time k + \u2206k1 is estimated using the past terrain sensor data at time k with respect to {B} as follows: \u2206\u03b8Pitch(k + \u2206k1) = tan\u22121 ( zbF(k) \u2212 zbF(k \u2212 \u2206k2) xbF(k) \u2212 xbF(k \u2212 \u2206k2) ) (22) where \u2206k2 is the minimum time satisfying the condition Lfr \u2264 |PbF(k)PbF(k \u2212 \u2206k2)|. Here, Lfr is the length between the front and rear points of the agent tracks, and |PbF(k)PbF(k \u2212 \u2206k2)| is the distance between the points PbF(k) and PbF(k \u2212 \u2206k2). The point PbF(k) is then defined by PbR(k) and PbL(k) as follows: PbF(k)= (xbF(k), ybF(k), zbF(k)) = ( min{xbR(k), xbL(k)}, 0, zbR(k)+ zbL(k) 2 ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003211_detc2007-34379-Figure15-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003211_detc2007-34379-Figure15-1.png",
        "caption": "Figure 15 : C s (magenta) omparison of FEM patch and elliptical patche",
        "texts": [
            "ashx NNEX 3 gives one example of one such FEM ent with the multirtzian method: Later 0 User's Manual g the Multicontact Wheel/rail the case of S1002 an UIC60 analytical wheel/rail profiles\" Vehicle System Solitons ailway wagons using mult dynamical codes\", 2nd ation 9-13 7. eport\", hm one body to an infinite plane ground [2] which is not appropriate to solve these conformal cases. A calculation made by Franck Jourdan at the LMGC lab of Montpellier University2 using ANSYS software. Results are in good agreem He Force Direction : + 17% (0.056/0.047) tangents al Force : -11% (10308/11574) N Patch Area (Fig.15) : X (27.2/28.4) \u2013 Y (18.7/17) mm 1. J.J. Kalker, \"Three-Dimensional Elastic Bodies in Rolling Contact\", 1st Ed., Kluwer Academic Publishers, Dordrecht/Boston/London, 1990 2. J.J. Kalker, \"CONPC9 1990,\" TU Delft , 1990 3. J.P. Pascal and G. Sauvage, \"New Method for reducin Problem to one equivalent Rigid Contact Patch,\" Proceedings 12th IAVSDSymposium, Lyon, August 26-30, 1991 4. J.P. Pascal \"The multi-Hertzian-Contact Hypothesis and equivalent conicity in d Dynamics 22-2 (1993), pp 57-78, Swets & Zeitlingrer, Lisse 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002916_jphyscol:1975138-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002916_jphyscol:1975138-Figure6-1.png",
        "caption": "FIG. 6. - Top view of the homogeneous mode. The molecules have an average twist as in solution 1. The transverse force FA gives rise to a lateral flow velocity v inside each domain. The nature of the flow next to the side wires and in the walls (dotted",
        "texts": [
            " - At very low frequencies the instability is a uniform distortion in domains limited by boundaries perpendicular to the flow and visible on the photograph of figure 4. The spacing between the domains clearly decreases with the cell width. In the narrowest cell, where the width is of the order of the wall thickness, no domains are obtained. This distortion corresponds to the homogeneous shear flow instability : In a given domain the conoscopic image indicates an average twist but no splay as for solution 1 of figure 3. Figure 6 gives a top view of the We describe here the results of microscopic visua observations. The wavelength of the roll instabilities was measured from the very regular diffraction pattern of a monochromatic laser beam going through the cell. All observations reported were done after a long enough time was allowed to let the structure stabilize. P correspond to instability states discussed in the text. lines) separating the domains has yet to be studied. configuration in different domains and points towards the most likely mechanism : As soon as the distortion is present, a transverse force appears, due to the effect A, which deflects the velocity along X"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002578_tmag.2006.871596-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002578_tmag.2006.871596-Figure2-1.png",
        "caption": "Fig. 2. Equivalent magnetizing current and applied external field on the surface of magnetic material in contact with air.",
        "texts": [
            " The magnetized material can be replaced by a superficial distribution of magnetizing currents with density in the air. The relation between the magnetic fields and is written as (1) 0018-9464/$20.00 \u00a9 2006 IEEE where is the air permeability, is the relative permeability, and is the residual magnetization of permanent magnet. From (1), the magnetization is expressed as (2) Using (2), the equivalent magnetizing current surface density is expressed as (3) where is normal unit vector on the surface. For calculating the external flux density on the surface current in Fig. 2, fields on both sides are written as and . They hold . and are self fields on both sides generated by . Therefore (4) By Lorentz\u2019 law, the resulting force density on the surface current is written as (5) The total force is obtained by the integration of the force density on the closed surface of the interested body. This conventional expression cannot apply to the situation where two materials, neither of which is air, are in contact with each other because it considers only one side surface current on the contacting interface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002954_1128888.1128914-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002954_1128888.1128914-Figure9-1.png",
        "caption": "Figure 9: The \u2018hammer in narrow notch\u2019 example. This example is modified from the \u2018hammer\u2019 example, where the size of the notch is decreased such that there is only narrow space for the \u2018hammer\u2019 to fit inside. (b) and (d) shows the placement of the \u2018hammer\u2019 at t=0 and t=0.5. (c) and (e) are their corresponding configurations respectively, which realize the UB1(PDg). The computed UB1(PDg) is tighter than the UB2(PDg) for most of time t.",
        "texts": [
            " We can cull some of the separators by making use of the currently known upper bound on PDg during any stage of the algorithm. If the separator is farther away from the object A than the current upper bound, we can discard this separator. We use the PDt between the two convex hulls of input models as an initial upper bound of PDg. We have implemented our lower and upper bound computation algorithms for generalized PD computation between non-convex polyhedra. We have tested our algorithms for PDg on a set of benchmarks, including \u2018hammer\u2019 (Fig. 6), \u2018hammer in narrow notch\u2019 (Fig. 9), \u2018spoon in cup\u2019 (Fig. 8) and \u2018pawn\u2019 (Fig. 10) examples. All the timings reported in this section were taken on a 2.8GHz Pentium IV PC with 2 GB of memory. Lower bound on PDg. In our implementation, the convex covering is performed as a preprocessing step. Currently, we use the surface decomposition algorithm proposed by [Ehmann and Lin 2001], which can be regarded as a special case of convex covering problem. In order to compute the PDt between two convex polytopes, we use the implementation available as part of SOLID [van den Bergen 2001]",
            " 7, the solid green curve highlights the value of UB1(PDg) between the \u2018hammer\u2019 and the \u2018notch\u2019 over all interpolated configurations. The dashed red curve, which corresponds to UB1(PDg), always lies between LB(PDg) and UB2(PDg). In this example, UB1(PDg) is less than UB2(PDg). The timing for this example is shown in Tab. 1. We run the PDg algorithm 5 times (b=5) for all the configurations (n=101). The average timing for LB(PDg), UB1(PDg), and UB2(PDg) is 1.901ms, 21.664ms and 0.039ms respectively. \u2018Hammer in narrow notch\u2019 example. We perform a similar experiment on \u2018Hammer in narrow notch\u2019 example (Fig. 9) to test the robustness of our algorithm. This example is modified from the \u2018hammer\u2019 example, where the size of the notch is decreased such that there is only narrow space for the \u2018hammer\u2019 to fit inside. Our algorithm can robustly compute the lower and upper bounds on PD for this example. Fig. 11 compare the lower and upper bounds on PDg over all sampled configurations (n=101). The third row of Tab. 1 shows the performance of our algorithm for this example. \u2018Spoon in cup\u2019 example. We apply our algorithm on more a complex scenario such as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003314_13506501jet315-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003314_13506501jet315-Figure1-1.png",
        "caption": "Fig. 1 FZG back-to-back hypoid gear test rig",
        "texts": [
            " A lot of influence factors are included in these calculation methods, but the influence of the oil level is not generally considered. Investigations were made in a back-to-back hypoid gear test rig for determining the detrimental effects on the scuffing load-carrying capacity of hypoid gears of a low oil immersion depth due to increased gear bulk temperatures and increased risk of lack of lubricant. JET315 \u00a9 IMechE 2007 Proc. IMechE Vol. 221 Part J: J. Engineering Tribology at WEST VIRGINA UNIV on July 24, 2015pij.sagepub.comDownloaded from The investigations were carried out on a FZG back-to-back hypoid gear test rig (Fig. 1), applying mechanical power circulation. In this type of test rig, two hypoid gear pairs, the test gear pair and a greater dimensioned transmission gear pair, are connected by two parallel shafts and a releasable mechanical coupling with a spur gear pair which closes the power circuit. The driving motor supplies the power losses. The cast test gear box of rigid design holds a sleeve where the test pinion is supported in taper roller bearings. The sleeve and the wheel can be axially adjusted for optimum contact bearing pattern and correct backlash. The load is applied by twisting the two halves of the load coupling against each other. The applied torque is measured with strain gages on the test pinion shaft. The test gear pair is dip lubricated without cooling or external circulation of the oil. The bath temperature is measured by a thermocouple located near the bottom of the oil sump (Fig. 1). The test gear set is a hypoid gear pair with an offset a \u2248 9 per cent of the outer pitch diameter of the wheel de2. The test gears are made of the same steel 17CrNiMo6. Both pinion and wheel are case carburized and ground. The main geometrical parameters, the mechanical properties, and surface conditions of the test gears are listed in Table 1. The investigations were carried out according to FZG oil hypoid test form A (modified) [4]. In this type of test, the load is increased in 11 steps between the pinion torques T1 = 60 and 680 Nm at otherwise constant test conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002260_j.mechmachtheory.2004.12.003-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002260_j.mechmachtheory.2004.12.003-Figure1-1.png",
        "caption": "Fig. 1. Coordinating manipulators.",
        "texts": [
            " For the fault tolerant operation of two coordinating redundant manipulators, the sudden change in joint velocity will damage the constraint relationship between a grasped object and manipulators and increase the internal force of the grasped object. Therefore, reducing the sudden change in joint velocity is more important for the fault tolerant operations of two coordinating manipulators. In following sections, a fault tolerant planning with avoidance of the sudden change in joint velocity for two coordinating redundant manipulators will be presented. When two manipulators grasp a common rigid object, the manipulators and the object constitute a closed-chain system shown in Fig. 1, where, B1XB1Y B1ZB1 is base frame; C1XC1Y C1ZC1 and C2XC2Y C2ZC2 are contact frames of end-effectors and object; OXOYOZO is object frame (O is the center of gravity of the object, i.e., c.g.; coordinate axes coincide the principal axes of the object). For convenient sake, the two manipulators are called master manipulator and slave manipulator respectively, whose relative parameters are denoted by subscript \u2018\u20181\u2019\u2019 and \u2018\u20182\u2019\u2019. Suppose that the two manipulator are identical, each with n joint DOFs and m end-effector s parameters (for spatial manipulators, m = 6; for planar manipulators, m = 3) and the end-effectors can grasp the object tightly so that there is no relative motion between the end-effectors and the object"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003094_j.mechmachtheory.2007.12.001-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003094_j.mechmachtheory.2007.12.001-Figure1-1.png",
        "caption": "Fig. 1. RR-RP-RP Assur group.",
        "texts": [
            " All the possible configurations of the Assur group of class 4 and order 2, with revolute and prismatic joints can be found by solving a sixth-order polynomial equation in one unknown [14,15]. Han et al. [16] using a method of vector with complex numbers solve the displacement analysis of the eight-link Assur group and obtain 48 assembly configurations. In the present paper five kinds of the class-three Assur group with revolute and prismatic joints are investigated. In all cases, using a successive elimination procedure, a final polynomial equation in one unknown is obtained. In Fig. 1 a RR-RP-RP triad with two internal prismatic joints is illustrated. To solve the position analysis of this Assur group, without loss of generality, a local Cartesian coordinate system, with origin the external joint A, and x-axis from A to external joint D is chosen. The position of the external joints A (0, 0), D (d, 0) and F (xF, yF) is known. Also the length lAB, the distances d1, d2, d3 and the angle a are given. The position of the triad links is described by a small number of parameters, such as the coordinates of the internal joint B (x,y) and the displacement s, to obtain a small number of equations",
            " (1), a final polynomial equation of fourth order with only variable s is derived: X4 i\u00bc0 Hisi \u00bc 0 \u00f017\u00de which is free from extraneous roots and where the coefficients Hi (i = 0, . . ., 4) depend only on the Assur-group data. Eq. (17) provides four solutions for s in the complex field. For every root sj (j = 1, . . ., 4), using back substitution, the coordinates x, y of the joint B and the displacement s1 are determined. The real solutions correspond to the assembly modes of the triad. The order of the polynomial equation (17) is minimal. This is confirmed by the following consideration: For a given position of the external joints A, D and F of the triad (Fig. 1), the internal joint B lies on the bicircular fourth order curve of the DCEF four-bar mechanism of the RPPR type [5,12]. Also B belongs to the circle centered in A, of radius BC. B is the intersection point of the fourth order coupler curve with the circle and eight intersection points exist at most. Due to the fact that this intersection contains two imaginary points as doubles points, there will be at most four real intersection points. Therefore the maximum number of the assembly modes of the RR-RP-RP triad is four",
            " The coordinates of the external joint A (0,0) and of the auxiliary points D (d,0) and F (xF, yF) situated on the sliding direction of the corresponding external prismatic joint are known, as well as the length of links lAB, lBC and the angles h1, h2 and a. The distances d1 d2, d3 and d4 are also given. The position of the triad links can be described by the coordinates of the internal joint B (x,y) and the displacement s3. The first constraint equation is given as Eq. (1). The second and third equations are obtained from the ABCDA loop: Table Data a Data Config 1 2 3 4 x\u00fe lBC cos u \u00bc d \u00fe s3 cos h1 d4 sin h1 \u00f066\u00de y \u00fe lBC sin u \u00bc s3 sin h1 \u00fe d4 cos h1 \u00f067\u00de where u \u00bc p=2\u00fe b\u00fe h2 a; cos b \u00bc r=lBC; sin b \u00bc \u00f0d1 d2\u00de=lBC; r \u00bc l2 BC \u00f0d1 d2\u00de2 1 2 \u00f068\u00de From Eqs. (66) and (67) taking into account Eqs. (68), after transformations, yields: x \u00bc s3 cos h1 \u00fe d d4 sin h1 r sin\u00f0a h2\u00de \u00fe \u00f0d1 d2\u00de cos\u00f0a h2\u00de \u00f069\u00de y \u00bc s3 sin h1 \u00fe d4 cos h1 r cos\u00f0a h2\u00de \u00fe \u00f0d1 d2\u00de sin\u00f0a h2\u00de \u00f070\u00de Eqs. (69) and (70) are inserted in Eq. (1) and a final polynomial equation of second order in variable s3 is derived"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002649_1464419jmbd12-Figure11-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002649_1464419jmbd12-Figure11-1.png",
        "caption": "Fig. 11 Calibration rig",
        "texts": [
            " Because the eccentricity and its associated harmonics still prevailed, it was necessary to avoid these frequencies during tests. These were located by scanning the frequency range while the shaft was rotating without excitation. Frequencies that displayed a signal strength on the spectrum analyser in excess of 50 mV were avoided. In order to convert the voltage readings from the spectrum analyser into real values of acceleration and displacement, it was necessary to calibrate the accelerometer and capacitance probe. This was done using the calibration rig shown in Fig. 11. By choosing steel discs of the appropriate thickness, mechanical vibrations were reduced to about the same order of magnitude as those experienced under test conditions. The base of the accelerometer was mounted on the head of the reference accelerometer and both were enclosed by a rigid yoke that provided a flat surface for the Wayne Kerr capacitance probe. Originally, the capacitance probe was held in an adjustable slide, enabling the air gap between the probe and the yoke to be easily altered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001274_robot.1986.1087415-Figure2-1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001274_robot.1986.1087415-Figure2-1-1.png",
        "caption": "Fig. 2-1 Object and finger",
        "texts": [
            " c) If column (low) vectors of matrix A are linearly independent one another, then A is a column (low) proper matrix. Matrix A is non-singular if and only if A is a colu#n and kow proper matrix. d) A and A are the pseudo-inverse matrix and the orthogonal projection matrix along R{AI of matrix A , respectively . If A is a column (low) proper matrix, then the following equations are satisfied: A # A = I and A*A=O (AA # = In and AA*=O). n LINEMATIGS In this section, a set of kinematic equations for an articulated finger and an object is obtained for a two dimensional system. Fig. 2-1 shows a configuration of an object along with the i-th finger of the hand, where relevant coordinate frames and variables are also shown. There are four frames; a hand frame (0-x Y,) at the center of the palm. an object Prames ( 0 - x Y ) at the appropriate location on the oBjeOct, a finger frame (0-x ) at he center of the i-th finger f~rpf! and a contact frame (0-x.Y.) at he contact point between the ilth finger tip and the object. The radius o f the finger tip is R. It is assumed that this hand has N fingers and each finger has M i joints (active joints)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000425_s0218127402005339-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000425_s0218127402005339-Figure2-1.png",
        "caption": "Fig. 2. Open-loop chaotic response.",
        "texts": [
            " (a) (b) (c) (d) (e) Fig. 3. Regulation to origin. (a) Vc1, Vc2, IL, (b) 3-D plot of Vc1, Vc2, IL, (c) Parameter estimate \u03b8\u03021, (d) Parameter estimate b\u03021, (e) Parameter estimate \u03c1\u03021. In t. J. B if ur ca tio n C ha os 2 00 2. 12 :1 59 9- 16 04 . D ow nl oa de d fr om w w w .w or ld sc ie nt if ic .c om by U N IV E R SI T Y O F N E W E N G L A N D L IB R A R IE S on 0 1/ 24 /1 5. F or p er so na l u se o nl y. (a) (b) Fig. 4. Nonzero set point control. (a) Vc1, Vc2, IL, (b) 3-D plot of Vc1, Vc2, IL. Fig. 2. The chaotic nature of the Chua\u2019s circuit is observed for the chosen initial condition. To examine the trajectory tracking ability of the controller, the complete closed-loop system is simulated. Reference trajectory yr is generated by a third-order filter (s+ 1)3(yr \u2212 y\u2217) = 0 with repeated poles at s = \u22121. The initial conditions chosen are yr(0) = 0.5, y (k) r (0) = 0(k = 1, 2). For the regulation of the state vector to the origin, y\u2217 is set to zero. The control parameters are set to ci = \u03b3i = 1 and \u0393 = I, the identity matrix, for simplicity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002947_robot.2005.1570219-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002947_robot.2005.1570219-Figure1-1.png",
        "caption": "Fig. 1. Ceramic capacitor 2012",
        "texts": [
            " Next, we conduct experiments to assess the feasibility of micro-parts feeding by the proposed method. Finally, we discuss how well the feeding model fits experimental results. II. PRINCIPLE OF UNIDIRECTIONAL FEEDING This section describes the principle of unidirectional feeding by a saw-tooth surface. We first examine the case of a ceramic chip capacitor, a typical micro-part used in electrical devices. Then, we analyse the feeding mechanism by developing a model for the contact between the micropart and saw-tooth. Fig. 1 shows a ceramic chip capacitor. Table I tabulates the specifications of TDK C-series ceramic chip capacitors. These capacitors were composed of a conductor with an electrode on either side. Fig. 2 shows the surface profile of a 2012-type ceramic chip capacitor. It was the electrodes of the micro-part that contacted the feeder surface as they were about 40 m higher than the conductor. The electrode surface exhibited concavities and convexities. the electrode surface are perfectly spherical with radius (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001930_s10665-005-9007-0-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001930_s10665-005-9007-0-Figure2-1.png",
        "caption": "Figure 2. Case 1 of fixator assembly.",
        "texts": [
            " The spherical joints B1, B2, B3 seen in Figure 1(a) belong to the moving platform fixed to the distal fragment. The center of the distal ring G1 will also be the origin of a movable uvw co-ordinate system attached to the moving platform, whereby the uv-plane is defined by the distal ring and the u-axis is defined by G1B1; see Figure 1(a). Based on the above assumptions and notation, a detailed analyses of the three cases will be presented. See Appendix D for a list of symbols. 2.1. First case We consider the situation as shown in Figure 2. Both bone fragments are perpendicular to the respective circles. First, it is necessary to recognize the parameters which characterize the initial and final configurations of the Stewart Platform, one of them being the neutral configuration. The values of these parameters are to be taken from measurements on the lateral, AP, radiographs and on the axial clinical examinations; see Figure 1(b\u2013d). Parameter h designates the distance between the proximal and distal ring planes along the z-direction, when the fixator is at its neutral configuration; see Figure 1(b)",
            " To this end, inserting (\u03b40 \u2212 \u03b4Ax) as \u03b1 in (7) and solving the equations resulting from comparison of (7) with (6) for the unknown angles we obtain the following: tan \u03b7= ewx cos(\u03b40 \u2212 \u03b4Ax)+ ewy sin(\u03b40 \u2212 \u03b4Ax) ewz , (8) cos\u03b3 = ewz cos\u03b7 . (9) The relationships (8), (9) now define the unit vectors eu, ev, ew. From the given set (bL, cL), one can calculate the fragment lengths on the proximal (b) and distal sides (c) of the fracture point. Since fragments are assumed to be perpendicular to their relevant planes of attachment in the first case, Figure 2(a), on the base part it is apparent that bL =b, whereas on the moving part, c will be estimated by the following: c= cL\u221a cos2 \u03b2wz + cos2 \u03b2Ax sin2 \u03b2wz . (10) With reference to Figure 2(a), G\u2032 1 is the fracture point on the distal fragment to be unified with its counterpart K on the proximal fragment. Accordingly, the following vector relationships can be written down in the fixed Gxyz-system: GG1 =GK +KG\u2032 1 +G\u2032 1G\u2032\u2032 1 \u2212G1G\u2032\u2032 1 (11) with GK =qx i +qy j+bk, (12) KG\u2032 1 = ex i + ey j+ ezk, (13) G1G\u2032\u2032 1 = rx i + ry j+ rzk, (14) G\u2032 1G\u2032\u2032 1 = cew = c(ewx i + ewy j+ ewzk). (15) Furthermore: GB1 =GG1 +G1B1, (16) GB2 =GG1 +G1B2, (17) GB3 =GG1 +G1B3. (18) Now, in order to calculate G1B1, G1B2, G1B3, one can imagine a triangle B1B2B3 with sides b1=B2B3, b2=B3B1, b3=B1B2 and describe the vectors in the moving G1uvw-system: G1B1 =R1eu, (19) G1B2 =\u2212R1 cos 2\u03b41eu +R1 sin 2\u03b41ev, (20) G1B3 =\u2212R1 cos 2\u03b43eu \u2212R1 sin 2\u03b43ev, (21) where: (see Appendix B) \u03b41 = \u03d51 +\u03d52 \u2212\u03d53 2 ; \u03b43 = \u03d53 +\u03d51 \u2212\u03d52 2 ; R1 = b2 2 cos \u03b43 , (22) \u03d51=cos\u22121 ( b2 2 +b2 3 \u2212b2 1 2b2b3 ) ; \u03d52=cos\u22121 ( b2 3 +b2 1 \u2212b2 2 2b3b1 ) ; \u03d53=cos\u22121 ( b2 1 +b2 2 \u2212b2 3 2b1b2 ) . (23) Since eu, ev have already been defined in terms of the Gxyz-system unit vectors by either (6) or (7), the vectors under consideration are clearly well-known now in the fixed Gxyz-system. With a similar reasoning in the proximal ring plane, A1A2A3 can be imagined as a triangle with sides a1=A2A3, a2=A3A1, a3=A1A2; see Figure 2(a). Then, the vectors GA1, GA2, GA3 in the fixed Gxyz-system will identify the co-ordinates of the points A1, A2, A3, respectively. GA1 =Ri, (24) GA2 =\u2212R cos 2\u03b21i +R sin 2\u03b21j, (25) GA3 =\u2212R cos 2\u03b23i \u2212R sin 2\u03b23j, (26) where: \u03b21 = \u03c61 +\u03c62 \u2212\u03c63 2 ; \u03b23 = \u03c63 +\u03c61 \u2212\u03c62 2 ; R = a2 2 cos \u03b23 , (27) \u03c61=cos\u22121 ( a2 2 +a2 3 \u2212a2 1 2a2a3 ) ; \u03c62=cos\u22121 ( a2 3 +a2 1 \u2212a2 2 2a3a1 ) ; \u03c63=cos\u22121 ( a2 1 +a2 2 \u2212a2 3 2a1a2 ) . (28) When the platform is in its first configuration, Figure 2(a), the bar lengths (L1\u2013L6) can be evaluated by taking into account distance formulae between the relevant points specified in the same system: L2i\u22121 =|GAi \u2212GBi | ; L2i = \u2223\u2223GAj \u2212GBi \u2223\u2223 , i =1,2,3; j =\u22122+5\u00b75i \u22121\u00b75i2 (29) For the final configuration of the platform, Figure 2(b), the link lengths L1s ,L2s ,L3s ,L4s ,L5s , L6s are computed in the same way by the formula (29), except that, GA1, GA2, GA3 being same, the vectors GB1, GB2, GB3 are replaced by GB1s , GB2s , GB3s as given below: GB1s = (R1 cos \u03b40 +qx\u2212rx)i + (R1 sin \u03b40 +qy\u2212ry)j+ (b+ c)k (30) GB2s = (\u2212R1 cos(2\u03b41 \u2212 \u03b40)+qx\u2212rx)i + (R1 sin(2\u03b41 \u2212 \u03b40)+qy\u2212ry)j+ (b+ c)k (31) GB3s = (\u2212R1 cos(2\u03b43 + \u03b40)+qx\u2212rx)i + (\u2212R1 sin(2\u03b43 + \u03b40)+qy\u2212ry)j+ (b+ c)k (32) 2.2. Second case The second case may result for several reasons. One of these might be that, after imposing the requirements of the first case and after fracture fixation, radiographs and clinical investigations might point to a residual deformity at the neutral configuration",
            " (65) Thus, the rotation angles (\u03b3 , \u03b7, \u03b1) about the x, y, z-axes are extracted in that order from the matrix above as follows [14, Chapter 2]: \u03b3i = tan\u22121(evzi/ewzi), (66) \u03b7i = tan\u22121 ( \u2212euzi/ \u221a e2 uxi + e2 uyi ) , (67) \u03b1i = tan\u22121(euyi/euxi). (68) With (59\u201361) and (66\u201368), the three translations (g1xi, g1yi, g1zi) and the three orderly rotations (\u03b3i , \u03b7i , \u03b1i) are now well-defined. In order to describe the trajectory to be traced by the distal fragment end G\u2032 1 during the treatment process in the fixed Gxyz-system, the following vector equation is written down for each step i: GG\u2032 1i =GG1i +G1iG\u2032\u2032 1i \u2212G\u2032 1iG \u2032\u2032 1i . (69) For the first case, Figure 2, vectors of interest are computed as follows: G1iG\u2032\u2032 1i = rueui + rvevi , (70) GG1i =g1xi i +g1yi j+g1zik, (71) G\u2032 1iG \u2032\u2032 1i = cewi, (72) where ru, rv are the same as in (45) and (46). For the second and third cases, however, Equations (70) and (71) remaining the same, the vector G\u2032 1i G\u2032\u2032 1i is determined in the following way: G\u2032 1iG \u2032\u2032 1i = cew\u2032i , (73) where ew\u2032 is the last column of the transformation matrix [A G\u2032\u2032 1u\u2032v\u2032w\u2032 Gxyz ]i is expressed as follows: [A G\u2032\u2032 1u\u2032v\u2032w\u2032 Gxyz ]i = [AG1uvw Gxyz ]i [AG1uvw G\u2032\u2032 1u\u2032v\u2032w\u2032 ] T "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001067_095441002760179771-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001067_095441002760179771-Figure4-1.png",
        "caption": "Fig. 4 Convex and concave tooth manufacture",
        "texts": [
            " Elastoplast ic analysis of curvic joints under a blade release condition has been dealt with elsewhere [11]. To obtain contact over the entire length of the coupling halves, one of the halves is machined by the external tool surface and the other by the internal tool surface. This produces a different geometry on either side of the coupling. If the coupling half is machined by the external tool surface then the teeth will have a concave geometry. If the coupling half is machined by the internal tool surface then the teeth will have a convex geometry; this is illustrated in Fig. 4. A large number of dimensions are required in order to de\u00aene the geometry of a Curvic coupling. Referring to F ig. 1, the dimensions used at the inside tooth radius for the present investigation were as follows: w, tooth width \u02c6 2.28mm; hc, chamfer height \u02c6 0.28mm; rf , \u00aellet radius \u02c6 0.6 mm; bh, bedding height \u02c6 1.10 mm; lg, angle of inclination of the gable (i.e. the gable angle) \u02c6 4.28; lc, angle of inclination of the chamfer \u02c6 458; y, tooth pressure angle \u02c6 308; a, addendum \u02c6 1.24mm; d, dedendum \u02c6 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002671_tsmcb.2006.870636-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002671_tsmcb.2006.870636-Figure3-1.png",
        "caption": "Fig. 3. ROBHAZ-DT with the terrain-prediction sensor.",
        "texts": [
            " Then, the vector (dn 0 1)T can be transformed into a vector (Xn Yn 1)T with respect to {B} as follows: Xn Yn 1   =   cos \u03b8n \u2212 sin \u03b8n xn sin \u03b8n cos \u03b8n yn 0 0 1     dn 0 1   . (4) Hereafter, the point Pn(Xn, Yn) \u2208 R2, with respect to {B}, is utilized as a range datum of obstacles instead of the distance dn \u2208 R1, where n = 1, 2, . . . , N . The ROBHAZ-DT used in this paper utilizes eight ultrasonic sensors, thus we haveN = 8. C. Vision Data Acquisition for Structured Laser Light A low-cost terrain-prediction sensor consisting of a laser-line generator, a web camera, and an inclinometer is attached to the ROBHAZ-DT, as shown in Fig. 3. The laser-line generator, the LM-6535ML6D of Lanics Co., Ltd., is used to project a line segment on the front terrain, and its fan angle and linewidth are 60\u25e6 and 1 mm, respectively. The wavelength of the laser beam ranges from 645 to 665 nm, and the optical output power is 25 mW. The CMOS web camera, the ZECA MV402 of Mtekvision Co., Ltd., is used to detect the laser-line segment. The inclinometer, the 3DM of MicroStrain, Inc., is used to measure the absolute angles from 0\u25e6 to 360\u25e6 on both the yaw and pitch axes, and from \u221270\u25e6 to 70\u25e6 on the roll axis with respect to the universal frame {U}"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003488_robot.2007.363548-Figure15-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003488_robot.2007.363548-Figure15-1.png",
        "caption": "Fig. 15. Voltage-induction-type slider is stacked on the stator",
        "texts": [
            " We fabricated stator and slider films with induction electrodes as shown in Fig. 14. The stator driving-electrodes and an induction electrode measure 8-mm wide by 30-mm long and 4.5-mm wide by 31.5-mm long, respectively. The slider driving-electrodes and an induction electrode measure 8-mm wide by 15 mm long and 4.5-mm wide by 15-mm long. The driving-electrode pitch of the stator is 200 \u03bcm and that of the slider is 400 \u03bcm. We operated the motor using the induction and measured the slider motion (see Fig. 15). The motion was measured using optical displacement sensor (ZIMMER, 200). The result is plotted in Fig. 16. The slider runs with a speed of about 0.8 mm/s with a smooth transition, showing the possibility of high-accuracy positioning. High-power electrostatic motors based on FPC technology are promising for many mechatronic applications because of their high output performance and unique features. Previous high-power motors require electric cabling to their sliders, which may cause troubles in some applications"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002244_s1064230706030063-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002244_s1064230706030063-Figure1-1.png",
        "caption": "Fig. 1. The pendulum.",
        "texts": [
            " Note that the problem of stabilizing the pendulum at the top position is of interest. In [5, 6], the pendulum was stabilized by vertical movements of the pendulum base. In [7], the problem of stabilizing the vertical unstable equilibrium position whose suspension point is fixed was solved using a revolving flywheel. Consider a pendulum that is able to rotate about a horizontal axis O and is controlled by a torque M applied to it. We use the following notation: \u03d5 is the angle between the pendulum and the vertical axis (Fig. 1), m is the pendulum mass, J is its moment of inertia relative to the axis O , l is the distance from the axis O to the center of mass of the pendulum, and g is the gravitational acceleration. The motion equation of the pendulum has the form (1.1) where the dot means the derivative in t . Assume that, on the control torque, the constraint is imposed (1.2) where M 0 is a given constant. J \u03d5\u0307\u0307 mgl \u03d5sin+ M,= M M0,\u2264 \u2014A time-optimal feedback control is synthesized that steers a nonlinear pendulum to the top unstable equilibrium position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003488_robot.2007.363548-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003488_robot.2007.363548-Figure9-1.png",
        "caption": "Fig. 9. Configuration of slider and stator in driving. The slider is simply stacked on the stator.",
        "texts": [
            " In this setting, the measured capacitance of Cm1 was 19.4 pF (The value is different from the measurement in Fig. 7. This is because the fixing condition of the slider in the experimental setup can be different at each time). Theoretical thrust force amplitude of the frequency-difference component is 0.305 N. This value agrees quite well with the experimental result. Finally, we operated the motor by the same voltage setting. The slider with electric wire was simply stacked on the stator as shown in Fig. 9, and then driven by voltage application. The motion of the slider was measured by an optical displacement sensor (Zimmer, 200). The measured motion is plotted in Fig. 10. The slider runs with a speed of about 0.8 mm/s almost same as the theoretical analysis predicted. In this section, we discuss the effect of electrostatic induction. Fig. 11 shows a capacitance network model of the motor with the induction. Driving electrodes and induction electrodes are modeled simultaneously. We assumed the induction electrodes as simple capacitors inserted between a voltage supply and the driving electrodes of the slider"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000958_s0094-114x(02)00049-6-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000958_s0094-114x(02)00049-6-Figure2-1.png",
        "caption": "Fig. 2. Transverse tooth profile and its radii of curvature.",
        "texts": [
            " The algebraic value of U is U \u00bc N n \u00bc v\u00f0p\u00de\u00f0ctg2b \u00fe cos2 a\u00de0:5\u00f0cos2 a \u00fe ctg2b cos2 w\u00de 0:5 sin\u00f0a \u00fe w\u00de \u00fe 0:5 1 r\u00f01\u00de 1 r\u00f02\u00de x sec a cos w \u00bc sin wffiffiffiffiffiffiffiffiffiffiffiffi sin2 w q v\u00f0p\u00de\u00f0ctg2b \u00fe cos2 a\u00de0:5 g2 cos2 a \" \u00fe \u00f0ctg2b \u00fe cos2 a\u00de dg da 2 # 0:5 g cos a \u00fe sin a 0:5 1 r\u00f01\u00de 1 r\u00f02\u00de g dg da : For 0 < w < 180 , sinw ffiffiffiffiffiffiffiffiffiffiffiffi sin2 w q \u00bc 1. Therefore U \u00bc v\u00f0p\u00de g2 cos2 af 2 \" \u00fe dg da 2 # 0:5 g cos a \u00fe 0:5\u00f0f \u00f01\u00de \u00fe f \u00f02\u00de\u00de dg da \u00f025\u00de where f \u00bc \u00f0ctg2b \u00fe cos2 a\u00de 0:5 ; f \u00f01\u00de \u00bc sin a \u00f0g=r\u00f01\u00de\u00de, f \u00f02\u00de \u00bc sin a \u00f0g=r\u00f02\u00de\u00de (the upper \u2018\u2018\u00fe, )\u2019\u2019 for quadrant I, the lower \u2018\u2018), \u00fe\u2019\u2019 for quadrant III). The value of U may be positive or negative, that is, the lubricant may be entrained into the contact region from one side or the other of the instantaneous contact line. Suppose the curve af as shown in Fig. 2 is a transverse tooth profile of pinion and q\u00f01\u00de ta is the radius of curvature of addendum profile ap at any point Ca, then q\u00f01\u00de ta \u00bc CaRa \u00bc CaEa \\ dda : Ca corresponds to contact point CI (see Fig. 1). Therefore CaOa \u00bc CIO \u00bc gI; EaBa \u00bc EaDa \u00fe DaBa \u00bc gI \u00fe dgI; DaBa \u00bc dgI: It is observed from Fig. 2 that ha \u00bc dda \u00fe 90 b \u00f0a \u00fe da\u00dec \u00bc dca \u00fe 90 b ac; i:e: dda \u00bc dca \u00fe da: Therefore OaDa \\ OaRa \u00bc OaBa \\ r\u00f01\u00de \u00fe da; dgItg\u00f0a \u00fe da\u00de q\u00f01\u00de ta gI \u00bc dgI sec\u00f0a \u00fe da\u00de r\u00f01\u00de \u00fe da or 1 q\u00f01\u00de ta \u00bc cos a \u00fe 1 r\u00f01\u00de dgI da gI cos a \u00fe sin a \u00fe gI r\u00f01\u00de dgI da ; similarly 1 q\u00f02\u00de ta \u00bc cos a \u00fe 1 r\u00f02\u00de dgIII da gIII cos a \u00fe sin a \u00fe gIII r\u00f02\u00de dgIII da : Suppose q\u00f01\u00de tf is the radius of curvature of dedendum profile pf at any point Cf , then q\u00f01\u00de tf \u00bc CfRf \u00bc CfEf \\ ddf : Cf corresponds to contact point CIII (see Fig. 1). Therefore CfOf \u00bc CIIIO \u00bc gIII; EfBf \u00bc EfDf DfBf \u00bc gIII \u00fe dgIII; DfBf \u00bc dgIII: It is observed from Fig. 2 that hf \u00bc ddf \u00fe b90 \u00f0a \u00fe da\u00dec \u00bc dcf \u00fe b90 ac; i:e: ddf \u00bc dcf \u00fe da: Therefore OfDf \\ OfRf \u00bc OfBf \\ r\u00f01\u00de \u00fe da; dgIIItg\u00f0a \u00fe da\u00de qIII tf \u00f01\u00de \u00fe gIII \u00bc dgIII sec\u00f0a \u00fe da\u00de r\u00f01\u00de \u00fe da or 1 q\u00f01\u00de tf \u00bc cos a \u00fe 1 r\u00f01\u00de dgIII da gIII cos a \u00fe sin a gIII r\u00f01\u00de dgIII da ; similarly 1 q\u00f02\u00de tf \u00bc cos a \u00fe 1 r\u00f02\u00de dgI da gI cos a \u00fe sin a gI r\u00f02\u00de dgI da : The values of radii of curvature (q\u00f01\u00de ta , q\u00f01\u00de tf , q\u00f02\u00de ta , q\u00f02\u00de tf ) may be positive or negative, that is, the corresponding transverse tooth profiles may be convex or concave",
            " As a rule, however, the shape can be approximated by a circle, whose center is close to the pitch center\u2019\u2019. \u2018\u2018The slight difference of the radii of (mating) profiles facilitates the tooth contact and allows for small errors in making and assembling\u2019\u2019. \u2018\u2018A farther purpose of the invention is to provide helical gearing, which is capable of rapid and accurate production and which may be ground without difficulty, if so desired\u2019\u2019. The related contents of [5\u20139]: The circular arcs, which were recommended by Novikov to be used as the theoretical transverse mating tooth profiles ([6] Fig. 2) for helical gearing with eb > 1, were sought out by means of Euler\u2013Savary equation. It is obvious that q\u00f01\u00de t \u00bc g, q\u00f02\u00de t \u00bc g and 90 > a > 0 satisfy Euler\u2013Savary equation 1 q\u00f01\u00de t g \u00fe 1 q\u00f02\u00de t g \u00bc 1 sin a 1 r\u00f01\u00de \u00fe 1 r\u00f02\u00de ; i:e: q\u00f01\u00de t \u00fe q\u00f02\u00de t \u00bc \u00f0q\u00f01\u00de t g\u00de\u00f0q\u00f02\u00de t g\u00de sin a 1 r\u00f01\u00de \u00fe 1 r\u00f02\u00de ; where the upper signs of , are for the contact point CI and the lower for CIII (see Fig. 1), q\u00f01\u00de t and q\u00f02\u00de t are curvature radii of transverse tooth profiles at contact point CI or CIII for pinion (1) and gear (2) respectively (the curvature radius of convex addendum profile is positive and that of concave dedendum profile is negative), a and g (gI or gIII) are polar coordinates of contact point CI or CIII, r\u00f01\u00de and r\u00f02\u00de are pitch circle radii of pinion (1) and gear (2) respectively. On this condition (q\u00f01\u00de t \u00bc g, q\u00f02\u00de t \u00bc g and 90 > a > 0 ) the relative curvature radius of the transverse mating profiles is qt \u00bc q\u00f01\u00de t q\u00f02\u00de t q\u00f01\u00de t \u00fe q\u00f02\u00de t \u00bc g2 0 \u00bc 1; that is to say, instantaneous circular-arc contact occurs in the transverse plane (refer to [6] p. 27). Such a circular-arc-contact helical gearing is highly sensitive to errors and elastic deformations, so it is necessary to substitute point-contact ([5] Fig. 2, [6] Fig. 6) for circular-arc-contact ([6] Fig. 2) on condition that the predetermined a and g remain unchanged (refer to [6] p. 30). For this reason the early Novikov gearing for practical application is a point-contact trans- verse-circular-arc gearing with q\u00f01\u00de t \u00fe q\u00f02\u00de t < 0 and eb > 1. The performance indexes of conjugate flanks were calculated on condition that the tooth profiles had already been predetermined. For the convenience of hobbing the late Novikov gearing substituted the normal-circular-arc profiles for the transverse and its normal module was standardized (refer to [9] p"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000982_ac00166a039-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000982_ac00166a039-Figure3-1.png",
        "caption": "Figure 3. Schematic view of the Pt cuvette cell: (A) sue view of the cell, (a) to vacuum system, reference electrode, and pump, (b) solution exit line, (c) working electrode cell compartment, (d) auxiliary electrode cell compartment, (e) Teflon plug, (1) quartz cuvette; (E) front vlew of the cell, (a) to vacuum system, (b) channel for electrical connections to the working and auxillary electrcdes, (c) solution exit port, (d) working electrode, (e) solutlon entrance port.",
        "texts": [
            " The solution in the cuvette cell was removed by applying a positive N2 pressure and then solution refilled by capillary action. The working electrode can be removed from the cuvette for pretreatment or surface analysis and reinserted very easily through the 3 24/40 inner joint (see Figure 2). The auxiliary electrode was a piece of Pt wire and the reference electrode was Ag/AgCl (saturated KC1). All potentials in the text will be referred to this reference. B. The construction of the second cuvette cell for a Pt working electrode (cell B) was similar to a design by Simone (18) and is shown in Figure 3. A piece of Teflon (Berghoff, Raymond, NH) A B was milled to press fit into a standard 10-mm optical path length quartz cuvette with an internal volume of 3 mL. Two channels (1 cm X 0.5 cm) were milled into the Teflon on opposite sides of this Teflon plug, which defined the working electrode compartment and the auxiliary electrode compartment. The depth of these channels was approximately 5 mm. Small holes (1.5 mm diameter) were drilled in the middle of each channel and through the length of the Teflon plug"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003304_j.msea.2007.11.032-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003304_j.msea.2007.11.032-Figure2-1.png",
        "caption": "Fig. 2. Devices for laser hardening of the flat specimens with borehole",
        "texts": [
            " The longitudinal direction of he specimens was the rolling direction of the bars. All fatigue pecimens were ground. The resulting residual stresses in lonitudinal direction in the region of the later hardened area can e seen in Table 6. .2. Laser hardening .2.1. Experimental setup At the flat specimens with borehole, a hardening zone had to e generated running around the borehole. In order to avoid the ormation of a tempered zone at the end of the circulation, the pecimen was fixed in a clamping device which was rotated with rotation frequency of maximum 3000 rpm (Fig. 2, left). This esults in a pulse repetition frequency of 50 Hz. The clamping ig. 1. Geometry of the flat specimens with borehole and of the bending speciens with shoulder. G. Habedank et al. / Materials Science and Engineering A 488 (2008) 358\u2013371 361 Ta bl e 1 C ro ss -s ec tio n of th e ba rs an d ch em ic al co m po si tio n (m ea n an d st an da rd de vi at io n) B at ch C ro ss -s ec tio n (m m 2 ) C Si M n P S C r M o N i C u 1 50 \u00d7 8 0. 41 0 \u00b1 0. 00 8 0. 16 4 \u00b1 0. 00 3 0. 83 2 \u00b1 0. 00 2 0. 01 6 \u00b1 0",
            " The laser beam impinged the specimens surface erpendicular or with an angle \u03b1 and was defocussed according o the desired width of the hardening track. A shielding gas to rotect the surface from oxidation was not used because of the urbulences induced by the high rotation speed. To determine he optimal process parameters for each specimen variant, the urface temperature, the process time and the position of the aser beam were varied. The bending specimens with shoulder had to be hardened in he region of the notch. For this purpose the laser beam impinged he specimens surface with an angle\u03b1= 45\u25e6 (Fig. 2, right) to get a ymmetrical hardened zone in the body and in the finger-shaped art of the specimen. The laser processing head was moved linarly along the angle with a feed rate of 130 or 150 mm/min. he pulsed mode in this case was realised by the laser itself ith frequencies of 25 and 100 Hz. .2.2. Measurement and controlling of the temperature The hardening temperature was measured independently rom temperature controlling with a line pyrometer of the model AND Infrared with a line of 12 side-by-side measuring fields"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000550_robot.2000.844843-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000550_robot.2000.844843-Figure2-1.png",
        "caption": "Fig. 2: Normalized impact geometry",
        "texts": [
            " (n E SE\"), (17) where Ft = %. This new geometry means the range of directional impact force for given n-directional task velocity like Eq. (16) . From Eqs. (10) and (13), the following equation is derived: where nTAp is the task velocity change along the normal direction of environment. And, as shown in Eq. (9), we can derive nTAp = nT(JM-' JT)nFimp, (18) nTAp = -(1+ e)nTp. (19) Therefore, if the magnitude is 1, the following relation is obtained: nT(JM-lJT)nFt = 1 (n E SE\"). (20) Consequently, the smallest axis in Fig. 2 is the preferable direction of impact reduction and this impact geometry has clear physical meaning as can be seen in the following examples. 3.3 Numerical example As shown in Fig.3, the end-effector is located at (O.O70.4)m and the pre-impact velocity to the normal direction of environment is about 0.24m/s. Then, for several task directions, impact forces are generated and depicted in Fig.4. Fkom this figure, we can find that the proposed normalized impact geometry agrees with physical intuition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003977_s12213-008-0010-1-Figure16-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003977_s12213-008-0010-1-Figure16-1.png",
        "caption": "Fig. 16 Structure of the micropump",
        "texts": [
            " The performance of the two- axial orthogonal microrobot is shown in Table 2. The volume of the two-axial orthogonal microrobot is tenth part of that of a typical conventional manipulator. We could arrange at least five robots simultaneously on a table of a conventional inverted microscope, although we could set up only two conventional manipulators to a conventional inverted microscope. 4 Cell processing organized by three orthogonal microrobots 4.1 Micropump We have developed a micropump driven by the piezoelectric actuator as shown in Fig. 16. The sequence of this micropump is very simple. The piezoelectric actuator pushes and pulls the liquid inside the silicon tube as depicted in Fig. 17. Table 3 shows the typical performance of the micropump. This tiny pump is so small and light that the orthogonal microrobot can carry. In several experiments, we have checked this tiny pump pushes 50\u00b10.5 nl when the inner diameter of the glass pipette is 15 \u03bcm and input voltage to the piezoelectric actuator is 30 V. This micropump can hold an egg cell with a diameter of 100 \u03bcm by decreasing the input voltage of piezoelectric actuator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000246_bf00312219-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000246_bf00312219-Figure9-1.png",
        "caption": "Fig. 9a-i. Functional model of the pleural wing joint if the first subunit of the tergo-pleural muscle is not active; the nob stands in position 3 (a-e), the angle ~ between the pleural wall and the insertion region of the first subunit is not increased, and the head of the pleural wing joint is not turned outwards (d-f > I); b, e, h downstroke; the tooth of the ventral radial rein lies in front of the joint, e, f, i downstroke; the tooth lies behind the joint; for the component parts see Fig. 8",
        "texts": [
            " 7 b 1 + 2) or back by the antagonistic contraction of pterale III muscle I (Fig. 7 III 1) around the vertical axis of pterale II (Fig. 7 pt II). The positions A, B and C are adjusted by the relative strength of the contraction of basal muscles 1 and 2 and antagonistic pterale III muscle 1. During the first half of downstroke the groove of the tooth connects with one of the peaks of the pleural wing joint. Diagrams of the functional movements of the gearbox are shown in Figs. 8-10. The operational parts of the wing joint and thoracic structures are shown in Fig. 8. In Fig. 9 the first subunit of the tergo-pleural muscle is not contracted. In Fig. 10 the first subunit is active and the tooth has been moved so that its groove connects with one of the peaks. The first and second subunit of the tergo-pleural muscle act as a tension muscle, supporting pleuro-sternal muscle 1. The two subunits put the pleural wall under additional tension (cf. Heide 1971) when the gears are in action. Contraction of the first subunit pulls its kidney-shaped insertion region (Fig. 8 ir) inwards; the nob (n) on the pulling wire (pw) is puUed from position 3 (Fig. 8 3) to position 5 (Fig. 8 5) on a ruler (ru). The angle between the pleural wall (PO and this insertion region (ir) increases [see Figs. 9 a (wing up), b, c (wing down); 10a, b, c, arrow (wing down)]. This inward movement of the insertion region also turns the V-shaped stem of the pleural wing joint with the gearbox (Fig. 8 g l -3) outwards (Figs. 9, 10, d, e, f, > 1). Figure 9 g-i shows the two possible ways of interaction of the tooth if the gears are not activated: (1) during flight the tooth moves into the anterior groove described above (Fig. 9h); (2) it lies behind the gearbox of the pleural wing joint (Fig. 9i). This position is used when the indirect flight muscles are active and the wings are not coupled to the wing-base-driving sclerites (Nachtigall 1968) or when the wing lies in the resting position (Fig. 4a). Figure 10g-i shows the different positions of the wing leading edge when the groove of the tooth connects with one of the peaks of the pleural wing joint (Fig. 4b-d). When the tergo-pleural muscle is not active during flight, the wing base moves up and down over the turning axis (Fig. 5 ta), consisting of the anterior and posterior turning point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002307_1.2406105-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002307_1.2406105-Figure10-1.png",
        "caption": "Fig. 10 The involute gear hob after been reground",
        "texts": [
            " Usually, it is recom- ended to assign the actual value of the hob-setting angle h ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ash equal to the pitch helix angle h of the hob. As was proved in our earlier work 14 , in order to satisfy the equality h= h this conditions is the best possible the actual value of the hob-setting angle is required to be computed from the equation tan h = m \u00b7 Nh do.h \u2212 2 \u00b7 1.25 \u00b7 m \u2212 do.h 2 \u2212 m2Nh 2 18 Here do.h designates reduction of the hob outside diameter do.h due to resharpening of the worn gear hob Fig. 10 . Figure 10 yields a very simple formula for computation of do.h= do.h new \u2212do.h worn . The idea of the hob-setting angle can be traced back to the publication by Buckingham 11 . As the vectors A, B, and C are located within the common lateral surface of the auxiliary rack R, the following identity A B \u00b7C 0 is observed. The last expression yields a determinant cos h 0 sin h sin n sin h \u2212 cos n \u2212 sin n cos h \u2212 cos r tan \u2212 cos r \u2212 sin r cos = 0 19 After exploding the determinant, and after the necessary formulae transformations are performed, one can come up with the equation of two unknowns, namely of r and ",
            "url=/data/journals/jmdedb/27844/ on 05/12/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use o c g p o g c i n o t h n w t = n o t = H i l t c n a s m c g = F t J Downloaded Fr f proper surface generating 10 . Pitch diameter of the new hob, of the completely worn hob ould not be used for computation of parameters of design of the ear hob. For accurate computations, it is recommended to use itch diameter of the partly worn gear hob that correlates with utside diameter of the cutting tool. Outside diameter of the new ear hob is equal to do.h Fig. 10 , while outside diameter of the ompletely worn gear hob could be computed from the equation do.h\u2212 do.h . For computation of the outside diameter reduction do.h, the following approximate equation do.h 2 \u00b7 L \u00b7 tan rh = 5.585 \u00b7 tan rh nh 25 s derived. Here it is designated that L is the distance between two eighboring hob teeth that is measured along the helix on the utside cylinder of the hob Fig. 10 ; rh is clearance angle at the op cutting edge of the hob tooth; and nh is the effective number of ob teeth. For involute hobs with straight slots, nh is always an integer umber, and it is always equal to the actual hob teeth number nh a hich is usually in the range of nh a =8 16 because of this, he distance L can be computed from the equation L \u00b7do.h /nh a . For gear hobs with helical slots, the effective hob teeth number h is always a number with fractions. Moreover, the actual value f nh depends upon the hand of helix of slots"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003092_20080706-5-kr-1001.02044-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003092_20080706-5-kr-1001.02044-Figure3-1.png",
        "caption": "Fig. 3 Model of steering mechanism with EPS",
        "texts": [
            " This study investigates the algorithms of EPS as follows: Assistance control, based on steering torque input value Damping compensation, based on the response of steering angle and vehicle state variables. The control block of EPS is shown as Fig. 5. The assistance control is based on steering torque sensor signal which represents the driver\u2019s steering input. The basic assistance torque value is proportional to the input steering torque, which can be described as: KATm TkT = (11) where ATk denotes the assistance coefficient, KT the torque sensor value. According to Fig. 3 and equation (6): )( fsK NKT \u03b4\u03b8 \u2212= (12) For emergency maneuver situations, extra assistance is needed to achieve higher vehicle response. So assistance torque value proportional to the steering torque derivative value is also applied, which can be described as: KATdm TkT &= (13) where ATdk denotes the assistance coefficient Assistance torque value of (11) and (13) are called as proportional and derivative control respectively. The aim of damping compensation control is to solve damping problem that affects steering stability and steering feel in high speed maneuver situations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003007_6.2006-6147-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003007_6.2006-6147-Figure3-1.png",
        "caption": "Figure 3. Rotor system response to directional pedals.",
        "texts": [
            " Directional control is achieved with the directional pedals by imparting equal but opposite (i.e., differential) lateral cyclic pitch to the forward and rear rotor blades respectively; thus causing the Tip Path Plane (TPP) of each rotor to tilt in opposite directions. For example, moving the right pedal forward causes the forward rotor TPP to tilt to the right, whereas the rear rotor TPP will tilt to the left, resulting in a clockwise directional moment about the center of gravity as illustrated in Figure 3. Conversely, a left pedal input causes a counter-clockwise directional moment. Lateral control is achieved by applying equal lateral cyclic pitch to the blades with the cyclic control stick. Moving the cyclic control stick to the left results in both rotors\u2019 TPP tilting to the left as illustrated in Figure 4. Conversely, a right cyclic input tilts both rotors\u2019 TPP to the right. Th h the cyclic control stick using Differential Collective Pitch (DCP); whereby the pitch of the forward and rear rotor blades are all collectively changed equally yet in the opposite direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003234_07ias.2007.328-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003234_07ias.2007.328-Figure3-1.png",
        "caption": "Figure 3. Cross section of a PM BLDC motor.",
        "texts": [
            " Referring to (6), the voltage equation of phase a is )()( dt diL dt diL dt diLirv c ac b ab a aaaaa +++= arc ac b ab a aa epi d dLi d dLi d dL ++++ \u03c9 \u03b8\u03b8\u03b8 )( (17) By defining that )( dt diL dt diLv c ac b abam += rc ac b ab a aa pi d dLi d dLi d dL \u03c9 \u03b8\u03b8\u03b8 )( +++ (18) one has aam a aaaaa ev dt diLirv +++= )( (19) a a aaaaamaa e dt diLirvvv ++=\u2212=\u2032 )( (20) Similarly, v\u2032b and v\u2032c are defined. According to (1)-(16), a complete Matlab/Simulink-based phase variable model is built as shown in Fig. 2, where vam, vbm and vcm, va, vb and vc, v\u2032a, v\u2032b and v\u2032c can be obtained from Matlab functions based on (17)-(20). The rest of work is similar to the modeling of a conventional DC motor, so the proposed model can be easily realized in the Simulink environment. III. PERFORMANCE SIMULATION OF A BLDC MOTOR Fig. 3 shows the magnetically relevant parts of the PM BLDC motor prototype [7-8]. The laminated stator has 12 slots, in which the three phase single-layer windings are placed (not shown for clarity). The rotor core and shaft are made of solid mild steel, and four pieces of NdFeB PMs are mounted and bound on the surface of the rotor. The stator core has an inner diameter of 38 mm, outer diameter of 76 mm, and axial length of 38 mm. The main air gap length and the height of PMs along the radial magnetization direction are chosen as 1 mm and 2.5 mm, respectively. The motor is designed to deliver an output torque of 1.0 Nm at a speed of not less than 5000 rev/min. Fig. 4 illustrates the plot of magnetic flux density vectors at no-load at \u03b8=0o, i.e. the rotor position shown in Fig. 3. From the no-load field distribution, the PM flux (defined as the flux of one coil produced by the rotor PMs), back emf of one phase winding, and cogging torque can be determined. The curves of these parameters against the rotor angular position or time can be obtained by a series of magnetic field FEAs at different rotor positions. Fig. 5 shows the no-load flux linking a coil (two coils form a phase winding) at different rotor positions. By applying the discrete Fourier transform, the magnitude of the fundamental of the coil flux was calculated as \u03c61=0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001153_analsci.6.541-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001153_analsci.6.541-Figure2-1.png",
        "caption": "Fig. 2 Potential change DE vs. ethanol concentration. Solid lines (A): calculated according to Eq. (6); the ratio of",
        "texts": [
            "4 542 The flow-injection apparatus5 consisted of a peristaltic pump (Model Minipuls 2, Gilson Inc.), a 6-way valve (HPV6, Gasukuro-Kogyo) with a loop for sample injection, a flow-through type ORP (oxidation-reduction potential) detector (which has a platinum-plated ORP electrode and a silver/ silver chloride reference electrode (Denki Kagaku Keiki, Co.) (DKK)), and a potentiometer (Model IOC-10, (DKK)) for measuring the potentials of the ORP electrode. The manifold was constructed with Teflon tubing (0.5 mm i.d.) throughout. The gas-diffusion separation unit is the same as that shown in Fig. 2 in a previous report4, except for the membrane. The gas-diffusion separation unit comprises two Daiflon blocks furnished with a shallow groove (37 mm long, 3 mm wide, 0.5 mm deep) and separated by the membrane, which allows the transfer of ethanol from a stream of the carrier water (C.S.) to a stream of dichromate solution (R.S.1) containing sulfuric acid. The microporous PTFE membranes used were 50 \u00b5m thick and had pore sizes of 0.1 \u00b5m -0.8 \u00b5m (Sumitomo Denko Co., Ltd.). Standard procedure The FIA system used is shown in Fig",
            " (9) is larger than 103, which means the 6[Cr2072-]o/([Fe2+]o-6[Cr20,2-]o)=2.0. [Cr20,2-]o and [Fe2+]o are assumed to be 0.015 M and 0.135 M, respectively. Solid lines (B) and (C): calculated according to Eq. (12). The values of kt: 100 for (B); 10 for (C). Open circles are observed values. Concentrations of Cr2072- and H2SO4 in the R.S.1 are 0.03 M and 8 M, respectively. Concentration of Fe2+ in the R.S.2, 0.135 M; length of R.C.1, 18 m, temperature of R.C.1, 60\u00b0C; sample volume, 1.66 ml. completion of the reaction (1). Curve (A) in Fig. 2 shows the relationship between DE and [C2H5OH]o calculated by using the initial concentrations of [Cr2072-]o 0.015 M and [Fe2+]o 0.135 M, which provide a ratio of 2.0. These initial concentrations are chosen for the standard analytical procedure. In addition, coefficient p is assumed to be unity in the calculation. Curve (A) has a linear response range up to ca. 1.OX 10-2 M C2H5OH, which corresponds to 5.72X10.2% (v/ v). The sensitivity for curve (A) is 3.2X103 (mV/ M). For ratios below about 1 or above 3, the curves become convex or concave. On the other hand, when reaction (1) does not come to completion, the relationship between DE and [C2H5OH]o can be calculated from Eq. (12). Curves (B) and (C) in Fig. 2 show the relations for the values of kt in Eq. (9) of 100 and 10, respectively. These curves are slightly convex. In fact, these relations for the latter were observed under the experimental condition of a short reaction time. This situation was found to hold even when the permeation of all ethanol in the sample does not come to completion, i.e., p<l, as judged from Eq. (12). Results and Discussion Sensitivity-governing factors in the f low system with the gas d ffusion unit The sensitivity of the proposed method depends on 544 ANALYTICAL SCIENCES AUGUST 1990, VOL",
            " 1 Temperature of the the sensitivity gas-diffusion separation unit the concentrations and acidity of reagent solutions (Cr20,2- and Fe2+), the reaction time and temperature. Among the sensitivity-determining factors, the concentration of sulfuric acid in R.S.1, the reaction time and temperature of R.C.1 are important for reaction (1). The peak heights increased markedly with a higher concentration of sulfuric acid, a higher reaction tem- perature and a longer reaction time. The results indicated by the open circles in Fig. 2 were observed by using an FIA system which took the place of the gasdiffusion unit in Fig. 1. The results showed that the calculated curve (A) could be confirmed by experiments carried out under the conditions indicated in Fig. 2. The solid lines in Fig. 3 show the observed relationships between the peak heights and the ethanol concentrations for three different lengths of R.C.1 in the system of Fig. 1. Reaction coils of 1, 2.5 and 5 m length provide reaction times of 36, 90 and 180 s, respectively. These periods are short for completion of reaction (1). The dotted lines in Fig. 3 were calculated from Eqs. (9) and (12) for the different values of kt in Eq. (9). As can be seen, the observed peak heights agree well with the calculated curves, even though a small deviation between them exists"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001461_03091908109009364-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001461_03091908109009364-Figure4-1.png",
        "caption": "Figure 4. Electrode assembly for Roche Lactate Analyser 640 (after Soutter et a1 [33u.",
        "texts": [],
        "surrounding_texts": [
            "procedures involved may themselves be responsible for substantial initial losses in enzyme activity. One of the simplest and mildest procedures is to adsorb enzyme physically on to a solid support such as alumina or carbon. Enzyme loading here tends to be low, and there is also the attendent possibility of ready desorption with use. Physical entrapment in a gel matrix such as polyacrylamide has proved a successful and widely used technique. This gives non-rigid membranes that are ideal for enzyme electrodes. To attain permanent attachment of an enzyme a covalent bond is necessary ie chemical immobilisation. Usually this entails more vigorous reaction conditions which lead to a greater initial loss in enzyme activity. A procedure that is frequently used is to crosslink chemically to an inert protein such as albumin; glutaraidehyde is a valuable bifunctional reagent for this. In future increasing utilisation is likely to be made of covalent attachment to water-insoluble supports eg glass and nylon. Whatever the immobilisation procedure, a loss of activity during use is almost inevitable. With the less robust enzymes this can be a serious problem, necessitating renewal of enzyme membranes within hours rather than days.\nWhen the electrode is brought intocontact with the substrate, a complex concentration profile develops within the enzyme layer which is a function of both diffusion and reaction processes. According to Fick\u2019s Second Law of diffusion:\n6 2 (PI 6 t 6 xz -- - Dp6 (P)\nWhere P = product D p = diffusion coefficient of the product t = time x = distance from the outer surface of the enzyme layer\nMichaelis-Menten Kinetics gives reaction velocity as\n6 (P) Vm (S) -- - 6 t K m + ( S )\nWhere V, = maximum rate of the reaction S = substrate K , = Michaelis constant.\nDiffusion and reaction have opposing effects on product concentration, and when\n6- P v, (S) Dp- = - ~\n6 x ? K , + (S)\nAgIAgCI Cat hod e.\nPt Anode\nEnzyme\nFigure 1 . An amperometric enzyme electrode based on the Clark sensor.\nthis reaches a constant value. The important consequence is that a n enzyme electrode is capable of a steady-state response. One simplified approach to events within the enzyme membrane was used by Bowers and Carr [8]. Neglecting external mass transfer and substrate partitioning between enzyme and solution these workers found that at equilibrium\nwhere D, is the substrate diffusion coefficient and (S),,,,<<K,. This simple relation applies to potentiometric electrodes with very active or thick enzyme membranes. For (s)b,,,>> K,, however, response is independent of bulk substrate concentration. With amperometric electrodes, the situation is further complicated as the product isconsumed a t the underlying sensor. This distorts the concentration profile in the enzyme layer, with the result that the linear range is extended to higher substrate levels. The amount of enzyme used also affects response [I]. A larger response is obtained with increasing enzyme concentration until a plateau value is reached and further increase has no effect. Any excess provides a reserve of enzyme, however, which prolongs the electrode operational life and also reduces the effects of enzyme inhibitors that may be present in solution. Response times are shortened by membranes with higher enzyme concentrations.\nA thin enzyme layer also makes for a faster response. Variables such as temperature, pH, buffer and ionic strength also affect performance through their influence on the enzyme reaction.\nGlucose electrodes The first enzyme electrode, proposed by Clark and Lyons [3], was for the measurement of blood glucose. This utilised a glucose oxidase-catalysed reaction:\nglucose glucose + O2 + H20 + H2 02 + gluconic acid\noxidase\nA thin layer of enzyme in solution was trapped between dialysis membranes and held over either a glass pH electrode or an oxygen electrode. They give few details, but the response of the pH-based electrode was found to be related to glucose concentration, buffer strength, flow rate, temperature and pH. Thus at a flow rate of 3 ml/min a 100 mg/l glucose solution produced a pH change of 1. Nilsson et al [9] found a ten minute response time for their pH-based glucose electrode making it too sluggish for practical use.\nUpdike and Hicks [ 101 used acrylamide gel-entrapped glucose oxidase over a dual cathode amperometric oxygen sensor. Active enzyme was placed over one cathode and heat-denatured enzyme over the other. By measuring the differential output from the\nFigure 2. A dual cathode amperometric electrode (after Updike and Hicks [ IOU.\n294 Journal of Medical Engineering & Technology\nJ M\ned E\nng T\nec hn\nol D\now nl\noa de\nd fr\nom in\nfo rm\nah ea\nlth ca\nre .c\nom b\ny M\ncM as\nte r\nU ni\nve rs\nity o\nn 02\n/1 2/ 15 Fo r pe rs on al u se o nl y.",
            "electrodes they were able to determine glucose concentration independently of background oxygen tension. Calibration curves with whole blood, plasma and aqueous solutions were similar. In order to reduce the effect of flow on electrode response, they used enzyme restricted to within a small area of the electrode surface to minimise substrate consumption. This reduced the difference between response in stirred and stagnant solutions to under 5%; any implanted electrode would have to have a response that was flow-independent. It was thought that their type of electrode could be used in glucose monitoring.\nBessman and Schultz [ l l ] , however, did not consider longterm monitoring to be feasible with an implanted version of this electrode. In their view the gas-permeable membrane would loosen with time and give rise to unstable and noisy responses. Even in the case of new electrodes, pressure changes from simple body movements were thought sufficient to cause signal oscillations. Instead their approach was to use a galvanic sensor with the gas-permeable membrane a small distance from the cathode. This reduced any impact that membrane distortion had on the signal, and there was the added advantage that current generation in the presence of oxygen does not require an externally applied voltage. The glucose oxidase they used was \u2018cross-linked in a cloth matrix and response was sluggish, requiring 6-7 minutes for 90% completion as compared with under three minutes for a 98% response with Updike and Hicks\u2019 electrode. Their cross-linked enzyme, nevertheless, proved highly resistant to degradation in body fluids, and Layne et a1 [ 121 found full retention of activity after three months of implantation in rabbits. This group, however, only carried out short-term (3 hr) extracorporeal monitoring of glucose. Blood was sampled from rabbits a t the rate of 2 ml/hr, and after dilution by anticoagulant passed through flow channels created over a twin galvanic electrode. They regarded lag times of up to 10 minutes as acceptable, but some of their electrodes required as much as 30 minutes for a steady response. Background oxygen affected the enzymic reaction; changes in the state of oxygenation produced altered readings despite the use of a blank electrode. The oxygen level was, in fact, maintained with a n anaesthetic machine. The electrode, furthermore, responded to glucose only in the plasma component of whole blood, making it necessary to allow for the haematocrit in any dilution. Of importance to future intracorporeal use was the finding that in undiluted plasma glucose levels were underestimated, and at high flow rates reduced oxygen currents were produced, the likely explanation being sample viscosity. It would appear therefore that even galvanic electrodes could not be used intracorporeally without a major modification in design.\nMeasurement of blood glucose in samples with a variable oxygen content was attempted by Romette et a1 [ 131. They used a single Clark electrode with gelatin-immobilised glucose oxidase. Oxygen is twenty times more soluble in gelatin than in aqueous solution, and during a single estimation only oxygen within the enzyme layer was utilised. The electrode, however, was used in\nthe kinetic mode where the initial slope of the electrode response was determined. Between analyses the electrode had to be exposed to air to recharge the enzyme layer with oxygen. As it stands, this electrode could not be used for continuous monitoring, but a gelatin membrane might usefully be employed in the above-mentioned twin-electrode systems. If the sample is diluted sufficiently in a standard buffer, then it is possible to use a single electrode. Thus Sokol et a1 [I41 made reliable kinetic mode measurements using an electrode with enzyme directly attached to the gas-permeable membrane. Even in vivo monitoring has been performed with this type of electrode [15]. The overall apparatus was cumbersome as sampling had to be intermittent and blood delivered to the electrode via a complicated system of valves, giving a glucose reading every 150 seconds.\nAn alternative to oxygen tried by Williams et al [16], as an electron acceptor, is benzoquinone:\nglucose gluconic acid f hydroquinone oxidase > glucose + benzoquinone + H20\nGlucose oxidase was used entrapped within a porous or gel layer covered by a dialysis membrane. Hydroquinone from the enzyme reaction was measured amperometrically at a platinum working electrode polarised at 0.4 V (vs sce):\nhydroquinone Pt > quinone + 2H\u2019 t 2e\nThough correction for background current was required, it was at least possible to optimise the concentration of the electron acceptor.\nHydrogen peroxide generated in the glucose oxidase-catalysed reaction has also been used to measure glucose by electrode [I 71. Background variation in oxygen had little effect on response according to Clark and Clark [ 181 who used such an electrode to make continuous glucose measurements on the surface of mouse brain. The electrode responded within 10 seconds of an intravenous injection of insulin and there was no effect of oxygen breathing in the animal. There was a small basal current thought to be due to other electroactive species and to the residual output of the electrode itself.\nA hydrogen peroxide-based glucose electrode is now commercially available for plasma and whole blood [ 19,201 (Yellow Springs Instrument Company, Yellow Springs, Ohio). This operates in the kinetic mode and functions as a discrete analyser. Enzyme is crosslinked with glutaraldehyde and protected from cells and protein in blood by an outer polycarbonate membrane. A low molecular weight cut-off membrane made of cellulose acetate prevents electrochemical interference at the underlying platinum electrode. Durin\nVolume 5 No. 6 November 1981 295\nJ M\ned E\nng T\nec hn\nol D\now nl\noa de\nd fr\nom in\nfo rm\nah ea\nlth ca\nre .c\nom b\ny M\ncM as\nte r\nU ni\nve rs\nity o\nn 02\n/1 2/ 15 Fo r pe rs on al u se o nl y.",
            "measurements an air-driven diaphragm stirs the sample, and serves also to maintain a supply of oxygen for the enzyme reaction.\nEquilibrium measurements with this electrode enabled Grooms et a11211 to monitorglucose continuously in normal and diabetic animals. A hydrogen peroxide-based glucose electrode is available for clinical monitoring (Miles Laboratories, Elkhart, Indiana) [22] and uses a similar multi-layer enzyme membrane. This device is also extracorporeal; venous blood is sampled continuously (2 ml/hr) and passed through the electrode flow cell after dilution in isotonic buffer. The lag time between the withdrawal of blood and the analysis is about three minutes. Clarke and Santiago [23] observed that the electrode itself was capable of a 90% response in under one minute. Membranes, on average, had to be replaced after 20 hours of continuous monitoring, though in some cases they remained functional for up to 140 hours of accumulated use. The drift in electrode response averaged 2% per hour while sensitivity remained unchanged. The electrode forms the sensor component of a complete artificial biofeedback system used for short-term control of diabetics. Other parts of the system are a minicomputer and infusion pumps. The arrangement allows a programmed dose of insulin (or glucose) to be delivered intravenously in response t o dynamic blood glucose changes.\nMicro glucose electrodes which could be inserted into soft tissue were constructed by Silver [24]. These comprised glassinsulated platinum with the enzyme present as a n adsorbed layer on the platinum. Response times down to two seconds were noted and glucose was measurable within the physiological range. A micro electrode such as this would have minimal dependence on either sample flow-rate or viscosity.\nUrea electrodes Hydrolysis of urea by urease takes place according to:\nurea + 2H20 + H + urease> 2 NH4+ + HCO,\nand this enzyme has been the basis of all urea electrodes. Guilbault and Hrabankova [25] used a urease-coated NHJ' glass electrode to analyse plasma and urine. The glass electrode lacked selectivity, and it proved necessary to eliminate Na' and Kt interference by adding ion exchange resin to samples and making measurements against an uncoated NH4' electrode. This complicates the approach to analysis by electrode. An NH4+ electrode, based on the antibiotic nonactin [26], had better selectivity and a urea electrode of this type has been employed in a clinical analyser (Photovolt corporation, New York).\nThough more sluggish, gas sensors have an excellent selectivity with regard to interferent ions. Mascini and Guilbault 1271 in this way measured urea in blood sera with an NH,-gas sensor. They used thin (Teflon)gas membranes with thin, highly active enzyme layers and were able to bring response times down to two minutes. Measurements required a compromise choice of p H between the high pH required for effective conversion of NH4+ to NHI and the optimum for the enzyme reaction. In the air-gap electrode of Ruzicka and Hansen [28] NH,diffuses across a space rather than through a membrane, and a higher speed of response may be obtained. Guilbault and Tarp [29] determined urea with an air-gap electrode, but enzyme had to be held at the base of the electrode chamber. Response depended largely on the speed of the reaction, requiring 3-4 minutes for completion. Immobilisation on a magnetic stirrer brought this down to 2-3 minutes [30]\nThe HCOI- generated by urease may be detected at a COZ gas sensor. Aqueous urea solutions have been measured with this type of electrode [31], but for blood a second COz electrode would be required to allow for background CO2 variation. variation.\nLactate electrodes Blood lactate measurement is a useful indicator in a variety of clinical situations such as shock and hypoxia. The first electrode for measuring lactate was devised by Williams et al [ 161 with yeast\nlactate dehydrogenase (cytochrome b2) held over a platinum electrode polarised at 0.4 V (vs sce):\nLactate i- 2 Fe ( CN)6-' -> pyruvate + 2 Fe (CN)L4 + 2H +\n2 Fe(CN)L4 Pt > 2 Fe (CN)6-3 + 2e\nThe ferricyanide cofactor used here had to be added to the assay so!utions, but such a n electrode enabled Durliat et a1 [32] to measure lactate in blood without any further sample preparation. Initially the working electrode was polarised at 0.25 V (vs sce), but later -0.08 V against an inert platinum electrode was found to be sufficient. Under their measurement conditions signal current reached maximum values that were linearly related to lactate concentration. A discrete analyser suitable for bedside use has now been marketed (Roche-Bioelectronics, Basel). The electrode operates in the kinetic mode, produces a result in 2-3 minutes and enables blood lactate measurements up to a concentration of 12 mmol/l[33]. Durliat et a1 [34] have proposed a continuous flow arrangement for extracorporeal lactate monitoring. This had a n unacceptably high requirement for blood (100 ml/hr), but they subsequently developed a reagentless electrode for intracorporeal use [35]. The enzyme was deployed without cofactor so' direct electron transfer now occurred between enzyme and electrode metal. This enabled change in lactate concentration to be followed directly a t the coronary sinus of a dog that had been subjected to an injection of noradrenaline. Results are given in arbitrary units for they were not able to calibrate the electrode under the exact flow conditions found at the coronary sinus. Another electrode was devised using a large molecular weight cofactor (ferricytochrome c) retained in the enzyme layer and this also enabled reagentless measurement. However, the cofactor had t o be electrochemically regenerated after each analysis and this precludes continuous measurement.\nOther electrodes There are numerous oxidoreductase enzymes requiring oxygen as a n electron acceptor. According to Clark [36] those which are sufficiently active, apart from glucose oxidase, are the oxidases for galactose, uric acid and xanthine. Taylor et a1 [37], for example, determined galactose in plasma and whole blood with a galactose oxidase membrane held over a hydrogen peroxide sensor. Measurement required 40 seconds, and response was linear up to a t least 5 g/l galactose. Dihydroxyacetone, glycerol and lactose are also substrates for the enzyme, and with this electrode Grooms et al [21] were able to follow blood levels during loading tests with these substances in animals. Uric acid has been measured with urate oxidase immobilised over an oxygen electrode [38]. Interference from other oxygenconsuming oxidisable species was sufficiently small to enable reliable estimation of both serum and urine. A hydrogen peroxide sensor was not used since free peroxide is not produced in the reaction. With cholesterol oxidase over an oxygen sensor, Satoh et al [39] measured free cholesterol in serum. They found that cholesterol did not penetrate the enzyme layer, but that a significant reaction took place at its surface. Improved sensitivity was achieved with a hydrogen peroxide-based system [40], though compensation for background interference was necessary.\nCreatininase catalyses the conversion of creatinine to N-methylhydantoin and NH3. Meyerhoff and Rechnitz [41] used the enzyme with a n NH,-gas sensor to determine levels in serum and urine. Sensitivity was less in serum owing to high viscosity, thus it was necessary to dilute the sample. For urine, NH, interference had to be eliminated with a cation exchange resin.\nOther electrodes based on NH,/NHd' sensors include those for 5'-adenosine monophosphate, and several aminoacids [4]. These have yet t o be tried in biological samples.\nSimultaneous use of two or more enzymes can extend the analytical range of enzyme electrodes. Sucrose in blood, for example, has been measured with a glucose electrode during an intravenous loading dose in a dog [21]. Invertase and mutarotase\n296 Journal of Medical Engineering & Technology\nJ M\ned E\nng T\nec hn\nol D\now nl\noa de\nd fr\nom in\nfo rm\nah ea\nlth ca\nre .c\nom b\ny M\ncM as\nte r\nU ni\nve rs\nity o\nn 02\n/1 2/ 15 Fo r pe rs on al u se o nl y."
        ]
    },
    {
        "image_filename": "designv11_28_0001905_j.aca.2004.09.021-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001905_j.aca.2004.09.021-Figure1-1.png",
        "caption": "Fig. 1. (a) PDMS plate with Y-shape microchannels and temperature sensor. (b) PDMS plate with Peltier element.",
        "texts": [
            " After engraving PDMS plate, there are carbon particles remaining in the obtained microchannels. They may be carefully removed using small pincers or blunt-end needle. This laser engraving technique is good enough to make test systems for the method optimization or reaction preliminary studies. Surface roughness does not interfere test measurements. It even helps in mixing reagent and sample much faster. For the final system the microchannels can also be made with a typical mould technique. The Peltier element drowned in the second plate (Fig. 1b) was used to control temperature of the microreactor zone. Stable reaction zone should be maintained to make the results liable and repeatable. Spontaneous adhesion of two prepared plates [12] was not strong enough to compensate the fluid pressure generated by the peristaltic pump and the leakage was observed. Thus, these two plates were sealed using a plasma bonding technique, what made the microreactor leakproof. The total calculated volume of the microreactor is 3.7 l. 2.3. Apparatus s a t t s p o a 2 w p s p c t ",
            " The alkaline icrate reagent was prepared daily by mixing picric acid and odium hydroxide solutions with a ratio 1:1. Post-dialysate nd urine samples were provided by hospitals. The samples ere analysed in clinical laboratory (creatinine determinaion using a standard clinical analyzer was performed), and hen creatinine determination was carried out in flow-through icrosystem on the same day when they were collected. .2. Microsystem design The microreactor contains two plates made of oly(dimethylsiloxane) (PDMS, Dow Corning Sylgard 84). First plate (Fig. 1a) was finely engraved with the elp of a laser to obtain Y-microchannel with 26 cm long A peristaltic pump Miniplus3 Gilson was used to pump olutions into the microsystem. Spectrophotometric measurements were performed using commercial optical flow cell positioned in a spectrophoometer (Specord S10, Carl Zeiss). The Peltier element was connected to a temperature conroller made in our laboratory. The controller utilized a typical emiconductor diode as a temperature sensor. The diode was laced over the microchannel (see Fig. 1a) in the process f PDMS plate fabrication. The whole temperature system llowed to maintain temperature with \u00b11 \u25e6C accuracy. .4. Measurements Calibration solutions (or clinical samples) and picric acid ere pumped simultaneously into the microreactor using a eristaltic pump with the tubings diameter of 0.05 mm intalled on the same pump head. In this way, solutions were umped with the same flow rate and their volume ratio was onstant. In the reactor\u2019s meander, a complexing reaction ook place. The detection was performed in an optical flow cell (8 l volume) with the use of classical spectrophotometer (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000327_01445150310501208-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000327_01445150310501208-Figure5-1.png",
        "caption": "Figure 5 Conformal (left) and traditional (right) cooling channel geometries employed in cooling channel efficiency evaluation",
        "texts": [
            " In conclusion, EDM of laminated inserts should, if at all possible, be avoided, which, for brazed inserts, necessitates the use of an annealing process to reduce the material hardness, thus permitting conventional CNC machining. This test was designed to enable an evaluation between conformal cooling and traditional cooling. A production tool with cooling problems in the runner system was chosen as it is typically the most affected area of a die in terms of wear, temperature, pressure etc. The conformal cooling channels were designed into an insert, following the runner system and biscuit area (Figure 5). FE moulding flow analysis of the design proved promising, showing improved cooling performance from the conformal cooled insert over that of the conventionally cooled system. Conformal cooling was found to offer a reduction in solidification time and hence increased production speed, indeed, the productivity of the die was improved by 11 per cent. However, both conformably cooled dies failed after a total of 450 components. The laminate insert failure was catastrophic due to de-lamination of an Rapid laminated die-cast tooling Gregory John Gibbons et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002559_tmag.2005.846213-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002559_tmag.2005.846213-Figure8-1.png",
        "caption": "Fig. 8. Distributions of nodal force of rotation direction F (z = 58 mm). (a) d = 0:0 mm. (b) d = 0:4 mm.",
        "texts": [
            " It is found that the force in the right part of the rotor is larger than the left part of that when the rotor is off-centered. Fig. 6 shows the characteristics of nodal force of radial direction and rotation direction on the node A. The fundamental frequency is 240 Hz. The cycle of waveform of nodal force is 90 . Fig. 7 shows the characteristics of nodal force of radial direction and rotation direction on the node B. In case of mm, there are mainly 12th and 24th harmonic components due to the slot of stator core. On the other hand, there are several harmonics components in case of mm. Fig. 8 shows the distributions of the nodal force of rotation direction . It is found that there are constantly nodal forces of rotation direction near the rotor of the off-center direction due to the off-center of the rotor. We analyzed the electromagnetic force of an IPM motor using the 3-D finite-element method. Consequently, the total force calculated by the nodal force method is almost the same as that calculated by the Maxwell stress tensor method. It was found that the average torque does not decrease though the torque ripple increases by the off-center"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002027_1.2179460-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002027_1.2179460-Figure6-1.png",
        "caption": "Fig. 6 Meshing co",
        "texts": [
            " The worm-gear angular misalignment occurs due to the manufacturing error of the planet worm-gear carrier and is reflected in the assembly as in Fig. 5. The ideal situation for four planet wormgears is that they are located symmetrically at a, b, c and d. While considering the angular misalignment , there are a number of possibilities in the assembly that the planet worm-gears are located away from their ideal locations. The latency errors impinge on meshing properties and load capacities of a toroidal drive. To study these errors, the coordinate frames between the planet worm-gear and the sun-worm is illustrated in Fig. 6. In the figure, a0 represents the theoretical center distance between the sun-worm and planet worm-gear, a is the center-distance offset, w the sun-worm lateral misalignment and the planet worm-gear angular misalignment. In the sun-worm system, the coordinate frame S1 o1 , i1 , j1 ,k1 is the reference frame of the sun-worm while not considering the error. The error-effect coordinate frame Sw ow , iw , jw ,kw is away from the coordinate frame S1 by shifting along the sun-worm axis by taking into account of the sun-worm lateral misalignment w",
            " The angular velocity vector of the planet worm-gear is 2= 2k2 = t21k2 , where t21 is the velocity ratio between the sun-worm to the planet worm-gear and is given by t21= 2 / 1= 1 / 2. Considering the angular velocity of the sun-worm is a unit vector as, 1=k1 =sin 2i2 +cos 2j2 , the first term of Eq. 9 can 2 1 r2 = 0 \u2212 t21 \u2212 cos 2 t21 0 sin 2 cos 2 \u2212 sin 2 0 x2 y2 z2 10 The latter two terms of Eq. 9 involve latency errors which are depicted by the error impinged center-distance vector as = o1 o2 = o1 o1 + o1o2 = a0 + a i1 \u2212 wk1 11 whose components are illustrated in Fig. 6. This center distance can be transformed to coordinate frame S2 by taking the transformation matrix integrated with latency errors in Eq. 6 . It follows that = a0 + a cos cos 2 \u2212 w sin 2 \u2212 a0 + a cos sin 2 \u2212 w cos 2 \u2212 a0 + a sin 12 Hence, the second term of Eq. 9 is obtained as 1 = 0 0 cos 2 0 0 \u2212 sin 2 \u2212 cos 2 sin 2 0 a0 + a cos cos 2 \u2212 w sin 2 \u2212 a0 + a cos sin 2 \u2212 w cos 2 \u2212 a0 + a sin 13 Taking derivative of the error impinged center distance in Eq. 12 gives the third term of Eq. 9 as d dt = \u2212 a0 + a t21 cos sin 2 \u2212 wt21 cos 2 \u2212 a0 + a t21 cos cos 2 + wt21 sin 2 0 14 In the derivative, the angular misalignment is constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000747_bf02458263-FigureI-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000747_bf02458263-FigureI-1.png",
        "caption": "Fig. I",
        "texts": [],
        "surrounding_texts": [
            "(i.e. microrotation vector). It is physically reasonable that lubricant liquid is regarded as micropolar fluid. In fact, the clearance in a bearing is so small that it may be comparable with the average grain or molecular size contained in non-Newtonian lubricant liquid. Moreover, in ordinary operating conditions, because of the mixed-up of both dirt and metal particle, the lubricant liquid could be considered as fluid suspension. Thus the micropolar model is a realistic and an acceptable model of lubricant liquid.\nTh'e early articles using the micropolar fluid theory to bearing are due to Allen and Kline00t, Green0 Jl and Cowin p21. Later, Shukla and Isa0S] proposed the generalized Reynolds equation of mieropolar fluid and used it to one dimensional slide bearing. Prakash and Sinhat~4J obtained the solution of journal bearing with infinite length and micropolar lubricant liquid. Tipeittsl considered the inner pressure distribution and friction characteristics of short bearing with micropolar lubricant liquid. In the present paper, we shall investigate the journal bearing of finite length with micropolar lubricant liquid.\nII. The Lubricant Equat ions of Micropolar Fluid\nThe field equations of micropolar fluid in vector form are\n0/9 Ot t-V.(pv)=O Dv } (~,+ 2/~)VV- v - 1 (2#+X)V \u2022 V \u2022 v+ ;('V \u2022 w-- v-F/+ PF = P--~\" T (2.1)\nDw ( a + f l +Y)VV 'W- - I~V XV X w + XV X V--2XW-t-pL = p j D t\nwhere 9 p is the mass density, v is the velocity vector, w is the microrotation vector, _/7 is the thermodynamic pressure, F is the body force of unit mass,/, is the body couple,j is the microinertia, ). and # are the viscosity coefficients ofthe classical fluid mechanics, X, a , fl and 3; are new material coefficients of micropolar fluid and D/Dt represents the material derivative. The constitutive equations of micropolar material are\nt , ,=(- - /7 + 2v,, ,)3, ,+( F --\"~-X1)(v.,'+vt,.) + X(Vt,.--e.,rw.) (2.2)\nm~ = aw, , ,~bz + flwk,: + ywl ,k (2.3)\nwhere tkl and mkl are the stress tensor and the couple stress tensor respertively. ~kt, is the permutation tensor, dr, is Kroneker delta. The index following a prime represents the partial derivative to spatial variable x k. For imcompressible fluid, ignoring body force and body couple, we havev-v=0,-F=0 and L = 0. Moreover, we may replace /7 by the fluid pressure F. Now consider the flow of thin lubricant layer in journal bearing and assume the velocity and microrotation have the following form:\nv=(u~, u2, us), w = ( w , , 0, ws) (2 .4)\nUsing the usual postulations for lubricant theory and ignoring infinitesimal quantities with high order we obtain the governing differential equations for lubricant flow\n1 . 8Zu, + #w3 8p = 0\nV x 2y \"1",
            "_ _ + ) OZu3 Owl Off 1 (2 , X ' - ~ ' - - Z Oy Oz = 0 2\n0 z t 0 3 C3tt I ^ _ _ , , e-~-ffa u, - x - ~ - - z x w ~ - ,\n8zw, 0% v--g-~-y~ + x - - ~ - - 2 x w , = 0\n( 2 . 5 a , b . c . d , e , f )\nnut Ouz Ous +W =~\nOp = 0 Oy\nFor the lubricant layer (Fig. 1) the ordinary boundary conditions are\ny = 0 : ul=Ul, uz=us=0 , w l = t ~\ny=h. u,=Uz, uz=Vz+U2-~x , us=0, t O 1 -~ - f l / da --~- 0\nwhere h represents the thickness of oil film, U L, the tangent velocity of surface l, U 2 and Y 2, the tangent and normal velocity of surface 2\nrespectively. Because p is independent of y, Eqs. (2.5a) and (2.5c) may be considered as ordinary differential equations with constant coefficients for u Z and w 3. According to the same reason, Eqs. (2.5b) and (2.5d) may also be considered as ordinary differential equations with constant coefficients for u 3 and w r Thus, the expressions for velocities u t, u 3 and microrotations w, w 3, as a result of the solutions of the above equations with boundary conditions (2.6) are\nU 1 - -\nN z (oh(my) - - 1) (ch(mh) - - 1) m [ sh(my)- - - sh(mh) ] }\nu I Op y' N~\" 3='-~ ---~-z ~ h ch(my) -- 1 m - s h ( m h ) 1 + Y\n(ch (my) -- 1) (eh (mh) -- 1 ) -- N' [ sh(mh) 3}\nD' . . . . . . + ~'~(my) h w , = - - { 2 ( I _ N . ) - (ca(my,--1) - s ~ [ 2.\n_ D t _ --1)] 1 8p 2 ( 1 - - N ' ) (ch(mh) 2g tgz y }\n. sh(my) [__~f ap D, -(oh (my) --1) \"l-~h(mh) \"Ox\" ms = 2(I_N z) Dl ] 1 #P\n-- 2 ( 1 _ N 2 ) ( c h ( m h ) - - l ) - 2t t /gx y\nI igP[fl_~z 2 N'h oh(my, - -17 1----~{ . Ox - m sh(mh) j + U ~ + y\nOp 0z\n(2.6)\n(2 .7)",
            "w here\nD r = ( l - - N 2 ) ( h Op / [ h N z ch(mh)- - I ]} 2 II Ox t- (Ut--U2) m sh(mh) \"\nD2= ( 1 - - N 2) h ap 2 t z Oz\nk 2 # + X / ' \\ ---~-] , m = - ~ -\nWe might also obtain u 2 from continuous Eq. (2.5 e). The quotations is omitted here. After the distribution of velocity is obtained, we may write the representation of flow flux as\n+ 1212- 6Nlh l + e h ( m h ) _] (2.8) sh(mh)\nQ,=II ufly = h Op l + c h ( m h ) / 12# Oz I h2 +121z-rNlh sh(mh) ]\nIntegrating continuous equations (2.5 e) along y orientation, we have\nO n Oh [ Ou, + Ou, ~ dy=__{__~_~__IQ utdy Vz+Uz-~ -=- - I i 'Ox Oz '\nOh 0 n - -U2~+-- -Oz lo u3dy)\nThen substituting u j and u 3 of (2.7) into (2.5 e) and considering V 2 to be time rate of h, i.e. Vz---- 0 h/Ot, we have\n0 ~ x ) OZp Oh Oh Ox ( G(x) +G(x)-o-~z2 =12-O-i-+6(U~+U2) Ox (2.9)\nwhere\nG(x) = h V hZ + ,2lZ_6Nlh l +eh(Nh/l)-] u L sh(Nh/l) _]\nEq. (2.9) is the lubricant Reynolds equation of micropolar fluid. When'N and I approach zero equation (2.9) is changed into the Reynolds equation of Newtonian fluid. Therefore, it is a generalization of the lubricant Reynolds equations in Newtonian fluid.\nIntroducing the dimensionless variables"
        ]
    },
    {
        "image_filename": "designv11_28_0000485_robot.2002.1014296-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000485_robot.2002.1014296-Figure9-1.png",
        "caption": "Figure 9: Graspable finger position regions for 3 fingers",
        "texts": [],
        "surrounding_texts": [
            "is met, the hypersphere is one of inscribed hyperspheres of the convex polyhedron (see Fig.G(b)).\nFor a convex polyhedron Vir or V$ formed by J hyperplanes, the number of inscribed hyperspheres for hyperplane combinations is JC(,+l). If the number of the hyperspheres satisfying eqs.(48)-(51) is N, the radius of the biggest inscribed hypersphere is given as\n(52) where, T I , ~ 2 , , rN represent the radiuses of the inscribed hyperspheres for hyperplane combinations.\nNrthermore, for the GFPR polyhedron, the biggest inscribed hyperspheres for Viv and V&.(q, r = 1, 2, ... ,m, q # r ) can be obtained. If the radiuses of these hyperspheres are given as rcmaxl, T c m a z , ***,rCmar&, the radius of the biggest inscribed hypersphere for GFPR is\n(53) The convex polyhedron containing the above hypersphere will be selected. If plural convex polyhedrons containing the biggest hypersphere with the same radius exist, it is need to compare their volumes further. 4.4 Volume of Convex Polyhedron\nThe volumes of convex polyhedrons can be obtained by the method expressed in [9].\nTo solve the volume for an nD convex polyhedron, at first, we must subdivide the nD convex polyhedron into simplexes, each of which can be given by its vertexes. For example, an nD simplex is given by the its vertexes as lull lu2, . , Then, its volume V, is\n= max (r1, rz, - * . , r ~ } ,\nrcma = max {TcmwIr r c m m 2 , ***,rcmaxfi}-\nkzi - IC = kza - Iijij If a nD convex polyhedron is subdivided into S sim-\nplexes, the volume of the polyhedron can be given as S - v = pa. (55)\nS=l\n5 Numerical Example We give a numerical example using the proposed ap-\nFor the object shown in Fig.7, the vertex positions proach to determine the Stable GFPR with 3 fingers. of the object with respect to CO are:\np7, 7.000 c o z = ~ . ~ ~ o ] , 2.000 y-q, 2.000 ro4=~.000~ 7.0 *\nThe direction vectors of the edges are:\nt l=[ - l :OOo] \u2019 tz=[O:OOO]\u2019 *=[ 0.704\u2019 t4=[ 0.00d *\nThe lengths of the edges are:\n0 000 1 000 -0.707 -1.000\nLi = 5.000, Lz = 11.000, Ls = 7.071, L4 = 6.000.\nThe coefficient of friction between the object and fin-\nrO.OOO 0.000 0.566 0.000 0.000 0.000 0.000 0.566 0.707 0.000 0.424 0.707 0.000 0.707 0.000 0.000 (56) 0.707 0.000 0.000 0.000 0.000 0.707 0.707 0.4241\n-\n-\ngers is set as 0.5, so that we have 0.894 0.894 -0.447 0.447\ne11=[0.447] \u2019 e1P\u2019[-0.447] \u2019 0.894] ezz=[0.894]1\nVertex 1\nVertex 3 Vertex 2\nFigure 8: Boundary hyperplanes and edge bounds of 3\nfinger grasp\n..............................",
            "0.000 5.000 1.125 0.000 2.500 0.000 11.000 6.098 6.000 3.500 0.000 0.000 ][U\u2019]. 5.000 5.000 0.000 0.000\n2.099 5.833 11.000 11.000 0.000 0.000 0.900 0.000 ps\nP I , . . . ,h L 0, PI + ... +@E = 1). (64)\nThe GFPR V I therefore has the following form 4\nVI = U (V;dJv&). (65) q,r=Lq#r\nThe regions of Vir and V 2 (q,r = 1,2,3,4, q # ;) and Vi dre illustrated in Cg.9, where Vir and Vqr, (q, r = 1,2,3,4, q # r ) are convex polyhedrons respectively, while the union set VI is a polyhedron but not a convex polyhedron. 5.2 Determining the Stable GFPR\nFor the convex polyhedrons Vkr and V:r (q,r = 1,2,3,4, q # r ) , the biggest inscribed hypersphere and volume of each polyhedron can be obtained based on the computing result. Let us see 3 bigger convex polyhedrons having bigger hypersphere shown in Fig.10.\nFor the convex polyhedron Vt2, the radius of the biggest inscribed hypersphere and volume 7:2 are\nr,l = 1.768, vf2 = 134.375. (66)\nFor the convex polyhedron VT4, the radius rC2 of the biggest inscribed hypersphere and volume i7:4 are\n(67) -2 rcz = 1.589, VI4 = 94.833.\nFor Vi3, the radius T 3 of the biggest inscribed hypersphere and volume &\nrd = 1.559, V23 = 99.532. (68) It can be seen that the radius value rg is the biggest. Therefore, the convex polyhedron VI, is the Stable GFPR for the edge candidate 1-2-4. If the radiuses for plural convex polyhedrons are the same, furthermore, the volumes of them are compared. 6 Conclusion\nWe presented an analytical approach to plan the stable Graspable Finger Position Region (GFPR). At first, we selected graspable candidates from all of the combinations of the object edges using the force equilibrium condition. Then, for a selected candidate, the regions of graspable finger position was analyzed by using the moment equilibrium condition. It was shown that the region is bounded by several boundary hyperplanes. With the combining these boundary hyperplanes, two propositions were proposed in order to obtain the GFPR exactly. The region was a polyhedron but not a convex polyhedron. Furthermore, the Stable GFPR was given by comparing the biggest inscribed hyperspheres and the volumes of the convex polyhedrons contained in the GFPR. The center part of the the biggest inscribed hypersphere is the stable finger position region. Lastly, numerical example were performed to show the effectiveness of the proposed approach.\nReferences [l] V.-D. Nguyen, \u201cConstructing ForceClosure Grasps,\u201d\nThe Internat. Jour. of Robotics Reseamh, Vo1.7, No.3,\n[2] Y.-C.Park, G.-P.Starr, \u201cGrasp Synthesis of polygonal Objects Using a Three-Fingered Robot Hand,\u201d The Intemat. Jour. of Robotics Research, Vol.11, No.3, pp.163184, 1992.\n[3] X.Markenscoff, C.H.Papadimitriou, \u201cOptimum Grip of a Polygon,\u201d The intemat. Jour. of Robotics Research,\n[4] J.Ponce, \u201cOn Computing Three-Finger Force-Closure Grasps of Polygonal Objects,\u201d IEEE Thaw. on Robotics and Automation, Vo1.11, No.6, pp.868-881, 1995.\n[5] T.Omata, \u201cFingertip Positions of a Multi-Fingered Hand,\u201d IEEE Internat. Conf. on Robotics and Autom-\n[6] Baker,B.S., Fortune,S. and Grosse,E, \u201cStable prehension with three fingers,\u201d Pmc. Symp. Theory of Cornputing, pp.114-120, 1985.\n[7] V. Chattel, \u2018Zinear Programming,\u201d Published in Japan by Keifuku Publishing Co., Ltd., 1983.\n[8] Y. Yu, Y. Li, T. Showaow, \u201cA Navel Analytical Method for Finger Position Regions on Grasped Object,\u201d IEEE Intemat. Conf. on Intelligent Robots and System,\n[9] X.-Z. Zheng, N. Tomochika, T. Yoshikawa, \u201cDynamic manipulability of multiple robotic mechanisms in coordinated,\u201d Jour. of the Robotics Society of Japan, In Japanese, Vol.11, No,6, 1993.\npp.3-16, 1988.\nV01.8, N0.2, pp.17-29, 1989.\ntion, pp.1562-1567, 1990.\npp.937-942, 2001."
        ]
    },
    {
        "image_filename": "designv11_28_0002425_j.sna.2006.01.016-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002425_j.sna.2006.01.016-Figure6-1.png",
        "caption": "Fig. 6. Fabricated shot-put sensor: (a) prototype and (b) schematic.",
        "texts": [
            " The overall structure has to be very firm in order to withstand the intense collision when the sensor falls onto the ground. The upper shell is connected with the sensing element via a screw joint. The lower shell is connected with the sensing element via screw fastening. The other parts are all installed inside the shells, including data-acquisition and processing cir- cuits, battery, mass balances, etc. The two mass balances are added into the structure in order to keep the sensor\u2019s weight at around 7.26 kg. And these mass balances can also compensate for deviation of the mass centre of the structure. Fig. 6 shows the photograph of the fabricated shot-put senor. Compared with the schematic, it is easy to identify the control buttons, ports and leds of the sensor. Fig. 7 shows the photographs of the shot-put sensor in contrast with the standard shot for open males. It can be seen that they are almost of the same shape. The Universal Serial Bus (USB) 1.1 port is used to transfer stored sensor data to PC or laptop. The hand position is marked on the surface of the lower shell for the shot-putters to locate where they should put there hands"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003975_j.jappmathmech.2008.08.016-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003975_j.jappmathmech.2008.08.016-Figure3-1.png",
        "caption": "Fig. 3.",
        "texts": [
            " These parts \u2013 \u2032 3 = { | 2 > 0, 2 > | 1|} (rolling), \u2032 1 = { |\u2212 1 > 2 > 0} (sliding to the left) and \u2032 2 = { | 1 > 2 > 0} (sliding to the right) \u2013 are centrally symmetric with the first three regions. For them, the mappings \u2032 1, \u2032 2 and \u2032 3 are specified by formulae similar to (1.10) but with a change in the sign of . Consequently, the conditions of existence and uniqueness (3.5) also remain unchanged. Example 3. Adding to the system from Example 1 a restriction in the form of a vertical wall (Fig. 3) against which the end C of the rod rests, we will obtain the well-known problem of the equilibrium of a ladder upon which a person is standing (see, for example, Refs 17 and 18). Suppose, to begin with, that the wall is smooth, and the constraint between the wall and the rod is bilateral. Then, q1 and q2 can be taken as generalized coordinates, and the angle q3 is defined by the formula (3.8) where d is the abscissa of the surface of the wall. In Eq. (3.1), the reaction of the wall N\u2032 will be added: (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002669_robot.2005.1570583-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002669_robot.2005.1570583-Figure4-1.png",
        "caption": "Fig. 4 Top View of Experimental Field",
        "texts": [
            " These levers consist of touch sensors which are electrically connected to the PIC and the logic level of each touch sensor is also sent to the PC through the PIC. It is possible to use this data as a parameter on the operation generator module on the PC. For example, in Fig. 3, WM-6 moves to the front of the food feeder when the lever is pushed. Therefore, we consider these levers to be the input devices of WM-6. We developed experimental setups as shown in Fig. 2. The interaction experiments between the rat and WM-6 are conducted within an experimental field of size 1000 x 1000 [mm] (Fig. 4) and containing the food feeder, water feeder and the battery exchanger. A CCD camera is positioned above the field and constantly sends an image of the experiment to the PC every 30 seconds. The PC controls WM-6, the food feeder, the water feeder and the battery exchanger. The food feeder consists of a microcontroller PIC (16F877) and a stepping motor. This machine releases a food pellet of 45 [mg] into a plastic bowl on the field when it receives an instruction sent from the PC. The water feeder consists of a microcontroller PIC (16F877) and a servo motor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001906_iros.2005.1545237-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001906_iros.2005.1545237-Figure6-1.png",
        "caption": "Fig. 6. Two ways to generate forces.",
        "texts": [
            " The tip of the left arm contacts with the valve handle at t = 0 (Fig. 5 (a)). Then the tip is smoothly moved 0.02 (m) upward along pz (Fig. 5 (b)). The tip position is kept for 1 [s]. Finally, the tip is moved to the initial position (Fig. 5 (c)). A 5th order polynomial interpolation is used to move the tip smoothly (Fig. 5 (d)). As described in Section (IV-A), there are various way to apply force to the environment. The following two ways are examined: 1) force is produced by moving the left arm (Fig. 6 (a)), 2) force is produced by moving the legs (Fig. 6 (b)). As for the arm configuration, the three typical configurations are considered: (i) horizontally extended (Fig. 7 (a)), (ii) folded (Fig. 7 (b)), and (iii) optimized posture. The postures (i) and (ii) are chosen ad hoc, while the posture (c) is calculated in the similar way discussed in Section (II) (the way is simplified for this case study as described below). Experiments are performed for the following five cases: Case 1 The left arm is horizontally extended as illustrated in Fig. 7 (a), and the arm is moved to produce the force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003740_1.2975154-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003740_1.2975154-Figure2-1.png",
        "caption": "FIG. 2. a Left handed helicoidal sector with rectangular section; b magnetization M oriented as the correspondent unit vector n and c sloped by angle S with respect to normal n\u2212n.",
        "texts": [
            " 8 n is the unit vector of the oriented straight normal line to the surface S in the point P. n is oriented so as to always come out from the volume V of the magnet Fig. 1 b . Then, from Eqs. 7 and 8 , we can write the explicit expressions of M P and M P by the M components Mx, My, and Mz, M P = \u2212 Mx P x + My P y + Mz P z , 9 M P = Mx P nx P + My P ny P + Mz P nz P . 10 III. VOLUME CHARGE MAGNETIC DENSITY M FOR HELICOIDAL MAGNETS WITH CONSTANT MAGNETIZATION MAGNITUDE Let us consider a left handed helicoidal sector with rectangular section. Figure 2 a schematically illustrates the solid shape that has been obtained by two helicoids that have a straight line perpendicular and passing through the relative common axis a\u2212a. From the descriptive geometrical point of view, each helicoid can be considered as a surface generated by a helicoidal motion of this line around the axis a\u2212a. The line is defined by the term \u201cgeneratrix of the helicoid.\u201d9 Let ri and re be the internal and external radii of the sector, respectively. In relation to the geometrical picture obtained as just described, we observe that it can also be thought of as a set of an infinite number of cylindrical helicoidal sectors that have an infinitesimal rectangular section. We can denote the sides of these infinitesimal rectangles as ds and dr. They are oriented along the radial and axial directions, respectively Fig. 2 a . Then, for each of these infinitesimal and helicoidal sectors, it is possible to consider a cylindrical helix that passes through the center of gravity of each planar infinitesimal rectangle previously defined. The radius r of changes from ri to re. In this way the complete helicoidal sector can be considered as a set constituted by an infinite number of points always belonging to coaxial cylindrical helixes that have the same pitch. Therefore, when we consider a point P of the sector just defined, only one [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: 131.230.73.202 On: Thu, 18 Dec 2014 07:41:10 curve passes through to P. Consequently, this point P is identifiable by the geometric parameters that characterize a cylindrical helix. To define quantitatively the helicoidal geometry just described, let us consider an orthogonal Cartesian coordinate system with origin O Fig. 2 b . The axis X represents the axis a\u2212a of the sector illustrated in Fig. 2 a . The angle fixes the angular position of the helicoidal sector with respect to a\u2212a or X . The generic point P of is identified by the angle measured from the initial rectangular section of the same sector. Here t\u2212 t and n\u2212n are the tangent and the normal straight lines to in P, respectively. The straight line g\u2212g represents the generatrix of the cylinder9 whose radius is indicated as r. The curve belongs to this cylinder. We observe that the normal n\u2212n is inclined with the helix angle with respect to the generatrix g\u2212g",
            " Then the n components along n\u2212n and g\u2212g are equal to n cos and n sin , respectively Fig. 3 a . The components nx, ny, and nz of n along the axes X, Y, and Z Fig. 3 b are nx = n cos , 11 ny = \u2212 n sin sin \u2212 , 12 nz = \u2212 n sin cos \u2212 , 13 where n= n =1 is the magnitude of n. Now we consider the magnetization of the helicoidal sector by applying to the generic point P of the magnet, a magnetization vector M characterized by a constant magnitude. This M is oriented as the correspondent unit vector n Fig. 2 b . The vector M just defined therefore is of a helicoidal kind. In Fig. 4 the distribution of M along a generic cylindrical helix with starting and ending points A and B, respectively, is illustrated by a qualitative picture. In this drawing we denote the radius of by r and suppose that the extension of is almost equal to two revolutions. In Fig. 2 b is quantitatively defined by fixing the suitable value of the angle . Now, since the orientation of M is the same one of n we straightaway obtain the components Mx, My, and Mz of M. In fact, with reference to O X ,Y ,Z and Eqs. 11 \u2013 13 , it follows that Fig. 5 a Mx = M cos , 14 My = \u2212 M sin sin \u2212 , 15 Mz = \u2212 M sin cos \u2212 . 16 Substituting Eqs. 9 and 10 in Eqs. 11 \u2013 16 , we obtain in each point P of the magnet the volume and surface charge density M P and M P , respectively. In particular, in order to compute M P by Eq",
            " 3 b we find that r = y2 + z2, 17 where y and z are just the two coordinates of P in the frame of reference O X ,Y ,Z . Because cos \u2212 = \u2212 y r , 18 sin \u2212 = z r , 19 from Eq. 17 it follows that [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: 131.230.73.202 On: Thu, 18 Dec 2014 07:41:10 cos \u2212 = \u2212 y y2 + z2 20 and sin \u2212 = z y2 + z2 . 21 Moreover, if we denote by p the pitch of the cylindrical helix shown in Fig. 2 b , the relationship among the helix angle , r, and p is see Fig. 5 b = arctan p 2 r . 22 Considering again Eq. 17 , we obtain = arctan p 2 y2 + z2 . 23 Substituting Eqs. 20 , 21 , and 23 in Eqs. 14 we find the following three equations: Mx = M cos arctan p 2 y2 + z2 , 24 My = \u2212 M sin arctan p 2 y2 + z2 z y2 + z2 , 25 Mz = \u2212 M sin arctan p 2 y2 + z2 y y2 + z2 . 26 Calculating the partial derivatives Mx / x, My / y, and Mz / z by using Eqs. 24 \u2013 26 , we obtain the following expressions: Mx x = 0, 27 My y = \u2212 Mp3yz 8 3 1 + p2 4 2 y2 + z2 3/2 y2 + z2 6 + Myz y2 + z2 1 + p2 4 2 y2 + z2 , 28 Mz z = Mp3yz 8 3 1 + p2 4 2 y2 + z2 3/2 y2 + z2 6 \u2212 Myz y2 + z2 1 + p2 4 2 y2 + z2 ",
            " 9 we get M P = \u2212 0 \u2212 Mz P z + Mz P z , 31 that is, M P = 0. 32 Consequently, in each point P of the helicoidal magnet, characterized by a magnetization M also helicoidal and M = M =constant, the volume charge density M P is always equal to zero. This result has been obtained in relation to a left handed helicoidal magnet and it is valid for right handed magnets too. In fact, we can repeat all the previous mathematical steps, but, only with reference to the quantities represented in Fig. 6, which is analogous to Fig. 2 b . In this case, Fig. 6 illustrates a right handed cylindrical helix . The symbols that are used in Fig. 6 are the same ones as Fig. 2 b and have the same meaning. The only differences between the equations relative to right handed magnets that we can write and the previous ones are limited to certain signs. In fact, with reference to Figs. 6 and 7 a relative to a right handed helicoidal magnet, Eqs. 11 , 13 , and 18 must be substituted by the following: nx = \u2212 n cos , 33 nz = n sin cos \u2212 , 34 cos \u2212 = y y2 + z2 . 35 Therefore, in relation to the magnetization M of the right handed magnet, it is necessary to substitute Eqs. 14 and 16 with the correspondent see Fig",
            " Downloaded to ] IP: 131.230.73.202 On: Thu, 18 Dec 2014 07:41:10 My = \u2212 M sin sin \u2212 + D , 51 Mz = M sin cos \u2212 + D , 52 we obtain again M P 0. In Eqs. 51 and 52 D is the rotation angle of M in the plane YZ with respect to the straight normal line n\u2212n. This case is defined when M, applied to the point P, always belongs to a plane that is tangent to the cylinder on which the cylindrical helix is defined. We denote the radius of the cylinder by r. Now, differently from what has been illustrated in Fig. 2 b , we substitute the helix angle of with the value + S. Therefore, in relation to a left handed cylindrical helicoidal magnet, S represents the sloping angle of M with respect to the normal straight line n\u2212n Fig. 2 c in the tangent plane previously defined. Then, we mark by M the sloping magnetization vector that, as usual, has magnitude M equal to a constant value. Substituting with + S S is a constant in the expressions of Mx , My , and Mz Eqs. 14 \u2013 16 , using in the equations just obtained, the expression of Eq. 23 , and calculating the correspondent partial derivatives with respect x, y, and z, it follows Mx x = 0, 53 My y = Mpyz cos arctan p 2 y2 + z2 2 1 + p2 4 2 y2 + z2 y2 + z2 2 + Myz sin S + arctan p 2 y2 + z2 y2 + z2 3/2 , 54 Mz z = \u2212 Mpyz cos arctan p 2 y2 + z2 2 1 + p2 4 2 y2 + z2 y2 + z2 2 \u2212 Myz sin S + arctan p 2 y2 + z2 y2 + z2 3/2 . 55 Observing Eqs. 54 and 55 we have My y = \u2212 Mz z . 56 Substituting Eqs. 53 and 56 in Eq. 50 we obtain M P = \u2212 0 \u2212 Mz P y + Mz P z , 57 that is, again M P =0 in each point P of the magnet. Then, we have obtained the following results: if i M always belongs to a plane that is parallel to the axis of the magnet and ii the angle S measured on this plane between M and the normal n\u2212n that passes through the generic point P of the magnet is constant Fig. 2 c , then the volume magnetic charge M P is always equal to zero. Consequently, in order to have M P =0, we have found that the M orientation along the normal n\u2212n is not necessary. As a matter of fact, in the above mentioned plane, the M orientation can be any, on condition that the magnitude of M does not depend on the coordinates x, y, and z of P, that is, the value of M must be a constant. In relation to a right handed cylindrical helicoidal magnet, we can substitute the angle S with D and define the components Mx , My , and Mz , as illustrated in Fig",
            " Now, if we apply the development sequence to all the infinite coaxial cylinders whose radius and height are ri r re and h, respectively, it is possible to stack up all the infinite development planes of the same cylinders, together with the relative M distributions that have all the corresponding bidimensional divergence equal to zero. Then, methodically stacking up the planes, we can build up the prismatic solid illustrated in Fig. 11 b . For example, this solid can be thought as symmetric with respect to the plane belonging to the axes X and Y of the coordinate system considered at the beginning see Fig. 2 b . In Fig. 11 b we have fixed a symmetric position of the prismatic solid in relation to the coordinate system. Then, on each rectangle with sides equal to 2 r and h the following equation is valid: Mx P x + Mz P z = 0. 80 Now, since on each rectangle it is always My P = 0, 81 it is obvious that the variation in the component My P of M along the axis Y is null in the whole prismatic solid, My P y = 0. 82 Then, Eqs. 80 and 82 give Mx P x + My P y + Mz P z = 0, 83 that is, from Eq. 9 , we obtain M P = 0. 84 In relation to the case that has been described in Sec. V where M was inclined by a generic and constant angle independent of x, y, and z see Fig. 2 c , we can repeat the whole previous procedure and obtain the same conclusions. We observe that the magnetic prism for which Eq. 84 is valid and has been carried out from the cylindrical helicoidal magnet by a simple development operation of developable ruled surfaces,9 that is the coaxial cylinders of radius r. Consequently, the arbitrariness of the method to identify a simple magnet equivalent to the real magnet is very small. Then, this procedure can be interpreted as a geometrical physical justification of the result obtained: a cylindrical helicoidal magnet with the magnetization previously considered has a volume magnetic charge M equal to zero because, in the equivalent magnetic prism, it shows a uniform bidimensional distribution of M, for which it is immediate to verify that \u00b7M=0 in the whole prism, as it happens in the simple parallelepiped or cylindrical magnets characterized by a uniform magnetization",
            "202 On: Thu, 18 Dec 2014 07:41:10 Therefore, if we use only a simple development operation on a plane, we are not able to define any equivalent magnet characterized by M =0. In the previous sections it has been shown that in cylindrical helicoidal magnets with helicoidal magnetization, the volume charge density M is equal to zero in each point of the magnet. In this section surface charge density M expressions for the same kinds of magnets are given. The surfaces to consider are six, and for each one we have to find the corresponding M expression. These surfaces are those that surround the left handed helicoidal sector with rectangular section illustrated in Fig. 2 a . In Fig. 12 a these surfaces have been denoted by S1, S2, S3, S4, S5, and S6. The surface S1, S2, S5, and S6 are coaxial and helicoidal. S3 and S4 are rectangular. Let us obtain the M1 expression for the surface S1. The inner and outer radii of S1 are ri and re, respectively. For each radius ri r re we can define the cylindrical helix illustrated in Fig. 2 b . Consequently S1 can be thought of as a set constituted by an infinite number of curves all adjoining and coaxial. As soon as a point P of is fixed see Fig. 12 a , we can apply one more time all the considerations illustrated in Sec. III for computing the components nx, ny, and nz of the unit vector n in P. However, in the present case of M evaluation we observe that n must always be going out from the surface where M is computed. If we consider again the magnetization M oriented along n and its magnitude M = M =constant, from Eq",
            " 1 b and 12 a , these components may be written as Bix px ,py ,pz = 0 4 Si Mi pix,piy,piz px \u2212 pix px \u2212 pix 2 + py \u2212 piy 2 + pz \u2212 piz 2 3/2dSi, A11 [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: 131.230.73.202 On: Thu, 18 Dec 2014 07:41:10 In these equations, px , py , and pz are the coordinates of the point P where Bi P has to be evaluated. The other symbols pix, piy, and piz denote the coordinates of the point P that is characterized by the correspondent Mi see Figs. 1 b and 12 a . Observing also Fig. 2 b , for the index i=1, we obtain the following p1x, p1y, and p1z expressions versus , , and d: p1x = \u2212 d \u2212 p 2 , A14 p1y = \u2212 r cos \u2212 , A15 p1z = r sin \u2212 . A16 In these equations , , and d are positive quantities. Analogously, for i=2 it results to p2x = \u2212 d \u2212 b \u2212 p 2 , A17 p2y = \u2212 r cos \u2212 , A18 p2z = r sin \u2212 . A19 In Eq. A17 b has a positive sign and represents the axial distance between the two helicoidal surfaces S1 and S2. Finally, the coordinates p3x, p3y, p3z and p4x, p4y, p4z, identifying the position of the surfaces dS3 and dS4, respectively, are p3x = \u2212 d \u2212 b 2 , A20 p3y = \u2212 r cos , A21 p3z = r sin , A22 p4x = \u2212 d \u2212 b 2 \u2212 p 2 , A23 p4y = \u2212 r cos \u2212 , A24 p4z = r sin \u2212 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003188_1.2919780-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003188_1.2919780-Figure2-1.png",
        "caption": "Fig. 2 Measurement of the reference cavity pressure by using a syringe \u201eschematic\u2026",
        "texts": [
            " In a normal unidirectional rolling contact, after a hort time, the early stage of a cavity would just breakthrough the il meniscus and an ambient pressure can be assumed, as shown n Fig. 1 b . In Ref. 15 , a cavity pressure as that of vacuum was defined. A elatively simple test is carried out, by measuring the vacancy ressure inside of a syringe filled with oil, as schematically shown ig. 1 Observations and schematic showing \u201ea\u2026 an enclosed ype cavity and therefore a cavity pressure lower than the amient pressure can be assumed; \u201eb\u2026 cavity breaking through he oil meniscus and therefore an ambient pressure can be ssumed n Fig. 2. 31502-2 / Vol. 130, JULY 2008 om: http://tribology.asmedigitalcollection.asme.org/ on 01/30/2016 Terms The pressure measured inside a visible vacancy, when pulling the piston of a syringe, was near absolute vacuum pressure \u22120.1013 MPa , smaller than \u22120.095 MPa, and first bubbles in the oil of the syringe have been also observed at about 70% of the vacuum pressure. In real EHL conditions, therefore, the authors assume that the cavity pressure can be around 70\u2013100% of vacuum pressure. For numerical simulations, a reference cavity pressure as that of vacuum \u22120"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001003_tmag.1984.1063164-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001003_tmag.1984.1063164-Figure3-1.png",
        "caption": "Fig. 3 . Structure and dimensions of the rotor.",
        "texts": [
            " Figure 2 shows a general view of a parametric synchronous motor built for experiments. We used the commercial cut cores as the magnetic circuit A I , A2 for excitation and the Fe-Si plates (0.35 mm thickness) as the common magnetic circuit B. A slit was provided in the common magnetic circuit in order to increase the output power. [ 21 The rotor is a non-salient pole type with a permanent magnet made of commercial strontium ferrite. The composition and the properties of the permanent magnet are shown in Table 1. The structure and dimensions of the rotor are shown in Fig. 3 . We used an external driving motor to start the parametric synchronous motor in experiments, although self-starting motor will be used in practically by using the rotor with amortisseur winding. Table 1. Composition and properties of strontium ferrite permanent magnet. Compositions Sr0-6FezO3 Residual Flux Density (Br) 0.42 (T) Intrinsic Coercive Force (IHc) 239 (kA/m) Coercive Force (BHC) 235 (kA/m) where N, is the synchronous speed, f is the supply frequency, p is the number of poles and T(N"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003779_1.2982500-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003779_1.2982500-Figure3-1.png",
        "caption": "FIG. 3. Sketch of the numerical domain showing boundary conditions applied on far field boundaries gray and on the projectile boundary black .",
        "texts": [
            " Computation of the perfect projectile shape requires that for each of the intermediate projectile shapes the coupled Navier\u2013Stokes and adjoint Eq. 2 be solved numerically. To do this, the physical and adjoint velocity fields, u and w, are discretized by quadratic finite elements and the pressure and adjoint pressure, p and q, by linear elements, and the complete finite element model is solved using COMSOL Multiphysics. We impose far field boundary conditions upon a cylindrical surface with radius R and length 2L see Fig. 3 . Over the analyzed range in Re it was found to be sufficient to take R =L =400. An irregular triangular mesh is constructed using the COMSOL built-in function \u201cmeshinit,\u201d with approximately 300 triangle vertices distributed along the boundary of the projectile, the same number along each of the symmetry axes, and the ratios of side lengths of adjacent triangles not permitted to exceed 1.18 away from these boundaries. N 60 equally spaced mesh points are selected on the shape boundary and evolved according to the update rule dx /d = n, with alpha the optimal-shape perturbation 4 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003868_s10015-008-0557-x-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003868_s10015-008-0557-x-Figure3-1.png",
        "caption": "Fig. 3. Control of direction",
        "texts": [
            " The manipulator has many passive joints that have lock mechanism. Two wires are installed around both sides of the manipulator, and a hose is installed in its center (Fig. 2a). A rail is installed on a side of the manipulator. Two manipulators are connected by the rail. They can be moved along the rail each other (Fig. 2b). 3.2 Mechanism of changing direction Wire is fi xed on top rink and tube is fi xed on the end rink. By pulling the wire, we can change head direction, and then lock the joints at the state (Fig. 3). 3.3 Lock mechanism Figure 4 shows structure of each joint. Each joint have two frictional materials.And, hose passed through the center. By putting water into the hose, the hose expands, and the expanded hose pushes inside friction materials, then, inside friction materials engages with outside friction materials. As a result, the joint is locked to the position (Fig. 5). The amount of the injected water into the hose is adjusted with the piston that is installed to the end part (Fig. 6). As described in subsection II-1, conventional robots have motors, sensors and controllers to operate the robot, and, require space for loading with them"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003082_1.2736431-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003082_1.2736431-Figure4-1.png",
        "caption": "Fig. 4 Solution strategy of the rolling tion of roller indentation \u201ea\u2026 and adhesio",
        "texts": [
            "org/ on 07/01/2013 Terms f The effect of adhesion induced bifurcation during progressive load, i.e., the\u201cjumping on\u201d stick discussed in 28 , is not taken into account. g Without loss of generality, it is assumed that Mappl=0 in Fig. 1. According to the approximation e , the noncontact adhesion zone II in Fig. 1 vanishes, so Xb\u2212=Xa\u2212 and Xb+=Xa+. Under these approximations, the boundary-value problem defined by the contact system in Fig. 1 is solved through the superposition of the displacement-based solutions of two independent boundary-value problems, as illustrated in Fig. 4. The corresponding contact analysis can be divided into the following stages: etween elastic bodies; \u201eb\u2026 proposed ntact ntact with JKR adhesion; superposi- ct b co -co n rotation \u201eb\u2026 Transactions of the ASME of Use: http://asme.org/terms p . d c u i a d t s a d fi t f J Downloaded Fr 1 The roller indents the substrate with the depth \u0303 at the time instance =0, Fig. 4 a . Let 2l to be the length of the contact zone, i.e., Xa0+\u2212Xa0\u2212=2l, and l\u0304 is the average elongation of the substrate at the two ends of the indentation-induced contact zone, then the average transverse strain on the contact surface, denoted as av, reads l\u0304 l = av 5 2 The roller rotates clockwise through an angle while the particles of the substrate surface within Xa0\u2212 X1 Xa0+ adhere to the roller surface until a detachment takes place where the contact zone becomes Xa\u2212 X1 Xa+, illustrated in Fig. 4 b . During this rotation, relative sliding between substrate and roller surface is permissible within the contact zone but the substrate material particles at the two ends of the contact zone are presumed to stick to the roller so there is no change in the contact zone size, i.e., Xa0+ \u2212 Xa0\u2212 Xa+ \u2212 Xa\u2212 6 which is identical to the approximations b , i.e., R =V and infinitesimal strain. 3 When the roller continuously rotates and steadily travels forward, once a detachment occurs at one end of the contact zone, a new attachment is assumed to occur simultaneously at the another end; thus the stick zone size remains constant in the coordinate system Xi that originated at the intersection of the vertical central line and the bottom of the roller",
            " This stress function is determined by z = Z z 2 i L h t dt Z t t \u2212 z + Z z Pm z 10 where Z and Pm are functions to be determined, which will be discussed in detail later; the integral of 10 is on the segment L along the entire real axis. When a stress boundary condition is prescribed on L, h z = p z + iq z 11 When a displacement boundary condition is given on L, then h z = 2G d dz u1 z + iu2 z 12 For the rolling contact problem in Fig. 1, the displacement boundary condition is given in the contact zone, as illustrated in Fig. 4; the traction free condition is given outside the contact zone so h z vanishes. Hence, the integral route L degenerates to the contact zone X1 a\u2212 X1 X1 a+ and the stress function is solvable when the displacement h z is given. When z is known, the stress distributions on the entire semi- infinite plane are determined 12 : 11 + 22 = 2 z + \u0304 z\u0304 13a 22 \u2212 11 + 2i 12 = 2 z\u0304 \u2212 z z \u2212 z \u2212 \u0304 z 13b For the problem of Fig. 1, at infinity z\u2192 the following condition should be satisfied: 11 = 12 = 22 = 0 14 Also, the global equilibrium requires that P = L p t dt Q = L q t dt 15 where L denotes the contact zone",
            "1 Two Boundary Value Problems. The problem addressed n Fig. 1, as discussed in Sec. 2.5, is solved by the superposition f the solutions of the following two boundary-value problems efined in Figs. 4 a and 4 b . Using the superscripts I and II to enote the variables associated with the problem I and II, these wo boundary-value problem can be stated as below. Problem I (roller indentation): find uI= u1 I ,u2 I that satisfies the lastic equilibrium condition and the boundary conditions which pecify the motion illustrated in Fig. 4 a , u1 I = u\u0303 t u2 I = \u2212 + t2 2R for X2 = 0 t l 17 nd 22 I = 12 I = 0 for X2 = 0 t l 18 here is constant, u\u0303 t is the surface transverse deformation to e determined, t is a coordinate defined as t = X1 \u2212 l\u0304 l\u0304 = Xa+ + Xa\u2212 2 l = Xa+ \u2212 Xa\u2212 2 19 he coordinate origin t=0 is the geometrically symmetric center f the contact zone size, see Fig. 4 a . In 17 and 18 and the nalysis hereafter, the superscript I indicates the quantities associted with the problem I and II to the quantities with the problem II o be discussed. In this analysis the quantities with the orders of t4 /R3 are omitted. Assuming that the surface transverse deformation in 17 can be xpressed as a series expansion of a self-similar solution, u\u0303 = u\u0303sym + u\u0303skm 20 u\u0303sym = l av a1 t l + a3 t l 3 + \u00af 21 u\u0303skm = sv t l 2 + a4 t l 4 + \u00af 22 here u\u0303sym is a skew-symmetric function that describes a transerse deformation symmetrical to t=0 while u\u0303skm is a symmetric unction that characterizes the antisymmetrical part of the transerse displacement u\u0303; the constants av , sv ,a1 ,a3 ,a4 , . . . are to be etermined. According to 5 and 6 and associated approximaions, we know that at t= \u00b1 l, u\u0303sym = l av u\u0303skm = 0 herefore a1 = 1 \u2212 a3 a4 = \u2212 1 22a Problem II (roller stick-rotation): find uII= u1 II ,u2 II that satisfies lastic equilibrium condition and the boundary conditions which pecify the motion illustrated in Fig. 4 b , u1 II = u\u0303skm + R 1 \u2212 1 2 t R 2 \u2212 2 6 + t R 2 for X2 = 0 t l 23 86 / Vol. 129, JULY 2007 om: http://tribology.asmedigitalcollection.asme.org/ on 07/01/2013 Terms u2 II = R 2 \u2212 t R for X2 = 0 t l 24 where u\u0303skm is defined by 20 and 22 . The derivation of the rotation induced surface deformation, i.e., the second part of 23a , is given in Appendix B. Also, 22 II = 12 II = 0 for X2 = 0 t l 25a and the detachment condition when the cylinder rolls forward is as follows \u2212 p \u2212 l = T0 25b When X1 2+X2 2\u2192 , 11 II = \u2212 11 I 22 II = \u2212 22 I 12 II = \u2212 12 I 26 3",
            "org/ on 07/01/2013 Terms a\u22121 = \u2212 Q + iP 2 36 An additional energy conservation equation is introduced, Q \u00b7 R = \u2212l l u1 II \u00b7 q t + u2 II \u00b7 p t dt 37 Equations 15 , 16 , 36 , and 37 , together with the adhesion condition 25b , are seven equations to determine the parameters l, , sy, av, a1, and to establish the relationships between these parameters and P, Q. Remark: For the case of steady-state rolling with stick and full sliding, the analysis procedure introduced in the previous sections is still applicable. Assuming that the roller rotates continuously with a sliding zone, within which there is no normal separation nor stick zone. Under such a steady-state the angular velocity should be given, denoted as a rotation angle \u0303 per unit time. Similar to Fig. 4, this problem can be divided into two individual motions per unit time: 1 the roller drags the substrate moving with an angle due to adhesion; 2 then the deformation field of the substrate and contact zone are \u201cfrozen\u201d while the roller rotates with the angle \u0303\u2212 . Hence, solutions obtained previously apply to stage 1 . Stage 2 has no effect on the structures of stress and displacement distribution, although it causes extra energy dissipation. Under this condition the energy conservation 37 becomes Q \u00b7 R = \u2212l l u1 + R \u0303 \u2212 \u00b7 q t + u2 \u00b7 p t dt 37a which leads to different values of l, sy, av upon the input \u0303",
            " Applying the coefficients listed in Appendix , the P, Q, and R can be expressed as follows: For the solution without JKR adhesive traction: P 2G = l 11 P l R + 12 P sv av + 13 P av + 14 P 2 41 Q 2G = l 11 Q l R + 12 Q sv av + 13 Q 42 here 11 P = \u2212 4 2 + 4 + 12 P = 16 3 4 + 8 3 2 + 1 13 P = 2 14 P 14 P = \u2212 1 11 Q = 11 P 12 Q = 8 4 2 + 1 + 4 2 3 1 \u2212 2 + 2 3 \u2212 1 13 Q = \u2212 2 14 P he corresponding rolling friction coefficient is R = l R + 12 Q 11 P av sv + 13 Q 11 P l R + 12 P 11 P av sv + 13 P 11 P av + 14 P 11 P 2 43 or the solution with JKR adhesive traction: R = l R + 11 av sv + 2 12 l R + 2 21 av + 22 2 44 here 11 = 1 22 \u2212 8 3 4 + 16 3 2 \u2212 1 3 12 = 21 = \u2212 1 11 P 22 = \u2212 2 2 \u2212 1 2 88 / Vol. 129, JULY 2007 om: http://tribology.asmedigitalcollection.asme.org/ on 07/01/2013 Terms 4 Results and Discussion 4.1 The Indentation With Nonsingular Adhesion. Let =0, av=0, the solutions 41 and 42 degenerate to a cylinder indentation contact defined by Fig. 4 a , P = 2G 11 P l2 R + 13 P avl Q = 0 45 Applying 25b to 34 see Appendix B , T0 = 2G \u2212 1 av \u2212 2 l R 46 where = log 2 = 3 \u2212 4v Combining 45 with 46 , the unknown av is cancelled and the resulting relation below establishes the relationship among contact zone size, applied normal load, and maximum adhesion, l = T0R 2G 1 + 4 2 1 + 1 \u2212 4 2 + 1 PG RT0 2 47 When no external force is applied, i.e., P=0, two bifurcated solutions of l, as illustrated in Fig. 5, are obtained, Solution I trivial : l = av = 0 Solution II: l = 2 \u2212 1 4 2 + 4 + R av By substituting the second solution into 46 , we reach the following estimate of the relation between contact zone size and maximum adhesion which is exact when no external force and the system is under infinitesimal deformation, T0 = G 4 2 + 1 l R 47a or l = T0R G 4 2 + 1 47b 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003196_s11012-006-9036-4-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003196_s11012-006-9036-4-Figure1-1.png",
        "caption": "Fig. 1 Stepped labyrinth seal geometries",
        "texts": [
            " We used the Colebrook\u2013 White friction factor model in the calculation of circumferential velocities. The pressure distribution is found by satisfying the leakage equation and circumferential velocity distribution is determined by satisfying the momentum equation. The validity of the bulk pressure approach was examined by using a Computational Fluid Dynamics (CFD) program in [6]. The approach is the same followed by Childs and Scharrer [2] for the straightthrough labyrinth seals. 2 Seal geometries and leakage Flowrate calculations The seal geometries for stepped labyrinth seals are given in Fig. 1. The clearance C between the teeth and the rotor surface, the number of teeth NT varying from 5 to 18, and the shaft radius Rs determine the annular flow area. In the stepped labyrinth seals the radius will be Rsi = Rsi\u22121 \u00b1 d. Continuity equation implies that the leakage flowrate remains constant in all cavities if the rotor rotates with constant speed, i.e. . m1 = . m2 = \u00b7 \u00b7 \u00b7 = . mNT = . m. (1) We use the Neumann model [13] to calculate the flowrate . m which is given as . m = \u00b51i\u00b52iAi \u221a P2 i\u22121 \u2212 P2 i RT "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000571_robot.2002.1013603-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000571_robot.2002.1013603-Figure3-1.png",
        "caption": "Figure 3: Representative Points for Surface Contact in Rot at ion",
        "texts": [
            " This is because all the contact forces on a half-line that passes the instantaneous COR have the same direction vector; therefore the resultant generalized force of all the contact points on the intersection between the half-line and the surface can be represented by the effect of point contacts at the intersections between the half-line and the boundary of the surface (see Figure 2, left). Similarly, when the instantaneous COR is on the surface, AOt can be replaced equivalently by the effect of all the contact points on the boundary of the surface and the COR (see Figure 2, right). However, we still have to consider infinite contact points to obtain Aot. Thus we approximate A r o t with the effect of contact forces at finite representative points as follows: 1. If the COR is outside the contact surface (Figure 3, left), we draw several half-lines that pass the COR. We choose intersections of these half-lines and the boundary of the surface as representative points. Besides, vertices of the surface are also chosen as representative points. 2. If the COR is on the contact surface (Figure 3, right), we also draw several half-lines that pass the COR. We choose intersections of these halflines and the boundary of the surface, vertices of the surface, and the COR as representative points. The COR is regarded as a non-sliding contact point. We can express the set of applicable contact forces by a union of polyhedral convex cones as Eq. (7) a p proximately using the above-mentioned representative points, even if the object has surface contacts in rotation. When we draw more half-lines and choose a lot of representative points, the approximation can be to arbitrary precision"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000034_robot.1992.220260-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000034_robot.1992.220260-Figure6-1.png",
        "caption": "Figure 6: (1.) Nelson curve, (I.) Left type-1 curve",
        "texts": [
            " If this technique isn\u2019t applicable, the appropriate blocked subpath BS is returned to the channel search level. 6. Path with Continuous Curvature A path with continuous curvature is computed, using ting appropriate curves into the corners si; simultaneously it has to be ensured, that the resulted path of the rectangular modeled vehicle lies inside (in-attribute) the DC. The actual DC will be enlarged, if it is necessary and possible. Our type-1 curve (standard curve) bases on a method introduced by Nelson (refer to [4], figure 6): the sequence S = (so,. . . . s,,) of line segments and fit- 0 r, 4: polar coordinates, IC: curvature Figure 6 shows our left type-1 curve fitted into the corner p2 defined by the subsequence (pl,pz,p~) of S. The start and the end of the curve are indicated by p , and pe. The center of the polar coordinate system is marked by c. If R is given, the other parameters and the resulting curve can be computed with well known methods. Two type-1 curves form one type-2 curve (figure 7). It is well suited to depart from small corridors, because p , = p2 . If RI and Rz are known, the two curves can be computed. Our type-3 curve is the dual one to the type-2 curve ( p , = p2) and is well suited to drive into small corridors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002056_iros.1992.594512-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002056_iros.1992.594512-Figure3-1.png",
        "caption": "Figure 3: Manipulator Configuration for Identification",
        "texts": [],
        "surrounding_texts": [
            "In general, the motion equation of a serial link manipulator is expressed as follows, by considering viscous damping coefficients and Coulomb friction. 7 = M(q, x)G + h(q, 4.1 + G(q, x) +ci4 + fisgn(q) (1) Where, 7 = ( 7 1 , 7 2 , e e ., T N ) ~ : joint torque, q = (q l , q2, - ., qN)t : Joint angle, q = (GI, q2, - - ., qN)t : Joint angular velocity, 2 = (21,x2, - e , xN)~: Composite parameters, ci = (c1, cp, . . ., C N ) ~ : Viscous damping coefficients, fi = (f f 2, . . -, f N ) : : Coulomb friction, M(q,x): Inertia matrix ( N x N ) , h(q, 4 , ~ ) : Centrifugal, Coriolis forces term ( N x l), G(q,x): Gravitational term (Nxl) . = q2, S . ., qN) t : Joint angular acceleration, In this paper, the following inertial parameters ai , pi and friction parameters q , f i are defined as dynamic parameters. Each joint torque can be expressed as a linear equation consisting of the dynamic parameters; their parameter coefficients Bi , Ci , Di, those are the functions of motion data (e.g., joint angle, joint angular velocity, joint angular acceleration ) and kinematic parameters. 7; = (Ai-lZo)\u2018n; + c;qi + f ;sgn(q;) (2) Where, A\u2019-l i:a transformation matrix, ni: the moment exerted on xi by p; = (Til, Ti,, T:3 T i 2 IfJ Ti,,) Moreover, ( 5 ) n y, = Cmj, I; = ri + rig + 7;+l(r;tri63 - r,r;\u2019) mi : Mass of joint j, n : Number of joints, si : Position vector from the origin of xi to the center of the mass expressed with xi , T ; : Position vector from the origin of to the origin of Xi expressed with Ci, l i s : Inertia matrix of link i around the center of the mass with xi , fi : Inertia matrix of link i around the origin of the xi expressed with xi, I j k \u2019 : j column and IC low element of f;, 63 : Unit matrix, xi : link i coordinate frames. j =a Then, coefficients B; , C; and D; are expressed as follows. Bi = [ r(e l ) , P(e2), m 5 3 ) 1 (6) C; = [ el x (A:%,-~), e2 x (A: -%;-~) , e3 x (A: -%;-~ )] (7) 13, = 1 &1 -WZW3 W 1 W 3 (;2 - W l W 3 63 + W l W 2 ( w 2 ) a - ( W 3 ) \u2019 W l W 3 6 - W l W 3 dl + W Z W 3 (Us)\u2019 - ( W 1 ) 2 & - W l W 2 - W l m W l W 2 & (W1)\u2019 - (W1)\u2019 & - W Z W 3 (;2 + W l W 3 (8) Where, r ( e i ) = e& + U ; x (w; x e;) r , : [ a,, &sinbj, d;cosb; I t ai: Common length between Zi-1 I Z;, d;: Length from Xi-1 to Xi along Zi direction, b;: Angle from 2,-1 to 2, around Xi, e;: Unit vector, e,= I, ej= O ( j # i ), w j : j- th element of angular velocity for link i, b i j : j- th element of angular acceleration of link i. By defining a coefficient matrix W ( B , , Ci, 0 4 , r ; ) , a dynamic parameter matrix X ( a ; , pi, e, f i ) and a joint torque vector 7 can be expressed as follows. 7 = wx (9) The least squares method is applied to equation (9) for the identification: here the joint torque and joint motion data are measured simultaneously. 2.2 Application of linear identification method In practice, based on the measured joint torque t and coefficient matrix W , the following equation is given. T = W X + S (10) Where, X is the value of the parameter and 9 is the error. Here, the optimally estimated parameter value under the minimum error condition of 9 can be given as follows. (11) x = ( W t q - I w t + To solve equation ( 11 ) correctly, the following condition number should be small [14]. 6 1 cond W = - un here, U,, is the maximum singular value, 6 1 is the minimum singular value. Equation ( 12 ) indicates that it is necessary not only to drive each joint independently but also to give no large imbalances between joints in the following experiment, therefore, special attention was paid to maintain the above conditions. Furthermore, a recursive least squares method requiring no inverse matrix computation was used to avoid restriction in the sampling number. 2.3 Parameter coefficient of manipulator Figure 1 shows a schematic diagram of the manipulator ( PUMA260 ) tested here and its link coordinates. Only three basic joints from the manipulator base that can cause large non-linear dynamic effects were considered for the identification. The dynamic modeling of the power transmission mechanisms such as reduction gears was ignored. Using equations (6) - ( 8 ) , the parameter coefficients of the manipulator were analytically derived. The coeficient equation for joint 3 is given as follows. The Y-axis of joint 3 is a rotational axis, therefore, the coefficient of 342, an element of the 1st order moment of joint 3 becomes zero. Moreover, inertial tensoils 3 1 1 1 and 3133 have the same parameter coefficient. Where, 34;: Element of a;, /3 : 8 2 +83. From the above considerations, the base parameters of joint 3 can be easily extracted. The base parameters of the other joints can also be extracted in a similar manner. 3 Identification experiment 3.1 Overview of experiment Figure 2 shows a schematic diagram of the applied experimental system. The manipulator was driven by feed-forward control (see eq. ( 14 )) based on approximate dynamic parameters, to achieve desirable motions for identification. The approximate parameters were determined by considering the mass, the manipulator geometry and adequately assumed friction parameters. 7i = Tf i (ed,ed,ed) + K,;(& - 6) + KPi(ed - e ) (14) where, &Joint angle, &Joint angular velocity, &Joint angular acceleration, K,; : Velocity feedback coefficient, K,; : Position feedback coefficient. Motor currents as joint torques were measured with current probes. The data sampling time and sampling count were set to 2ms and 5000, respectively. The joint angular velocity and angular acceleration were calculated by smooth numerical differentiation of angular displacement data in the following manner. First, a sampled signal y(i) is assumed to be expressed by eq. ( 15 ). y(i) = .(j - i ) 2 + b ( j - 1) + c (15) where, j = (i - m), ..., i, ..., (i + rn) Coefficients a, b and c are determined by applying the least squares method to the measured motion data, Consequently, the velocity and the acceleration can be accurately estimated. In the experiment, the number was set to 8. 3.2 Motion planning for identification As discussed before, adequate manipulator motion is necessary for accurate parameter identification. In this study, the following indexes were introduced. (1) Suppression of mechanical vibrations: If the motion required for identification includes discontinuous acceleration changes, generally speaking, the accuracy of the identification computation is believed be degraded because joint torques may contain high-frequency components. (2) Persis tent ly Existing (PE) condition : To maintain the independence of each parameter coefficient , the manipulator motion should be randomized. Each parameter coefficient is expressed as a function of joint angle, angular velocity and angular acceleration. Thus, considering this nature, each joint should be driven with a different angular frequency and displacement amplitude. (3) Adequa te manipulator configuration and motion conditions: Identification accuracy is degraded when significant imbalances exist between the parameter coefficients. These imbalances are considered to appear under certain motion conditions because the parameter coefficients depend on the joint variables. Therefore, an experiment was performed to determine the adequate conditions of manipulator , joint angular velocity, and angular acceleration for identification. The motion conditions are summarized as follows. [l] The displacement of joint i is represented as a sinusoidal function with amplitude 8,o and angular frequency wi. [ Z ] All joints are driven at the same velocity; however, the displacement amplitude of each joint differs from that of the others. [3] The joint velocity can be changed within a certain range by changing Oi. [4] For link 2, whose posture can significantly affect the total configuration, the following configurations are used: Vertical Configuration (VC), Neutral Configuration (NC) and Horizontal Configuration (HC) (Figure Table 1 summarizes the manipulator operating conditions. The amplitude of the joint displacement and the angular frequency in these conditions are listed in Table 2. 3). 4 Experimental results Figure 4 illustrates an example of measured motion data. The measurements are taken from joint 3. As clarified by the figure, there is no significant noise, even for the acceleration data. An example of identified parameters for link 3 is shown in Figure 5, which also shows that the dynamic parameters converge when the sampling count increases."
        ]
    },
    {
        "image_filename": "designv11_28_0001657_tmag.2004.824772-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001657_tmag.2004.824772-Figure3-1.png",
        "caption": "Fig. 3. Structural finite-element model of the motor.",
        "texts": [
            " The 60 Hz wave in this case may be a fairly high phase belt harmonic [5]. The second flux density pair, under \u201cSource 2,\u201d consists of waves having mode numbers of 150. The wave at 60 Hz is the product of the fundamental MMF and stator slot permeance wave. The wave at 1814 Hz appears to be a slot ripple harmonic [6]. The third flux density pair, under \u201cSource 3,\u201d has 42. The \u201c60 Hz\u201d wave is the seventh phase belt harmonic. The 1814 Hz wave is a slot flux density harmonic. A structural finite-element model of the motor, illustrated in Fig. 3, was analyzed. The model is composed of solid, plate, beam, and linear elastic elements. The rotor and stator back iron, rotor shaft, and motor housing are modeled with solid elements, the end plates and motor teeth are modeled with plate elements, and the two cradles are modeled with a combination of plate, beam, and linear elastic elements. All materials are steel except for the copper teeth windings and aluminum end plate covers. Linear elastic elements are used to model the angular contact rolling element bearings that couple the rotor and stator through the rotor shaft and stator end plates"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003685_s1061934808090189-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003685_s1061934808090189-Figure2-1.png",
        "caption": "Fig. 2. Absorption spectra of an optode in the absence ( a ) and presence ( b ) of silver ions.",
        "texts": [
            " As PDR is known as a sensitive and specific spectrophotometric reagent for silver [29], we prepared an optode based on PDR for the spectrophotometric determination of silver without any organic solvents. For this purpose, the prepared sensor was placed in a solution containing silver ions and, after a given time, the color of the membrane changed from yellow to orange. To select a suitable wavelength, the absorption spectra of an immobilized form of PDR on triacetylcellulose membrane in the absence and presence of silver ions are measured. As is obvious from Fig. 2, the maximum absorption wavelength of PDR in the membrane is 450 nm, whereas it shifts after the formation of the Ag-PDR complex. The absorbance of the optode was measured at 550 nm against a blank membrane in further studies, because only the Ag-PDR complex absorbs at this wavelength. Effect of variables and optode characteristics. In order to provide a stable, sensitive, and homogeneous membrane, the effect of the variables on the preparation of an optical sensor was investigated. In preliminary experiments, the effect of ethanol, THF, DMF, acetonitril, and ethylenediamine as solvents for the preparation of the PDR solution was investigated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002372_1.2167651-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002372_1.2167651-Figure2-1.png",
        "caption": "Fig. 2 Two different locations of point C with respect to A and O",
        "texts": [
            "org/about-asme/terms-of-use Downloaded F denoted by x and y, respectively. Also we assume the link AB b2 to be lengthy enough for the link OAA to be a crank. From the geometric point of view it is clear that the path of point C is the locus of all points having the same distances a from a fixed reference circle in the line of sight of a fixed reference point at the origin. The center and radius of the fixed circle are OA \u2212b3,0 and b1, respectively. It is important to note that point C during its motion can be located on two different sides of point O. Figure 2 shows these two places. First we assume that point C is located on the left side of the axis y Fig. 2 a . The equation of the fixed circle which is the locus of point A is as follows: xA + b3 2 + yA 2 = b1 2 1 To derive the equation of the path of point C we define two vec- tors OA =xAi\u0302+yAj\u0302 and OC =xCi\u0302+yCj\u0302. First let assume point C to be on the same side of A with respect to the origin as shown in Fig. 2 a . In other words, a b3+b1. From dot and cross product of two vectors OA and OC the following relationships can be written: OA \u00b7 OC = xCxA + yCyA = a + xC 2 + yC 2 xC 2 + yC 2 2 OA OC = xAyC \u2212 yAxC = 0 3 Solving Eqs. 2 and 3 , xA and yA are found with respect to xC and yC as follows: xA = 1 + a xC 2 + yC 2 xC, yA = 1 + a xC 2 + yC 2 yC 4 Now with the aid of the relation OA \u2212 OC =a, Eq. 1 , and the result 4 , the equation of the path of point C is derived as follows: rom: http://mechanicaldesign"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002852_iros.2006.281799-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002852_iros.2006.281799-Figure6-1.png",
        "caption": "Fig. 6 The sudden change in joint velocity at an arbitrary initial posture",
        "texts": [
            " 1, the initial joint configurations of master and slave manipulators can be decided uniquely when the initial position of c.g. of the object and the initial angles of joint 4 of master and slave manipulators are given. Therefore, the initial position and the initial angles are taken as variables for this optimization problem. In order to indicate the influence of the sudden change in joint velocity on a manipulator's behavior, an arbitrary initial position of c.g. of the object and initial angles of joint 4 for the two manipulators are chosen as respectively: (1.033,0,0.88) m, 041 = -180.40 and 042 = -160.40. Fig. 6 shows the sudden change in joint velocity at the arbitrary initial posture. For this case, the sum of the sudden change in joint velocity for the two manipulators is 81rad/s. When joint 2 of the master and slave manipulators fails and is locked at t=2.25 s, the sudden change of surviving joint 3 for the two manipulators reaches maximum value A=0.2rad/s and A=0.4rad/s respectively. In contrast, when joint 2 of the master and slave manipulators fails and is locked at t=3.35 s, the sudden changes in surviving joint 3 for the two manipulators reaches minimum value A =0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000949_20.92216-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000949_20.92216-Figure5-1.png",
        "caption": "Figure 5 shows a model of 4-pole rotating machine. Both the stator and rotor windings carry currents, and the eddy current is neglected. In this case, as the machine has 4 poles, Q is equal to 9O(deg.). Therefore, the transformation from the local coordinates to the ordinary coordinates is denoted as follows:",
        "texts": [],
        "surrounding_texts": [
            "The introduction of a periodic boundary condition in 3-D magnetic field analysis is especially important in order to reduce the computer storage and the CPU time[l]. The periodic boundary condition in 3-D analysis, however, has not been examined systematically until now. The reasons why it has not been examined are as follows: (a) The definition of 3-D periodic phenomena has been obscure. (b) Though the periodic phenomena are defined by the flux and current distributions, the boundary conditions for the periodic phenomena must be given by the vector potential A and the electric scalar potential @ or the current vector potential 7 and the magnetic scalar potential Q . (c) The periodic conditions of A and q5 o r T and I2 cannot be directly obtained from B and J , because the A or T vector at a point cannot be directly obtained from 8 and J\" at. the point, and the scalar quantity qj or Q cannot be imagined from the vector quantities B and J . In this paper, firstly, the periodic boundary conditions in 3-D analysis using the A-q5 method are clarified by investigating the above-mentioned problems. Secondly, the usefulness of the periodic boundary conditions is shown by examing the CPU time when the periodic conditions are applied. Lastly, the periodic conditions are applied to the analysis of an actual induction motor. 2. PERIODIC BOUNDARY _ _ -. ~~ ___ - 2.1 Definition of 3-D periodic phenomena In usual rotating machines, the flux and current are distributed periodically in the 2-D plane, even if the construction of the machine and the flux and current distributions are 3-dimensional. In this case, as the flux and current, distributions are point symmetric, there is a center line. The case when the center line is a straight line and is perpendicular to 2-D plane on which the phenomena are periodic is considered. The definition of the periodic phenomena in 3-D magnetic field is as follows: B and .J vectors have three components and are distributed periodically on a flat plane which is perpendicular to the center line of symmetry. Let u s consider two points p and q on a plane Spq as shown in Fig.l. The line 0-01 is perpendicular to the plane Spq and it is the center line of symmet.ry. The points p and q are chosen so that the distance between two points o and p is equal to that between o and q, and the angle between two lines 0-p and 0-q is equal t o 8 on the plane Spq. Next, let u s consider t.he plane Sp including the point p and the cent.er line and the plane Sq including the point q and the cent,er line, which are perpendicular t o the plane Spq. Sp coincides with Sq when Sp is rotated by the angle 8 along the line 0-oL. The definition of the periodic boundary in 3-D magnetic field analysis is as follows: In order to define periodic boundaries, 1/2 period of the change of phenomena is considered. If the flux I densities 3 p and B q and current densities at the points p and q satisfy the following the planes Sp and Sq are called the boundaries\". q x ' 9 Y ' B = - B P X P Y P Z P X B = - 0 B = - J = - J B c l Z ' c l X ' q Y ' J p y = - J J = - J P Z q z ' G p and .Iq equations, I' pe r i odic (1) ( 2 ) ( 3 ) ( 4 ) ( 5 ) (6) Where Bpx, Bpz and Jpx, Jpy, Jpz are the x-, y;, and z-components of W p and J p respectively. Bqx , Bqy', Bqz' and Jqx', Jqy', Jqz' are the x'-, y'- and 2'-components of B q and 9 q respectively. x', y' and z ' are the local coordinates and the angle between xand x'-axes is equal to 8. The planes Sp and Sq may also be curved as shown in Fig.2. The points p' and q' which are on the plane Spq should satisfy the same conditions as those mentioned above for the points p and q. Bpy, f X ' Y ' F i g . 1 Periodic boundaries. Fig.2 C u r v e d periodic boundaries. 0018-9464/88/ 1100-2694%01.000 1988 IEEE 2695 2.2 Periodic conditions of A and @ __ .- - - . - - - - - __ As the magnetic fields are determined from .4 and @ in the A - @ method, the boundary conditions for the periodic phenomena should be given by A and 9. Therefore, the periodic conditions of A and @ have to be examined. As the vector potential A corresponds to the current density 9 [2], the following relationships between the x-, y- and z-components Apx, Apy and Apz at the point p and those Aqx', Aqy' and Aqz' at the point q can be obtained: A = - A P X q x ' ( 7 ) A = - A P Y Q Y ' ( 8 ) P Z Q 2 ' (9 ) A = - A J e can be written using A and @ as follow: (10) aA Ye=-u (- +grad#) a t As the direction of J e is the same as that of A , the direction of grad @ should be also the same as that of A . Also, the direction of A vector at the point p is opposite to that at the point q as denoted by Eqs.(7)( 9 ) . Therefore, the sign of grad@ at the point p is different from that at the point q. As a result, the following relationship between #p at the point p and $ q at the point q is obtained. o p = - @ q (11) -3. APPLICATIONS AND-DISCUSSIONS 2.1 Simple models The usefulness of the boundary condition has been examined by applying it to simple models. Figure 3 shows a cylinder with two slits at symmetrical positions. The magnetic field is uniformly applied in the y-direction and decays exponentially with time as follows: (TI (12) B y le-t'0.0009 The flux distribution is point syametric with respect to the line 0 1 - 0 2 as shown in Fig.4. The angle Q is equal to 180(deg.) in this model. It corresponds to a 2-pole machine. The flux distribution and the starting current of a 3-phase 4-pole induction motor with a massive rotor shown in Fig.6 are analyzed using 3-D finite element method, and compared with t.hose of 2-D analysis. It is assumed that the relative permeabilitiw of the rotor and stator cores arc constant(linear), and each is assumed to be 1000. The conductivity of the rotor core is l.OxlO'(S/m). The m.a.f. per one slot is 250(AT). The frequency is 50(Hz) . In 3-D model(Fig.G(a)), the planes p-o-ol-p~-p and 9-0-01- ql-q are the periodic boundaries. The vector potential Az on the z-axis is equal to zero. It is assumed that the flux is parallel to the plane p-9-91- 2696 pl-p, namely A is equal to zero on the plane. In 2-D model(Fig.G(b)), the lines p-o and q-o are the periodic boundaries, and Az at the point o is zero. The curved line p-q is the Dirichlet boundary. Figure 7 shows the equipotential contour plots of Az on the plane z=O in 3-D and 2-D analyses. The Figures denote that the flux in 3-D model is larger than that in 2-D model. This is because the eddy current density in 3-D model is smaller than that in 2- D model due to the longer eddy current path length in 3-D model as shown in Fig.8. Starting currents of induction motor are calculated by assuming that the applied voltages (=200(V)) to 3-D and 2-D models are the same. The calculated starting current of 3-D model is smaller than that of 2-D model by 25(%). a windins A d ' Y + a P - ' X e- (a) bird's-eye view (b) cross section Fig.6 3-phase induction motor. \" I ( a ) 3-D model p 1 (b) 2-D model F i g . 7 Equipotential contour p l o t s . (a) 3 - D model ( b ) 2-D model Fig.8 Eddy current p a t h s in rotor. 4 . CONGLUSIONS .- Although the periodic boundary conditions for A - @ method is examined, the periodic conditions for other methods, such as T-62 method, can also be treated in the same way. The boundary condition which appear, for example, in the linear induction motor[l] is different from that examined in this paper. This will be reported in an another paper later. ACKNOWLEDGEMENT _______ This work was partly supported by the Grant-in-Aid from the KiKai Kogyo Shinko Zaidan, Tokyo Japan. REFERENCES ~- [ l ] J.R.Brauer, G.A.Zimmerlee, T.A.Bush, R.J.Sande1 and R.D.Schultz: \"3D Finite Element Analysis of Automotive Alternators under Any Load\", IEEE Trans. on Magnetics, MAG-24, 1, 500 (1988). [ Z ] T.Nakata and N.Takahashi: \"Finite Element Method in Electrical Engineering\", (book), Morikita Publishing Co., Tokyo (1987). [3] D.S.Kershaw: \"The Incomplete Cholesky-Conjugate Gradient Method for the Iterative Solution of Systems of Linear Equations\", Journal of Computational Physics, 2 6 , 4 3 (1987). [4] T.Narita, M.Kawabe and H.Nakagawa: \"Performance Analysis of Linear Pulse Motor by Finite Element Method\", Shinko Electric Journal, 29, 2, 18 (1984). The periodic boundary condition for 3-D A - @ method has been examined, and the usefulness of the condition is demonstrated. The obtained results can be summarized as follows: (a) The definition of 3-D periodic phenomena has been clarified. (b) The periodic conditions of A and @ is obtained. ( c ) The CPU time can be considerably decreased by using the periodic condition."
        ]
    },
    {
        "image_filename": "designv11_28_0001063_imece2002-33568-Figure27-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001063_imece2002-33568-Figure27-1.png",
        "caption": "Figure 27. Location of residual stress measurement in IMS-T1 part (see Table 2 for measurement values)",
        "texts": [
            " This helped to develop a strategy to build up multiple layers before the accumulated residual stress can lead to cracking. After the deposition of a predetermined number of layers, stress relieving is carried out before further layers are deposited. This strategy led to successful fabrication of full size components as shown in Figure 20-22. As an example, the fabricated IMS-T1 sample was sent to a service company (Lambda Research) for residual-stress measurements by x-ray diffraction technique. Figure 27 shows the points where stress was measured. Locations 2, 5, and 6 are deposited during the last run and thus, show residual compressive stress, since they were not stress relieved. The other locations were deposited in earlier runs and were subsequently stress relieved. They show negligible residual stress, whereas the maximum stress at the location without stress relieving is +49.4 ksi (Location 6, Table 2). loaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/31/2016 Term This paper presented scientific accomplishments and fabrication technique development related to rapid manufacturing by laser aided direct metal deposition process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003704_ecce.2009.5316465-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003704_ecce.2009.5316465-Figure9-1.png",
        "caption": "Fig. 9. Finite element analysis results of magnet flux distribution for (a) healthy motor; and (b) faulty motor with 3 broken rotor bars",
        "texts": [
            " FINITE ELEMENT ANALYSIS To verify the equivalent circuit based analysis provided in III, a finite element analysis (FEA) simulation was performed. The 2 dimensional (x-y or r-\u03b8) cross-sectional view of the entire machine with appropriate circuit connectivity was modeled using the FEA program so that the physics of broken bar is represented accurately. The entire 360\u00b0 of the machine cross section of a multi-pole machine is required to be modeled, as the broken bars upset the inherent exploitation of the one pole-pitch based electromagnetic symmetry, as shown in the machine model outline in Fig. 9 (a 4 pole machine with 44 bars is considered). It is assumed that the end rings provide ideal short circuits at both ends of the rotor for simplicity as this does not significantly impact the overall results of the given problem. The FEA program is run in the time transient mode without motion to replicate the standstill excitation conditions used in the proposed method. The standard magnetic vector potential and electric scalar potential based formulation of Maxwell\u2019s equations that has been reported in the literature from the early 1970\u2019s is used. As an illustration, an instant of the magnetic flux distribution for healthy and faulty motors are shown in Fig. 9(a)-(b), respectively. It can be seen that the 4 pole magnetic flux symmetry is evident in the healthy case (Fig. 9(a)). For evaluating of the impact of broken bars, 3 broken bars that are not electrically conductive were placed at the x-axis location (Fig. 9(b)). The location of the broken bars is 90 electrical degrees apart from the \u03b8=0o location as in the Fig. 4 case. It can be seen in Fig. 9(b) that the magnetic flux penetrates deeper in the rotor at the x-axis location since there is no current induced in the broken bars, while the rest of the machine maintains the four-pole flux pattern. The pattern of Req, Xeq, |Iqs|, and Pin in the presence of 3 broken bars was calculated using (6)-(8) from the steady state voltages and currents of the stator 3-phase windings \u201cmeasured\u201d from the external circuit connectivity. The % variations in Req, Xeq, |Iqs|, and Pin with respect to the healthy motor under 10hz excitation are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001016_0954405011518430-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001016_0954405011518430-Figure6-1.png",
        "caption": "Fig. 6 Strategy of an uncoupled FE simulation",
        "texts": [
            " Today, a coupled FE simulation using deformable dies for complex threedimensional FE models needs substantially longer CPU (central processing unit) time than with rigid dies. Therefore, the IFUM has developed a software tool that uses an uncoupled calculation of the workpiece and dies with FORGE3 for the mechanical model and MSC.MARC for the thermal analysis [12]. At IFUM, helical gear wheels have been formed in a precision forging process. Characteristics for this process are the high local stresses in the dies. For this reason, the thermal die loading due to the forging process was investigated by the uncoupled method (Fig. 6). Firstly, an FE simulation of the forging process was performed with rigid dies. This simulation was performed with the commercial FE package FORGE3. The thermal \u00af uxes into the rigid dies were then determined during this simulation. Subsequent calculation of the thermal die loading was performed with the previously determined external \u00af uxes. The split nodal \u00af uxes are brought on to the meshed dies as boundary conditions. This strategy leads to short CPU times. A previous investigation of a three-dimensional FE simulation of an orbital forging process resulted in a reduction in CPU time of about 50 per cent in comparison with the coupled method [12]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000778_s0045-7949(02)00294-8-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000778_s0045-7949(02)00294-8-Figure4-1.png",
        "caption": "Fig. 4. 78-node cantilever rectangular plate.",
        "texts": [
            " The natural frequencies and generalized mode shape of each order of total system can be obtained by solving Eq. (28). By using coordinate transformation of Eq. (27), the real mode shape of each order of total system under physical coordinates can be obtained. In order to check out the approach outlined in the preceding sections, one example is used to illustrate the effectiveness of the proposed method. Example: The free vibration of a cantilever plate taken from Ref. [14] is considered. The dimensions and properties of the plate are shown in Fig. 4. FEM method of the full-plate, Craig\u2013Bampton method, and the proposed method are used to calculate the mode shapes and frequencies of the plate. When Craig\u2013 Bampton method is used, the substructure boundary b1 is located on the plate, as shown in Fig. 4. However, when the proposed method is used, boundaries b1 and b2 are located and the elements between them in the cantilever plate are regard as a flexible substructure. Tables 1 and 2 show respectively the frequencies and the amplitudes of several node points for modes 3 and 6 obtained by the three methods indicated previously. Further results of this investigation are given in Ref. [14]. It can be found from Tables 1 and 2 that the proposed method gives acceptable mode shape as well as frequency results when compared with the full-plate solution obtained by FEM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001749_icarcv.2002.1238554-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001749_icarcv.2002.1238554-Figure4-1.png",
        "caption": "Fig. 4: Sunibcr of sectors and center point of a. sector",
        "texts": [
            " etc) as shown in Fig 3 Find tlic point iiisidc this area lying on tlic iiitcrscction of bisccting ra.tlia1 linc of each sector a.nd tllc a.rc diridiiig this a,rca. into two equal parts. Thicsc poiiits arc shown as point for area ubcrl. point n i p for area d e f. point m a for area e f bu. point ~ n 1 for axca ghij etc. A detailed discussion rcgardnilg these poiiits follow. Let 11s sa>-: radius of thic 0'\" circle is '1-0. Then i\"* conccutric circle lias a. radius 0.4:) of 1.0 +i*rleh.. . n e dcsircd unit arc3 is ILr; (Fig 4). The circular area. lying bctwecn thc two coiicciitric circles of radius rj 1 and T+ has to be dicidcd in sectors of cqud unit area. of IIra. So. the number of (uilit area.) sectors (ti..o..s:) bctwccn i l h a i d ( i + l ) ' / l circle is (I.? -./::)/I.;. higle made by the two radial lines of tliosc sections is 3FO/n.o..~. One of such a sector is shown as pqrs in Fig 4. &iter point of sector pyrs is sliowii as in,,. This point lies on the intersection of bisecting radial linc wluch bisects the a.iiglc made by the arc. ad at tlic center and tlic a.rc r ~ l r ~ 2 w'tiicli dividcs the sector pyrs iiito t m equa.1 parts of arcas -41 and -4.3. Thus radius of point ' i n p will i)c vj = w. Coorclinatcs of the center point of ca.cli scctor arc found oiit. Consc qucntlx. the roordiiiatcs of a11 the four points of cach wctor arc a.1~0 dctcni~icd. for csmiiplc poults y. y. Y and s for pp.s sector in Fig 4- It mi be observed tkit that if T O and dclr are of sane valuc then t.hc iiiuiibcr of sectors hctwwn i f I'h circIc aid i'\" circ.1~ is 4i + 1. Step 4 : Pcrforin inverse ki1icniatic.s at the points m.1~ i n d . 9~1.1 ... ctc following Padcii-Iiahi's method [I 11. Esistciicc or iioncxistciicc of iiivcisc khiciiiatics dctcrininc wvhcthcr tlic corresponding sector is iiisidc tlic workspacc or outside ttic rvoskspacc. If the iiiverse kiiicmatics exists a t any such poiiit tlicii thc corresponding sector is imide tlic workspacc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003307_1377999.1378055-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003307_1377999.1378055-Figure3-1.png",
        "caption": "Figure 3. Test system configuration",
        "texts": [
            " We used Logitech\u2019s MONO Racing Force Feedback Wheel, an 11-inch wheel with six programmable buttons, acceleration and brake pedals, two shifting option buttons, and the force feedback function (Figure 2-(a)) for the steering wheel type interface. This is the only interface that uses foot pedals for certain functions in our study. The key mapping used for the steering wheel with pedals is as follows: the pedal #1 was mapped for moving the robot in the forward direction, while the pedal #2 moved the robot backward. Turning the wheel counterclockwise controlled the robot for turning towards left, while turning the wheel clockwise rotated the robot towards the right (Figure 3-(a)). Button #5 signaled the end of task. Joystick. The last interface is a joystick with conveniently placed action buttons. We used Logitech\u2019s Extreme 3D Pro that supports an eight-way rubberized hat, a twist handle, and a rapid-fire trigger function (Figure 2-(b)). The key mapping for the joystick was pretty straightforward. The robot moved forward when the subject pushed the joystick forward. The robot moved backward when the subject pulled the joystick the other way. Moving the joystick to left rotated the robot towards left, and moving the joystick to right rotated the robot towards right. Button #5 also signals the end of task (Figure 3-(b)). 9th Intl. Conf. on Human Computer Interaction with Mobile Devices and Services (MobileHCI\u201907) 463 The system configuration for measuring user performance with 4 types of input interfaces is shown in Figure 3. The input device for a button and acceleration sensor, the Wiimote, could communicate with an Ultra-Mobile PC through the Bluetooth protocol with a BCM2042 chip set. The joystick and the steering wheel with pedals communicated through the Universal Serial Bus port in the Ultra-Mobile PC. The Ultra-Mobile PC, model Q1 from Samsung Electronics, used the Intel Pentium M processors and Microsoft Windows XP Tablet OS. Its display was a 7-inch touch screen. The user performance measuring program was executed on the Ultra-Mobile PC"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000781_la020411o-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000781_la020411o-Figure3-1.png",
        "caption": "Figure 3. Border of a water puddle: schematic representation of the three menisci at the liquid/liquid/air contact line (cross section).",
        "texts": [
            " If R is the angle of the meridian tangent with the x axis, where p(x, z) is the hydrostatic pressure (excluding the atmospheric pressure p0): p(x, z) ) Fg(e - z). Equation 15 simply reduces to The integral that gives the tension EA (eq 14) then becomes where we have introduced two successive changes of variable dx ) dz/tan(R) and dz ) -dR\u03ba-1 cos(R/2). The procedure yields In the limit of small angles, eq 18 reduces to This holds for one meniscus. In the liquid/liquid case, we have to add the three values for each meniscus, characterized by the three capillary lengths \u03baA -1, \u03baAB -1, and \u03baB -1 and the three contact angles RA, RAB, and RB shown in Figure 3. We have 2.3. Energy of a Modulated Line. We consider now the contact line which borders the water puddle. We note u(x) the deformation of the line with respect to the unperturbed position (straight line or arc of circle) and u(q) the Fourier transform of the contour. In the capillary regime, we can generalize the Joannyde Gennes expression. where \u03b3\u0303-1 ) \u03b3A -1 + \u03b3B -1.14,16 In the gravity regime, deformations are screened at \u03baij -1. The energy (as for a guitar string) is proportional to the increase of the contour length: \u03a0A - \u03a0B ) u R (12) 1 2 F\u0303ge2 ) 1 2 F\u0303gec 2 + u R (13) EA ) \u222b0 \u221e[\u03b3(ds dx - 1) + 1 2 Fg(e - \u00fa)2] dx (14) \u03b3(1 - cos R) - 1 2 Fge2 + \u222b0 \u00fa(x) p(x, z) dz ) 0 (15) 2 sin(R2) ) \u03ba(e - \u00fa(x)) (16) EA ) \u222b0 \u221e dx ( 1 cos R - cos R) ) -\u222bRA 0 2 sin(R2) cos2(R2)\u03b3\u03ba -1 dR (17) EA ) 4 3 \u03b3\u03ba -1(1 - cos3(RA 2 )) (18) EA ) 1 2 \u03b3\u03ba -1RA 2 (19) u ) EA + EB + EAB (20) Eel q ) 1 2 \u03b3\u0303\u03b8E 2 |q||uq|2 (21) Eel q ) 1 2 uq2|uq|2 (22) with u given by eqs 18-20"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002192_pes.2004.1372764-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002192_pes.2004.1372764-Figure6-1.png",
        "caption": "Fig. 6. Zone 2 element with Lenticular characteristic",
        "texts": [
            " In other cases the reach settings are changed to reduce the probability for tripping under load conditions. However, this reduces the effectiveness of Zone 3 as a remote backup protection element. All of the above has been taken into consideration in the design of modern microprocessor based transmission line protection relays with distance characteristics. To avoid the operation of a Zone 3 distance element with Mho characteristic one can select to use instead a \u201clenticular\u201d (lens-shaped) characteristic. From Figure 6 it is clear that the resistive coverage of this characteristic is restricted. The aspect ratio of the lens a/b is adjustable. By selecting the configuration parameter a/b the user can provide the maximum fault resistance coverage and at the same time avoid the operation under maximum load transfer conditions. However, it is clear that the resistive coverage is not consistent along the length of the line and varies with the location of the fault. Faults at the end of Zone 2 will probably be cleared by Zone 3 in the cases when there is arc resistance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003658_13506501jet540-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003658_13506501jet540-Figure2-1.png",
        "caption": "Fig. 2 Schematic diagram of the block-on-ring tribometer [17]",
        "texts": [
            " The model relates the coefficient of friction to the chemical sensitivity of the lubricant and its relevance at different points within the cam/follower cycle and describes the relationship between friction coefficient and the chemical concentration of a molybdenum dithiocarbamate in PAO6 base oil containing 1.2 wt% zinc dialkyldithiophosphate (ZDDP). Considerable research has been reported on the friction at the cam/follower interface, explaining the dominance of high contact pressure and sliding between the surfaces in the lubricated contact zones of the flank and the nose region of the cam, leading to boundary and mixed lubrications [21]. A bench tribometer \u2018block-on-ring\u2019 (Fig. 2) was selected to study the friction response of the tribofilm formed by a typical friction modifier, molybdenum dithiocarbamate, in a model automotive engine lubricant (also containing ZDDP in a synthetic polyalphaolefin base oil) under boundary and mixed lubrication conditions, representative of severe conditions at the cam and follower interface in an automotive engine. The ring and block specimens were manufactured from the same batch of AISI 52100 alloy steel for uniformity and were through hardened to 64 Rockwell C, a representative measurement for a valve train cam and follower"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003554_978-3-540-30301-5_4-Figure3.14-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003554_978-3-540-30301-5_4-Figure3.14-1.png",
        "caption": "Fig. 3.14 The Adept robot uses closed-loop control and variable-reluctance motors",
        "texts": [
            " They are relatively low in cost and interface easily to electronic drive circuits. Microstep control can produce 10 000 or more discrete Part A 3 .7 robot joint positions. In open-loop step mode the motors and robot motions have a significant settling time, which can be damped either mechanically or through the application of control algorithms. Power-to-weight ratios are lower for stepper motors than for other types of electric motors. Stepper motors operated with closedloop control function similarly to direct-current (DC) or alternating-current (AC) servomotors (Fig. 3.14). Permanent-Magnet DC Motor. The permanent-magnet, direct-current, brush-commutated motor is widely available and comes in many different types and configurations. The lowest-cost permanent-magnet motors use ceramic (ferrite) magnets. Robot toys and hobby robots often use this type of motor. Neodymium (NEO) magnet motors have the highest energy-product magnets, and in general produce the most torque and power for their size. Ironless rotor motors, often used in small robots, typically have copper wire conductors molded into epoxy or composite cup or disk rotor structures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002607_analsci.22.29-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002607_analsci.22.29-Figure2-1.png",
        "caption": "Fig. 2 Optimized flow-assembly. Q1, Bromoxynil in ethanol and KOH medium; Q2, water as a carrier; Q3, KMnO4 in a polyphosphoric medium as an oxidative system; V, injection valve; B, peristaltic pump; PR, photoreactor; PMT, photomultiplier tube; W, waste. (a) confluence for mixing solutions (sample and photo-degradation medium solutions) in the assembly for preliminary assays.",
        "texts": [
            " Other used reagents were: KMnO4, H2SO4, K3Fe(CN)6, NaCl, Triton X-100, Na2B4O7\u00b7 10H2O, Fe(NO3)3\u00b79H2O, Cr(NO3)3\u00b79H2O, N,N-dimethylformamide, 2-propanol, formic acid, KCl, N-bromosuccinimide, NaNO3 from Panreac; polyphosphoric acid from Riedel-de Ha\u00ebn; Ce(NH4)2(NO3)6, NH4OH, NH4Cl, Na2HPO4\u00b712H2O, Na2SO4, CaCl2\u00b72H2O, NiCl2, CuSO4\u00b75H2O, NaNO2, KOH from Probus; ethanol, acetonitrile, N-cetyl-N,N,N-trimethylammonium bromide from Merck; NaOH, HCl, acetic acid, KH2PO4 from J. T. Baker; FeSO4\u00b77H2O, sodium dodecyl sulfate, hexadecyl pyridinium chloride, \u03b2-cyclodextrine from Fluka; acetone, glycine, polysorbate 80, quinine sulfate, benzalkonium chloride, KHCO3 from Guinama; KH2PO4\u00b72H2O from UCB; ZnCl2 CuSO4\u00b75H2O, KI from Scharlau; MgCl2\u00b76H2O, H2O2 from Prolabo. Ioxynil, a pesticide from the Bromoxynil family and assayed as an interferent, was also from Dr. Ehrenstorfer, 99.8% according to the label claim. The flow system is illustrated in Fig. 2. It consisted of a photo-reactor made of 173 cm of a PTFE coil, 0.8 mm internal diameter (Omnifit), helically coiled around a 8 W low-pressure mercury lamp (Sylvania) for germicidal use; a Rheodyne Model 5041 injection valve, and a Gilson Minipuls 2 peristaltic pump provided with flexible pump tubing from Omnifit. The measurement of the chemiluminescence emission was achieved by means of a home-made flow-cell that consisted of a flat spiral-coiled quartz tube (1.0 mm i.d., 3 cm total diameter, without gaps between loops)",
            " From an analytical point of view, the most interesting photo-induced chemiluminescence effects were included in groups (d) and (e), and they were suitable for developing new and sensitive chemiluminescent analytical procedures. These two groups comprised 25% of the pesticides tested. Bromoxynil presented a very weak response with the lamp OFF in all media (three folds the noise of the base line) and increased the chemiluminescent outputs by a factor of 30 in 10\u20133 mol l\u20131 NaOH as the medium of photodegradation. The flow system and solutions adopted for further Bromoxynil determinations are shown in Fig. 2a. Bromoxynil was selected as the result of the reported wide screening test on pesticides. The flow system illustrated in Fig. 2a was also used for preliminary assays while trying to observe the best medium for the photo-degradation of Bromoxynil. A suitable oxidant was established by testing some strong oxidant systems, namely: 4 \u00d7 10\u20134 mol l\u20131 potassium permanganate or 6 \u00d7 10\u20133 mol l\u20131 Ce(IV) (both of them in 1.5 mol l\u20131 H2SO4); 6 \u00d7 10\u20133 mol l\u20131 Fe(CN)6 3\u2013 and 4 \u00d7 10\u20132 mol l\u20131 N-bromosuccinimide (both in 1.5 mol l\u20131 NaOH). As illustrated in Fig. 3, the best outputs were obtained with potassium permanganate and hexacyanoferrate(III)",
            "22% polyphosphoric (which provided the highest outputs) were compared by testing different concentrations of Bromoxynil from 0.1 to 10 mg l\u20131). Figure 4 shows the results obtained with the best sensitivity for the 0.22% polyphosphoric acid medium. Influence of the medium on the photodegradation and/or the chemiluminescence Modifications on the pH as well as the presence of some substances, e.g. Fe(II) or Fe(III), H2O2, organized media or sensitizers, can strongly affect the photodegradation process and the chemiluminescence behavior. The following substances were assayed by merging with the sample solution (shown in Fig. 2a) at the indicated concentration, between branches variation vs. reference (aqueous solutions containing 5 mg l\u20131 of Bromoxynil\u2013): \u03b2-cyclodextrine 0.73%, (+20%); benzalkonium chloride 0.54%, (\u201397%); N-cetyl-N,N,N-trimethylammonium bromide 0.11%, (\u201370%); hexadecylpyridinium chloride 0.11%, (\u201399%); sodium dodecylsulfate (SDS) 0.68%, (+83%); Triton X-100 0.064%, (+74%); Tween 80 0.06%, (+47%); 2-propanol 20%, (+294%); acetone 0.5%, (\u201393%), acetonitrile 20% (\u201397%); dimethylformamide 5%, (+40%); dioxane 5%, (\u201324%); ethanol 5%, (+465%); formic acid 0",
            "42,44,45 Hidroxylated compounds (bromine is substituted by an OH), as 3,4-dihydroxy-5-bromobenzonitrile and 3,4,5-trihydroxy- benzonitrile, and hydrogenated compounds (substitution of bromine by a H) as 3,4-dihydroxybenzonitrile and 4-hydroxybenzonitrile, were observed by GC-MS42 after 10 min of irradiation at 254 nm (low-pressure vapor mercury lamp) at pH 7 in a phosphate buffer. With the new flow conditions, each chemical parameter was re-optimized (univariant method) by testing other values around that previously selected as optimum. The substitution of NaOH by KOH resulted in higher outputs. The confluence between the sample and the medium of photodegradation was removed to avoid any unnecessary dilution of the sample. Finally, the selected manifold was as illustrated in Fig. 2 where Q1 is the sample in 0.014 mol l\u20131 KOH and 1% of ethanol flowing at 4.4 ml min\u20131, V is a loop of 644 \u00b5l, Q2 is the carrier (pure water) at 9.8 ml min\u20131, and Q3 is 1.4 \u00d7 10\u20134 mol l\u20131 KMnO4 in 0.21% H4P2O7 flowing at 2.9 ml min\u20131. The dynamic range was found to be between 5 \u00d7 l0\u20133 and 5 mg l\u20131 of Bromoxynil, and fitted with the equation I = (\u201310400 \u00b1 1500)C2 + (82000 \u00b1 8000)C + (7000 \u00b1 4000) with a correlation coefficient of 0.9993, where I is the chemiluminescent emission in counts and C is the pesticide concentration in mg l\u20131"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002660_iros.2006.282408-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002660_iros.2006.282408-Figure3-1.png",
        "caption": "Fig. 3. Applied wrench and imposed wrench at the foot.",
        "texts": [
            "\u201d The notation in the model is as follows: m0 Mass of the foot link m1 Mass of the first link (leg) m2 Mass of the second link (upper body) lb Distance from CoM of the foot link to the first joint lg1 Distance from the first joint to CoM of the first link lg2 Distance from the second joint to CoM of the second link l1 Length of the first link \u03a3i Inertial coordinate frame \u03a3f Foot coordinate frame \u03b80 Angle from the inertial coordinate frame to the foot coordinate frame \u03b81 Angle of the ankle joint \u03b82 Angle of the hip joint I0 Inertia moment of the foot link I1 Inertia moment of the first link I2 Inertia moment of the second link r0 Position vector from inertial coordinate frame to foot coordinate frame The equation of motion of the three link model can be written as follows:[ Hf Hfl HT fl H l ] [ x\u0308 \u03b8\u0308 ] + [ cf cl ] + [ gf gl ] = [ 0 \u03c4 ] + [ RT fp JT ] [ f n ] (7) where H l \u2208 R2\u00d72 Inertia matrix of the leg and upper body links Hf \u2208 R3\u00d73 Inertia matrix of the foot Hfl \u2208 R3\u00d72 Inertia coupling matrix cl \u2208 R2 Velocity dependent nonlinear terms of the links cf \u2208 R3 Velocity dependent nonlinear terms of the foot link gl \u2208 R2 Gravity terms of the links gf \u2208 R3 Gravity terms of the foot \u03c4 \u2208 R2 Joint torque x\u0308 \u2208 R3 Acceleration of the foot \u03b8\u0308 \u2208 R2 Joint angular acceleration We assume that an external wrench [fT n]T is acting at the upper body link at a point displaced by a units from the CoM of this link outward. This is illustrated in Fig. 3. We expand the external wrench term in Eq. (7), as:\u23a1 \u23a2\u23a2\u23a2\u23a2\u23a3 ffx ffz nf \u03c4 \u2032 1 \u03c4 \u2032 2 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a6 = [ RT fp JT ] [ f n ] (8) where ffx x-component of the imposed wrench at the foot ffz z-component of the imposed wrench at the foot nf Moment component of the imposed wrench at the foot \u03c4 \u2032 1 Ankle joint torque due to applied external wrench \u03c4 \u2032 2 Hip joint torque due to applied external wrench RT fp = [ I2\u00d72 0 [rfp\u00d7] 1 ] = \u23a1 \u23a3 1 0 0 0 1 0 \u2212rfpz rfpx 1 \u23a4 \u23a6 (9) [rfp\u00d7] = [\u2212rfpz rfpx ] (10) rfp = [ rfpx rfpz ] = [ xb + l1C1 + (lg2 + a)C12 l1S1 + (lg2 + a)S12 ] (11) In addition, the Jacobian matrix for the point where the wrench is applied, is: J = \u23a1 \u23a3\u2212l1S1 \u2212 (lg2 + a)S12 \u2212(lg2 + a)S12 l1C1 + (lg2 + a)C12 (lg2 + a)C12 1 1 \u23a4 \u23a6 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001914_05698190490439346-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001914_05698190490439346-Figure1-1.png",
        "caption": "Fig. 1\u2014Connecting rod assembly.",
        "texts": [
            " The analysis was based on the finite element method, which includes effects of interference fitted bearings and pre-loaded bolts. The rod inertia force associated with the gas pressure was found to have a significant effect on the varia- tion of the rod bearing shape. The shape variation of a connect- ing rod assembly is commonly ignored in rod bearing analyses. Investigation of bearing deformation was conducted in order to evaluate the lubrication characteristics. Elastohydrodynamic Lubrication; Connecting Rod Bearing; Inertial Force; Bearing Deformation A connecting rod assembly (see Fig. 1) in an engine, which consists of rod, cap, bolts, big-end (or connecting rod) bearing, and small-end bushing, links the piston pin and the crank pin and transmits force between them. The connecting rod bearing serves as an important joint between the connecting rod big-end and the crank pin. The connecting rod participates in the conversion of reciprocating motion into rotational motion. The connecting rod bearing is compressed into the big-end bore through interference in order to prevent relative rotation and to promote the conduction of heat",
            " By considering the elasticity of the connecting rod and bearing, the strain equations can be written as (\u03bb + G)\u2207(\u2207\u00b7u) + G\u22072u + Fi = 0 [7] where u(uX\u2032 , uY\u2032 , uZ\u2032 ) is the displacement vector and Fi(F X\u2032 i , FY\u2032 i , F Z\u2032 i ) is the inertial force vector. The boundary condition on Eq. [7] involves the contact problem, which will be discussed in the next section. Note, \u2207\u00b7u = \u2202uX\u2032 \u2202 X\u2032 + \u2202uY\u2032 \u2202Y\u2032 + \u2202uZ\u2032 \u2202 Z\u2032 is the total volume strain. From the previous section, the inertia forces (in the X\u2032 and Y\u2032 directions) are known at all nodal points. Due to contact, forces and moments are transmitted between contact surfaces accompanying surface deformations. There are 12 (2 \u00d7 6) contact surfaces in the connecting rod assembly (Fig. 1). These include: 1) interferenced upper and lower bearing shells; 2) rod and cap joints; 3) bearing shell back surfaces and the big-end bore; 4) bolt heads and supporting surfaces in the cap; 5) pre-loaded bolts and threads in the bolt holes; and 6) rigid shaft and bearing shell inner surfaces. For these contact surfaces, the equilibrium between internal stress components and external surface contact forces can be written as F X\u2032 s = \u03c3X\u2032 cos \u03b8X\u2032 + \u03c4X\u2032Y\u2032 cos \u03b8Y\u2032 + \u03c4Z\u2032 X\u2032 cos \u03b8Z\u2032 FY\u2032 s = \u03c4X\u2032Y\u2032 cos \u03b8X\u2032 + \u03c3Y\u2032 cos \u03b8Y\u2032 + \u03c4Y\u2032 Z\u2032 cos \u03b8Z\u2032 F Z\u2032 s = \u03c4Z\u2032 X\u2032 cos \u03b8X\u2032 + \u03c4Y\u2032 Z\u2032 cos \u03b8Y\u2032 + \u03c3Z\u2032 cos \u03b8Z\u2032   [8] where Fs(F X\u2032 s , FY\u2032 s , F Z\u2032 s ) is the surface force vector, (\u03b8X\u2032 , \u03b8Y\u2032 , \u03b8Z\u2032 ) is the angle between the surface normal direction with the (X\u2032, Y\u2032, Z\u2032) direction, and the stresses are \u03c3X\u2032 = 2G \u2202uX\u2032 \u2202 X\u2032 + \u03bb\u2207 \u00b7 u, \u03c3Y\u2032 = 2G \u2202uY\u2032 \u2202Y\u2032 + \u03bb\u2207\u00b7u, \u03c3Z\u2032 = 2G \u2202uZ\u2032 \u2202 Z + \u03bb\u2207 \u00b7 u, and \u03c4X\u2032Y\u2032 = G ( \u2202uY\u2032 \u2202 X\u2032 + \u2202uX\u2032 \u2202Y\u2032 ) , \u03c4Y\u2032 Z\u2032 = G ( \u2202uZ\u2032 \u2202Y\u2032 + \u2202uY\u2032 \u2202 Z\u2032 ) , \u03c4Z\u2032 X\u2032 = G ( \u2202uX\u2032 \u2202 Z\u2032 + \u2202uZ\u2032 \u2202 X\u2032 ) There are two kinds of boundary conditions involved in the contact problem: the prescribed surface displacement and the specified surface force",
            " Initially, the bearing shells were pressed into the big-end bore and the bolts were pre-loaded. Figure 4 shows that this process affects the initial shape of the big-end bore and the bearing. The big-end bore is expanded because of the bearing shell press-fit. The expansion in the connecting rod axis direction is smaller than in the transverse direction. Initial clearance shapes of the big-end bore and its bearing are given in Fig. 5. Minimum diametrical expansion is 0.0007 mm and is located at 126\u25e6 where the wall is thicker because of the bolthead seat (see Fig. 1). In addition, the bolt pretension loading may have a significant effect. Maximum expansion is 0.0107 mm near the clamp joint between the rod and the cap. The two bearing shells are in contact at their ends and impose higher pressure on the big-end bore. From Figs. 4 and 5 it can be observed that the bearing initial clearance shape is not uniform and certainly not circular. The clearances in the area near the clamp joint are strongly affected because of the bearing shell press-fit and the bolt pre-loading"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000808_s1000-9361(11)60181-7-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000808_s1000-9361(11)60181-7-Figure3-1.png",
        "caption": "Fig . 3 Illustration of determination o f location and",
        "texts": [],
        "surrounding_texts": [
            "The distort ion of the tooth surface caused by manufacturing processing makes the real tooth surface deflect f rom the theoret ical one. It induces tw o kinds of errors: the pitch error and the deviation of the real tooth surface f rom the theoretical one. As shown in Fig. 1, ! t is the theoret ical tooth surface and ! a is the real tooth surface. Assume that the real tooth surface rotates to ! b; M is the contact point of ! t and ! b(M is the M ean Point of the gear tooth surface) . F ig . 1 Ef fect of the toot h sur face dist ortion Because of the same manufacturing process- ing, all the teeth of the gear have the same and . According to the circle closeness principle [ 2] , is counteracted. Therefore, it is only compensat ion of that is requested to guarantee the precision of the tooth surface. 1. 2 Definition of deviation of tooth surface T he real tooth surface !a may be considered as a pile of the theoret ical tooth surface and dif ference surface[ 3] caused by distort ion of the tooth surface. Assume that the theoret ical tooth surface ! t gener- ated w ith the theoret ical machine-tool sett ings i0( i = 1, \u22ef, n, n is the number of machine-tool set ting s) is r t( u, v ) , nt ( u, v ) ( 1) w here u, v are surface coordinates, and nt is the unit surface normal. Because of the rest riction of the manufactur- ing processing, the real tooth surface does not coincide w ith the theoret ical one. The deviation of the real tooth surface from the theoret ical one is defined as the dif ference between real tooth surface and the theoretical one along the normal direct ion. Therefore, the deviat ion is independent of the coordinate sy stem . T he vector function of !a is ra = rt + ( u, v ) nt ( 2) 2 Measurement of Real T ooth Surface"
        ]
    },
    {
        "image_filename": "designv11_28_0003414_icma.2007.4303747-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003414_icma.2007.4303747-Figure1-1.png",
        "caption": "Fig. 1: A suspended mobile robot which can move on a rough terrain.",
        "texts": [
            " This may be the main reason for development of their expanding applications such as fire fighting, forestry, dismantling bombs, toxic waste cleanup, transportation of nuclear materials, and even in housekeeping tasks. Exploiting a wheeled mobile robotic system in uneven environments, it is inevitable to use some kind of suspension/tire compliance module. In addition, the use of suspension subsystem increases the safety of the base as well as its mounted arm(s), in response to shocks and jerks transmitted to them due to irregularity of the open terrain. So, a suspended wheeled mobile robot can be considered as an appropriate system for motion on rough and gentle uneven terrain, Fig. 1. Attempts for attaining the dynamical equations of motion for mobile manipulators have presented successful results. However, most of them have ignored the compliance characteristics of the structure/tire(s). A systematic method for the kinematics and dynamics modeling of a two degree-offreedom (DOF) Automated Guided Vehicle (AGV) has been presented by Saha and Angeles, [1-2]. They have employed the notion of Natural Orthogonal Complement to eliminate the Lagrange multipliers. The idea of direct path method, [3], has been utilized for deriving the dynamics of differentially-driven mobile manipulators equipped with multiple arms, [4]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001016_0954405011518430-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001016_0954405011518430-Figure1-1.png",
        "caption": "Fig. 1 Closed-die technology for the forging of a helical gear wheel",
        "texts": [
            " Keywords: metal forming, \u00ae nite element simulation, thermal die loading, drive mechanism, noncircular gears NOTATION a centre distance am, bm coeYcients of Fourier series A surface area of the die C quality of the transmission function regarding kinematic demands e distance between the centre and the pivot of an eccentrically mounted circular gear i\u2026\u2019\u2020 transmission ratio as a function of the driving angle n number of the cycle _q \u00af ux Q quantity of heat r1\u2026\u2019\u2020 pitch curve radius of the driving gear as a function of the driving angle r2\u2026\u2019\u2020 pitch curve radius of the driven gear as a function of the driving angle R radius of a circular gear s ram stroke Tdie local temperature of the tool Twp local surface temperature of the workpiece vs slide velocity x record of Fourier coeYcients \u00actr heat transmission coeYcient \u00bd cycle time \u2019 angle of the driving gear \u00c1 angle of the driven gear Owing to its working principle and the higher accuracy of parts, closed-die hot forging calls for higher requirements on process parameters and tool technology. Figure 1 shows the concept of the closed-die forging of a helical gear wheel. Closed-die forging is mostly used for the manufacturing of near net shape or net shape parts by precision forging. The punch or additional closing elements close the die during the deformation. To operate the closing elements, multi-acting presses, spring assemblies or separate closing devices are needed to provide the necessary closing pressure. B02200 # IMechE 2001 Proc Instn Mech Engrs Vol 215 Part B The MS was received on 14 March 2000 and was accepted after revision for publication on 30 June 2000"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000991_0094-114x(87)90035-8-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000991_0094-114x(87)90035-8-Figure1-1.png",
        "caption": "Fig. 1. A 6-loop fractionated degree-of-freedom chain.",
        "texts": [
            " TEST FOR FRACTIONATED DEGREE-OF-FREEDOM (DOF) The following deals with the test for fractionated freedom using loop paths (CoCjkCkt, CuCjkCkiCt~, etc.) and path LOCM [equation (1)] of kinematic chains. Method 1 This method may be called as loop path method as the test is based on the concept that no path exists between independent loops belonging to separate subchains when peripheral loop LK+ ~ [i.e. (K + l)th loop] is removed, or in other words when CIK+I = C2K+I = 0 are put in path LOCM. For example, Fig. 1 shows a 6-loop kinematic chain in which loop Lj of subchain 1 (SCI) is connected (SCIII) through peripheral loop L 6 only. In general, loop(s) of one subchain of FFKC may be connected with the loop(s) of other subchains through a peripheral loop only. The path LOCM of the chain is written as ,46(KC, C)Lop L1 L2 L3 L4 L5 1 C12 0 0 0 Ci2 1 0 0 0 0 0 1 0 C35 0 0 0 i 0 0 0 C35 0 1 C16 C26 C36 C46 C56 L 6 Loops Ci6 Ll C26 L2 C36 L3 (2) C46 L4 C56 L5 1 L 6 when, path LOCM becomes 1 CI2 As(KC, C)eor, = 0 0 0 CI6 = C26 = C36 = C46 = C56 = 0, the above C12 0 0 1 0 0 0 1 0 0 0 1 0 C35 0 0 0 C , (3) 0 1 It can be seen from the permanent of the above resulting path LOCM (after making terms representing 2-loop subchain C 2, and closed cycles of loops C o, Cjk ",
            " (iv) If at least one path does not exist between loop U and remaining independent loops, the kinematic chain has fractionated degree-of-freedom, otherwise not. Method 2 It may be noted that peripheral loop Lr+~ [i.e. (K + 1)th loop] connects separate subchains of a FFKC. On deleting the row (and column) corresponding to the peripheral loop, the separate subchains (though connected through separation link) are not connected with each other through independent loops. The path LOCM of the chain shown in Fig. 1 can be written as Ar(KC, C)Lop l Cl2 0 0 0 Cj6 Ct2 0 0 0 1 0 0 0 0 1 0 C35 0 0 I 0 0 C35 0 1 C~ C~ C,~ C~ C16 C~6 C~ (4) C,6 C56 1 On deleting the (K + l)th sponding to peripheral loop, the above becomes row (and column) corre- As(KC, C)Lop LI 1 Ct2 = 0 0 0 L2 L3 L4 C12 0 0 1 0 0 0 1 0 0 0 1 0 C35 0 L 5 Loops 0 L~ 0 L 2 C35 L 3 . (5) 0 L, 1 L5 On interchanging the 4th and 5th rows, and then interchanging the 4th and 5th columns, the above K x K square matrix becomes As(KC, C)Lop Lj I-i [C12 = 0 0 0 L2 L3 L5 L4 Cl2 ] 0 0 0 1 J 0 0 0 0 [ 1 C35 ] 0 0 [C35 1 J 0 0 0 0 [1] which may be written as Ascl As(KC, C)eop = 0 0 0 0 Ascn 0 0 Asc m Loops Ll L2 L3 L5 L, (6) (7) Permanent of the above matrix becomes per As(KC, C)Lop = (per Aso) ' (per Ascii). (per Ascm). (8) As the non-zero elements of the K x K square matrix (6) can be arranged into square subsets lying along the leading diagonal with other elements equal to zero as above, the kinematic chain shown in Fig. 1 has fractionated degree-of-freedom. On the basis of the above discussion, the following test for fractionated degree-of-freedom is proposed. (i) Make Clx+ l = C2x+ i . . . . . Crx+ i = 0 in path LOCM of the kinematic chain. (ii) If, by interchanging rows (and columns) of the resulting matrix Ax(KC, C)top, it is possible to arrange non-zero elements into square subsets lying along the leading diagonal with other elements equal to zero, the chain has fractionated degree-of-freedom, otherwise not. LOOP FREEDOM MATRIX (LOFM) Loop freedom matrix of a (K + D-loop kinematic chain in general symbolic notation is written as[10] Ax + l (KC, f , F)Lop Ll L2 L3 \u2022 \u2022",
            " (28) Calculation technique A set of independent loops of the chain are identified analytically by first finding any spanning tree of its graph, and the number of independent loops K is obtained as K = J - N + I . The loop expressions are easily obtained from closed form expressions developed in [10]. The number of subehains nL into which the peripheral loop of a F F K C is divided by the separation link is calculated as nL = (degree of separation link)/2. The joints Ju of interloop junction C o are obtained by finding common joints between loop expressions. For computational details one may refer to [10]. An example is worked out to illustrate the application of the equations derived above. Example 1 Figure 1 shows a 6-loop F F K C which gives nL=3, K = 5 , K + l = 6 , D = 3 , J = 1 8 , N = 1 4 , FJ,~=L2 ..... is = 1. DOF of the chain can be obtained from the following equation[10] J K F ~ - E F ~ - - Z D j i ~ l j = l F = 18 - (5 \u00d7 3) = 3. (29) From Fig. 1, numbers of joints Jij in Cij are written a s J~: = 1, J , = Jl4 = Jl5 = 0, J23 = J24 = J25 = O, ,]'26=3, J35=2, ,1736=2, ,/45=0, therefore, El2 = 1, El3 = El4 = F15 = 0, F23=F2,=F25=O, F26 = 3, F3s=2, F36=2, F45=0, From equation (29) , f ~ = l , A = I , f4=1, A=2, -1 1 1 i 0 0 A6(KC, f , F)Lop = 0 0 0 0 3 3 From equation (15), J16 ~ 3 ,/34 = 0 ']'46 ----- 4 , \"]56 ----- 3 Fi6---3 F34 = 0 F46 ----- 4, F56 = 3. ~ = 1 f f f = 6 0 0 0 3 - 0 0 0 3 1 0 2 2 0 1 0 4 2 0 2 3 2 4 3 6 frr+~ = ( 3 + 3 + 2 + 3 + 4 ) - 3 \u00d7 3 = 6 (true)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000184_s0956-5663(00)00051-8-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000184_s0956-5663(00)00051-8-Figure1-1.png",
        "caption": "Fig. 1. Disk configuration: two widely separated enzyme-coated sensors, each with a an accompanying blank uncoated anode, are contained in each housing. Each blank anode was separated by 2 min from its accompanying enzyme-coated anode. Contained in the interior of the housing is a transimpedance amplifier, battery pack, and a pulse-period modulated transmitter.",
        "texts": [
            " The catheter was then tunneled in a superior direction and eventually was exteriorized in the posterior neck. The protruding catheter was protected by a cylindrical pillbox attached to the skin with stainless-steel sutures. The catheter lumen was plugged with stainless-steel stylets and the animals recovered. 2.2. Sensor fabrication Two widely separated glucose sensors, each of which included an enzyme-coated indicating electrode and an accompanying blank indicating electrode (without an enzyme coat) were placed in each housing disk (see Fig. 1). A single common Ag/AgC1 reference electrode (cathode) in each disk served all four of these indicating electrodes (anodes). Each disk housing, made of baked epoxy resin with rounded outside edges, had a diameter of 50.8 mm and a height of 15.2 mm (Resdel Corp., Rio Grande, NJ 08242). The disks were scribed with three concentric rings with diameters of 8, 32, and 36 mm. The two outside rings were machined to a depth of 1 mm and width of 0.3 mm. Material internal to the inner ring was completely removed to create a central cavity for the cathode",
            " A glucose oxidase enzyme solution (35 mg glucose oxidase (GOX, Sigma G-6125), 14 mg bovine serum albumin (BSA, Sigma A-4378) dissolved in 230 ml DW, 10 ml 100% isopropyl alcohol, and 100 ml of 25% glutaraldehyde) was applied via a stationary fiber wick while the disk rotated at 100 RPM on an electronic spin-coater (P6204-A, Specialty Coatings Systems, Indianapolis, IN 46241). In this fashion, approximately seven units of GOX was applied to each of the outer two platinum electrodes in each housing thus creating the active glucose sensors. The two inner blank indicating electrodes were left uncoated for the purpose of measuring background current (see Fig. 1 for sensor diagram). The sensors were allowed to dry for 30 min in room air and then immersed in DW for 15 min. Immersion for 15 min was then repeated twice in fresh DW followed by drying with an N2 stream. The sensors were then heated in an oven at 40\u00b0C for 30 min. While maintaining this temperature, the sensors were rotated at 2000 RPM on the spin-coater. Three milliliters of warmed BBF polyurethane (Polymer Technology Group, Berkeley, CA 94610) were then applied directly over the spinning disks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003414_icma.2007.4303747-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003414_icma.2007.4303747-Figure4-1.png",
        "caption": "Fig. 4: A virtual structure for movement of platform on rugged terrain where each wheel will be on a different height.",
        "texts": [
            " The MHS measure has been utilized for stability investigation of wheeled mobile robotic manipulators with rigid elements. Different manoeuvres have been implemented on flat and slopping surfaces and the efficiency of this metric as well as computational simplicity compared to other metrics have been illustrated in previous works, [13-14]. Here, the MHS will be extended for operation of wheeled robotic systems with flexible suspension. Since, the proposed MHS measure is based on the contact points between the base and ground, by considering a virtual structure (see Fig. 4) the MHS can be generalized to this case. Note that, the virtual structure consists of the tires and a variable-form fictional body connecting the positions where the suspension attaches to the tires. In addition, the whole overall system is founded above this structure. Therefore, when this imaginary structure tends to tip-over the complex system consists of the mobile base/machine and manipulator arm(s) has a tendency to experience the instability. To generalize the MHS criterion, first the applied forces/torques (except the forced exerted to the tires) on virtual structure should be computed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002641_tmag.2006.872518-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002641_tmag.2006.872518-Figure4-1.png",
        "caption": "Fig. 4. Magnetic bearing system (1=8 region).",
        "texts": [
            " When the thickness of the element in the gap becomes thin, of the ordinary method increases rapidly, but that of the leaf element does not change so much, as shown in Fig. 3(a). Moreover, the numerical error of the obtained from the ordinary method can be also removed by the leaf element as shown in Fig. 3(b). In Fig. 3, the difference by the treatments for the leaf element is not appeared. This means that the ill-condition of the matrices can be removed by using any types of leaf elements. The leaf element is applied to the analysis of eddy currents in the surface layer of a laminated core in an actual magnetic bearing system. Fig. 4 shows a magnetic bearing system. Only of the whole region is shown due to symmetry. This model is composed of the stator with the coil and the rotor with the shaft. It is assumed that the coil is excited by dc biasing current and the rotor rotates with constant speed. In this case, the eddy currents flow only in the rotor and shaft, and the magnetic fields and eddy currents become constant in time. Therefore, the iron losses occur only in the rotor and the shaft. In order to reduce the eddy current losses, the rotor core is made by laminating the steel sheets, of which the thickness is 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003977_s12213-008-0010-1-Figure19-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003977_s12213-008-0010-1-Figure19-1.png",
        "caption": "Fig. 19 Cell processing organized by three orthogonal microrobots on an inverted microscope",
        "texts": [
            " However, we could not control the discharge rate Displacement of the pump when the inner diameter of injection pipette is smaller than 10 \u03bcm. Generally, inner diameter of the injection pipette should be less than a few micrometers at the artificial insemination and nuclear cell transfer. We plan to improve the sensitivity of this small pump. 4.2 Collaboration of three two-axial orthogonal microrobots We attach small manual stages to two-axial microrobots for positioning pipettes and a dish in Z direction as shown in Fig. 18. We positioned pipettes and the dish in focal height by manual Z stage in experiments. Fig. 19 is the photograph of the experimental set up and the working area for a cell processing organized by the three two-axial orthogonal microrobots on an inverted microscope. We put the holding pipette on the left robot for sample capturing. We also put the injection pipette on the right robot. Between these robots, we arrange another microrobot that moves the dish. The whole cell-processing device is very small, 200 mm in length, 150 mm in width and 60 mm in height, so we can easily arrange the device to the microprocessing instruments even if the working area is very small"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002724_978-1-4684-1033-4_13-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002724_978-1-4684-1033-4_13-Figure2-1.png",
        "caption": "FIGURE 2. RIB, SKIN AND GENERAL INSTABILITY BUCKLING MODES",
        "texts": [
            " Strengths were conservatively estimated based upon experience with similar composite material systems. CONTINUOUS FILAMENT ADVANCED COMPOSITE ISOGRID: STRUCTURAL CONCEPT 221 Design Analysis Methodology The design of stiffened plates and shells to resist buckl ing is facil itated by considering three limiting types of buckling modes. They are rib crippling, skin buckl ing and general instability. Each mode is assumed to be independent and distinct in a buckle resistant design. They are illustrated in Figure 2. An intuitive design approach that, although not rigorous nor always reI iable, has often been used in the past is the simultaneous mode design (SMD) method. The premise upon which the SMD method is based is the assumption that the optimum (least weight) design results if all failure modes occur simultaneously. This is not always a valid assumption. Furthermore, this assumption can result in buckle resistant designs that are far from optimum in a practical sense; the reason for this is that nonlinear model interactions can be present that render an SMD based upon independent, distinct failure modes highly sensitive to imperfections"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003094_j.mechmachtheory.2007.12.001-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003094_j.mechmachtheory.2007.12.001-Figure4-1.png",
        "caption": "Fig. 4. PR-PR-RP Assur group.",
        "texts": [
            " This is confirmed by the following consideration: For a given position of the external joints A, D and F1 of the triad (Fig. 3), the internal joint C lies on the second order curve (circle) of the ABEF1 four-bar mechanism of the RRPP type [5,12]. Also C belongs to the circle centered in D, of radius CD. C is the intersection point of two circles and there will be at most two real intersection points. Therefore the maximum number of the assembly modes of the triad is two. In this section the position analysis of the PR-PR-RP Assur group with one internal prismatic joint and two external prismatic joints (Fig. 4) is solved. A local Cartesian coordinate system, with origin point A, and x-axis from A to D is chosen. The auxiliary points A and D are situated on the sliding direction of the corresponding external prismatic joint. The coordinates of the points A (0, 0) and D (d, 0) and of the external revolute joint F (xF, yF) are known, as well as the distances di (i = 1, . . ., 5), the angles h1, h2 and the link length lBC. The position of the triad links is described by a small number of parameters, such as the displacements s1, s2 and s3",
            " Using the Sylvester theorem, the variable s3 is eliminated from Eqs. (62) and (63) yielding: F 12\u00f0s1; s2\u00de \u00bc 0 \u00f064\u00de Again, using the Sylvester theorem and eliminating the variable s2 from Eqs. (61) and (64) yields the fourth order final polynomial equation with only unknown s1: X4 i\u00bc0 P isi 1 \u00bc 0 \u00f065\u00de Eq. (65) provides four roots for s1 in the complex field. The fourth order final polynomial equation is minimal. This is confirmed using a similar consideration as at the previous triad: For a given position of the external joints A1, D1 and F of the triad (Fig. 4), the internal revolute joint C lies on the fourth order curve of the A1BEF four-bar mechanism of the PRPR type [5,12]. Also C belongs to the straight line parallel to the sliding direction of the external prismatic joint D1 and located at distance d4. The point C is the intersection point of the fourth order curve with a straight line and four real intersection points exist at most. Therefore the maximum number of the assembly modes of the PR-PR-RP triad with one internal and two external prismatic joints is four",
            " For each real value of the displacement s1, the coordinates of the internal revolute joints B and C are determined using Eqs. (39), (40) and (43), (44), respectively. The two configurations of the triad corresponding to the real solutions are presented in Fig. 8. Table 3 Data and solutions of the RR-RR-PP Assur group Data lAB = 48, lBC = 51, lCD = 58.5, a = 118 , h = 53 , d = 90, d1 = 35, d2 = 43.5, d3 = 49.5, xF = 92, yF = 49 Config. s1 x y s2 Fig. 8. Assembly modes of the RR-RR-PP Assur group. Example 4. The geometrical data and the coordinates of the points A, D and F of the PR-PR-RP triad (see Fig. 4) are inserted in the upper part of Table 4. The solving of the final fourth order polynomial equation (65) leads to two real roots and two complex roots (see Table 4) for the input data here considered. For each real value of the displacement s1, using back substitution, the displacement s2, s3 and the coordinates of the internal revolute joints B, C and E are calculated. The corresponding two assembly modes of the PR-PR-RP triad are illustrated in Fig. 9. Example 5. The geometrical data and the coordinates of the points A, D and F of the RR-PR-PP triad (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002620_sbrn.2006.29-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002620_sbrn.2006.29-Figure4-1.png",
        "caption": "Figure 4. Half ellipse trajectory[9]",
        "texts": [
            " Care is taken to ensure that the di- rections remain linearly independent. The iteration is terminated when either the convergence rate or the error between the predicted and the exact solutions are smaller than prescribed values. The Powell\u2019s method described above will converge to the minimum of a quadratic function in a finite number of iterations[4]. Initially, the robot gait control was accomplished modeling the endpoints trajectory through a cyclical function, specifically a half ellipse. The Figure 4, extracted from[9], illustrates the half ellipse used. For the trajectory generation, the endpoints positions in the x axis are obtained through the equation: x(t) =      x0 \u2212 l 2 + 2lt T if t < T/2 x0 + l cos(\u03b1) 2 if t \u2265 T/2 , (2) where x(t) is the endpoint position at time t, x0 is the ellipse origin (center) in the x axis (see Figure 4), T 3 Proceedings of the Ninth Brazilian Symposium on Neural Networks (SBRN'06) 0-7695-2680-2/06 $20.00 \u00a9 2006 is the cycle time (one complete step), t is the current time, l is the ellipse length and \u03b1 is the current endpoint angle in relation to ellipse center, calculated through the equation: \u03b1 = 2\u03c0 T ( t \u2212 T 2 ) . (3) The endpoint position in the y axis is obtained through the equation: y(t) = { y0 if t < T/2 y0 + h sin(\u03b1) if t \u2265 T/2 , (4) where y(t) is the endpoint position at time t, y0 is the ellipse origin in the y axis, and h is the ellipse height (see Figure 4). When t >= T , the current time t is reseted to 0 and a new robot step starts. The ellipse parameters using in the above equations are optimized using the Powell\u2019s method[4]. The Table 3 shows the parameter values used in our simulations. The positions x0 and y0 are in relation of the origin (hip) of the leg. After the endpoints coordinates generation, the inverse kinematics was calculated using the Powell\u2019s method, to obtain the expected angles of each joint. In order to control the joints, the torque applied to each joint angular motor was calculated by[3]: \u03c4t+1 = max(I(\u03c9t \u2212 k(\u03b8 \u2212 \u03b8d)), \u03c4max), (5) where where \u03b8 is the actual joint angle, \u03b8d is the desired joint angle, \u03c4max is the maximum torque ceiling, \u03c9 = \u03b8\u0307 (joint angular velocity), and I is the inertia matrix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002307_1.2406105-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002307_1.2406105-Figure3-1.png",
        "caption": "Fig. 3 Determining base helix angle b.h of an involute hob",
        "texts": [
            " For solving the problem of determining the ob base helix angle, actual values of normal pressure angle n nd the hob-setting angle h must be known. The solution to the problem under consideration is represented n the system of three planes of projections. They are 1, 2, and 3, respectively. An auxiliary plane of projections 4 is also used. In order to determine the hob base helix angle b.h using the G based method, the lateral tooth surface of the auxiliary rack R s required to constructed. Let\u2019s start from an arbitrary plane A hat is orthogonal to the axis of projections 1 / 2 Fig. 3 . The 3The DGB approach proved to be useful for solving a variety of gear related roblems see, for example, the monograph by Buckingham 11 , as well as more ecent publications 8,12 . 4The DG/K approach is based on fundamental results obtained in differential eometry of surfaces, and in kinematics of multiparametric motion of a rigid body in 3 space. The method is disclosed in two monographs 1,4 by the author. Both the onographs are available from the Library of Congress. 36 / Vol. 129, MARCH 2007 om: http://mechanicaldesign",
            "h in this particular configuration location and orientation of the plane R, an auxiliary plane of projections 4 is constructed. The axis 1 / 4 is orthogonal to the trace R1. The hob base helix angle b.h is the angle that the lateral rack surface R makes with a plane that; 1 is orthogonal to the horizontal plane of projections 1 , and 2 is orthogonal to the trace R4. Use of conventional descriptive geometry rules yields construction of the hob-base helix angle b.h, as well as the hob-base lead angle b.h that complements the angle b.h to 90 deg Fig. 3 . The derived solution Fig. 3 to the subproblem of determining the base helix angle b.h gives an insight into how an expression for computation of b.h can be derived. Using the above solution Fig. 3 , one can come up with the following equation 1,13,14 cos b.h = cos n cos h 6 Equation 6 could also be represented in the form tan b.h = sin2 n + tan2 h cos n 7 Here is designated that n=normal pressure angle; and h =hob-setting angle. Base lead angle b.h can be computed from the equation b.h =90 deg\u2212 b.h. 2. Base diameter of an involute hob. The generating surface T of a gear hob can be represented as an enveloping surface to consecutive positions of the plane R that is performing a screw motion around the hob axis of rotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002244_s1064230706030063-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002244_s1064230706030063-Figure4-1.png",
        "caption": "Fig. 4. The time-optimal feedback control for k = 0.25.",
        "texts": [],
        "surrounding_texts": [
            "Following the maximum principle [4], we introduce the Hamiltonian of system (1.5) (2.1) x1 0( ) x1 0, x2 0( ) x2 0,= = x1 T( ) \u03c0 2\u03c0n, x2 T( )+ 0,= = H p1x2 p2 x1 ku+sin\u2013( ).+= Here, p 1 and p 2 are the adjoint variables corresponding to the equations (2.2) The optimal control that satisfies constraint (1.6) is determined from the condition (2.3) Equations (1.8), (2.1), and (2.3) imply that, at the terminal time instant t = T, the condition holds which is one of the necessary optimality conditions [4]. The results of Chapter 7 of book [8] imply that, in the considered problem, singular controls do not exist. It follows from (2.3) that the optimal control takes the values u = \u00b11, and to obtain it in the feedback form, it is sufficient to find the switching curves and dispersal curves in the plane x1x2 confining the domains where u = +1 and u = \u20131. p\u03071 p2 x1, p\u03072cos p1.\u2013= = u p2sgn .= HT k p2 T( ) 0\u2265= 386 JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL Vol. 45 No. 3 2006 RESHMIN, CHERNOUS\u2019KO Note that switching curves consist of the points where the control reverses sign in the course of motion along the optimal trajectory. The dispersal curves are generated by the points at which the optimal control can be equal to either +1 or \u20131, and two optimal trajectories starting at each of these points reach the terminal state (1.8) (for the same and different n) in the same time."
        ]
    },
    {
        "image_filename": "designv11_28_0002637_iecon.2006.347864-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002637_iecon.2006.347864-Figure1-1.png",
        "caption": "Fig. 1. Schematic of a humanoid robot system",
        "texts": [
            " For each phase, the analytic solution of center of mass is found for the given ZMP pattern. Then using the periodic condition of ZMP pattern, unique solution of the center of mass can be obtained. The obtained center of mass trajectory is embedded to the whole-body closed-loop inverse kinematics (CLIK) of the center of mass Jacobian method. This paper is organized as follows: In next section, we derive the simplified model of the humanoid robot. Then, the analytical method to generate the center of mass trajectory will be given. Consider a humanoid robot system shown in Fig. 1. In the figure, nk and \u03c3k denote the moment and force applied to both feet and hands, respectively. pcm is the center of mass of whole system, pi denotes the center of mass of ith link, pzmp means the zero moment point (ZMP) of the whole system and g denotes the gravity vector given by g = (0, 0, g)T . 41591-4244-0136-4/06/$20.00 '2006 IEEE From the fundamental mechanical principle, we know that if the reference point is chosen at the center of mass of the system, then the time rate of change of the angular momentum of a system about the center of mass is equal to the moment about that point of the external forces/moments acting on the system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002287_10739140600809421-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002287_10739140600809421-Figure1-1.png",
        "caption": "Figure 1. Schematic diagram of the flow system for determination of the studied drugs. a) K3Fe(CN)6 solution; b) luminol solution; c) sample solution; P1 and P2, peristaltic pumps 1 and 2; V, six-way injection valve; F, flow cell; PMT, photomultiplier tube; HV, high voltage (operated at 2400 V); COM, computer; W, waste solution.",
        "texts": [
            " Luminol working solution (5.0 1025 mol L21) was prepared by directly diluting the luminol stock solution with 0.1 mol L21 sodium hydroxide solution. Potassium ferricyanide stock solution (0.01 mol L21)was prepared by dissolving 0.3293 g potassium ferricyanide in water and diluting to 100 mL with water. Potassium ferricyanide working solution (1.0 1024 mol L21) was prepared by diluting above stock solution with water. A schematic diagram of the flow-injection chemiluminescence (FI-CL) system used in this work is shown in Fig. 1. The peristaltic pumps were D ow nl oa de d by [ U ni ve rs ity o f B at h] a t 0 3: 36 2 2 O ct ob er 2 01 4 used to deliver all solutions. The tubes, a, b, and c were used to deliver potassium ferricyanide solution, luminol solution, and sample, respectively. Then, a certain amount of sample solution was injected into the emerged stream through the six-way injection valve. PTFE tubing (0.8 mm i.d.) was used to connect all components in the flow system. A six-way injection valve was used to inject sample solutions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000371_elan.1140020807-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000371_elan.1140020807-Figure4-1.png",
        "caption": "FIGURE 4. Calibration plots obtained for flow-injection glucose determination using a Pt disk electrode covered with a polyester Nucleopore membrane in (A) manifold types A and B (B) from Figure 1. Injected sample volume, 6 pL.",
        "texts": [
            " Flow Systems with the CPG-GOD Reactor without a Dialyzer In the optimization of the flow-injection-measuring system for clinical glucose determination with an enzyme flow-through reactor, attention should be paid to linear range o f the amperometric detector and t o the interferences caused by the electroactive constituents of physiological samples. For the platinum disk electrode covered with the polyester Nucleopore membrane, even for a very small injection volume (6 pL), the linear response was observed only up to 10 mM glucose (Figure 4A) using the simplest configuration o f the flow-injection system (Figure 1A). In a flow system in which part of the carrier solution with the injected sample was pumped to waste (which is a convenient method of on-line dilution) (Figure lB), the linear response range was extended to 50 mM (Figure 4H). This allows the utilization of such mea- 61 0 Matuszewski and Trojanowicz suremetits for natural serum samples with high patholog- Among the particular potential interfering species, the effect o f ascorbic acid, urea, uric acid, and citrate o n glucose determination was examined i n various flow-injection system configuration. Detailed results of these studies are discussed here. The effects of the presence o f creatinine, glutathione, lactic acid, and salicylate were also examined, but the results ohtained for those species ical level of glucose"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001855_1.2000270-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001855_1.2000270-Figure2-1.png",
        "caption": "Fig. 2 Pico slider with a crown of 30 nm and a camber of 5",
        "texts": [
            " The multiple layers at the head disk interface cannot be treated as bulk material. And also the changes in the thickness and the material properties of the lubricant and the head-disk overcoats change the magnitude of the total intermolecular force. To analyze the effect this has on the stability of the system, we considered three different values of the Hamaker constant A1=0.5 10\u221219J ,A2=10\u221219 J, and A3=2 10\u221219 J. Static simulations were performed using the 3 DOF air bearing model to calculate the steady-state fly height for the slider shown in Fig. 2. A multi-equilibrium region is shown using the fly height diagram in Fig. 3. It is seen that as the value of the Hamaker constant increases from A1 to A3, the rpm range of the unstable region also increases from 1400 to 3800. Therefore, for higher values of the Hamaker constant, more hysterisis will be observed in touchdown-takeoff Fig. 3 Fly height diagram with different values of Hamaker constant rom: http://tribology.asmedigitalcollection.asme.org/ on 08/30/2017 Terms experiments and hence the system has more instability. The desired fly heights for various values of the Hamaker constant are shown in Table 1. We observe that the desired fly height also increases from 4.08 to 5.39 nm with the increase in the Hamaker constant from A1 to A3, which in turn limits the areal density that can be achieved. Static simulations were performed for the slider design shown in Fig. 2 for three different radial positions. The fly height diagram Fig. 4 shows the equilibrium fly heights at the three radial positions. We observe that the rpm range of the unstable region is least at the outer diameter OD position and greatest at the inner diameter ID position. The desired fly height also decreases from ID 6.07 nm to MD 5.07 nm to OD 3.57 nm as shown in Tables 2 and 3. A stable fly height of 4 nm is greater than the desired fly height value at the OD 3.57 nm , but is less than the corresponding value at the MD 5",
            " To analyze the effect of the slider form factor on the stability of the HDI, static simulations for the femto design were carried out at two different suspension preload values. This was done for two different slider designs. It was observed in both cases that lower stable fly heights can be achieved with higher suspension preloads. Hence it is important to study the effect of suspension preload on the stability of the system. Static simulations at five different suspension preload values varying from 1 to 3 gm were done for the pico design at the same radial position for the slider shown in Fig. 2. The fly height diagrams are shown in Fig. 9. r of 2.5 nm. The base recess is 2.5 m. Femto slider ecess is 2.3 m. be e r different suspension preloads Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F We observe that the pico designs with higher suspension preloads have smaller unstable rpm range. Hence less hysterisis will be observed with higher suspension preloads in touchdowntakeoff simulations. The desired fly height for the five cases is shown in Table 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001231_robot.1986.1087722-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001231_robot.1986.1087722-Figure1-1.png",
        "caption": "Figure 1 . The finite element model of the six-bar mechanism",
        "texts": [
            " If the actual driving force or torque does not coincide with a primary system coordinate, then it is modeled as an externally applied load and a primary force of magnitude zero is applied in the direction of a system coordinate. The primary s stem coordinates are numbered last to distinguish them from the ordinary system coordinates. The primary force can be a function of time, system coordinates positions and velocities, or any combination of them. The number of primary forces can not exceed the value of the degree of freedom of the system. illustrate the modeling procedure, consider the six-bar mechanism shown in Figure 1. The mechanism is driven with known input torque applied at 02. Q5 is the primary system coordinate and the restrained rotary freedom 31 is the primary freedom. The primary force PI can take the form: P, = K(q5 0 - Q5) representing a torsional spring. The same model can be used to analyze the behavior of the six-bar mechanism when it moves under its own weight. This is done by applying a ::wo primary force in the direction of Ji5 and ap9lying the force due to the weight of the lumped masses in the direction of the corresponding freedoms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002785_1.3438180-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002785_1.3438180-Figure2-1.png",
        "caption": "Fig. 2 The RRSS mechanism",
        "texts": [
            ":-) ]-'-( b_-_b-=-:o )--,-4>2 (a - b)t[P(Ud)](b - bo) where the input link motion is specified in terms of 8 and 0, and ;j = Vo(a - ao) (16) a = Ao(a - ao) Plane Four\u00b7Bar Function Generation Mechanism. It is obvious that the solutions derived for the RSSR linkage are also valid for the plane four-bar linkage when uo' = (0,0, 1) and Ud t = (0,0, 1) and the z-coordinates for all other parameters are zero. We may further assume, without loss of generality, that aot = (0, 0, 0), and bot = (1, 0, 0). Kinematics of the RRSS Mechanism An RRSS mechanism, referring to Fig. 2, may be identified by (17) The equation of the constant length constraint on the follower link BD can be expressed as Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/20/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use E s'[T(u)]r F s'[P(u)]r G s'[Q(u)]r + t(llrl12 + 115112 - L2) The displaced position X(x) of any coupler point X(XI) due to a ro(,ation 0 of the driving link CA is now given by x = [R(a, U)[X1' - a] + a (20) where the fictitious intermediate position Xl' is Xl' = [R(O, uo)] [X, - ao] + ao The kinematic equations for velocity and acceleration are ob tained by differentiating the displacement equation (18) with re spect to time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000880_ijcat.2002.000288-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000880_ijcat.2002.000288-Figure3-1.png",
        "caption": "Figure 3 Angular displacement distribution.",
        "texts": [
            " When a straight spline is misaligned, the splines rotate by the angle of misalignment g around a point midway along the spline face length. This hinge is determined by the centering action of the spline teeth. One end of the spline, therefore, moves upward and the other moves downward by a value of Imax, normal to the tooth pro\u00aele, Figure 2 Imax b=2 sin g cosf 5 which is the downward shift of the two teeth at a plane perpendicular to the plane of misalignment. The shift of the other teeth is less than Imax, and depends upon the angular position of the tooth as shown in Figure 3. The displacement at the nth tooth pair In is related to Imax as follows: In Imax cos n\u00ff 1 y 6 where y Angle between two adjacent teeth 360 N degrees N Number of spline teeth n Index number Since the teeth cannot physically overlap with those of the mating spline, the clearance between teeth varies with angular position ny, Figure 4, and the interference at the pair of teeth which is shifted by an angle f from the axis of misalignment in the direction of rotation equals zero [10]. The clearance Cn at the nth tooth is then given by: Cn Imax \u00ff In Imaxf1\u00ff cos n\u00ff 1 y g b=2 sin g cosf f1\u00ff cos n\u00ff 1 y g 7 The clearance distribution, shown in Figure 4, exists only under light loading"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003704_ecce.2009.5316465-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003704_ecce.2009.5316465-Figure4-1.png",
        "caption": "Fig. 4. Pulsating magnetic field located at (a) \u03b8 =0o and (b) \u03b8 =90o position; broken bar fault located at \u03b8=90o",
        "texts": [
            " Rotating the pulsating magnetic field with the rotor fixed (proposed method) is equivalent to rotating the rotor with the location of the pulsating field fixed (single phase rotation test). Since the inverter can be used to generate pulsating fields at any arbitrary location, the rotor is excited at multiple circumferential locations, as shown in Figs. 3-4. If the field vector angle, \u03b8, is 0o, the field sinusoidally distributed in space pulsates between the 0o and 180o position, and if \u03b8 is 90o, the field pulsates between the 90o and 270o position, as shown in Fig. 4(a)-(b), respectively. The pulsating vector at \u03b8 can be produced with squarewave-triangle PWM with the three phase voltage references set at ),()3/2cos(),( ),()3/2cos(),( ),()cos(),( * * * tsquVtv tsquVtv tsquVtv cs bs as \u03c9\u03c0\u03b8\u03c9\u03b8 \u03c9\u03c0\u03b8\u03c9\u03b8 \u03c9\u03b8\u03c9\u03b8 \u22c5+= \u22c5\u2212= \u22c5= (2) where V is the excitation voltage magnitude and squ(\u03c9t) represents a squarewave with an excitation frequency of \u03c9. The pulsating field induces voltage in the rotor bars resulting in rotor current flow, but the motor does not rotate since the average induced torque is zero",
            " If the rotor is healthy, the equivalent circuit input impedance, Zeq(\u03b8), is constant independent of the pulsating field location, \u03b8, since the motor is symmetrical. However, if a broken bar is present, the motor symmetry is lost and Zeq(\u03b8) changes with \u03b8. It is shown in [23] that the rotor resistance, Rr, and rotor leakage inductance, Xlr, increase with a broken bar for the field component perpendicular to the broken bar location. If the broken bar is located at \u03b8=90o and the pulsating field is at \u03b8=0o, as shown in Fig. 4(a) (field perpendicular to broken bar), Rr increases since the bar where the maximum voltage is induced is broken. At \u03b8=0o, Xlr also increases since the reduced current in the broken bar makes it easier for the rotor flux produced by the adjacent bars to leak. If the fault and pulsating field are at the same location, as shown in Fig. 4(b), Rr or Xlr do not increase significantly since the induced voltage or current in the broken bar(s) or adjacent bars is small. Analytical expressions for the equivalent resistive and reactive components, Req and Xeq, of the equivalent input impedance, Zeq, of an induction motor excited with a pulsating field can be derived from Fig. 6 as (3)-(5), where Xr = Xm+Xlr. eqeqeq XjRZ \u22c5+= , (3) )/( 222 rrrseq XRXRRR m ++= , (4) ( ) )/( 222 rrrmrmlseq XRXXRXXX +++= . (5) From (3)-(5), it can be shown that increase in the rotor parameters Rr and Xlr due to a broken bar results in an increase in the Req and Xeq components",
            " The standard magnetic vector potential and electric scalar potential based formulation of Maxwell\u2019s equations that has been reported in the literature from the early 1970\u2019s is used. As an illustration, an instant of the magnetic flux distribution for healthy and faulty motors are shown in Fig. 9(a)-(b), respectively. It can be seen that the 4 pole magnetic flux symmetry is evident in the healthy case (Fig. 9(a)). For evaluating of the impact of broken bars, 3 broken bars that are not electrically conductive were placed at the x-axis location (Fig. 9(b)). The location of the broken bars is 90 electrical degrees apart from the \u03b8=0o location as in the Fig. 4 case. It can be seen in Fig. 9(b) that the magnetic flux penetrates deeper in the rotor at the x-axis location since there is no current induced in the broken bars, while the rest of the machine maintains the four-pole flux pattern. The pattern of Req, Xeq, |Iqs|, and Pin in the presence of 3 broken bars was calculated using (6)-(8) from the steady state voltages and currents of the stator 3-phase windings \u201cmeasured\u201d from the external circuit connectivity. The % variations in Req, Xeq, |Iqs|, and Pin with respect to the healthy motor under 10hz excitation are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002461_s0022-0728(79)80193-x-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002461_s0022-0728(79)80193-x-Figure1-1.png",
        "caption": "Fig. 1. (a) Plots of (i'-/i--d) vs. qM as ca lcu la ted for c~) = 5 X 10 .6 tool cm -3 and g O = K R = 0 u p o n se t t ing t he d i f fe ren t ia l capac i ty Cd equal t o 40 /~F cm -2 and t he charge dens i ty qM at E = E0 equal to +10 (sol id curves) and to + 5 / I C c m -2 (dashed curves) . N u m b e r s o n each curve are ~ values in ~ cm. The ver t ical l ines 1 and 2 m a r k the s t a n d a r d p o t e n t i a l E 0 for the solid a n d dashed curves, respect ively . (b ) P lo ts o f log(ira/id) vs. log W for K O = K R = 0, qM(E0) = 10 btC c m -2, C d = 40 /~F cm -2 and for c~) ffi 5 x 10 .6 (1) and 5 x 10 -7 tool cm -3 (2 ) The dashed s t ra igh t l ine has s lope 0.7.",
        "texts": [
            " On the other hand, ni tromethane is not appreciably adsorbed and, accordingly, is reduced to CH3NHOH without maximum formation [41]. A typical behaviour is shown by the azo-hydrazobenzene redox system in water-ethanol solutions, where the oxidized species is strongly adsorbed whereas the reduced one is not [42--44]. Thus, at pH 9, the reduction wave of azobenzene, which lies at potentials negative to the p.z.c., shows a maximum [44]. On the contrary, at pH 6, the oxidation wave of hydrazobenzene, which lies at potentials positive to the p.z.c., does not show maxima (Fig. 1A of ref. 44); only at high pH values, at which the oxidation wave of hydrazobenzene lies at potentials negative to the p.z.c., does this wave show a maximum (Fig. 1B of ref. 44), due to the flow of an anodic current at a negatively charged electrode (cf. eqn. 48). It is also significant that the so-called \"normal\" waves, which follow adsorption prewaves and are characterized by preferential adsorption of the product, do not show streaming maxima. 731 In view of the present approach the increase in the supporting-electrolyte concentration is expected to exert a particularly high depressive effect upon those first-kind maxima which are due to preferential \"non-specific\" adsorption of the reactant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003778_j.cirp.2009.03.122-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003778_j.cirp.2009.03.122-Figure2-1.png",
        "caption": "Fig. 2. Typical BMW rear axle differential.",
        "texts": [
            " The knurl pattern comprises fine triangular teeth of 0.4 mm height and 1 mm pitch. The mating component remains in its original \u2018\u2018soft\u2019\u2019 state. The component with the mill knurled teeth is then pressed on to the mating component in an axial direction to make an interference fit. The joint is formed by action of the unhardened material plastically flowing over the hardened knurled teeth. A typical rear axle differential (from a BMW car) uses a bolted bevel wheel differential case assembly configuration shown in Fig. 2. This bolted assembly method is gradually being replaced with laser welding. Laser welding enables a more compact joint * Corresponding author. 0007-8506/$ \u2013 see front matter 2009 CIRP. doi:10.1016/j.cirp.2009.03.122 than the bolted one as can be seen in Fig. 3, thus reducing the weight, the number of components and the overall size. Other OEMs such as Volkswagen AG are following suit by adopting laser welding instead of bolting [3]. Although laser welding has yielded the desired benefits over the bolted assembly regarding size and weight reduction, there are also some drawbacks associated with laser welding"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003953_s00170-009-2272-8-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003953_s00170-009-2272-8-Figure4-1.png",
        "caption": "Fig. 4 Relationship between the axel of the channel and Z axis. a Perpendicular, b between perpendicular and parallel, c parallel. qSG heat flux density of convection, qSS heat flux density of conduction",
        "texts": [
            " It is obvious that T2 is not equal to T0, and T1 is higher than T2. Therefore, heat from a current layer will transmit to the previous one, i.e., the heat from the previous layer will be sealed by the new one coming for T1>T2, and the direction of heat flux between the two successive layers will point to the previous one. Increasingly, heat will be accumulated layer by layer, and the temperature of the whole SLS green part will become high enough to raise the risk of binding the extra loose powders outside the process cross-sections. Shown as Fig. 4, cooling channels have three positions according to the relationship between the axel of the channel and the Z axis. Their positions are perpendicular, parallel, and the position which is between other two ones, respectively. Cross-sections of the channels are surrounded by heat flux from circumference of sintered sections (Fig. 4a\u2013c), and it is different according to the different relationship between channels and laser beam. Such heat accumulation and transmission will induce the excessive temperature augment over the softening point of epoxy powders within the closed zones where the unsintered powders are. Among these three position relationships in Fig. 4, loose powders in the channel whose axel is in parallel with the laser beam has the most probability of being binded. That is because the heat accumulation and transmission will become larger under such conditions that the area of the channel cross-section is smaller in Fig. 4c than those of the other two ones in Fig. 4b and Fig. 4a, respectively, and there are more layers needed to be built-up to finish the whole channel in Fig. 4c than those in Fig. 4a, b. The channels are blocked when loose powders are binded additionally. The precision of the green part will be damaged if the extra loose powders are binded on the surfaces of the part. Therefore, the forming procedures and the corresponding parameters should be adjusted to avoid the extra binding problem. One creative method is to change the combination SSqPrevious layer Previous layer Next layer 1 2 T 1T T Laying and scanning SGq SGqConvectionFig. 3 Heat transmission between the successive layers (T1>T2>T0) limL outV inV outV f f 2 1 2 1 Powder a b 21 pp \u2206>\u2206 Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000462_s0263574701003691-Figure12-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000462_s0263574701003691-Figure12-1.png",
        "caption": "Fig. 12. Radius of curvature.",
        "texts": [
            " The ground represents a part of the moon surface including pits, smooth hills and rocks. Rocks and steep terrain are considered as obstacles. Three paths are found: Two of them go through the pit and the third turns around it and follows a contour line. Pinchard4 has proposed a comparison with path generation based on the principles of genetic algorithms. A real robot is not able to follow any trajectory. Inertial forces and mechanical limits force the robot to follow trajectories with a bounded curvature: = 1 R (19) where R is the local radius of curvature (Figure 12). T and N are, respectively, the tangent and the normal vector to a trajectory. The relation between the curvature K, the velocity and the heading is: = v2 x2 v1 x1 sin cos v1 x2 sin2 + v2 x1 cos2 || v || (20) In this section we introduce a constraint in our model in order to control the curvature of the trajectories. In this way, we guarantee that a mobile robot can follow any particle. A fluid particle which moves in a complex environment, is affected by a combination of deformations like elongation, crushing shear but no extension or compression because our assumption of fluid incompressibility (Figure 13)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002947_robot.2005.1570219-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002947_robot.2005.1570219-Figure6-1.png",
        "caption": "Fig. 6. Slope contact between micro-part and saw-tooth",
        "texts": [
            " It was the electrodes of the micro-part that contacted the feeder surface as they were about 40 m higher than the conductor. The electrode surface exhibited concavities and convexities. the electrode surface are perfectly spherical with radius (Fig. 3) and the feeder surface is saw-toothed (Fig. 4). Let be the elevation angle of a saw tooth, as illustrated in 0-7803-8914-X/05/$20.00 \u00a92005 IEEE. 825 the figure. A saw-tooth contacts an electrode in one of two ways: point contact (Fig. 5) and slope contact (Fig. 6). A micro-part moves in the desired direction if it stops during point contact but slips during slope contact. We will analyse point- and slope-contact to derive a set of conditions for unidirectional feeding. Let us formulate the point-contact illustrated in Fig.5. Let be the force vector generated by the vibration of a parts feeder. Let be the angle between a horizontal line (parallel to the electrode surface) and one connecting the contact point and the center of a concavity or a convexity. The driving force on a capacitor can be represented as the sum of a tangent component and a normal conponent defined as: = cos (1) = sin (2) Assuming that the weight of a micro-part is negligible, the micro-part stops when the inequality = sin cos 0 (3) is satisfied. is the coefficient of friction at the contact point. Similarly, let in Fig. 6 be the force vector generated by the vibration of a parts feeder. Again, the driving force can be represented in terms of the tangent component and the normal component . = sin (4) = cos (5) Then, the slip condition during slope contact is expressible as: = cos sin 0 (6) where is the coefficient of friction at slope contact. Combining Eqs. (3) and (6) yields the following inequalities as conditions for the unidirectional motion of a micropart: tan (7) cos sin (8) Next, we investigate the case of feeding without directionality"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001930_s10665-005-9007-0-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001930_s10665-005-9007-0-Figure3-1.png",
        "caption": "Figure 3. Case 2 of fixator assembly.",
        "texts": [
            " One of these might be that, after imposing the requirements of the first case and after fracture fixation, radiographs and clinical investigations might point to a residual deformity at the neutral configuration. In that case, all the characteristic data pertaining to the parameters described in the first case, as shown in Figure 1, should be determined again and re-evaluated in such a way that, with proper bar lengths, the bone is finally brought to its anatomically correct position, as shown in Figure 3(b). Here it is to be understood that proximal parts retain their normal positions, while the relative positions of the distal parts have taken on an arbitrary appearance, as shown in Figure 3(a). In addition to the co-ordinate systems Gxyz and G1uvw defined earlier, (cf . Figure 1(a)), one more reference frame G\u2032\u2032 1u \u2032v\u2032w\u2032 with origin at the point of intersection, G\u2032\u2032 1, of distal fragment axis (w\u2032) with the distal ring plane B1B2B3 is needed to formulate the process. Unit vectors of each reference system will be obtained through the transformation matrices both at the initial and final configurations of the fixator assembly, as shown in Figure 3. Since the Guvw system is obtained by rotating the Gxyz reference system through an angle \u03b40 about the z-axis, the transformation matrix [AG1uvw Gxyz ]1 and hence the unit vectors [eu e v ew]1 at the initial configuration \u201c1\u201d, are determined by setting \u03b3 = 0, \u03b7 = 0 and \u03b1 = \u03b40 in (7). Following a very similar procedure as in the first case by taking into account the recorded data as well as Equations (1\u20139) except that \u03b1 is set equal to \u03b4Ax in (8) and (9), we may compute the rotation matrix [A G\u2032\u2032 1u\u2032v\u2032w\u2032 Gxyz ]1 which expresses the unit vectors [eu\u2032 ev\u2032 ew\u2032 ]1 of the G\u2032\u2032 1u \u2032v\u2032w\u2032system with respect to the fixed Gxyz-system in configuration \u201c1\u201d. Then, because of the orthonormal properties of rotation matrices, the transformation of the G1uvw-system relative to the G\u2032\u2032 1u \u2032v\u2032w\u2032-system, represented by the matrix [AG1uvw G\u2032\u2032 1u\u2032v\u2032w\u2032 ]1, is estimated from the following matrix product: [AG1uvw G\u2032\u2032 1u\u2032v\u2032w\u2032 ]1 = [A G\u2032\u2032 1u\u2032v\u2032w\u2032 Gxyz ]T1 [AG1uvw Gxyz ]1, (33) where superscript T denotes the transpose. In configuration \u201c2\u201d of the fixator assembly, Figure 3(b), similar to (33), the following can be written for the rotation matrices: [AG1uvw Gxyz ]2 = [A G\u2032\u2032 1u\u2032v\u2032w\u2032 Gxyz ]2 [AG1uvw G\u2032\u2032 1u\u2032v\u2032w\u2032 ]2. (34) However, since the axes of the G\u2032\u2032 1u \u2032v\u2032w\u2032 and those of the fixed Gxyz systems become parallel, we have [A G\u2032\u2032 1u\u2032v\u2032w\u2032 Gxyz ]2 =\u2217 [eu\u2032 ev\u2032 ew\u2032 ]2 =   1 0 0 0 1 0 0 0 1   . (35) It is also clear that, since both the G1uvw and the G\u2032\u2032 1u \u2032v\u2032w\u2032 systems are attached to the same distal platform, a relative transformation amongst them remains invariant under any change of configuration. Thus: [AG1uvw G\u2032\u2032 1u\u2032v\u2032w\u2032 ]2 = [AG1uvw G\u2032\u2032 1u\u2032v\u2032w\u2032 ]1. (36) From (34), in the light of (35) and (36), it follows: [AG1uvw Gxyz ]2 =\u2217 [eu ev ew]2 = [AG1uvw G\u2032\u2032 1u\u2032v\u2032w\u2032 ]1. (37) Based on the above discussion, first the link lengths (L1\u2013L6) are computed to correspond to the initial configuration, Figure 3(a), by evaluating GB1, GB2, GB3 as given below under (38\u201340) and then substituting them in (29): GB1 =R1 cos \u03b40i +R1 sin \u03b40j+h0k, (38) GB2 =\u2212R1 cos(2\u03b41 \u2212 \u03b40)i +R1 sin(2\u03b41 \u2212 \u03b40)j+h0k, (39) GB3 =\u2212R1 cos(2\u03b43 + \u03b40)i +\u2212R1 sin(2\u03b43 + \u03b40)j+h0k, (40) where h0 is the initial height between the base and the moving platforms along the z-axis and R1 is the distal ring radius associated with \u03b41, \u03b43 in (22) and (23). As for the link lengths (L1s\u2013L6s) in the final configuration, these are calculated by the following vector relationships, with reference to Figure 3(b): GG1 =GG\u2032 +G\u2032G\u2032\u2032 1 \u2212G1G\u2032\u2032 1, (41) GG\u2032 =qx i +qy j, (42) G\u2032G\u2032\u2032 1 = (b+ c)k, (43) G1G\u2032\u2032 1 = (rueu\u2032x + rvev\u2032x)i + (rueu\u2032y + rvev\u2032y)j+ (rueu\u2032z + rvev\u2032z)k. (44) Here b, c are the proximal and distal fragment lengths, respectively; eu\u2032x , eu\u2032y , eu\u2032z, ev\u2032x , ev\u2032y , ev\u2032z, ew\u2032x , ew\u2032y , ew\u2032z are the entries of the matrix [A G\u2032\u2032 1u\u2032v\u2032w\u2032 Gxyz ]1 and ru,rv are the components estimated from (rx , ry) radiographic data as follows: ru = rx cos \u03b40 + ry sin \u03b40, (45) rv =\u2212rx sin \u03b40 + ry cos \u03b40. (46) Completion of evaluations is realized by considering Equations (16\u201329) with the help of (37)",
            " (52) By comparison of (48) with (47), the following is deduced: tan \u03b7\u2032 = cos\u03b2z\u2032x cos\u03b2z\u2032z , (53) cos\u03b3 \u2032 = cos\u03b2z\u2032z cos\u03b7\u2032 . (54) Thus the rotation matrix [AG\u2032x\u2032y\u2032z\u2032 Gxyz ] in (47) is now well-defined. The third case is also characterized by the initial and final configurations of the fixator assembly, as shown in Figure 4(a), (b). Since the description of the first configuration in the third case is not affected by the oblique position of the proximal part, the neutral position will be handled in the same way as in the second case, as shown in Figure 4(a) and in Figure 3(a). The distal part being the same in both cases, equations and conditions like (33), (34), (36), (37) will hold true for the third case too. Different, however, from the second case is the fact that the axes of the G\u2032x\u2032y\u2032z\u2032 and G\u2032\u2032 1u \u2032v\u2032w\u2032 systems are to be parallel in the final configuration of the third case, Figure 4(b), which is expressed by the following: [A G\u2032\u2032 1u\u2032v\u2032w\u2032 Gxyz ]2 = [eu\u2032 ev\u2032 ew\u2032 ]2 = [ex\u2032 ey\u2032 ez\u2032 ]. (55) Thus, in order to get [AG1uvw Gxyz ]2, specific for the third case, Equation (55) is substituted in (34) together with (33) and all other calculations are the same as in the second case",
            " For the calculated leg lengths at each step, direct kinematics together with the theory presented in Section 3 is implemented yielding the B1, B2, B3 co-ordinates and the fracture opening (KG\u2032 1) as shown in Table 3. While there is a totally (linear and angular) misaligned position of the bone fragments at the initial configuration (i.e., step 0), all the misalignments have been removed in the final configuration (i.e., step 10). 4.2. Example 2 The dimensions of the fixator, the lateral and AP views, as well as the clinical data, are input to the second case; see Figure 3. The output are the link lengths and motion results. The specified lateral data are as follows: ey =1\u00b703 cm; ez =1\u00b700 cm; cL =7.05 cm; b=12 cm; \u03b2L =\u22126\u00b7750. The AP data: ex =\u22123\u00b758 cm; \u03b2AP =28\u00b734\u25e6. The Axial data: qx =0\u00b750 cm; qy =0\u00b760 cm; rx =0\u00b770 cm; ry =0\u00b780 cm; \u03b40 =60\u25e6; \u03b4Ax =20\u00b700\u25e6. After implementation of the theory of Section 2.2, the inverse kinematic results turn out to be the following: c=8\u00b700 cm; L1 =20\u00b782; L2 =20\u00b782; L3 =20\u00b782; L4 =20\u00b782; L5 =20\u00b782; L6 =20\u00b782. L1s =21\u00b710; L2s =21\u00b763; L3s =17\u00b758; L4s =18\u00b732; L5s =21\u00b791; L6s =22\u00b789"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003826_s1064230708020019-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003826_s1064230708020019-Figure4-1.png",
        "caption": "Fig. 4. Trajectories with two control switches and the FLAG domain.",
        "texts": [
            " For \u03d52 \u2208 [0, \u03c0) their difference is negative since, first, the lower limit of integration in (4.14) exceeds the lower limit of integration in (4.15), and, second, the integrand in (4.14) does not exceed the integrand in (4.15) for the same values of y because of the trigonometric inequality Problem 4. Assume that the only terminal point is (0, 0). In the domain S (see Section 2), it is necessary to find optimal trajectories with two switches. We also need to specify the value k for which they are absent with guarantee. Solution. First, we consider an auxiliary trajectory (Fig. 4) that starts at a point ( ) and comes at the point (0, 0) and has two control switches at the points (\u03d51, ) and (\u03d53, ). The trajectory crosses the abscissa axis at the point (\u03d52, 0) (see Remark 3). Assume that all specified points and, consequently, the whole trajectory belong to the set S. A trajectory with two switches of only this type can be optimal in problem 4. Remark 3. The points (\u03d51, ) and (\u03d53, ) lie on different sides of the abscissa axis. This fact follows from the theorem in [5] on the alternation of roots of the function and its adjoint, whose sign determines the sign of the optimal control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002425_j.sna.2006.01.016-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002425_j.sna.2006.01.016-Figure5-1.png",
        "caption": "Fig. 5. Exploded view of the shot-put sensor.",
        "texts": [
            " Simplified analysis model of the sensing element under a concentrated oad. F denotes the concentrated load, h denotes the thickness of the flat sheet, 0 denotes the radius of the rigid centre, R denotes the radius of the flat sheet. bridges composed of the strain gauges convert the strains into raw electrical signals for the forces Fx (x-direction force), Fy (y-direction force) and Fz (z-direction force), respectively. A specially designed layout of the strain gages can assure very small couplings among those raw electrical signals. 3.2. Fabrication of sensor Fig. 5 shows the structural model of the proposed shot-put sensor in an exploded view. Owing to very limited inner space, each part of the sensor has to be carefully designed with emphasis on size and mounting position. The overall structure has to be very firm in order to withstand the intense collision when the sensor falls onto the ground. The upper shell is connected with the sensing element via a screw joint. The lower shell is connected with the sensing element via screw fastening. The other parts are all installed inside the shells, including data-acquisition and processing cir- cuits, battery, mass balances, etc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000880_ijcat.2002.000288-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000880_ijcat.2002.000288-Figure4-1.png",
        "caption": "Figure 4 Angular clearance distribution.",
        "texts": [
            " One end of the spline, therefore, moves upward and the other moves downward by a value of Imax, normal to the tooth pro\u00aele, Figure 2 Imax b=2 sin g cosf 5 which is the downward shift of the two teeth at a plane perpendicular to the plane of misalignment. The shift of the other teeth is less than Imax, and depends upon the angular position of the tooth as shown in Figure 3. The displacement at the nth tooth pair In is related to Imax as follows: In Imax cos n\u00ff 1 y 6 where y Angle between two adjacent teeth 360 N degrees N Number of spline teeth n Index number Since the teeth cannot physically overlap with those of the mating spline, the clearance between teeth varies with angular position ny, Figure 4, and the interference at the pair of teeth which is shifted by an angle f from the axis of misalignment in the direction of rotation equals zero [10]. The clearance Cn at the nth tooth is then given by: Cn Imax \u00ff In Imaxf1\u00ff cos n\u00ff 1 y g b=2 sin g cosf f1\u00ff cos n\u00ff 1 y g 7 The clearance distribution, shown in Figure 4, exists only under light loading. Under heavy load application, the teeth de\u00afect and the clearances are redistributed to accommodate teeth de\u00afection. The individual tooth stiffness depends upon its geometry and the location of the applied load along the surface of contact. The tooth stiffness is calculated from the tooth de\u00afection under a given load due to: elastic beam bending, shear de\u00afection, Hertzian de\u00afection and foundation (rim) de\u00afection. A Finite Element Analysis (FEA) may be used in this regard, or the procedure outlined in [11]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003458_icelmach.2008.4799998-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003458_icelmach.2008.4799998-Figure2-1.png",
        "caption": "Fig. 2. Homopolar flux magnetic path (involving frame, bearings and shaft) considered in [1], [2] as a consequence of the air-gap eccentricity.",
        "texts": [
            " Even if valid numerical models have been obtained for the UMP analysis, by FEM [4] or series development [5] solution of the 2D magneto-static field equations, the analytical approaches, based on the m.m.f. concept, are still used, even if under some simplifying hypotheses, because they allow to better understand the phenomenon. In [1], referred to a two-pole induction machine, a homopolar flux is considered, as strictly correlated to the airgap eccentricity and to the UMP. In [2], the homopolar flux is explained in terms of Ampere\u2019s law integration constant and correlated with the reluctance of the magnetic path external to the machine core (see fig.2); nevertheless it is neglected, as in [3] and in [6]. Also in [7], [8], [9] the homopolar flux is ignored. Anyway, all the analytical approaches adopt the same m.m.f. formulation used in the magnetically symmetrical machines: in fact, only alternative components are included. In this paper, a more general formulation of the m.m.f. is developed, that leads to consider a homopolar m.m.f. component, but zero homopolar flux. The analysis will be developed with reference to any isotropic a.c. machine",
            " (11) Of course, depending on the machine roto-dynamical behaviour (static and/or dynamic eccentricity), \u03b5 and \u03b2 may depend on time; therefore, in general: \u03b5 = \u03b5(t) and \u03b2 = \u03b2(t). Hence, again neglecting the ferromagnetic core m.v.d.s, from (9) and (11), the flux density results: ( ) ( )( ) ( )( )0 cos 1 cos p o o M n M b g \u22c5 \u22c5 \u03be \u2212 \u03b8 + \u03be = \u03bc \u22c5 \u22c5 \u2212 \u03b5 \u22c5 \u03be \u2212\u03b2 . (12) Eq. (12) shows that the flux density distribution b(\u03be) is known, provided that the integration constant Mo is defined. Differently from what represented in fig. 2, it is reasonable to impose the solenoidal property of b(\u03be): ( )2 0 0b d \u22c5\u03c0 \u03be \u22c5 \u03be =\u222b . (13) As known, the meaning of (13) is that no homopolar flux exists in each normal section of the machine stack length. The insertion of (12) in (13) leads to evaluate Mo: o p hM M= \u2212 \u22c5\u03b7 , where (14) ( )( ) ( ) ( ) 2 2 0 0 cos 1 cos 1 cosh n dd \u22c5\u03c0 \u22c5\u03c0\u22c5 \u03be \u2212 \u03b8 \u03be\u03b7 = \u22c5 \u03be \u2212 \u03b5 \u22c5 \u03be \u2212\u03b2 \u2212 \u03b5 \u22c5 \u03be \u2212\u03b2\u222b \u222b . (15) III. HOMOPOLAR FUNCTION AND FIELD DISTRIBUTION The function \u03b7h defined in (15) can be called homopolar function. Its manipulation is easier with the following variable transformation (corresponding to considering the rotating frame x-y instead of the stationary frame Xs-Ys): \u03b1 = \u03b8 \u2212 \u03b2 ; \u03b6 = \u03be \u2212 \u03b2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000207_1.1436087-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000207_1.1436087-Figure2-1.png",
        "caption": "Fig. 2 Notation for the double butterfly linkage",
        "texts": [
            " The revolute joints connecting the moving links are denoted as A, B, C, D, E, F and G and the Cartesian coordinate reference frame, denoted as XO2Y, is henceforth referred to as the fixed frame. The ternary links 3 and 7 are referred to as the coupler links and the coupler point that is used in this paper is taken to be coincident with the revolute joint B that connects the two coupler links. Note that point B is only one of three revolute joints on the two coupler links that follows a complex path; the other two revolute joints are C and F. The vectors that are used to describe each link are shown in Fig. 2. The vector R\u03041 n ~n5I, II, and III! connects two ground pivots, vector R\u0304i ~i52, 4, 6, and 8! is directed along binary link i. The X-axis of the fixed frame is arbitrarily chosen to pass through the ground pivot O8 and for convenience is shown to be horizontal; i.e., R1y I 50. The vectors R\u0304B/A and R\u0304B/C are directed along coupler link 3, vectors R\u0304B/F and R\u0304B/G are directed along coupler link 7, and vectors R\u0304D/O5 and R\u0304E/O5 are directed along ternary link 5. The vector from the origin O2 of the fixed frame to the coupler point B is denoted as R\u0304B and can be written as R\u0304B5XBi\u03041YBj\u0304 (1) where XB and YB are the Cartesian coordinates of point B in the fixed frame",
            " is measured from the beginning of the vector R\u0304j and the absolute angular displacement of ternary links 3, 5, and 7 are 40 \u00d5 Vol. 124, MARCH 2002 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/23/20 measured from the beginning of vectors R\u0304B/C, R\u0304E/O5 and R\u0304G/F , respectively. The angular displacement of the moving link m, henceforth referred to as the joint variable and denoted as um , is positive when measured in the counterclockwise direction from the X-axis. The interior angles of ternary link k ~k53, 5 and 7! are denoted as ak , bk and gk as shown in Fig. 2. The cosine and sine of an angle are denoted consistently throughout this paper as c and s, respectively. 3 Polynomial Equation for the Coupler Curve The first step to obtain the closed-form polynomial equation for the curve traced by the coupler point B ~as a function of the link dimensions only! is to write the independent vector equations which describe the position of point B with respect to the ground frame. Since the mechanism is comprised of three independent five-bar loops then there are four such equations; i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003740_1.2975154-Figure16-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003740_1.2975154-Figure16-1.png",
        "caption": "FIG. 16. a Example of cylindrical graphic of the normalized component Bny of B relative to rc9=95.5 mm; b cross section of the cylindrical graphic at x=\u22120.1968 m and interpretation of the Bny values.",
        "texts": [
            " In the outer and inner regions defined by this surface the positive and negative values of the B components have been reported, respectively. Furthermore, to better visualize these three-dimensional polar diagrams, all normalized values have also been multiplied by a reduction scale factor equal to 25. It has been necessary to carry out this operation to avoid that high negative values of the components may generate confused intersections among more or less close regions of each interpolation surface. Figure 16 a illustrates what we have obtained by this procedure for the normalized component Bny of By. In this case Bny has been computed on the cylindrical surface with radius rc9=95.5 mm. Using an opaque coloration for the cylinder with unitary radius, the positive values of Bny are represented by the dark regions of the surface that are external to the same cylinder. Vice versa, the negative values of Bny are defined by light regions that are internal to the cylinder. Figure 16 b clearly indicates the meaning of the cylindrical graphics reported in Fig. 16 a : a transversal section with respect to the axis of the opaque cylinder at x=\u22120.1968 m from the origin O of the reference system O X ,Y ,Z is illustrated see also Fig. 13 d . In this way we see the polar diagram of Bny versus . In Figs. 17 and 18, some graphics obtained by the above mentioned procedure and relative to the cylindrical surfaces with radius rc7 ,rc8 ,rc9, and rc10 are reported. These figures also indicate the normalized components Bnx and Bnz, all multiplied by the usual reduction scale factor equal to 25. Figures 19 and 20 show the polar diagrams similar to that one illustrated in Fig. 16 b . These diagrams have been drawn performing four sections at x=\u22120.0984, \u22120.1968, \u22120.2952, \u22120.3936, and \u22120.4920 m on each one of the cylindrical graphics reported in Figs. 17 and 18. By this representation, therefore, it is possible to get a better space evaluation of the field configuration around the magnet. As predictable, the graphics show a helicoidal configuration of the B components that are variously modulated on magnitude versus x and rcj. This modulation depends on the radial distance between the cylindrical surface where B is computed and the two cylindrical helicoidal surfaces of the magnet"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000811_s0142-9418(02)00113-7-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000811_s0142-9418(02)00113-7-Figure6-1.png",
        "caption": "Fig. 6. True stress versus relative deformation (st e) for natural rubbers. Carbon black N220 content: 1: 0; 2: 15; 3: 30; 4: 45; 5: 60, mass part. : knee points.",
        "texts": [],
        "surrounding_texts": [
            "A new characteristic of rubbers is proposed, i.e. the knee-point strain. Occurrence of knee point is caused by the limited stretchability of the vulcanization network. Deformation and true stress in the rubber phase are equal in the bending point both for pure-gum and filler-loaded rubbers, therefore the stress\u2013strain functions of the said rubbers can be combined into one curve. Thus, the bending point on the stress\u2013strain curve is not a geometrical feature, but a structural characteristic of rubber related to the density of its vulcanization network, i.e. to its modulus of elasticity."
        ]
    },
    {
        "image_filename": "designv11_28_0001930_s10665-005-9007-0-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001930_s10665-005-9007-0-Figure5-1.png",
        "caption": "Figure 5. Projections of a rod with w axis in the Oxyz-system.",
        "texts": [
            " In case the surgeon could describe the trajectory along which the distal bone end could be moved most conveniently to bring it in complete alignment with the proximal bone end, then it should be possible to set up a procedure for the evaluation of necessary bar lengths for that purpose. In this work, bones are only represented by their mid-points. However, if they are badly deformed to the extent that they can no longer be represented as cylinders, then points outside their axes might have to be taken into consideration as well. In such cases, the work can be extended to cover these points. A rectangular prism with the sides Cx , Cy , Cz along the axes x, y, z of an orthogonal reference system is shown in Figure 5. The axis (w) of a rod having length c coincides with the diagonal of the prisms as seen in Figure 5. If the angles measured between the projections of the rod onto the zx, zy and yx-planes and the corresponding z, z, y-axes are denoted by \u03b2AP , \u03b2L, \u03b2Ax , respectively, as shown in Figure 5, then the following relationships can be written: Cx =CL cos\u03b2L tan \u03b2AP ; Cy =CL sin \u03b2L; Cz =CL cos\u03b2L, (A-1) where CL is the length of the projected rod in the yz-plane. Now, in the light of the relationships (A-1), Equations (1\u20134) can be obtained by successive substitutions among the following relationships written from Figure 5: tan \u03b2Ax = Cx Cy ; tan \u03b2wz = Cx Cz sin \u03b2Ax , (A-2) tan \u03b2wy = \u221a C2 z +C2 x Cy ; tan \u03b2wx = \u221a C2 y +C2 z Cx , (A-3) where \u03b2wx , \u03b2wy , \u03b2wz are direction cosine angles of the axis w in the Oxyz-reference system. The distal triangle B1B2B3 is drawn in Figure 6. Given the sides b1, b2, b3 of the triangle, the angles \u03d51, \u03d52, \u03d53 can be determined by the application of the cosine law, leading to the equation set (23). Since points B1, B2, B3 are on a circle with center at G1 and with radius R1, it follows that the triangles B1G1B2, B2G1B3, B3G1B1 are isosceles triangles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001930_s10665-005-9007-0-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001930_s10665-005-9007-0-Figure4-1.png",
        "caption": "Figure 4. Case 3 of fixator assembly.",
        "texts": [
            ", \u03b2 \u2032 L, \u03b2 \u2032 AP) one can define the orientation of the z\u2032-axis as follows: ez\u2032 = i cos\u03b2z\u2032x + j cos\u03b2z\u2032y +k cos\u03b2z\u2032z, (48) where \u03b2z\u2032x , \u03b2z\u2032y , \u03b2z\u2032z are determined according to the following relationships: tan \u03b2 \u2032 Ax = tan \u03b2 \u2032 AP tan \u03b2 \u2032 L , (49) tan \u03b2z\u2032z = tan \u03b2 \u2032 AP sin \u03b2 \u2032 Ax , (50) tan \u03b2z\u2032y = \u221a 1+ tan2 \u03b2z\u2032z sin2 \u03b2 \u2032 Ax tan \u03b2z\u2032z cos\u03b2 \u2032 Ax , (51) tan \u03b2z\u2032x = \u221a 1+ tan2 \u03b2z\u2032z cos2 \u03b2 \u2032 Ax tan \u03b2z\u2032z sin \u03b2 \u2032 Ax . (52) By comparison of (48) with (47), the following is deduced: tan \u03b7\u2032 = cos\u03b2z\u2032x cos\u03b2z\u2032z , (53) cos\u03b3 \u2032 = cos\u03b2z\u2032z cos\u03b7\u2032 . (54) Thus the rotation matrix [AG\u2032x\u2032y\u2032z\u2032 Gxyz ] in (47) is now well-defined. The third case is also characterized by the initial and final configurations of the fixator assembly, as shown in Figure 4(a), (b). Since the description of the first configuration in the third case is not affected by the oblique position of the proximal part, the neutral position will be handled in the same way as in the second case, as shown in Figure 4(a) and in Figure 3(a). The distal part being the same in both cases, equations and conditions like (33), (34), (36), (37) will hold true for the third case too. Different, however, from the second case is the fact that the axes of the G\u2032x\u2032y\u2032z\u2032 and G\u2032\u2032 1u \u2032v\u2032w\u2032 systems are to be parallel in the final configuration of the third case, Figure 4(b), which is expressed by the following: [A G\u2032\u2032 1u\u2032v\u2032w\u2032 Gxyz ]2 = [eu\u2032 ev\u2032 ew\u2032 ]2 = [ex\u2032 ey\u2032 ez\u2032 ]. (55) Thus, in order to get [AG1uvw Gxyz ]2, specific for the third case, Equation (55) is substituted in (34) together with (33) and all other calculations are the same as in the second case. After transforming the co-ordinates of the points B1, B2, B3 into the fixed reference-frame co-ordinates in the initial \u201c1\u201d and final \u201c2\u201d configurations, Equation (29) can be employed to obtain the leg lengths"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002307_1.2406105-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002307_1.2406105-Figure2-1.png",
        "caption": "Fig. 2 Generation of the auxiliary rack R of an involute hob",
        "texts": [
            " The auxiliary rack R makes contact with the gear tooth surface G along the straight-line segment AB, which is often referred to as the characteristic Eg. An intuitive understanding of the shape of the lateral tooth surfaces of the rack R is helpful but not sufficient. For further consideration, equation of the rack R tooth surface is required to be derived. The major coordinate systems to be used in this research are as follows: 1 the coordinate system XgYgZg imbedded in the gear; 2 the coordinate system XRYRZR associated with the auxiliary rack R Fig. 2 and ultimately XhYhZh connected to the involute hob. Few more intermediate coordinate systems were used as well. The auxiliary rack tooth surface R could be represented as an enveloping surface to consecutive positions of the gear tooth surface G, while the pitch plane WR rolls without sliding over the pitch cylinder of diameter Dg. This concept can be used for derivation of equation of the surface R. In order to derive equation of the surface R, it is necessary to represent 1 the gear tooth surface G; 2 the pitch plane WR; and 3 their relative motion in a common coordinate system XRYRZR. Therefore, the operator Rs g0 R1 of the resultant coordinate system transformations is required to be composed. The resultant coordinate system transformation could be analytically represented as a superposition of several elementary coordinate system transformations Fig. 2 . The elementary coordinate system transformations could be analytically described by: 1 the operator Rt ,Zg of rotation about the Zg axis through an angle ; 2 the operator Tr \u22120.5Dg ,YR of translation along YR axis at a distance \u22120.5Dg; and 3 the operator Tr \u2212l ,XR of translation along XR axis at a distance \u2212l. The considered operators of the elementary coordinate system transformations yield equation for Rs g0 R1 Rs g0 R1 = Tr \u2212 l,XR \u00b7 Tr \u2212 0.5Dg,YR \u00b7 Rt ,Zg 2 The interested reader may wish to go to Refs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000721_s0022112001005699-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000721_s0022112001005699-Figure1-1.png",
        "caption": "Figure 1. Sketch of the experimental setup for buoyancy-driven motion of deformable drops.",
        "texts": [
            " By using a mixture of glycerol and water for the drop phase to control the viscosity ratio relative to a castor-oil medium, the experiments described here were performed to evaluate the theoretical findings and move beyond the limitations of the simulations to provide a more comprehensive picture of the possible behaviours. The details of the experimental procedures are provided in \u00a7 2. Then, in \u00a7 3, experimental results and comparison with theory are presented. Concluding remarks make up the final section, \u00a7 4. The experimental apparatus, which is similar to those used previously for slightly deformable drops (Zhang et al. 1993) and highly deformable bubbles (Manga & Stone 1993, 1995), is shown in figure 1. Made of 3/4 in. Plexiglas, the tank is 40 cm\u00d7 40 cm in the horizontal plane, with a height of 120 cm. A Pulnix 7-CN CCD camera is mounted on a motor-driven stand, so that the drops remain in the image as they fall. The interactions are then recorded on a Sony SLV-400 VCR, viewed on a Sony SSM-125 monitor, and analysed. For a few experiments, still photographs were taken for illustrative purposes at successive times with an Olympus OM-1 35 mm camera. To illuminate the drops, the tank was lit from behind by two Phillips 34 W fluorescent light bulbs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000554_robot.2001.933186-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000554_robot.2001.933186-Figure2-1.png",
        "caption": "Fig. 2: Forces acted on the link",
        "texts": [
            " The displacement of the joints and the displacement of the gravity center of the links, thus can be given by where t, is length of link i , tc, is the distance of gravity center of link i from joint i, and i = 0 ,1 ,2 , . . . , n - 1. Moreovcr, n~ is the displacement of head. The velocity and acceleration of the joints and those of the gravity center of the links can be derived through time-differentiation. For simplicity, we set sk = sin(&) and ck = cos(4k) in the formulation. On the other hand, we model each link as that shown in figure 2 . On the basis of the Newton-Euler equation, the robot dynamics can be derived and summarized as D~ = f7 + O7 + M ~ O 'i. + NI$ ( 2 ) f7 = {fq2,} E 8\" n-1 n-1 n-1 n-1 n-1 z-I j=i+l k=O Therein, r, is the torque at joint i, m, and I, are the mass and the moment inertia of link I, and i = 0,1 ,2 , . . . , n - 1. Note that at the tail and the head there are'no actuators, thus TO = 0 and rn = 0. Moreover, since the snake-like robot has no fixed base, the forces must satisfy f f + O f + moo* + m& = 0 (3) where n-1 r n-1 n-1 m = { m ( j ) } E xZxn in equation (7)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001058_bf00510418-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001058_bf00510418-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the organelle sensor for sulfite. 1. Pt cathode. 2. Teflon membrane. 3. Immobilized organelle. 4. Porous Teflon membrane. 5. The cell with glycine-HC1 buffer. 6. Water bath. 7. Pb anode. 8. Recorder. 9. Air pump",
        "texts": [
            " Deionized water was used in all procedures. Immobilization of Microsome. Rat liver $9 fraction (100 ~tl) containing microsome was filtered through the porous acetylcellulose membrane (Millipore filter, cat. no. VC, 0.10 ~m pore size, 25 mm diameter, and 150 ~xm thickness, Millipore Co., Bedford, Mass., USA). The quantity of organelle immobilized was equivalent to 2.7 mg protein. The microsome was retained on the acetylcellulose membrane. Preparation of Organelle Sensor. A diagram of the organelle electrode is shown in Fig. 1. The oxygen electrode consisted of a Teflon membrane (50gin thick), a platinum cathode (lcm diameter), a lead anode, and an electrolyte (1 N potassium hydroxide). The organelle membrane was attached to the surface of the Teflon membrane and covered with another Teflon membrane (Miltipore filter, cat. no. FASP 2500, Millipore Co.). Procedure. The system for the determination of sulfite ion was composed of the organelle sensor, a cell (2.8 cm diameter, 3.8 cm high), an incubator, and a recorder (Model EPR-200A, TOA Electronics Ltd"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002087_tsmcb.2002.806488-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002087_tsmcb.2002.806488-Figure1-1.png",
        "caption": "Fig. 1. Energy and utility function.",
        "texts": [
            " Let (6) be rewritten as _xi = w j iA j ixi + N w k i A k i xi +Bu = w j iA j ixi +D j i : (8) From the equilibrium point _xieq = w j iA j ixieq +D j ieq = 0 (9) one obtains xieq = 1 w j i A j i 1 D j ieq: (10) Let, furthermore, the energy function (5) be reformulated ~Jji = _xTi _xi = a j i + b j iw j i + c j i w j i 2 =Dj i D j i + w j i 2 xTi A j i D j i + w j i 2 x T i A j i A j ixi (11) where a j i = D j i D j i ; b j i = 2 xTi A j i D j i ; c j i = x T i A j i A j ixi: For w j ieq = b j i 2c j i (12) the energy function (11) reaches its minumum at ~J j ieq = a j i b j i 2 4c j i = 0: (13) Since cji 0 and wj imin 0 it follows bji 0 Substitution of (10) into (11) yields b j i = 2 1 w j i D j ieq A j i T A j i D j ieq= 2 1 w j i D j ieqD j ieq 0 (14) where u 6= 0 and wj i > 0. Then for xi = xieq one obtains ~J j ieq = _x T ieq _xieq = a j i b j i w j i + c j i w j i 2 : (15) For the price pj = 1 and if the system is in balance the maximum of the utility function (3) is reached at the minimum of the energy function (15) at which ~J j ieq = _xTieq _xieq = 0 (see Fig. 1). For all other points xi one obtains xi = 1 w j i A j i 1 _xi D j i and b j i =2 1 w j i _xi D j i T A j i T A j i D j i =2 1 w j i _x T i D j i D j i D j i : (16) So, bji < 0 as long as D j i D j i > _x T i D j i (17) which means that for high velocities (accellerations) condition (17) might be violated. Since the system, however, tends to move to the equlibrium point, condition (17) will be fullfilled for _xi ! 0. It was shown that near the equilibrium _xi = 0 and for pj = 1, the energy function (5) reaches its minimum and the utility function (3) its maximum, respectively",
            " Characterization of the model in respect of its pattern recognition capability along with other associated parameters has been reported from extensive study of the model. The storage capacity of the model has been found to be higher than 0.2n for a pattern size of n bits. Pattern recognition is the study as to how the machines can learn to distinguish patterns of interest from their background. The Associative Memory model provides an elegant solution to the problem of identifying the closest match to the patterns learnt/stored [3]. The model, as shown in Fig. 1, divides the entire state space into some pivotal points (say) a, b, c. The pivots (patterns) are assumed to be learnt by the machine during its training phase. The states close to a pivot are the noisy vectors (patterns) associated with that specific pivotal point. The process of recognition of a pattern with or without noise, amounts to traversing the transient path (Fig. 1) from the given pattern to the closest pivotal point learnt. As a result, the time to recognize a pattern is independent of the number of patterns stored. Since early 1980\u2019s the model of associative memory has attracted considerable interest among the researchers [4], [5]. Both sparsely connected machine (Cellular Automata) and densely connected network (Neural Net) have been explored to design the associative memory model for pattern recognition [4], [6], [7]. The Hopfield\u2019s neural net [7]\u2013[9] models a \u201cgeneral content addressable memory,\u201d where the state space is categorized into a number of locally stable points referred to as attractors (Fig. 1). An input to the network initiates flow to a particular stable point (pivot). However, the complex structure of neural net with nonlocal interconnections has partially restricted its application for design of high speed low cost pattern recognition machine. The associative memory model around the simple structure of cellular automata has been explored by a number of researchers [6], [10], [11]. Most of the CA based designs concentrated around uniform CA [6], [10], [11] with same rule applied to each of theCA cells"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000040_robot.2001.933027-Figure12-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000040_robot.2001.933027-Figure12-1.png",
        "caption": "Fig. 12 Experimental result (Rotation ,about Y - , Z- axis)",
        "texts": [
            " Tanie, \"Virtual Nonholonomic angle about the X-axis and the: object can reach the target position and posture. This result shows that the proposed constraint for Human-Robot cooperation in 3 - ~ method can control Position Posture of 6 degree of Proc. 2000 IEEE Int. Conf. on Intelligent Robots and freedoms in 3-D space. Systems (IROS'OO), to appear, 2000. b X * b Y ~ b Z ~ c X ~ c Y ~ c Z are viscoUs friction and [3] y, Hayashibara, K. Tanie, H, k a i and H. Tokashiki, absolute coordinate, respecti\\rely, Fig.12 shows the of a Robot for Cooperation with a Human,\" Proc. 1995 y - , Z- axes is that the operator can easily control the Roll Constraint,\" 2ooo IEEE Int. Robotics and"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000691_cdc.2001.980577-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000691_cdc.2001.980577-Figure1-1.png",
        "caption": "Figure 1: Decomposition of X . (a) X , cc 1.; and Pd h. (b) The initial decomposition of X . We suppose",
        "texts": [],
        "surrounding_texts": [
            "3.1 Old L P W e rewrite ( 5 ) and (6) as Iiteq([; k , j , 0) : 7 h:5k,J CY -I- s; go,e(xe, , ) Q 2; h:xk,3, (7) e a and 111 (7)-(9), xk, , j : h,j and qe are given, but E is the vector of parameters we can choose. To determine these parameters, let us consider the following LP : (LP1) : I = --E sub. to Ineq(S; k,j,q), q E = (0) UQ, Z k , j E node xk, X k , j f 0, k E 1 min & E R , a > 0 , K E R ~ Let (LP1) has ml number of Ineq(E; k,.j,y)'s, and let the standard form of (LP1) be ~ (LPl) min 2 =: -& sub. to Gil t + (TI = bl , E = [C CY i & E R , a > 0 , K E R \" , OERY', where 01 2 0 is the vector of slack variables, G11 E R'W x(2-bL) and bl E RnU, Remark 1 If Q > 0 is suficientlll small and if --E > 0 suficiently large then (E Q f c T I T , where K = 0, is a feasible solution of (LP1). Moreover, E i s bounded from above because of constraints corresponding to (8), the valrie of objective function --E must be bounded from below. Uherefore, (LPZ) must have an optimal solution. ?'his is the rea8on why we haue the first term in (4). If the op!imal value 2 = -2 < 0, then the optimal solution E of (LP1) satisfies the conditions of Theorem 1, and wc have a PLLF. If -E^ 2 0, then we increase the number of parameters, that is, we add some dividing hyperplanes, so that we can find parameters satisfying the conditions of Theorem 1. Remark 2 In genero,l, f o i different nodes X k . j and xk,,j,, Ineq(E; k , j , q ) arid Ineq(6; k',j ',y') might be 21 74 eqiiivalent constraint. In the following, let KJ Q1 ,I ( r ) = { ( k , j , q ) } be the set of indices of nodes X k , j and q, which generates the r-th constraint i n (LP1). Sometimes we use the notation r ( k , j , q ) to denote that the r-constraint is generated b y x k , j and q. 3.2 New LP Suppose that we add a hyperplane X(QT,+~) 5 {z I = 0) which does not intersect any old node zk,j E Xk, k E K , and that, for a subset I C D of IC, Xk ( k E KD ) is decomposed into X k , Ujk;;,. Let Kp: = K\\Kr,, and let Xk = Xk for k E K N and I&, k E K } , where f = I C N U(UkEK,, {kl? k.2)). Then a new candidate of PLLF is given by P(z) = hTz + K&Q;X t n~.+1$.+,{~+,z e\u20ac 1: V X E X k C c c q . (10) where $ is defined by (3) in which :Ek is the center point of &. N7e note here that for any f L, we have 5; = s$ for all k E K N and B!\u2019 = j;? = s$ for all k E KD. Corresponding to S(z) of (IO), we have a new LP which has the additional variable K L + ~ and its standard form is given bj - (LP2) : min z = - E sub. to G11( t ( 2 1 2 ~ ~ 1 - 1 t 6 1 = 61 GzlE t G22~1,+1 t ~2 = 62 G a t t GWL+I t 0 3 = 63 < = [E OI KTIT, E E R , CY > 0, hl ER\u2019,, K L + i E R, 1 ui E : U , 2 0, i = 1,2,3, where ul, u2, and (73 are vectors of slack variables. 1 k r each old node z k , l E node A\u2019+, ic F IC, lei us define i1;,1 by Note that &,j = IZ+ , for all zk,, E node xk, k E IC, since H ( v ~ + 1 ) does not intersect any old node xkj. Let KJQ2,1(r) and KJQz,z(r\u2019) be !;he set of indices { ( k , j , q ) } such that node x ~ , j and q generates the rlh constraint of the first. __ kind and the r\u2019-th constraint of the second kind in (LP2), respectively. We note the following propertie: 1131: Tlie following resnlt has been shown 113). is generated by new nodes. the optimal vuluc of (LP1). 21 75 3.3 St ruc tu re of the N e w LP By Theorem 2, we have a basic feasible solution [fr 8:' 0 8; of 0. By utilize this advantage, we had pro& a fast method to compute the simplex tabular of (LP2) for this feasible solution [13]. Since E and {~e}ecz, need not be nonnegative, we will solve LPs by using the upper bounding method. We note that in the upper bounding method, non-lxisic .variables must take either their lower or upper bound. Therefore, we suppose 0 is either the upper boimd or t,lie lower bound of t i ~ + l , which is a non-basic variable. 111 the following, we suppose 0 is the lower bound of K . I , + ~ . This means that we restrict the domain of &!,+I, but this does not cause any trouble as we will explairi later. We further assume that the lower bound of CY is sufficiently small positive number; lower bounds of E and . ( t i e } e c ~ are negative numbers whose absolute values are sufficiently large; lower bounds of [ 0 1 ] i , [ u z ] ~ and [oQ]~ are 0; and upper bound of all variables are sufficiently large numbers. Let, ( = [iT 671: be an optimal solution of ( L P I ) , and let <B and [Q czJT be the vectors of basic and nonbasic variables, where elements of &r and &, take their upper and lower bounds. Moreover, let &3 = [e: 6TBIT, where &i E Rmc and 8 1 ~ E Rm\", rn,, + in5 = ml, are vectors of basic variables chosen from elements of 5 and 01, respectively. For this feasible solution, without loss of generality, we c a n a p o s e that the objective function and const,raints of (LP2) are represented as follows: _- 4 Generat ion of an Effective Hyperp lane 4.1 Decreasing the Opt ima l Value From the condition for the optimality, C ~ J 5 0 and E L 2, 0 in (17), we have the following result: The sufficient condition in Theoreni 3 means that the value of object.ive function strictly decreases at the first pivoting in the upper bounds method. 4.2 Outl inc of M e t h o d We will propose a method to generate a dividing hyperplane ' H ( ~ L + ~ ) which satisfies the conditions (18)-(24) and does not intersect any old node x k , j E &, k E IC. w e note that { X k } k E I C , {n(17e))~~, WJQl. , l ( r ) )21, Gciiu, G a ~ ~ ~ I GEIU, GCIL, G ~ I I J , G o l ~ , hc i , bLTi, i r l ~ , ( [ I and Cr. are given data (sec? (a) in Remark 3), and that G I B , Gzu, GL, bz, 82, G ~ I B , GXJ, G ~ L , b:jr 63, Gt12, G,lz, Gzz, and G32 are not determined. When ( { D k , j } , {(KJ&~, I (T) , KJ$z,z(r')))) is given, Gzls, GZU, G ~ L , bz, 82, Gelz, G,IZ and G ~ z are det,ormincd (sce (b) in Remark 3 arid Theorem 2). On ti-,(: other bands, C31~, GBIJ, G31,. b:3, 83 and G32 are not completely determined since there is a.n uiicertain paranietc!r X E ( 0 , l ) in (14) - ( l a ) ; however, as we will show, we can derive a known linear constraint of r j L + l , which is a sufficient condition for (24) (if we choose [up,]+ > 0 sufficiently large, then [63 IT , < [up,Jr,, and, hence, we will ignorc (23) in the following). 21 76 Note that (11) generates linear constraints for 71L4.I and conditions (18)-(22) give linear constraints of (+y, a,,+~). 'We minimize the objective function --y under the linear constraints mentioned above. If the optimal value -y <: 0, then the optimal solution [y qT+l]'r determines a hyperplane which we want to generate. If the optimal value -y 2 0, t.hen we choose another set of ( { & , j } , {r<JQz,i(r), KJQ2,2(r'))}). This is the basic idea of the method that we will propose. Headers suspect that this need enumeration of sets of ( { & , j } , {KJQ2,1(r), KJQ2,2(r'))}) and requires huge computing time. We will discuss about this later. We now derive a sufficient condition for (24). Let Z k , j E CO { ~ k , t ~ , xk,jz}n'F1(q~+l) - I be a new node, where X k . j , E xkl, x k , j , E xk,, x,, U X k 2 = ~ k , and k c; KO. This new node genera.tes two constraints, say the r;-tli and the ri- th constraints of the third kind for ewh q. [Gsi],,;, [b3Ir; and [Gs2lr; (i = 1,2) are given by (14), (15) and (lG), respectively, and where A E ( 0 , l ) is not determined since ' X ( q ~ + t ) liar not been determined; however, since A E (0, l), it suffices that we consider (24) only when [61],.1(k,j1,Q) = [ e ~ ] r z ( k , , j z , q ) = 0. Let If EP,o({ik,j}) = U, then [&IT: > 0 because of (25), and, hence, (24) is satisfied. Suppose now Ep,~({S^l;,j}) # CI. From (14) and (16), we havc where Gcl l~12 = G;&Gc12. Therefore, (24) holds if 4.3 Remarks on Implementat ion Let x, = [G;,l,B]v when r 5 'm< and x,. = ! G , , ~ I ~ G ~ ~ ~ ~ ] , . when r : me. R.elating wit,h (18). (19) - (22) and (as), we define NA 'I'hen, to generate ?i(7/L+l), it is sufficient to consider 21N,\\I number of enurneration of {S^k,j. ( k , j , q ) E N A } . According to our experience, JNA 1 5 1.2(2+L), which is not so large. oreo over, we note t.11at most of21NAl number of { . $ h , j , ( k , j , q ) E NA} do not satisfy constraints generated by (11). Therefore, we adopt, the branchaid-boimdiiig method in the enumeration of { b k j , j j , (k,:j,q) E NA}: \\'e execute SET-S-ILJ(1,l). Procedure SE-r-s-I(-J(iiit i , int .s) Step 1. if (done-Hag = 1) stop; Step 2. &,,jj := s; Step 3. if (11) does not hold then return; Step 4. if ( i < INAI) then begin Step 5. SET-S-K-J(~ i-1, 1); Step 6. SET-S-K-J(~ + 1, -1); Step 7. end; Step 8. else begin Step 9. Step 10. Step 11. Step 12. !jt.ep 13. n?t,urn; Step 14. end; Skep 15. end Step 16. return; for all ((KJQ2,1(1-), KJQ2,2(r'))} do begin solve 1 2 3 for (7, q ~ + i ) ; if (y > 0) then { done..flag = 1; set (-/, 7j t+1) ; } At Step 3, we search a feasible solution of LP satisfying constraints derived by (11) according to { ik2 , , j , , }&, . Most of enumerations of { .4k6 , j j } )2 ' are skipped at Step 3. This is the key point of our method. When { , ? k j , , j j } i 2 1 is given, we know all of constraints of t,hc first and the second typeti; however, { (KsJQL,l(r), 1.(,JQ2,2(r'))} is not uniqiiely deteriniIiec1 and we need to eou~I~eratc d l possible {(KJQz,, (P), KJQ2,2(r'))}. This 21 77 process will be very time consuming. But according to our experience, in most of cases, we find ti optimal solution such that y > 0 at the first choice of {(I<JQ~,I(T), KJQZ,z(r\u2019))} So this repetition is not necessary in practical sense. At Step 10, LP3 means tha LP whose objective function is -y and constraints derived by (ll), (18) - (22) and (28). Finally, we note that by the first pivoting in the upper bounds method K L + ~ becomes one of basic variablos when conditions of Theorem 3 are satisfied. Then, we change the lower bound of I E L + ~ to a ngativc constant whose absolute value is sufficiently large. 5 An Example To show the usefulness of the proposed method, we show an example. This system is not quadratically stahlc(l4]. Let us consider a system given by (1) where n = 2, X = [-7,7] x [-7,7], Q = 2, We choose an initial polytope P = X , divide X into XI, &, X3 and X4 by 2 hyperplanes. Therefore, at the initial, K: = { 1 , 2 , . . ,4}. By the proposed method, we generate 12 hyperplanes. In [9], a PLF is constructed, where the corresponding polytope has 30 nodes. In our case, the number of nodes is 28 < 30. The computing time to construct PLLF including generation of these 12 hyperplanes is 0.750 (Sec) on Pentium I11 lGIlz PC with Linux OS. - \u2018In our program, for each r , KJQ, l(r) has its generator ( ~ k , , , ~ , ~ , q ) . When KJQ,,,(r) is dividid into KJQ2,1(r) and KJQ2,2(rf), we set KJQ2,*(r) so that it includes ( k o , j o , q ) at tho Rrst enumeration at Step 9."
        ]
    },
    {
        "image_filename": "designv11_28_0001872_s0022-0728(77)80109-5-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001872_s0022-0728(77)80109-5-Figure4-1.png",
        "caption": "Fig. 4. Flow cell assembly. (a) Schematic view, (b) Detailed view of electrolyte compartment and electrode units: buret unit (BU): buret (B), buret drive (BD), sample cell (SC) and nitrogen-rinsed stopcocks (S1, $2); damping unit (DM): standpipe (S), capillary (CP), flexible glass spiral (FS), planar precision connection (PC); cell unit (CU): adjustable electrode stand (ES), electrolyte compartment (EC), degassing cell (DC), indicator unit (IU) with indicator",
        "texts": [
            " electrode (I) and conditioner electrode (C), detector unit (DU) with detector electrode (D); spacer (SP), auxiliary electrode (A) and reference electrode (RE). damping unit DM equipped with standpipe (R = 0.4 cm) and capillary (r = 0.08 cm, l = 10 cm); the demountable cell unit CU, mounted on a movable stand, is composed of a pyrex bulk electrolyte compar tment housing working and reference electrode, a degassing cell separated from the main cell by a two-way s topcock and the indicator and detector electrode units. The electrode units (Fig. 4b) are built f rom cylindrical PVC-blocks and kept apart at distance 5 by a specially shaped polyester spacer. The f low entry into the cylindrical thin layer is located in the center of the detector unit and ends in a circular mouth of 0.12 cm diameter. Its upstream end is fi t ted to the downstream end of the damping unit by means of a planar pyrex joint connect ion \u2022 (of optical precision) on top of a flexible pyrex spiral mounted downstream from the capillary in the damping unit. The annular de tec tor electrode (inner radius 0",
            " This potential controlled electrode may be used either to scavenge trace amounts of electroactive species interfering with the adsorption process to be studied or (at sufficiently low flow rates to assure coulometric funct ion of this electrode) for quantitative removal of the depolarizer in order to measure residual currents at both indicator and detector electrodes. The entire flow path as well as the electrolyte compartments can be degassed before and between single measurements of a series by means of the various stopcocks shown in detail in Fig. 4a. A multiple-electrode potentiostatic circuitry described previously [ 13] was used to control the potentials of detector, indicator and conditioner electrode. The continuous and discontinuous potential ramp signal required for the polarisation of the indicator electrode [10] was generated by means of an electronic signal generator [ 14]. In the experiments described below the detector eiectrode (made from high purity silver, Cendres et Mfitaux SA, Bienne) was amalgamated in order to achieve a high hydrogen overvoltage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003384_wcica.2008.4593288-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003384_wcica.2008.4593288-Figure2-1.png",
        "caption": "Fig. 2. The tilt error between the end effector and the base board",
        "texts": [
            " Despite the characteristics of connectors differ from each other, their underlying frictional force models are similar during a mating process. Therefore, instead of enumerating all possible cases, we investigate a special type of connectors to exemplify the whole procedure. The typical connectors studied in this paper are illustrated in Fig. 1. There are two prerequisites of the assembly task in our study. First, the tilt error between the end effector and the base board is very small. This kind of error is evaluated by the angle be between two z-axes of frame }{ eF and }{ bF , which is depicted by Fig. 2. A small tilt error ensures that the research focus shifts from the dynamics of the assembly to the problem of searching for alignment. In this case, the mating process of electric connectors is actually a multiple hole-in-peg assembly problem because the end effector is a female connector. From the point of view of the hole search strategy, this kind of assembly is similar to a rectangular hole-in-peg problem. The second prerequisite of this study is that the initial translational and rotational errors on the contact surface are small and bounded"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003891_s0263574709990683-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003891_s0263574709990683-Figure2-1.png",
        "caption": "Fig. 2. The reference frames for the analysis of the kinematics.",
        "texts": [
            " The manipulator consists of a fixed base and a moving platform (M) connected to each other by three legs, each with a RRUR kinematic chain. The R pairs connected to the frame are to be considered actuated. As can be observed in Fig. 1, at the nominal pose (zero rotation of the moving platform), each manipulator\u2019s leg belongs to a face of a cube, i.e., the nominal cube. From Fig. 1 it can be seen that the actuated R pairs coincide with three vertices of the nominal cube and that, due to the symmetry, the moving platform is a tetrahedron. The following reference frames are defined in studying the kinematics of the manipulator (Fig. 2). A fixed reference frame OX0Y0Z0, hereafter {0}, with origin O coincident with a vertex of the nominal cube and axes which are pointing along the edges of the nominal cube. A reference frame PXGYGZG, hereafter {G}, attached to the moving platform and with P coincident with a vertex of the tetrahedron. At the nominal pose the rotation matrix of {G} with respect to {0}, hereafter 0RG, coincides with the identity matrix I. For each leg a fixed reference frame {Ji} is determined which has its axis xJ i pointing along the axis of the R pair connected to the frame",
            " Depending on which leg is considered, the rotation matrix 0RJ i takes different forms such that Leg1 : 0RJ1 = I, Leg2 : 0RJ2 = Rz0 (\u03c0/2), (1) Leg3 : 0RJ3 = Rx0 (\u03c0/2)Rz0 (\u2212\u03c0/2). Rx0 , Rz0 denote the basic rotation matrices about the x0 and z0 axes, respectively. Traversing the ith leg the xjiyjizji (j = 1, . . . , 5) local reference frames are defined with xji pointing along the axis of the j th R pair. \u03d1jixji denotes the rotation of the j th with respect to the (j \u2212 1)th reference frame, except for \u03d11ix1i which locates the first reference frame with respect to the fixed reference frame {Ji}. With reference to Fig. 2 we define the following vectors: ai = AiBi , a = |ai |, bi = BiCi , b = |bi |, di = CiP, d = |di |, hi = EiP, h = |hi |, (2) v\u0302i = \u2212hi h , w\u0302i = \u2212di d , where notation QiTi indicates a vector with direction from Qi to Ti , |u| indicates the length of vector u and u\u0302 is the unit u vector. From the geometry of the manipulator it follows that a + d = b, which is the length of the nominal cube edge. The synthesis of the architecture being studied as a spherical manipulator is due to the exhaustive work of Herve\u0300 and Karouia6, 7 who proved that the 3-RRUR is a SPM by displacement Lie group algebra and by Kong and Gosselin11\u221213 who worked with screw\u2013wrench systems. An alternative proof may be carried out by differential kinematics (Fig. 2). The velocity of point P can be written as vP = \u03d1\u03071ix1i \u00d7 ai + 2\u2211 j=1 \u03d1\u0307jix1i \u00d7 bi + \u23a1 \u23a3 3\u2211 j=1 \u03d1\u0307jix1i + \u03d1\u03074ix4i \u23a4 \u23a6 \u00d7 (di \u2212 hi) + \u23a1 \u23a3 3\u2211 j=1 \u03d1\u0307jix1i + \u03d1\u03074ix4i + \u03d1\u03075ix5i \u23a4 \u23a6 \u00d7 hi , (3) where all vectors are expressed in {0} (no leading superscript). Considering that x4i \u00d7 di = x5i \u00d7 hi = 0, after simple manipulations we obtain vP = \u03d1\u03071ix1i \u00d7 si + \u03d1\u03072ix1i \u00d7 li + \u03d1\u03073ix1i \u00d7 di , (4) where si = ai + bi + di , li = bi + di . (5) Dot multiplying by x1i both sides of Eq. (4) and observing that x1i is perpendicular to si , li and di : vP \u00b7 x1i = \u03d1\u03071ix1i \u00d7 si \u00b7 x1i + \u03d1\u03072ix1i \u00d7 li \u00b7 x1i + \u03d1\u03073ix1i \u00d7 di \u00b7 x1i = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001681_robot.2004.1307975-FigureI-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001681_robot.2004.1307975-FigureI-1.png",
        "caption": "Fig. I . Insertion of Peg into Tandem Shallow Hole",
        "texts": [],
        "surrounding_texts": [
            "PrOWdlngs ot the 2004 IEEE Irdernational Conhnnu on RoboUcs h Automation\nNew Ortsans. LA ApdI2004\nInsertion o f Long Peg into Tandem Shallow Hole Using Search Trajectory Generation\nwithout Force Feedback Takayuki Matsuno Toshio Fukuda Yasuhisa Hasegawa\nNagoya University Nagoya University Gifu University Nagoya, Japan Nagoya, Japan Gifu, Japan\nDept. of Micro System Engineering Dept. of Micro System Engineering Dept. of Mechanical System Engineering\nEmail: matsuno@robo.mein.nagoya-u.ac.jp Email: fukuda@mein.nagoya-u.ac.jp Email hasegay@gifu.cc.gifu-u.ac.jp\nA b s e f - In this paper we propose a method to insert a long peg into a tandem shallow hole using search trajectorygeneration without force feedback. Automation of the assembly in a factory progmssed in recent years. However the many processes where workers should assemble products by themselves st i l l remain now. We call these processes \"difficult assembly\". The difficult assembly has the feature that a mating part has a unique shape. The RCC (Remote Center Compliance) is an effective method for assembly, but it is no longer useful on the condition that mating parts are complex. The RCC device has no durability since it is a produd made from rubber, in addition a force sensor is expensive. If a robot could accomplish the assembly task without using those devices there is a advantage in terms of expense and durability. In our approach, the manipulator system inserts a long peg into the hole with switching the trajectory generation methods depending on the task condition.\nkeywords - Peg-In-Hole Problem, Search Trajectory Generation, Force Sensor-less\n1. INTRODUCTION\nAutomation of assembly task in a factory has been improved up to now. However, factory workers must still assemble many parts by their hands in the processes which could not have been automated. We call those processes \"difficult assembly\". The difficult assembly has a specific feature that each of parts to assemble has a unique shape. In this paper, we focus a long peg as a mating part and tandem shallow hole as a body which are shaped uniquely. Whitney proposed the RCC (Remote Center Compliance) method [ I ] and the RCC device[2] for Peg-InHole problems. They explicated mechanisms of jamming and wedging phenomena which cause failure of assembly task. They raised only the issue of the insertion of a cylindrical object into a hole with clearance. However more complex parts are used to make products[3][4] in a factory. A method to assemble complex parts is required, because the RCC method could not been adapted to assembly of the complex parts.\nThere are previous works which proposed the method that robot behaves correspondent to the condition of contact of complex parts. Yoshikawa[S] expressed the transition of condition of the contact between a body and mating part as a network, and proposed the method to generate a task planning automatically with the evaluation of task difficulty\nSuarez[6] described how sensory information can be used in an assembly fine-motion planner and also during the task execution. Kosuge[7] proposed a method for planar assembly to mate a square part onto the comer of body using structured compliance. However, there is no experimental results in the papers which deal with complex contact state. Probably it is difficult to actualize contact states which are required by the algorithm in the experiment. To apply those methods to a experiment using manipulator, a method to acquire sensor information with active sensing and a method to recognize the contact state are required [SI-[IO].\nTherefore, currently the RCC is the most useful method for an assembly task in a factory in terms of a cost. The RCC method has problems as follows.\n1) The task become difficult as a peg to insert is long. 2) There is no durability on the RCC device, because it is\n3) A peg must be fixed with high precision on the gripping\nThere is an advantage in terms of expense and durability to achieve a assembly task without force sensor and RCC device.\nWe focus a task to insert a peg into tandem shallow hole as a example of task which a robot cannot achieve with the RCC method. Then, we propose the method to insert the peg into tandem shallow hole using the search trajectory generation to acquire correct peg posture. We also propose the method to estimate the inclination of an insertion axis. In the sectionV, we verify the effectiveness of those method by the experiment.\nmade from rubber material.\npoint to exert the effect of RCC method.\n0-7803-8232-W04/$17.00 02004 IEEE 1123",
            "I I . EXPERIMENTAL ENVIRONMENT In this section. the difference between nroblems in urevious\n..... works and the focused problem is presented. The target task is shown in Fig.1. A peg is inserted into a tandem shallow\nassembly tasks in processes making an automatic transmission. In this paper we focus the task to insert a peg into a tandem\na 12.0\";;. 2 0 1\nhole through a floating part which has a hole. This is one of i....\nshallow hole ignoring assembly of the floating part. A. Influence of Shallowness of Hole\nFig. 2. Tolerance of Insertion Hole\nFirstly, we describe the influence of the shallowness of a hole. The tolerances of a hole and peg are shown in Fig.2. Consider a condition of contact between the hole and the peg depicted in Fig.3, where F, is insertion force on a tip of peg, Fz is force which press the peg against the inside of a hole,\nthe length of the inserted peg. Whitney[l] explicated the relation the possibility of insertion and the contact force using the Jamming Diagram. the\nM is moment of rotation, r is the radius of the peg and 1 is Fx Fx\n(a) Shallow Insenion (b) Deep Insertion\nJamming Diagram is shown in Fig.4, where Fig. 3. Insertion Depth\n1 A = - -^.. A' P\nand , 1.1 is friction coefficient between the inside of hole and the peg. Two contact states are defined to express the force condition between the hole and the peg. One is the one-point contact, another is twcFpoint contact. When a state is onepoint contact, the combinations of F,,F,, and ill are located on the inside of parallelogram. On the other hand, when a state is twopoint contact, the combinations lie on the upside line and the downside ones. The combinations on the outside of parallelogram cause the jamming of the peg, because the insertion force become less than the friction force.\nThe insertion length of the peg have an influence on the acute angles of Jamming Diagram. Because the vertex of an acute angle moves vertically in proposition to A, the capacity of parallelogram increases depending on the insertion length of the peg. In the case the insertion is shallow (Fig.3(a)), the Jamming Diagram became small parallelogram on vertical direction as shown in FigA(a). n l / rFz should be held down in order to keep availability of insertion. On the other hand, the deeper the peg is inserted as shown in Fig.3(b), the bigger the Jamming Diagram gets above and below as shown in Fig.4@). Compared with condition of Fig.3(a), an upper limit on M / r F z which provides the insertion availability grows larger. At our focused task, even if a peg is inserted deeply, the Jamming Diagram still keeps thin shape because the hole is shallow. Therefore, the condition for insertion possibility on focused task is more strict than when a hole and peg are same depth.\nIn addition, compliance center must be fixed when the RCC device is used. As for general Peg-In-Hole problems, the compliance center is set on the tip of a peg as shown in Fig.S(a). On the other hand, in the case of a through-hole the compliance center should be set behind the through-hole as shown in Fig.S(b). The fact shows that link length from\nmanipulator to compliance center always should be renewed when the manipulator system proceeds with the insertion operation. Therefore, manipulator system will not achieve the insertion operation with the RCC devices.\nB. Influence of Length of Peg\nNext, we describe the influence of the length of a peg. The length of the peg which we deal with for an experiment is 270 mm. As indicated above, the necessity to change the link length of the compliance center requires to use not the RCC devices but the force sensors for the achievement of the task. We express the force i moment on the compliance center as follows (See Fig6).\nFyr = Fw, Fzr = F,,, (2)\nai,, = ai,, + F,,L, - F,,L,,\nwhere, Fy,,Fz, and ,Ifzr are force i moment on compliance center, Fy,,F,, and M,, are force I moment on force sensor, and Ly,L, are the deflection from force sensor to compliance"
        ]
    },
    {
        "image_filename": "designv11_28_0000817_s0007-8506(07)60577-0-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000817_s0007-8506(07)60577-0-Figure2-1.png",
        "caption": "Figure 2: Localization of the maximum contact pressure on the punch",
        "texts": [],
        "surrounding_texts": [
            "Traditional metal stamping processes involve relevant ms ts linked to the equipments to be utilized and to the required set-up times. The industrial application of traditional metal stamping tech- is therefore e m c a l t y suitable only for large scale produdion (mass produdion). where the m s t s linked to die manufadure and set-up are distributed over a very large n u m e r of starrped parts. On the other hand in the last few decades new relevant and irrpellent needs have arisen such as the produdion of small batches of sheet metal m r q m e n t s . the inaeasing demand of process Rexibillty and finally the necesslty to reduce the time to market of the produds. The m e n t h e d needs are inmsistent Mh the traditional metal stamping processes. As a msequence two major adions are followed: first of all new forming processes Mich do not require expansive mventional equipments and time m s u m n g set-up operations have been recently proposed [MI; f u r t h e m e rapld tooling techniques have been recently introduced mainly to reduce the time to market of new produds [66]. It should be observed that the -em layer manufaduring technokgies saentmmlty support the mncept of \u2018Rapld Produd Development\u2019. The former applications of rapld tooling for plastic parts manufaduring have been successful and the efforts are ongang irproving materials productrvlty and quallty. On the other hand. when rapd tooling is aimed to the produdion of tools for sheet metal stamping no rapld t d i n g first choice technokgy is evident. T w approaches can be r e q n k e d : thredimensional printing m or seledive laser sintering [KIO] optrons. Layer CNC mt ro l l ed 9 D printing machines are in development for medium and big sized parts. Small sized parts may be mt effedivety produced using other rapld tooling options such as Seledive Laser Sintering. The research here addressed a i m to explore the use of SLS (Seledive Laser Sintering) tech- for this applimtion a m d i n g to the adual state of the art and identny M u r e research diredions."
        ]
    },
    {
        "image_filename": "designv11_28_0000354_ic00282a015-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000354_ic00282a015-Figure1-1.png",
        "caption": "Figure 1. Neutralization curves of N-dansylglycine in the presence of Cd2+ in methanolic solution (mhBly = 6 X lov5): (a) ma2+ = 0; (b) mCd2+ = 1.5 X M NaOH solution in anhydrous methanol was used as titrant. N-tosylglycine shows identical behavior.",
        "texts": [],
        "surrounding_texts": [
            "Materials. Reagent grade Cd(C10,)2.6H20 (Alfa Chemicals) and N-dansylglycine, N-tosylglycine, and N-benzoylglycine (Sigma) were twice recrystallized before use. Cadmium-1 13 oxide (91.67 atom % 13Cd), obtained from Oak Ridge National Laboratory, was converted to the perchlorate for use in the N M R study in aqueous solution. Doubly distilled water and anhydrous methanol (C. Erba) were used throughout. In aqueous solution measurements were performed on 1 X M cadmium(2+) perchlorate solutions with ligand-to-metal molar ratios in the range (2:1)-(10:l). NaCIO, was used as the base electrolyte, and the ionic strength was kept constant ( I = 0.1 M). In order to characterize the electronic transfer process, concentrations of Cd2+ ion ranging from 1 X loT4 to 5 X M and dropping times of 2, 3, 4, and 6 s were used. The same experimental conditions were maintained in methanolic solution: Cd(C10,)2.6H20 and NaC104 were recrystallized from this solvent before use. The pH of the solutions was adjusted by adding small amounts of concentrated NaOH in the same solvent. Polarographic measurements were carried out with an Amel 472 Multipolarograph at 25 * 0.1 OC. A saturated calomel electrode (SCE) was used as reference for the aqueous solution and an Ag/AgNO, (0.1 M) electrode for the methanolic solution. However, all Polarographic Analysis. (3) Fenyo, J.-C.; Beaumais, J.; Selegny, E.; Petit-Ramel, M.; Martin, R.-P. J , Chim. Phys. 1973, 299. (4) (a) Antolini, L.; Battaglia, L. P.; Battistuzzi Gavioli, G.; Bonamartini Corradi, A,; Marcotrigiano, G.; Menabue, L.; Pellacani, G. C. J . Am. Chem. SOC. 1983, 105,4327. (b) Ibid. 1983, 105,4333 and references cited therein. (c) Antolini, L.; Menabue, L.; Pellacani, G. C.; Battistuzzi Gavioli, G.; Grandi, G.; Battaglia, L. P.; Bonamartini Corradi, A,; Marcotrigiano, G. J . Chem. SOC., Dalton Trans. 1984, 1687. ( 5 ) Battaglia, L. P.; Bonamartini Corradi, A.; Menabue, L.; Saladini, M.; Sola, M.; Battistuzzi Gavioli, G. Inorg. Chim. Acta 1985, 107, 73. (6) (a) Battistuzzi Gavioli, G.; Grandi, G.; Menabue, L.; Pellacani, G . C.; Sola, M. J . Chem. SOC., Dalton Trans. 1985, 2363. (b) Antolini, L.; Menabue, L.; Sola, M.; Battaglia, L. P.; Bonamartini Corradi, A. J . Chem. SOC., Dalron Trans. 1986, 1367 and references cited therein. (7) (a) Smith, R. M.; Martell, A. E. In Critical Stability Constants; Plenum: New York, 1976; Vol. 4. (b) Yatsimirskii, K. B.; Vasil'ev, V. P. In Stability Constanrs of Complex Compounds; Pergamon: Oxford, England, 1960. (c) Charlot, G. In L'Analyse Qualiratiue er Les Reactions en Solution; Masson et Cie: Paris, 1963. (8) Wang, S. M.; Gilpin, R. K. Talanta 1985, 32, 329. (c) mCd2+ = 3 X m = number of moles. A 5 X El,, values are referred to the SCE. The pH measurements were performed with an Amel 337 pH meter using, in aqueous solution, an Ingold HA 405-60-K1 pH combination electrode and, in methanolic solution, an Ingold B7213 glass electrode as the indicator electrode and an Ag/ AgNOp (0.1 M) electrode as the reference electrode. For pH measurements in methanolic solution two buffers at pH 5.79 * 0.05 and pH 7.53 * 0.05 referred to the pH scale in methanol were used.9 All pH (and pK,) values in methanolic solution, reported in this paper, refer to this pH scalelo (pH*). \")Cd NMR Spectra. All measurements were made at 44.385 MHz on a Varian XL-200 spectrometer equipped with a multinuclear broadband probe. Spectra were obtained by using 10 mm 0.d. tubes and are externally referenced to 0.1 M aqueous Cd(CIO,), solution at 23 OC. Positive chemical shifts correspond to lower shielding. Natural abundance 0.1 M Cd(C104), was used for spectra in methanolic solution (CD30D) at ambient temperature. In aqueous solution, due to the high T I value for the 'I3Cd nucleus in D20,\" spectra were obtained with the minimal amount of D 2 0 required for internal spectrometer lock. For solubility problems of the ligands, the temperature was raised to 60 OC and 7 X M lI3Cd-enriched perchlorate solutions were used. A ligand-to-metal molar ratio of 2:l was used throughout. Standard acquisition parameters were as follows: spectral width, 4 kHz; pulse delay, 6-8 s; acquisition time, 2 s; pulse width, 10 ps (45\" pulse); collected number of scans, 200-2000. Due to the negative gyromagnetic ratio of the ]I3Cd nucleus, all spectra were obtained with no decoupling. No correction for diamagnetic susceptibility was applied. Preparation of Solid Complexes. Crystals of formula CdL2(H20), (L = N-tosylglycinate, N-dansylglycinate) were obtained by slow evaporation at room temperature of aqueous methanolic 1:l solutions containing cadmium(2+) hydroxide and amino acid in a 1:2 molar ratio. X-ray Powder Spectra. X-ray data were obtained with a Philips PW 1050 diffractometer at 298 K with a Cu K a source."
        ]
    },
    {
        "image_filename": "designv11_28_0000550_robot.2000.844843-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000550_robot.2000.844843-Figure3-1.png",
        "caption": "Fig. 3: Schematic diagram of simulation",
        "texts": [
            " (10) and (13), the following equation is derived: where nTAp is the task velocity change along the normal direction of environment. And, as shown in Eq. (9), we can derive nTAp = nT(JM-' JT)nFimp, (18) nTAp = -(1+ e)nTp. (19) Therefore, if the magnitude is 1, the following relation is obtained: nT(JM-lJT)nFt = 1 (n E SE\"). (20) Consequently, the smallest axis in Fig. 2 is the preferable direction of impact reduction and this impact geometry has clear physical meaning as can be seen in the following examples. 3.3 Numerical example As shown in Fig.3, the end-effector is located at (O.O70.4)m and the pre-impact velocity to the normal direction of environment is about 0.24m/s. Then, for several task directions, impact forces are generated and depicted in Fig.4. Fkom this figure, we can find that the proposed normalized impact geometry agrees with physical intuition. Namely, the proposed geometry indicates the impact force when the velocity component normal to the environment is equal to 1. 4 A new impact performance index Many former researchers used the denominator of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003173_12.768866-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003173_12.768866-Figure4-1.png",
        "caption": "Figure 4: (a) Illustration of the dipolar mechanism of flexoelectricity for bent-core (banana shape) liquid crystals. Model of the bent-core molecules used in microscopic theory.",
        "texts": [
            "org/ on 03/16/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx sponds to 50 m. The flexoelectric effect23,24 (coupling between electric polarization and elastic flexure) yields a polarization, fP in normally apolar nematic LC when the average direction for orientational order or director, n is subjected to splay or bend deformations. The effect is enhanced for molecules which possess a permanent dipole moment and shape anisotropies, specifically for pear-shaped or banana-shaped molecules. In these cases (see Figure 4a), orientationally deformed structures having nonzero fP have both closer molecular packing and lower free energy than non-polar arrangements. The flexoelectric polarization of a standard uniaxial nematic LC can be expressed in terms of two flexoelectric coefficients e1 and e3, corresponding to splay and bend deformations, respectively, such as shown in Eq.(1). 1 3fP e n n e n n (1) A molecular \u2013 statistical approach for calculating the flexoelectric coefficients was subsequently developed by Helfrich25. This model states that the bend flexoelectric constant e3 can be related to the kink angle as: 2 3 133 3 3 2 o B K b e N k T a (2) In this expression is the molecular dipole moment along the kink direction, a, and b are length and width of the molecules, o is the kink angle (Figure 4/b), T is the absolute temperature and N is the number density of the molecules. Helfrich\u2019s approach assumes that the molecules have no positional ordering, i.e. the molecules fluctuate independently. For rod-shaped molecules <1o; however for typical banana-shaped molecules ~60o. In conventional rod-shaped nemat- Proc. of SPIE Vol. 6911 691105-4 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 03/16/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx ics, the flexoelectric coefficients are typically 10-11-10-12C/m; based on Helfrich\u2019s model, we estimate that BCNs may have coefficients ~50 times greater"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003391_coase.2008.4626479-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003391_coase.2008.4626479-Figure2-1.png",
        "caption": "Fig. 2 Change of size and shape in non-uniform shrinkage compensation.",
        "texts": [
            " Moreover, there is a directional effect considering the direction in which laser scanning takes place and the direction perpendicular to it. In this work, an attempt is made to study the effect of geometry i.e. scan length on shrinkage in the direction of the laser scanning. The non-uniform shrinkage compensation applies different shrinkage values at different portion of the geometry. Uniform shrinkage compensation changes only the size of the part whereas a non-uniform compensation will change the size and shape of the part as shown in Fig. 2. B. Scan length and shrinkage Ragunath and Pandey [10] studied the effect of process parameters on the process and material shrinkage. They found that scan length mostly influences shrinkage in the X-direction. They also predicted that scaling factors can have a linear relationship with scan length. They derived empirical relations for percentage shrinkage in terms of scan length using Taguchi method. However they used scaling factors based on the maximum dimensions not on the individual scan lengths because of the nonavailability of a dexel based compensation system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002179_s11432-006-0397-z-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002179_s11432-006-0397-z-Figure2-1.png",
        "caption": "Fig. 2. Schematic structure of the amperometric transducer. (a) Top view; (b) cross section view.",
        "texts": [],
        "surrounding_texts": [
            "An amperometric immunoassay for determination of HIgG was developed. In the first step, the immunosensor was incubated for 30 min in 2 \u00b5L PBS (pH 7.4) containing HIgG, the target analyte, in various concentrations (0\u2015800 \u00b5g/L). The three-microelectrode system was then washed with PBS repeatedly. Next, the three-microelectrode system was incubated for 30 min in 2 \u00b5L PBS containing anti-HIgG-HRP (1 mg/L). Finally, the electrode system was washed repeatedly with PBS prior to amperometric measurements. The amperometric detection of HIgG was monitored by addition of 20 \u00b5L of the substrates (1 mmol/L H2O2 and 3 mmol/L KI) solution into the SU-8 micro pool of the immunosensor. The immuno-enzymatic reaction was investigated by chronoamperometry at 0.15 V (vs. reference), and the cathodic current at 30 s was taken as the amperometric signal. At 30 s, current values reached steady state. All measurements were carried out at room temperature (20\u2103)."
        ]
    },
    {
        "image_filename": "designv11_28_0002894_3.49377-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002894_3.49377-Figure2-1.png",
        "caption": "Fig. 2 Radio Astronomy Explorer\u2014 Lunar (RAE/B) Satellite.",
        "texts": [
            "0)'fe where, assuming that p\u00a3 = const, we have 0 0 0 0 1 0 0 0 1 (33) It follows that 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 \"0 0 0~ 0 1 0 0 0 1 The explicit form of Eqs. (26) is Ji<?.[4s01s02c02s03c03 + S01c01s203(c202 - 3s202)] - 92 - 3s202)+Ji\u00b02 )[4c01s02c02(c203 - s203) + 2s0iC0iS03C03(c202 \u2014 3s202)] + 3-s93(c291-s291)(c292-ls292)]- (34) 9 )'] = 0 (35a) 3) - s9lS93c93(c292 - s202)] - J^[s92c92(s293-s291c293)-s91s93c93(c292-s292)] 2 - s202)] - = 0 (35b) S92c92s93c93} - 3s202)] = 0 (35c) Before deriving the explicit form of Eqs. (27), it is necessary to specify the system configuration. We shall consider the system shown in Fig. 2, which simulates a Radio Astronomy ExplorerLunar (RAE/B) satellite. From Fig. 2 we conclude that 0 [/!]= ca sa -sa ca 0 0 0 1 (36) Hence, considering Eq. (14a) in conjunction with Eqs. (16, 25, 34, .and 36), and letting i = 1 in Eqs. (27a), we obtain the differential equation D ow nl oa de d by U N IV E R SI T Y O F ST R A T H C L Y D E o n M ar ch 2 7, 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .4 93 77 894 L. MEIROVITCH JULY 1974 3(c02c03-501s02s03)2] + [(/iyl + t;1)s2a(/ixl + xOsaca] [(s02s03 - s0iC02c03)2 - 3(c02s03 + 50!502c03)2] + (fiy! + Vl) x \\2 + c2e^(c2Q2- 3s202)] - [2(/iyl +i",
            " (12) to produce the elements of the Hessian matrix \\2tf~\\, enabling us to test the stability of the nontrivial equilibrium by testing \\3f\\ for positive definiteness. However, before the solution of Eqs. (46-55) is obtained, the element of [Jf ] evaluated, and the sign properties of \\3tf] determined, it appears desirable to use specific values for the various system parameters. In addition, the coefficients ari0, brio (i = 1,2,3,4) are given in Table 1. Illustrative Example: The RAE/B Satellite As an illustration of the theory developed above, we shall first determine the nontrivial equilibrium of the RAE/B Satellite (Fig. 2), and then test the stability of motion in the neighborhood of this equilibrium. The system parameters are as follows: A0 = 87.75 slug ft2, B0 = 83.74 slug ft2, C0 = 18 slug ft2 p1 = p2 = p3 = p4 = 4.348 x 10~4 slug ft\"1 , p5 = P6 = 4.596 xKT4 slug ft\"1 mi = m2 = m3 = w4 = 2.40 x 10\"3 slug, m5 = w6 = 0 /! = 12 = /3 = /4 = 600 ft, 1S = 16 = 315 ft EIyl = EIzl = EIy2 = \u2022- = EIz4 = 15.278 Ib ft2, a - 30\u00b0 EIy5 = EIZ5 = EIy6 = EIZ6= 13.889 Ib ft2, ft = 25\u00b0 hxl = hx4 = 0.973 ft, hx2 = hx3 = 0.878 ft, hx5 = hx6 = 0 hyl = -hy4 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003740_1.2975154-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003740_1.2975154-Figure6-1.png",
        "caption": "FIG. 6. Magnetization M in a right handed helicoidal magnet.",
        "texts": [
            " 27 and 30 in Eq. 9 we get M P = \u2212 0 \u2212 Mz P z + Mz P z , 31 that is, M P = 0. 32 Consequently, in each point P of the helicoidal magnet, characterized by a magnetization M also helicoidal and M = M =constant, the volume charge density M P is always equal to zero. This result has been obtained in relation to a left handed helicoidal magnet and it is valid for right handed magnets too. In fact, we can repeat all the previous mathematical steps, but, only with reference to the quantities represented in Fig. 6, which is analogous to Fig. 2 b . In this case, Fig. 6 illustrates a right handed cylindrical helix . The symbols that are used in Fig. 6 are the same ones as Fig. 2 b and have the same meaning. The only differences between the equations relative to right handed magnets that we can write and the previous ones are limited to certain signs. In fact, with reference to Figs. 6 and 7 a relative to a right handed helicoidal magnet, Eqs. 11 , 13 , and 18 must be substituted by the following: nx = \u2212 n cos , 33 nz = n sin cos \u2212 , 34 cos \u2212 = y y2 + z2 . 35 Therefore, in relation to the magnetization M of the right handed magnet, it is necessary to substitute Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002998_robio.2006.340097-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002998_robio.2006.340097-Figure2-1.png",
        "caption": "Fig. 2. Link i and reference frames.",
        "texts": [
            " This section will first give an overview of the coordinates used to describe the position and orientation of the snake robot. Subsequently, the gap functions for contact with external obstacles and the ground will be presented. The snake robot consists of n links that are connected by n \u2212 1 cardan joints, each having two degrees of freedom (DOF). The distance Li between two adjacent cardan joints equals the length of link i. The surface of link i is defined as a cylinder of length 2LGSi and radius LSC . Two halfspheres, each with radius LSC are mounted on each end of the cylinder, see Fig. 2. Denote the centre of the front and rear disc that constitute the ends of the cylinder as SFi and SRi, with positions rSF i and rSRi , respectively. Fig. 2 also depicts the earth-fixed coordinate frame I = ( O, eI x, eI y, e I x ) used as an approximation to an inertial frame where its centre O is fixed to the ground surface and the eI z-axis is pointing in the opposite direction of the acceleration of gravity vector g. External objects (obstacles) are included in the model for the snake robot to push against during locomotion. The external object j is modeled as a cylinder of radius LHj and infinite height with its mid-line parallel to eI z . The position of the point Hj where the mid-line of obstacle j intersects with the( eI x, eI y ) -plane is denoted by rHj "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000564_pola.1991.080290216-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000564_pola.1991.080290216-Figure4-1.png",
        "caption": "Figure 4. Effect of the pH value of the acetate buffer solution (0.1 M) on the relative activity of the free ( 0 ) and immobilized enzyme; M7 = M-BSA-HMD-GOD (m) , M13 = M-HMD-HMD-GOD (+ ) .",
        "texts": [
            " The characteristics of the immobilized enzyme were studied electrochemically in the flow-through suggest that the influence of the pH value on the mini-reactor shown in Figure L7 The effect of pH, activity of the free enzyme is lower than is its influconcentration of glucose in solution, and ionic ence on the immobilized form. Analysis of the results strength were studied for different membranes as (Fig. 5 ) shows that the activity of the immobilized shown in Figures 4 and 5. The results show that the enzyme is more dependent on the ionic strength of optimum pH value for the free and immobilized en- the buffered solution than on other factors. zyme is the same ( N 5.0). From Figure 4 we can Considering that the glucose oxidase electrode is going to be used for the analysis of undiluted blood serum, the influence of some of the serum\u2019s inorganic components on the enzyme activity was determined. The results obtained (Fig. 6 ) suggest that the activity of the enzyme is affected by the concentration of the synthetic serum solution and by chloride ion, whereas the influence of phosphate on enzyme activity is very low. The activity of the glucose oxidase in the membranes was not affected when blood serum samples were used to test the flow-through glucose mini-reactor with wall-jet electrochemical detection using real samples for a t least one month of use"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001055_s0304-3886(01)00096-1-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001055_s0304-3886(01)00096-1-Figure3-1.png",
        "caption": "Fig. 3. The six basic electrophotographic steps of charging, exposure, development, transfer, fusing and erase/cleaning are illustrated for a belt photoreceptor.",
        "texts": [
            " It is interesting to note that the images required for indirect marking, direct marking and paper displays are produced by controlling either light exposure or charge deposition, particle deposition, and either particle orientation or translation, respectively. For the most part, the proposed (future) concepts are enabled by advances in the microfabrication of devices and materials. Much of the literature that describes the industry's advances and new concepts is published in journals and proceedings of digital printing conferences sponsored by `The Society for Imaging Science and Technologya (www.imaging.org) and `The Imaging Society of Japana (www.mls.eng.osaka-u.ac.jp/isj/isj.html). The electrophotographic process illustrated in Fig. 3 is an excellent example of an indirect marking concept based on Q( E) imaging physics. The electrostatic image is formed by exposing a photoreceptor to light from either a scanning laser (illustrated in Fig. 3) or light emitting diode array [3]. The electrostatic image is developed with insulative toner particles charged by the phenomenon of triboelectricity. In recent years, there have been signi\"cant advances in full-color electrophotographic printers [1]. Electrography represents an alternative method for forming an electrostatic image by image-wise charge deposition on a dielectric layer called an electroreceptor. This printing method is also called ionography and electron beam imaging. A microfabricated aperture array can be used to control the image-wise charge deposition [4]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000774_ac0012501-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000774_ac0012501-Figure2-1.png",
        "caption": "Figure 2. Schematic drawing of the setup. The microelectrode is screwed through the bottom into the electrochemical cell, which is filled with 0.1 M KCl solution as electrolyte. The microelectrode is positioned just beneath the liquid surface and polarized to a potential sufficiently high to oxidize or reduce the investigated redox species under diffusional control. The position of the dispenser, which is filled with a solution of the redox species, and the droplet stream relative to the microelectrode can be adjusted by moving the electrochemical cell using micrometer screws. The dispenser triggers the data acquisition software, allowing recording of the time-vs-current response of the microelectrode after the dispensing of droplets containing the redox species into the electrolyte in close proximity to the site of the microelectrode.",
        "texts": [],
        "surrounding_texts": [
            "To establish a new method for the determination of diffusion coefficients of electroactive species, we used a setup that combines the specific properties of the microdispenser and of microelectrodes.The electrochemical cell was mounted on positioning tables equipped with micrometer screws that allowed exact movements in all directions. The microelectrode was inserted in the electrochemical cell through the bottom. The cell was filled with 0.1 M KCl solution so that the electrode surface of the microelectrode was just beneath the liquid surface. The dispenser was filled with a redox species dissolved in the same supporting electrolyte as was used in the electrochemical cell. The position of the dispenser was adjusted so that the droplet stream was almost perpendicular to the liquid surface and aiming on the glass surrounding the microelectrode. This perpendicular droplet stream minimized unidirectional convective effects after the droplets hit the liquid phase, thus avoiding preferential movement of the redox species in one direction. To minimize misdirection of the droplet stream by air movements, the dispenser and the electrochemical cell were placed in a box. The microelectrode was set to a potential high enough to establish a diffusion-controlled heterogeneous electron transfer reaction, with the redox species filled in the dispenser. The pulse generator was operated in burst mode, allowing the exact number of droplets in each experiment, which is equal to the number of generated pulses, to be defined. Each dispensing experiment was started manually by activating the internal trigger of the pulse generator. The pulse generator triggered the acquisition software of the laptop computer to simultaneously start data acquisition, recording the current-vs-time response of the potentiostat at a rate of 0.3 kHz. The dotted line in Figure 3 represents a typical current-vstime curve of the amperometric response of a microelectrode after dispensing 10 droplets of ferrocyanide(II) (c ) 20 mM) to a spot located close to the electrode surface. At the beginning of the experiment, the current was close to zero, because no redox species was present in front of the electrode surface. After a short delay time the current increased quickly to a maximum peak value, after which the current decreased slowly. This observation is indicative of the time that is needed by the dispensed ferrocyanide(II) ions to diffuse from their dispensing point (the spot where the droplets are entering the electrolyte solution) to reach the microelectrode surface. The current decrease after the peak maximum is caused by dilution of the dispensed ferrocyanide within the bulk of the supporting electrolyte. Because the overall electrolyte volume in the electrochemical cell (\u223c5 mL) was a factor of 5 \u00d7 106 higher than the total volume of the dispensed droplets, the equilibrium concentra(18) Kranz, C.; Ludwig, M.; Gaub, H. E.; Schuhmann, W. Adv. Mater. 1995, 7, 38-40. 2470 Analytical Chemistry, Vol. 73, No. 11, June 1, 2001 tion of ferrocyanide in the bulk electrolyte was negligible. Hence, the microelectrode current is decreasing to the baseline. The delay time (which is defined as the time to attain the maximum current) and the peak shape are strongly dependent on the distance between the active microelectrode surface and the spot where the dispensed droplets are shot into the electrolyte solution. The delay time increases with increasing distance; concomitantly, the peak height decreases and the peak becomes broader (see Figure 3, solid line). By plotting the peak time against the distance between the first dispensing spot and subsequent spots after repositioning of the electrochemical cell with respect to the microdispenser, the electroactive surface of the microelectrode can be visualized. A coarse prepositioning was attained by continuously dispensing droplets and recording the resulting current through the microelectrode while moving the electrochemical cell relative to the dispenser by using the micrometer screws. High currents indicated that the dispensing spot was close to the active electrode surface, thus allowing a coarse identification of the site of the microelectrode. After this, the electrochemical cell was moved relative to the dispenser in 100 \u00b5m steps, leading to a rectangular grid of 400 \u00d7 500 \u00b5m. At each position of the grid, the delay time to reach the current peak was recorded after dispensing of 10 droplets (with a single-droplet volume of 100 pL) of ferrocyanide. In Figure 4 these delay times are plotted versus the grid position. Dark areas correspond to short delay times, indicating that the dispenser is positioned in close proximity to the electroactive part of the microelectrode. The black area (showing a diameter of \u223c100 \u00b5m) indicates the closest possible distance between the dispensing site and the microelectrode. When one considers the influence of the thickness of the electrolyte layer over the microelectrode surface and the rather coarse grid distance of 100 \u00b5m, together with the fact that it is a coarse assumption to treat the dispensing site as a point source, the determined size of the microelectrode and the actual size of 50 \u00b5m are in good agreement. A similar approach can be used to determine diffusion coefficients of redox active species without any additional knowledge about the concentration of the redox species or the active area of the microelectrode. The following assumptions are necessary: 1. The square in the grid between 100 \u00b5m < x < 200 \u00b5m and 200 \u00b5m < y < 300 \u00b5m (the site of the active electrode surface; see Figure 4) is set as the zero position for distance measurements. 2. The distance between two points measured radially from the zero square is equal to the distance that the redox species diffuses from the dispensing point to the electrode surface. This approximation is essential, because the depth of the liquid layer over the microelectrode is unknown, which makes an exact calculation of the diffusion distance impossible. 3. The dispensing points and electrode surface can be treated as a point source and a point collector, respectively. 4. Convective effects can be neglected. 5. The Einstein-Smoluchowsky equation19 describing the correlation between diffusion distance d and diffusion time t for one dimension is valid. The distance between a first dispensing point and the electrode surface is x. The redox species needs a time t1 after dispensing to reach the electrode surface indicated by the maximum current. The distance between a second dispensing spot which is lying on the same radial line from the 0 position as the first spot and the electrode surface is d + x. After dispensing the redox species, current peak height is attained after time t2, which is somewhat larger than t1. The distance x is not known; however, the distance d between dispensing spots 1 and 2 can be exactly determined from the grid. Using the prerequisites listed above, the following (19) Atkins, P. W. Physical Chemistry, 3rd ed.; Oxford University Press: Oxford, 1986; p 692. d ) x(2Dt) (1) Analytical Chemistry, Vol. 73, No. 11, June 1, 2001 2471 equations are derived from the Einstein-Smoluchowsky equation. and Equations 2 and 3 can be combined and solved, leading to an equation for the diffusion coefficient. Table 1 shows calculated values for the diffusion coefficient of ferrocyanide(II) using different points of the grid. The average value of 5.38 ( 0.58 \u00d7 10-6 cm2 s-1 is close to the values reported in the literature. Stackelberg et al.20 reported a value for ferrocyanide(II) in 0.1 M KCl of 6.50 \u00d7 10-6 cm2 s-1. Taking a deeper look into literature shows that the reported values for the same electroactive species differ over quite a large range. Depending on the method of determination and the calculation algorithm, values for the diffusion coefficient of ferrocyanide(II) in 1 M KCl from 5.19 \u00d7 10-6 cm2 s-1 up to 7.98 \u00d7 10-6 cm2 s-1 can be found4,6. The deviation of the value for the diffusion coefficient of ferrocyanide(II) from the values reported in the literature can be explained by the assumptions made above. We have assumed that the diffusion pathway of the redox species is equal to the movements of the electrochemical cell; however, the real diffusion path is given by the rectangular triangle between the dispensing point, the active electrode surface, and the height of the liquid layer above the microelectrode. Obviously, as a consequence, the distance d used for the calculation is too small. Because in eq 5 the distance d is only present in the numerator, the calculated value of the diffusion coefficient will be too low. On the other hand, convective effects, which are not considered in this approach, result in a positive error. Convective effects are mainly attributed to the hitting of the droplets into the liquid phase. Because the time period between the dispensing of the redox species and the detection at the microelectrode is quite long, convective effects that are induced by the shooting should play a minor role. To overcome these limitations, we made use of a second redox species for calibration purposes. The microdispenser was filled with a solution containing both redox species. At first, we used a mixture of ferrocyanide(II) and ferrocene monocarboxylic acid. By applying a potential of 500 mV to the microelectrode, both of the redox species would be simultaneously oxidized under diffusional control. If the difference of the diffusion coefficient of both species were large enough, two separated peaks in the current-vs-time curves caused by the different diffusion times of both redox species should occur. Unfortunately, only a peak broadening could be observed, which does not allow accurate separation of the peak heights. Thus, the diffusion coefficients of ferrocyanide(II) and Fc-COOH could not be determined (graph not shown). To circumvent this problem, for calibration we used a second redox species that is not electrochemically converted at the electrode potential necessary to oxidize the first one. As a prerequisite, however, both redox species have to be stable in the same supporting electrolyte without affecting each other. A mixture of Fc-COOH and ruthenium hexamine ([Ru(NH3)6]3+) in 0.1 M KCl meets these requirements. The dispenser was filled with a solution containing 10 mM [Ru(NH3)6]3+ and 10 mM Fc-COOH, and the setup was completed as described above. In contrast to the experiment described for dispensing one redox species, here two measurements had to be made at each grid point, thus changing the microelectrode potential to the setpoints dictated by the dispensed redox species. At first, the potential of the microelectrode was adjusted to +500 mV, allowing the oxidation of Fc-COOH under diffusional control. An exact number of droplets was dispensed and the resulting current-vs-time curve was recorded. Then the microelectrode was polarized to -300 mV in order to reduce [Ru(NH3)6]3+ under diffusional control. The same number of droplets was dispensed again and a second current-vs-time curve was recorded. After this, the electrochemical cell was displaced by a defined distance, and the measurements were repeated similarly for the other grid points. The obtained peak time of the current was evaluated. Figure 5 shows an example for current-vs-time curves of Fc-COOH and [Ru(NH3)6]3+ dispensed at the same position (the currents are normalized with respect to the respective peak current). In the current-vs-time curve of Fc-COOH, the current reaches its maximum at t ) 1.33 s, but for [Ru(NH3)6]3+, the peak current is reached at t ) 1.15 s. Because all system parameters remained unchanged, the different peak times reflect the different diffusion coefficients of [Ru(NH3)6]3+ and Fc-COOH. The dispenser position relative to the 0 position is changed gradually, the described measurements are repeated at each position, and the peak times for both of the redox species are derived. Solid curve 1 in Figure 6 shows a plot of the peak times obtained for Fc-COOH at different dispensing spots vs the peak times for [Ru(NH3)6]3+ at the same locations. The points are fitted with a linear regression, and the resulting straight line shows an expected intercept close to zero (i ) 0.03) and a slope of 0.90. (20) v. Stackelberg, M.; Pilgram, M.; Toome, V. Z. Elektrochem. 1953, 57, 342- 50. D ) x2/2t1 (2) D ) (x + d)2/2t2 (3) D ) (- dx2t1 2(t1 - t2) - x( dx2t1 2(t1 - t2)) 2 - d2 2(t1 - t2)) 2 (4) 2472 Analytical Chemistry, Vol. 73, No. 11, June 1, 2001 This slope gives the direct correlation between the diffusion coefficients of both redox species. If one knows the diffusion coefficient of one of the redox species, the unknown diffusion coefficient of the second redox species can be easily calculated. A control experiment was performed to prove that the proposed measuring principle is independent from the concentration of the redox species. While keeping all other parameters constant, the concentration of [Ru(NH3)6]3+ was reduced to 50%, and a series of analogous measurements was carried out again. The dashed curve in Figure 6 shows a plot of the resulting peak times for Fc-COOH vs the peak times for [Ru(NH3)6]3+. The linear regression of the data points has a slope of 0.88 and an intercept of nearly zero (i ) 0.04). As expected, no significant deviation from the slope of the solid curve in Figure 6 can be found, thus proving the hypothesis that the measured peak times are independent from the concentration of the redox species. As already pointed out above, the slope of the linear regression of a plot correlating the peak times of one redox species to the peak times of another redox species depends on the ratio of their diffusion coefficients. Substitution for Fc-COOH by a ferrocene derivative having a higher molecular weight and, therefore, a lower diffusion coefficient should, hence, result in a decreased slope in its correlation curve vs [Ru(NH3)6]3+. The dotted curve in Figure 6 shows a plot of the peak times of ferrocene derivative 1 (compare Figure 1) vs the peak times of [Ru(NH3)6]3+. The slope of the linear fit is 0.63 and the intercept is i ) 0.13. The diffusion coefficient of a second ferrocene derivative, 2, (see Figure 1) was evaluated in the same way. The plot of the peak times of ferrocene derivative 2 vs the peak times of [Ru(NH3)6]3+ shows a straight line with a slope of 0.87 and an intercept of -0.07 (not shown). Ferrocene derivative 2 has a molecular weight comparable to Fc-COOH, and hence, a similar diffusion coefficient is expected. In fact, both compounds show similar relative diffusion coefficients with respect to [Ru(NH3)6]3+ (ferrocene monocarboxylic acid, 0.89; ferrocene derivative 2, 0.87). Until now, we have demonstrated that it is possible to determine the relative diffusion coefficients of different ferrocene derivatives with respect to [Ru(NH3)6]3+ on the basis of the presupposition that it is possible to determine independently the diffusion time of two redox species having different formal potentials and oxidation states. However, it should also be possible to determine the relative diffusion coefficients of redox species having similar formal potentials but a large difference in their diffusion coefficients. It should be possible to measure the transit time of both species at a microelectrode potential that is sufficiently high to oxidize both redox species under diffusional control. If the difference between the diffusion coefficients were large enough, the current-vs-time curve should show two single peaks or at least a split peak with two detectable peak maxima. To confirm this hypothesis, a mixture of ferrocene derivative 1 and Fc-COOH was dispensed with the microelectrode polarized to +500 mV. For most combinations of the parameters, such as distance between dispensing spot and microelectrode, number of dispensed droplets, and height of the electrolyte layer above the microelectrode, no peak separation could be observed. If the distance between electrode surface and dispensing spot was short, the transit times for both species was similar and no peak separation was observed. If the distance between dispensing point and electrode surface was very long, the current peaks became broad so that a clear peak identification was very difficult. However, with an optimized set of parameters, the expected peak separation could be detected. A corresponding current-vs-time Analytical Chemistry, Vol. 73, No. 11, June 1, 2001 2473 curve is shown in Figure 7. Plotting the time of the first peak versus the time of the second peak results in a straight line with a slope of 1.37 and an intercept of 0.04 (not shown). To prove that the developed method for the determination of the diffusion coefficient of redox-active compounds is self-consistent, the relative values of the diffusion coefficient of Fc-COOH vs [Ru(NH3)6]3+ and of ferrocene derivative 1 vs [Ru(NH3)6]3+ can be compared with the relative value of Fc-COOH vs ferrocene derivative 1. The calculated value for the quotient of the diffusion coefficients of Fc-COOH and ferrocene derivative 1 of 1.41 is close to the experimentally determined value of 1.37. This good accordance demonstrates the self-consistency and generality of the described method for determining diffusion coefficients. To prove the consistency of the proposed method using an independent method, we determined the diffusion coefficients of ferrocene derivatives 1 and 2 by following a method previously described by Bard et al.6 Chronoamperometric experiments with a potential pulse from 0 mV to 500 mV vs Ag/AgCl with diskshaped microelectrodes were performed. The resulting current was normalized with respect to its steady-state value and plotted versus the inverse square root of the time. The diffusion coefficient of the redox species can be calculated from the slope of the resulting straight line and the radius of the microelectrode (s ) slope, r ) radius of the microelectrode) By means of linear regression, a slope of 0.132 and an intercept of i ) 0.677 has been determined (r ) 0.992) for ferrocene derivative 1, and a slope of 0.113 and an intercept of 0.973 (r ) 0.993) for ferrocene derivative 2. As can be derived from eq 5, the ratio of the inverse square roots of the slopes of ferrocene derivatives 1 and 2 corresponds to the ratio of their diffusion coefficients. By comparing the resulting value of 0.733 with the value calculated from the time-of-flight experiments, a good agreement is obtained Thus, the consistency of our novel method could be clearly confirmed."
        ]
    },
    {
        "image_filename": "designv11_28_0000475_irds.2002.1043911-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000475_irds.2002.1043911-Figure6-1.png",
        "caption": "Figure 6: Various following pattern",
        "texts": [
            " From the results, the validity of the proposed control law is verified. 3.4 Various following pattern Based on the control law as described above, a mobile robot follows walking human. It is possible for a robot to follow a human from his back as well as other various position. It can be an example that a robot moves side by side with a human. Such various following patterns can be achieved in the proposed control method. The fixed angle between the virtual springs and the human\u2019s walking direction can be set as various pattern (Fig.6). Fig.7. shows various following patterns of the mobile robot. In this computer simulation the target human walked straight. The values of Bsh were set to -90, -45, -25, 25, 45 and 90 degree in this simulation. The results clarified that the human following pattern changes based on Osh. With the proposed control method, there are the following advantages. First, when a human walks in a complicated course, situation-adapted following is possible by changing Osh. Second, even though there are obstacles in the space, it is possible to avoid conflict between output from obstacle avoidance layer and human following layer by controlling e s h "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002863_j.diamond.2006.06.018-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002863_j.diamond.2006.06.018-Figure1-1.png",
        "caption": "Fig. 1. Integrating process of carbon nanotubes electrodes (\u2460 holes with diameter of about 400 \u03bcm prepared in plate glass Awith laser welder; \u2461 copper disks and lines prepared on plate glass B through DC magnetron sputtering; \u2462 bonding of glass A and B; \u2463 electrodepositing of copper column, platinum films and nickel catalyst in holes; \u2464 synthesis of carbon nanotubes electrodes through MWPCVD).",
        "texts": [
            "diamond.2006.06.018 In this article, MWCNTs were grown directly in the holes of glass by microwave plasma chemical vapor deposition (MWPCVD). These electrodes were characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM), XPS (X-ray photoelectron spectroscopy), Raman spectra and the electrochemical performance of the integrated CNT electrodes had been investigated by cyclic voltammetry (CV). The fabrication process of carbon nanotubes electrodes was showed in Fig. 1. Hole arrays with diameter of about 400 \u03bcm were prepared in plate glass Awith pulsed laser welder. Copper micro-disks, the locations of which are corresponding to the locations of holes in glass A, and copper lines, which were used as conductors during the electrodeposition process and electrochemical measurement process, were prepared on glass B by magnetron sputtering method. 50% sodium silicate solution was spread on the position of glass B where no copper disks or lines existed. Then glass A and glass B were welded at the temperature of 450 \u00b0C"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003694_jst.104-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003694_jst.104-Figure4-1.png",
        "caption": "Figure 4. Forces and moments acting on the ball; FI: inertial force, FC: centrifugal force, FG: gravitational force; forces and moments with suffix ball are produced by the bowler; note that the ball\u2019s velocity and acceleration are positive in x-direction of the ball coordinate system.",
        "texts": [
            " the inclination angle of the tubes (Figure 3), Fy0Th \u00bc FyTh cos \u00f029 \u00de \u00fe FzTh sin \u00f029 \u00de \u00f02\u00de Fz0Th \u00bc FyTh sin \u00f029 \u00de \u00fe FzTh cos \u00f029 \u00de \u00f03\u00de Fy0MiRi \u00bc \u00f0FyMi \u00fe FyRi\u00de cos \u00f029 \u00de \u00fe \u00f0FzMi \u00fe FzRi\u00de sin \u00f029 \u00de \u00f04\u00de Fz 0 MiRi \u00bc \u00f0FyMi \u00fe FyRi\u00de sin \u00f029 \u00de \u00fe \u00f0FzMi \u00fe FzRi\u00de cos \u00f029 \u00de \u00f05\u00de Sports Technol. 2009, 2, No. 3\u20134, 97\u2013110 & 2009 John Wiley and Sons Asia Pte Ltd www.sportstechjournal.com 99 Instrumented bowling ball where the subscripts Th, Mi, and Ri denote thumb, middle and ring finger respectively. The ball forces (Figure 4) are Fxball \u00bc Fy0Th Fy0MiRi \u00f06\u00de Fyball \u00bc Fz0Th \u00fe Fz0MiRi \u00f07\u00de Fzball \u00bc FxTh FxMi FxRi \u00f08\u00de Fball \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fx2ball \u00fe Fy2ball \u00fe Fz2ball q \u00f09\u00de Fxball is the reaction force of the inertial force FI and the gravitational force FG times sin y (5FG sin y), where y is the angle of the ball coordinate system during the swing relative to the ground (Figure 4; 01 if Fxball is pointing forward, 901 www.sportstechjournal.com & 2009 John Wiley and Sons Asia Pte Ltd Sports Technol. 2009, 2, No. 3\u20134, 97\u2013110100 Research Article F. K. Fuss if Fxball is pointing downward when holding the ball with a horizontally retroverted arm at the transition from back to forward swing). Fyball (Figure 4) is the reaction force of the centrifugal force FC and the gravitational force FG times cos y (5FG cos y). The pinch force is Fpinch \u00bc jFy0Th \u00fe Fy0MiRij 2 \u00f010\u00de The pinch force vectors at thumb and fingers are by definition in line and opposite to each other, have the same magnitude, and thus are mutual reaction forces. The COP position results from COPd \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Mx2d \u00feMy2d Fx2d \u00fe Fy2d s \u00f011\u00de The COP refers to the origin of the resultant force of each finger applied to the finger tubes, and thus to the distance between the origin of the resultant force and the origin of the sensor coordinate system. Equation (11) implies that jatan2\u00f0Fyd;Fxd\u00de atan2\u00f0Myd;Mxd\u00dej \u00bc p 2 \u00f012\u00de where the atan2 function returns the resultant of the xy-force and the xy-moment in any quadrant (in contrast to the inverse tangent function, which returns the angle in the first and fourth quadrant only). The ball moments (Figure 4) are defined as follows: Roll (rightward/leftward spin): Mxball \u00bc0:0175\u00f0Fz0Ri Fz0Mi\u00de FxMi\u00bdCOPMi cos \u00f029 \u00de FxRi\u00bdCOPRi cos \u00f029 \u00de \u00fe FxTh\u00bdCOPTh cos\u00f029 \u00de \u00f013\u00de Yaw (inward/outward spin): Myball \u00bc0:0175\u00f0Fy0Ri Fy0Mi\u00de FxTh\u00bdCOPTh sin \u00f029 \u00de \u00fe 0:025 FxMi\u00bdCOPMi sin \u00f029 \u00de \u00fe FxRi\u00bdCOPRi sin\u00f029 \u00de \u00f014\u00de Pitch (back/top spin): Mzball \u00bcFz0Th\u00bdCOPTh sin \u00f029\u00de \u00fe 0:025 Fy0Th\u00bdCOPThcos \u00f029 \u00de \u00fe Fy0MiCOPMi cos \u00f029\u00de \u00fe Fy0RiCOPRi cos \u00f029 \u00de Fz0MiCOPMi sin \u00f029\u00de Fz0RiCOPRi sin \u00f029 \u00de \u00f015\u00de Resultant moment: Mball \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Mx2ball \u00feMy2ball \u00feMz2ball q \u00f016\u00de The beginning of the backward swing was set to the last point with zero force rate before the first force peak (Figure 5)",
            " The same applies to the ratio of forward to backward swing period and impulse (Figure 7, Table 2). The coefficient of determination of the pinch impulse ratio is slightly higher than the one of the pinch force ratio. The magnitude of the second peaks of Fxball, Fyball, Fzball, and Fball, correlates well with the average score (Table 2). As mentioned above, Fxball is the reaction force of the inertial force FI and the gravitational force FG times siny (5FG siny), where y is the angle of the ball coordinate system during the swing relative to the ground (Figure 4). Thus, Fxball corresponds to the acceleration during the forward swing. Better bowlers produce a higher acceleration during the forward swing, which results in a higher ball velocity. The linear ball velocity, in turn, is reflected in the angular velocity of the ball-arm system and therefore in the centrifugal force of the ball. The larger the velocity and consequently the centrifugal force, the larger is Fyball. Fzball is negative, corresponding to a leftward acceleration in right-handed bowlers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000773_jmaa.2001.7531-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000773_jmaa.2001.7531-Figure3-1.png",
        "caption": "FIG. 3. Typical phase trajectories of the feedback-controlled system.",
        "texts": [
            "2 2 n 2 2 y x 1 sin xy cos x .\u017d . \u017d . \u017d .\u017d .\u017d . From the simulation results, all trajectories of the feedback-controlled \u017d .system reach the observation map H x in a finite time and remain on \u017d . \u017d . \u017d .H x thereafter. Moreover, all trajectories x t of the system 1.2 satisfy the tracking control property with asymptotic stability along the line \u017d .Z x x to 3, that is, Theorem 4.4 holds. By the modified Runge Kutta method, some typical phase trajectories of the feedback-controlled system are depicted in Fig. 3. REFERENCES 1. J. P. Aubin and A. Cellina, \u2018\u2018Differential Inclusions,\u2019\u2019 Springer-Verlag, Berlin, 1984. 2. J. P. Aubin and H. Frankowska, \u2018\u2018Set-Valued Analysis,\u2019\u2019 Birkhauser, Boston, 1990. 3. J. P. Aubin, \u2018\u2018Viability Theory,\u2019\u2019 Birkhauser, Boston, 1991. \u017d .4. S. Behtash, Robust output tracking for nonlinear systems, Internat. J. Control 51 1990 , 1381 1407. 5. J. W. Chen, J. S. Cheng, and J. G. Hsieh, Tracking control for nonlinear uncertain \u017d .dynamical systems described by differential inclusions, J"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003740_1.2975154-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003740_1.2975154-Figure8-1.png",
        "caption": "FIG. 8. A right handed conchospiral helicoid with rectangular section.",
        "texts": [
            " VOLUME CHARGE MAGNETIC DENSITY M FOR MAGNETS WITH CONCHOSPIRAL GEOMETRY AND MAGNETIZATION M The helicoidal permanent magnet of cylindrical kind can be considered as a particular case of a more general class of magnets characterized by a conchospiral geometry10 and magnetization. Therefore, in this section, we want to evaluate the volume magnetic charge M for the conchospiral magnets, on the usual assumption of a constant magnitude value M of M. The main aim of the subsequent considerations consists in finding if nontrivial conditions exist in order to obtain M =0 for the conchospiral magnets. Let us consider Fig. 8. A right handed helicoid with rectangular section is illustrated. The directrices of this helicoid are right handed conchospiral helices. They are coaxial with the axis a\u2212a. The generic conchospiral has been denoted by . P is the generic point of . The rectangular section of the helicoid has radial and axial dimensions of constant values, [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: 131",
            " If we suitably choose O, then the conchospiral will always belong to the surface of the cone. Successively, let us take into account the origin S of , whose radial distance from the axis a\u2212a has been denoted by R. An infinitesimal rectangular neighborhood of S can be defined and oriented by putting its sides parallel to those of the finite rectangular section of the helicoid. This infinitesimal rectangular neighborhood can be considered as a rectangular section of another conchospiral helicoid whose directrix is just the curve . In Fig. 8 this helicoid has been shown by the dash line. The correspondent rectangular section that passes through the point P of has also been drawn. Here ds and dr are the infinitesimal sides of the rectangular section. Now, we can think of the infinite number of points S belonging to the rectangular starting section of sides re\u2212ri and b. Then, there is a correspondent infinite number of conchospiral helices that are associated with the relative infinitesimal helicoids that have an infinitesimal rectangular section. These helices are joined one after the other. Therefore the shape of the helicoid illustrated in Fig. 8 can be completely described by using a set of infinite coaxial circular cones whose axis, common vertex, and height are a\u2212a, O, and OT, respectively. Then, the generic point P of the mass of this helicoid is geometrically identifiable as a point of the correspondent conchospiral that passes through all the helicoidal body. Figure 9 a shows a part of with reference to a right handed orthogonal Cartesian system O X ,Y ,Z whose origin corresponds to the vertex of the cone on which is defined. In this figure the point P of is geometrically identified by the generatrix gc\u2212gc, the radius r that has the starting point A, and the oriented angle that has been measured from the plane XY. The angle is a function of the angles and , = \u2212 . 58 In order to describe the generic angular position of the conchospiral around the axis X that corresponds to the axis indicated in Fig. 8 by a\u2212a, the angle has been considered. Observing Fig. 8 we also verify that enables us to specify the angular rotation around X of the whole helicoid. Moreover, as soon as we fix the value of , it is possible to identify the position of P that belongs to by defining the value of the angle Fig. 9 a . Then, we can define the whole curve by changing . Now, to identify the position of P for successively computing the volume magnetic charge M, it can be useful to consider a spherical coordinate system. The origin of this coordinate system is the vertex O, that corresponds to the origin of the orthogonal Cartesian system previously defined",
            " 58 = \u2212 , 67 Equation 65 gives c as a function of the spherical coordinate associated with the generic angular rotation of around the axis X, c = arctan \u2212 sin ln g cos h . 68 Here also represents the rotation of the whole conchospiral helicoid characterized by a finite rectangular section with sides re\u2212ri and b. Finally, by Eq. 68 , the components ng, n , and n of the unit vector n can be explicitly expressed versus the spherical coordinates g, , and , ng = \u2212 n cos arctan \u2212 sin ln g cos h , 69 n = n sin arctan \u2212 sin ln g cos h , 70 n = 0. 71 Now, let us fix the magnetization M of the magnet illustrated in Fig. 8. We choose direction and orientation of M equal to those of the unit vector n represented in Fig. 10. Then, we obtain a conchospiral magnetization whose magnitude is constant and equal to M in each point of the magnet. Substituting in Eqs. 69 and 70 the magnitude n of n with M, we get the components Mg, M , and M of M versus the spherical coordinates g, , and , Mg = \u2212 M cos arctan \u2212 sin ln g cos h , 72 M = M sin arctan \u2212 sin ln g cos h , 73 M = 0. 74 From Eq. 74 , in relation to the fixed orientation of M, we note that the component M is always zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003630_icelmach.2008.4800141-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003630_icelmach.2008.4800141-Figure3-1.png",
        "caption": "Fig. 3. Equipotential lines in the FE-model, under no-load conditions (a) and during the two phase short circuit (b)",
        "texts": [
            " 3d Finite Element investigations in [9] showed that \u2013 depending on contact conditions - a considerable part of the amortisseur currents did not close over the end connections but over the pole end plates. The existence of substantial pole plate currents can also be inferred from photos showing thermally induced discolorations of the varnish on the pole plates near the bars. To avoid lengthy 3d FE calculations, estimations for idealised configurations were obtained by the 2d Finite Element Method serving as limiting values for the real case. A. Induced Voltage, Two-Phase Sudden Short Circuit A 2 MVA, 2p=32 hydroelectric generator with a fractional winding of q=7/4 (Fig. 3) was investigated using FLUX2D. In [2], an equation determining the maximum of the induced voltage in the open phase during the two-phase sudden short circuit, 0 2 1, \u2032\u2032 = \u2212 \u2032\u2032 q Phase d xU U x (1) can be found. Using (1), the ratio \u2032\u2032 \u2032\u2032q dx x was estimated from the peak voltages in the open phase prior to and after the beginning of the two-phase short circuit (Figs. 4 and 5). For the evaluation of (1), the ratio between the first voltage peak after the short circuit and the no-load voltage crest value was taken"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000359_s1388-2481(02)00337-5-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000359_s1388-2481(02)00337-5-Figure4-1.png",
        "caption": "Fig. 4. Cyclic voltammograms recorded at a carbon electrode (3 mm diameter disc) of poly 1 (obtained by potentiostatic method at 0.80 V; Q \u00bc 0:5 mC) transferred in THF+0.1 M TBAP. Potential measured vs Ag=Ag\u00fe 10 mM in CH3CN\u00fe TBAP 0:1 M. (A) \u2013 Scanning the positive region first. Scan rate: 100 mV s 1. (B) \u2013 Scanning the negative region first. Scan rate: 50 mV s 1.",
        "texts": [
            " Effectively, the reversible one-electron oxidation of the Ni(II) porphyrin dication into Ni(III) complex as well as that of Ni(II) isobacteriochlorin cation radical into Ni(III) cation radical complex have already been observed due to the stabilizing effect of macrocycle on the nickel [25,26]. This constitutes one of the few examples of metallochlorin exhibiting six quasi-reversible one-electron processes leading from the Ni(I) state to the Ni(III) state. As previously reported for the electrogeneration of metalloporphyrin films [27], the electrochemical polymerization of 1 was carried out by controlled potential electrolysis (0.5 mC) at 0.8 V in THF+0.1 M TBAP. Fig. 4 shows the cyclic voltammogram of the resulting electrode transferred with thorough rinsing in THF+0.1 M TBAP solution free of monomer. Upon oxidative scanning, a redox system is observed at E1=2 \u00bc 0:22 V (Fig. 4(A)). Owing to the similarity in shape and potential value with the peak system for the monomer oxidation in THF, this redox process was attributed to the two overlapping oneelectron oxidation of 1. In addition the intensity of the anodic peak is proportional with the potential scan rate \u00f0R \u00bc 0:998\u00de. This indicates the formation of an electrogenerated film (poly 1) on the electrode surface as a consequence of the oxidative polymerization of the two pyrrole groups. As expected, a redox peak system appears in the negative region at the same potential value, namely E1=2 \u00bc 1:7 V, than the reversible one-electron reduction of Ni(II) chlorin into Ni(II) chlorin anion radical. A prepeak appears at 0.10 V and may be ascribed to electroactivity of the functionalized polypyrrolic skeleton (Fig. 4(B)). The current efficiency of the electropolymerization process was determined by dividing the charge recorded under the two electron oxidation wave of polymerized 1 by the charge passed during the controlled potential electrolysis (0.5 mC) and multiplying by 3.33. Indeed, the electropolymerization process requires 6.66 electrons per monomer (2.33 electrons per pyrrole group plus two electrons for the oxidation of 1 into the dication form). The resulting electric yield, 6%, is similar to those (1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003001_icarcv.2006.345243-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003001_icarcv.2006.345243-Figure1-1.png",
        "caption": "Fig. 1. Geometric parameters of a general-2-trailer.",
        "texts": [
            " An experimental system which is capable to execute these steps is available since a few years and has been steadily improved to integrate handling and safety issues. The maneuver is based on the well known dependencies for a general-2-trailer (see [1]): 1The project Fahrassistenz beim Ru\u0308ckwa\u0308rtsfahren is funded by Stiftung Rheinland-Pfalz fu\u0308r Innovation, Mainz, Germany.   x\u03071 y\u03071 \u03b8\u03071 \u03b8\u03072 \u03c6\u0307   =   cos(\u03b81) 0 sin(\u03b81) 0 tan(\u03c6)/L1 0 \u03b8\u03072/v1 0 0 1   ( v1 v2 ) (1) The parameters on the left side are the temporal derivatives of the geometric description of an articulated vehicle with a one-axle trailer given in figure 1. The input parameters are the velocity v1 of the fixed axle of the tractor and the steering velocity v2. The most decisive value in the matrix above is the change of the angle of the trailer. Here the dependency is: \u03b8\u03072 v1 = ( sin(\u03b82 \u2212 \u03b81) tan(\u03c6) L2 + M1 cos(\u03b82 \u2212 \u03b81) L1 L2 ) (2) Driving into a parking box requires taking into account a variety of constraints which restrict the degree of freedom that is given by the formula above. Two major constraints are: \u2022 Limitations to the steering angle given by the mechanics of the tractor: \u2212\u03c6max \u2264 \u03c6 \u2264 \u03c6max \u2022 Jack-knifing limitations to the angle between tractor and trailer: \u2212jkmax \u2264 \u03b82 \u2212 \u03b81 \u2264 jkmax Further constraints which consider practical aspects of parking a real vehicle in real traffic situations will be considered in a later section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003612_978-1-4020-8600-7_6-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003612_978-1-4020-8600-7_6-Figure1-1.png",
        "caption": "Fig. 1 (a) Four-DOF robot from Gallardo-Alvarado et al. (2006), (b) reciprocal screws, (c) equivalent structure.",
        "texts": [
            " These instructions follow the steps listed in Section 2. This guidance, showing each result algebraically, graphically and as a geometric statement, enables non-experts to obtain the singularity in an easy manner. 55 P. Ben-Horin et al. We exemplify the tool by means of the singularity analysis of a 4-DOF robot, first presented in Gallardo-Alvarado et al. (2006). This robot consists of three different legs, having PS, UPS and PRPS (or CPS) kinematic chains, respectively (the underlined labels stand for actuated joints), see Figure 1a. The constraint screws of leg 1 are reciprocal to the spherical and prismatic joints. Thus they form a two-system perpendicular to the prismatic and passing through the spherical joint. Then the reciprocal screw to the passive joint of leg 1, $1, is a screw directed along the leg. In leg 2 the passive joints are the spherical and the universal joints thus their reciprocal screw, $2, is directed along the leg that connects them. The third leg has two prismatic actuators P3 and P4. The reciprocal screws to the passive joints form a two-system of zero pitch, being a planar pencil with center at the spherical joint and containing the axis of the revolute joint. Particularly, $3 and $4 pass through the spherical joint center and are directed along the leg and parallel to the revolute joint axis, respectively. With these screws known, the equivalent structure to be entered into SinguLab is as appears in Figure 1c. The interface analyzing this robot is shown in Figure 2, where the singularity condition is that at least one of the tetrahedrons composed by S1A1B1C1, S1S3A3B3 and S1S3S2A2 (according to the labels in Figure 1c) is coplanar. This paper presents SinguLab, a graphical user interface for the singularity analysis of parallel robots. The theoretical background behind this analysis is based on Grassmann\u2013Cayley algebra, which provides a coordinate-free approach for treating geometric entities and their incidences. The identification of the geometric entities and the singularity conditions are made automatically. The results are based on pre- 56 SinguLab \u2013 A Graphical User Interface for the Singularity Analysis of Parallel Robots vious studies on certain classes of Gough\u2013Stewart platforms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001914_05698190490439346-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001914_05698190490439346-Figure3-1.png",
        "caption": "Fig. 3\u2014FEM model of the connecting rod assembly; (a) connecting rod and attached pin, (b) connecting rod bearing.",
        "texts": [
            " Input necessary parameters of connecting rod assembly solid model. Step 2. Mesh all components of the model. Step 3. Calculate nodal inertial and gravitational loadings. Step 4. Solve the contact problem with an interference fitted bearing and pre-loaded bolts, i.e., solve Eq. [8]. Step 5. Solve Eq. [7] and obtain the nodal displacement and stress (the bearing global deformation is thus obtained). Step 6. Output the results. In the present study, a three-dimensional element meshed connecting rod assembly model (Fig. 3) was investigated at 6,500 rpm. The connecting rod and attached pin are meshed by 10-node tetrahedral elements. The bearing shell and bolts are meshed by 8-node hexahedral elements. Details can be found in Wang (23). The information regarding the connecting rod assembly is given in Table 1. The displacement boundary conditions of the connecting rod assembly in the XYZ coordinate system are listed in the following: 1. Only half of the connecting rod assembly model is considered. Along the symmetry plane Z = 0, the symmetry displacement boundary conditions are uZ = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003891_s0263574709990683-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003891_s0263574709990683-Figure3-1.png",
        "caption": "Fig. 3. Geometry of the ith leg as a four-bar planar linkage.",
        "texts": [
            " The procedure proposed consisted of three steps: \u2022 (i) Define the range limits \u03d11imin and \u03d11iMax for the actuated angles; \u2022 (ii) For each value \u03d11i (i = 1, 2, 3) given, evaluate the passive angles \u03d13i , \u03d12i ; \u2022 (iii) Solve the nonlinear Eqs. (47), (48), and (49). (i) The actuated pairs \u03d11i must respect the limits imposed by the leg geometry varying between \u03d11imin and \u03d11iMax . Indeed, a single leg can be analyzed just as a planar fourbar linkage, with Ai and P as fixed revolute pairs and d as virtual link (Fig. 3). The lower limit position of the linkage is set when \u03d12i = 0 (first and second link aligned). The upper limit position is obtained by geometry, considering a symmetric rotation \u03b2 of the virtual link around a direction perpendicular to the plane of motion and passing through P , which coincides with each of the {G} axes at the nominal pose. By a procedure similar to those exploited for both the direct and inverse position analyses the planar linkage geometry at First we square both Eqs. (61) and (62) and add them; then we use a trigonometric relation to obtain: \u03b2\u0303 = \u03d11imin + \u03b2 = acos ( Pyi 2 + Pzi 2 \u2212 [(a + b)2 + d2] 2(a + b)d ) (63) Therefore Eqs",
            " (64), (65) lead to: Pyi = R1c\u03d11imin + T1s\u03d11imin (66) Pzi = R1s\u03d11imin \u2212 T1c\u03d11imin (67) where R1 = (a + b) + dc\u03b2\u0303 T1 = ds\u03b2\u0303 Equations (66), (67) can easily be solved for \u03d11imin: \u03d11imin = asin ( PziR1 + PyiT1 R2 1 + T 2 1 ) (68) Calculation to obtain \u03d11iMax starts from the analysis of the linkage at the upper position: Pyi \u2212 dc\u03b2 = ac\u03d11iMax + bc\u03b5 (69) Pzi \u2212 ds\u03b2 = \u2212as\u03d11iMax + bs\u03b5 (70) where \u03b2 = \u03b2\u0303 \u2212 \u03d11imin \u03b2 is known from previous calculation, \u03b5 is the angle that BiCi forms with a reference direction (Fig. 3). We square Eqs. (69), (70), add them and use a trigonometric relation to Therefore Eqs. (69), (70) can be rewritten as: PYi = ac\u03d11iMax + bc(\u03b5\u0303 \u2212 \u03d11iMax) (72) Pzi = as\u03d11iMax \u2212 bs(\u03b5\u0303 \u2212 \u03d11iMax) (73) Eqs. (72), (73) lead to: PYi = R2c\u03d11iMax + T2s\u03d11iMax (74) Pzi = \u2212R2s\u03d11iMax + T2c\u03d11iMax (75) where R2 = a + b + c\u03b5\u0303 T2 = bs\u03b5\u0303 Equations (74), (75) can easily be solved for \u03d11iMax : \u03d11iMax = asin ( PYiT2 \u2212 PziR2 R2 2 + T 2 2 ) (76) (ii) \u03d11i\u2019s i = 1, 2, 3 vary between \u03d11imin, \u03d11iMax to cover a full combination of given data"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000855_jra.1986.1087062-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000855_jra.1986.1087062-Figure3-1.png",
        "caption": "Fig. 3 . Link coordinate frames for rotational joints.",
        "texts": [
            " The acceleration ai is given by (6), i.e. ' a i - 1 + h ; - 1 X s j - l + t j - 1 X ( o j - l X s - 1 ) , if joint i- 1 is rotational ai = ai-l+ si-1/i-1+cj;-lX~j-1+2W;-lX;;-1/i-1 (16) + 0;- 1 x (Wj- 1 x si- I ) , if joint i- 1 is translational. 00 Note that (15) and (16) have a recursive form which permits us to compute the velocity and accelerations beginning with the first link and then moving forward. The position rei, velocities uc; and acceleration aCi of the center of mass of link i shown in Fig. 3 are given by rci = ri + scj (17) u,i = u; + i c i / j + ai x s,i (18) a c i = a i + ~ c ; + h i X s c j + 2 w i X ~ c ; + w j X ( o i ~ s c i ) (19) where x,; is the vector from the origin of the ith frame to the center of mass of link i. For determining the vebcities and accelerations of the center of mass of link i d a revolute arm it is convenient to use the ith frame since'di, e;, &, and q ; are measured about or along the zi axis. DYNAMICS U ING THE NEWTON-EULER QUATIONS From the balance principles of linear and angular momen- tum it follows that where F is the resultant of the external forces acting on the body, Mc is the movement of the external forces about the center of mass, and H, is the angular momentum vector of the body with respect to the center of mass",
            " (25) k c = I , h + w x ( I c w) . (26) From (22), (24), and (25), it follows that Note that the above vector-tensor equation is coordinate free, i.e. when written in terms of components a convenient choice of coordinate frames can be made. The evaluation of (26) is simplified when the axes of the corotational frame and the principal directions of the inertia tensor coincide. For the Newton-Euler equations we need the resultant force Fi and the moment Mci of the forces about the center of mass of each link. As shown in Fig. 3, letfi be the force applied to link i by link i - 1, and let -fi+ be the force applied to link i by link i + 1. Then F i = f i + ( - f i + 1 ) + m i g = f i - ~ + 1 + m i g . (27) Also, let Mi be the moment applied to link i by link i - 1 ; and let -Mi+ I be the moment applied to link i by link i + 1. Then Mci=Mi+(-Mi+I)+(-Sci)xJ;.+(Si--ci)X(-if+l) = M i - M ; : + , - S c i X f , - ( S j - S c i ) X f i + l . (28) By projecting Mi onto the direction of zi axis, we obtain the input torque ~i on the ith linl, , i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000545_rob.4620060405-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000545_rob.4620060405-Figure3-1.png",
        "caption": "Figure 3. Revolute joint.",
        "texts": [
            " (21) described above will be formed by merely grouping the equations of all the links and by adding the constraint penalty terms to those equations. Constraint Equations Serna and Bayo: Forward Dynamics of Elastic Robots 373 is not limited to any particular sort of constraint, however for the sake of simplicity and brevity the authors will only deal with the most common types of planar constraints such as those corresponding to the revolute and prismatic joints. Let us first consider two different links with origins Oi and Oi, respectively, that arc interconnected by a revolute joint as illustrated in Figure 3. If ul: is the axial elastic displacement at the end of link i (whose position coincides with the origin of link j ) the constraint conditions can be expressed as xi +(Li + u!) cos@, - xi = 0 yi + (Li + 1.4:) sin Qi - = 0 where Li is the length of the link i in its undeformed configuration. If axial deformations are neglected Eq. (30) can be used to eliminate the Cartesian coordinates of the joints as generalized coordinates. On the other hand Figure 4 illustrates a typical case of prismatic joint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001306_ias.1996.556992-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001306_ias.1996.556992-Figure2-1.png",
        "caption": "Fig. 2. Quadrature (q-d) Versus Physical (a-b-c) Reference Frames.",
        "texts": [
            " The inverter converts the q-d voltage commands V* and v * from the regulator to the applied line voqtages Va , v b , vc , to the motor. In this example, there is no position or velocity feedback to the controllers. Two of the line currents, I, and I b , are measured and fed back to both the observer and current regulator. In addition to the line currents, the q-d current commands and voltage commands are fed into the observer. The voltage commands would be readily available in a digital implementation of the current loop. Fig. 2 shows the q-d reference frame defined with respect to the three phases a-b-c of the physical system d d \u2019 The three stationary phases of the stator a-b-c are transformed to a two phase stationary frame a-p. The a-axis is usually defined as the a-axis. The p-axis is 90 degrees away from a-axis. Measuring the angle between the a-axis and a vector passing through the north pole of the rotor finds the synchronous frame d-axis. Since the rotor may have multiple magnetic pole pairs, the electrical frequency is a function of the mechanical frequency and the number of pole pairs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000652_0470867906-Figure8.5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000652_0470867906-Figure8.5-1.png",
        "caption": "Figure 8.5 Natural coordinate system for a rotationally symmetrical plane element",
        "texts": [
            " In this way the approach described here, see [333] and [33], differs significantly from the (later) work of Haase et al. [131] in which a system matrix of the mechanics constructed using a FE simulator is imported into a circuit simulator via a hardware description language. The construction of the element matrices should be represented for an isoparametric, rotationally symmetrical plane element, see also Bathe [19]. For this purpose a natural coordinate system is introduced for the element, which has the coordinates s and t, which each run from \u22121 to +1 see Figure 8.5. The first step is to approximate the coordinates of arbitrary points of the plane elements on the basis of the coordinates of the four nodes. To this end the form functions hi are introduced, which are formulated as follows in the natural reference system of the element: h1 = 1 4(1 \u2212 s)(1 \u2212 t) h2 = 1 4(1 + s)(1 \u2212 t) h3 = 1 4(1 + s)(1 + t) h4 = 1 4(1 \u2212 s)(1 + t) (8.1) The fundamental property of these functions is that the hi becomes equal to 1 at node i and becomes equal to 0 at all other nodes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002916_jphyscol:1975138-Figure11-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002916_jphyscol:1975138-Figure11-1.png",
        "caption": "FIG. 11. - Effect of the horizontal transverse force FA on the type 2 solution. Figures 10 and 11 show two limiting cases for the same type 2 distortion. The analysis of these nonlinear problems is not very clear at present.",
        "texts": [],
        "surrounding_texts": [
            "Cl-206 E. GUYON AND P. PIERANSKI\nAlthough we do not intend to discuss here the threshold problem, an estimate is consistent with the z Ericksen number evaluation (2). In a typical experiment with a L = 8 cm long cell, d = 200 p, the low frequency threshold corresponds to a pressure head - 2 mm of water. Using an estimate of APC JK, K, - 4 X 1 0 - ~ cgs we get an experimental value\nI I Er, - 10.9. The fact that this estimate is lower than the\nI I result (2) may be due in part to the transverse flow effects which did not play a role in the shear flow problem but give a first order destabilizing contribution here of magnitude comparable to the ordinary a, torque contribution. Only this last effect was evaluated\nraiapii in (2). I , - 1 - 4 .\nI - I dt'her instability modes with rolls of axis parallel to I the flow are seen (Fig. 7). The wavelength of the rolls is 1 independent of the width of the cell and is of the order or smaller than the thickness : I l a\nc w r c ~ - c 'Z e B \" S\n4 ' FIG. 8 - (Fig. 8, 10, 1 1 are viewed along the velocity axis). The proposed distortion corresponds to the linear instability\nS 4 * . mode taking place at point PIU. Thc vertical hydrodynamic W ; B h d i % a $ ~ i $ ? ~ ~ d d * i f r . r ,\nw r 'tb 3 I p z - r - l t . l a s ( ~ .a(rvpp*t* focusing forces F ln are of opposite signs in both halves of the e cell and should cause the formation of two rolls over the cell\nthickness.\nF'IG. 7. - A photograph showing, with the same scale, the rolls for the unstable points PZA (a), P213 (b), PIB (C).\nPOINT P I B (of Fig. 5). -We consider a large frequency (0.5 Hz) flow and a state just above threshold. The observations, in particular the absence of double imaging of dust particles located at the bottom plates, point towards the existence of a solution 1 instability. The dark and light lines (which indicate the lines of maximum curvature of n) along the rolls remain the same when the sign of the flow changed. This shows that the alternating distortion involves a change of sign of ny and not of the vertical component n, :\nIn the shear flow problem [2] we called this regime a y mode. The mechanism for the instability involves a vertical destabilizing hydrodynamic focusing force F, (Fig. 8). This term couples with a vertical hydrodynamic torque which splays the molecules off the xz plane.\nWe have characterized the y instability mode at point P,, by 1 B (solution 1 plus mechanism B).\nLet us note that FB is of opposite sign in each half of the sample thickness. If, as assumed, FB induces the formation of convective rolls, two rolls should be formed across the cell thickness. The diagram of figure 9 gives the wavelength of the rolls, h, measured from a laser light beam diffraction pattern, as a function of the pressure head just above threshold. At low frequencies, il is nearly equal to d/2. However, when Ap increases, the wavelength decreases as Ap-'l2 [9]. This result is clearly understandable : The rolls in both halves of the sample are decoupled. At threshold, the frequency f varies linearly with Ap (see Fig. 5) . When f increases, the distortion takes place near the plate over a smaller and smaller thickness of the order of il such that the elastic time constant for the relaxation of n, proportional to i12 is of the order o f f - l (see also formula B 6 and B 7 in reference [2] : when 2 decreases, the increase of the hydrodynamic focusing force F, is compensated by that of the viscous terms in the coupl-",
            "ing terms p). The variation of Ap as ,lv2 can also be obtained directly by considering the expression (2b) for Er, :\nEr, cc S , 12 cc Apd;12 . POINT PZB. - This state corresponds to a relatively large frequency and a finite amplitude instability. It is quite different from state 1 B. A dust particle gives a double image through the cell. The dark and bright lines of the longitudinal rolls exchange over each half period. The first point indicates a solution of type 2 (finite average splay) whereas the second one is compatible with the z mode instability solution described in reference [2] such that\nHere the vertical distortion oscillates around zero. Again the interpretation (see Fig. 10) involves the destabilizing vertical force F, ; we cbaracterize this regime as a 2 B mode.\nHere, F, has the same direction for two points on the same vertical in both halves of the cell. Contrarily to the 1 A case, a simple roll formation across the sample is expected. We indeed found that the wavelength of the rolls increased discontinuously going from point P,, to P,, (compare in Fig. 7 the wavelength of the small amplitude rolls (c) to the larger wavelength of the rolls for point PI* (h)).\nPOINT PzA. - Finally we come back to a state at very low frequency but involving a large enough distortion. The experiments show the existence of rolls parallel to the flow but of wavelength 2 to 3 times the thickness (Fig. 7a). One can check that it is a type 2 solution. A possible explanation of the instability involves the horizontal force due to the anisotropic stress tensor mechanism of type A, the twist of the molecule off the xz plane giving rise to the horizontal\nforce FA (Fig. 10). There is no sharp distinction between this description and that of figure 9 as in fact FA and FB are present at the same time in both cases.\nWe feel that a detailed description of the mechanism at the last two points is probably very difficult, first because it is a finite amplitude problem, secondly because of the coupling of the solutions in both halves of the cell.\nMore work and in particular quantitative measurements on thresholds is in progress. It is of interest to study the effect of fields. In particular the application of a large enough vertical electric field decreases the elastic time constant for the relaxation of n, and moves the z mode into the linear instability regime.\nAcknowledgments. - We thank P. G. de Gennes for pointing out to us the original features of the Poiseuille flow problem and L. LCger for useful exchanges of information.",
            "Note. - The Poiseuille cell is remarkably simple purposes : first, it shows a case of a hydrodynamic to assemble and to handle. Then by gently blowing instability problem (this is a remarkably simple case, as on one end of a tube attached to an end of the cell, one many hydrodynamic instabilities have only finite obtains easily the roll structures and the strong decrease amplitude solutions) ; secondly, it provides the most of transparence due to dynamic scattering. We feel that simple demonstration of the coupling between flow this simple device should be useful for pedagogical and molecular orientation in nematics.\nReferences\n111 PIERANSKI, P. and GUYON, E., Solid State Commun. 13 (1973) 435. [2] PIERANSKI, P. and GUYON, E., Phys. Rev. A 9 (1974) 404. 131 DE GENNES, P. G., Les Houches Lectures Notes (1973). In the\nproblem, Er represents typically the ratio between a time constant associated with the stabilizing elastic\neffect d2 and one due to the destabilizing hydrodyK 7 namic mechanism - . is a hydrodynamic viscosity. as\n141 'A comparative description of the mechanism of the shear flow instabilities is given in GUYON, E. and PIERANSKI, P., Physica 73 (1974) 184.\n[ S ] GAHWILLER, Ch., MO[. C w t . , Liqu. Cryst. 20 (1973) 301.\n[6] We have shown that in materials where a2 a3 was negative, the homogeneous mode was absent as the small positive torque a3 had a stabilizing effect ; PIERANSKI, P. and GUYON, E., Phys. Rev. Lett. 32 (1974) 924.\n[7] PIERANSKI, P. and GUYON, E., Phys. Lett. 49A (1974) 237. [8] See DE GENNES, P. G., The Physics of Liquid Crystals (Oxford University Press) 1974. [g] This mode provides a remarkably simple and efficient\nvariable wavelength grating which could possibly be used for practicaI purposes."
        ]
    },
    {
        "image_filename": "designv11_28_0000980_jjap.28.l1480-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000980_jjap.28.l1480-Figure9-1.png",
        "caption": "Figure 9. The configuration of the system (18 cm \u00d7 6 cm \u00d7 10 cm).",
        "texts": [
            " W was maximized and each Wi was designed over the target value as a typical micro-force measurement specification, shown in table 3. A typical instrument has under 1 mgf resolution, over 200 gf measurement range and under 1 s settling time. In general, W2 is not specified for a typical instrument. However, for a meaningful measurement,W2 must be large. In detail, the variation caused by a change in position of application of a force must be lower than the resolution. A weighing system was constructed as shown in figure 9 by using the results of optimal design and geometry conditions. 4.1. Resolution and range of measurement (W1) Figure 10(a) shows the sensitivity characteristic for the change in mass. A small change of mass or force should be detected by the position sensor for high resolution. The sensitivity of the position sensor to the change in mass is 67.567 V gf\u22121. The analogue-to-digital converter (ADC) used in this experiment could reasonably detect potentials under 5 mV, i.e. 0.074 mgf. If control error, external vibration and other factors are considered, the performance related to the resolution could be reduced, but a resolution under 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000490_j.ijmecsci.2003.10.010-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000490_j.ijmecsci.2003.10.010-Figure2-1.png",
        "caption": "Fig. 2. Geometry of the toggle linkage during real-mold clamping.",
        "texts": [
            " (2) The inertia forces, the weights, and the friction forces at the slider connections can be neglected when compared to the total deformation force of the tiebars and the thrust of the crosshead. (3) The deformation e ects of the mold and the mold platens are negligible. (4) Coulomb friction is valid for the friction at pin joints. (5) The friction coe6cients are the same for all pin joints. Due to assumption (1), the equilibrium equations of the toggle clamping system are constructed at the undeformed con\"guration of the toggle clamping system during real-mold clamping operation in this study. Fig. 2 depicts a skeleton drawing for the lower half of the toggle clamping mechanism shown in Fig. 1 during real-mold clamping operation. The dashed lines denote the con\"guration when the moving platen is just in contact with the stationary platen. It is assumed that the toggle mechanism and the tiebars are not yet deformed in this con\"guration. After the contact, the toggle linkage is subjected to compressive force. Thus, besides the rigid body motion, there arises the compressive deformation for the toggle linkage. It can be seen from the solid line shown in Fig. 2, the moving platen is at rest and the tailstock platen moves backward after the contact. The \"nal position of real-mold clamping operation is achieved when the toggle is fully extended in a straight line. In this paper, the symbol (\u223c) denotes that the quantity in parentheses is in the state of the \"nal position of mold clamping operation. From Fig. 2, the geometry of the \"nal position of the mold clamping operation, and the assumption of small deformation, we may have L2 sin C \u2212 L1 sin C = (L2 \u2212 BC) sin \u2212 (L1 \u2212 AB) sin = dA; (1) L4 sin( C + C) + L3 sin C =(LCF \u2212 CF) sin + L4 sin C cos + (L3 \u2212 DE) sin = dE; (2) \u0303= \u2212\u0303; (3) LCF = L4 cos C; (4) tan = L4 sin C (LCF \u2212 CF) ; (5) SC = (L1 \u2212 AB) cos \u2212 L1 cos C + (L2 \u2212 BC) cos \u2212 L2 cos C = HSC \u2212 AB cos \u2212 BC cos ; (6) HSC = L1(cos \u2212 cos C) + L2(cos \u2212 cos C); (7) UE = L1 cos C \u2212 (L1 \u2212 AB) cos +(L2 \u2212 LCF) cos C \u2212 (L2 \u2212 LCF \u2212 BF) cos +L4 sin C(sin C \u2212 sin ) + L3 cos C \u2212 (L3 \u2212 DE) cos ; (8) where Li (i = 1\u20134) and LCF are the distance between joints A and B, B and C, D and E, C and D, and C and F , respectively, at the undeformed state of the mechanism, SC is the elongation of the tiebars; AB, BC and DE are the axial shortened length of links 1, 2 and 3, respectively, BF and CF are the shortened length of axial segments BF and CF of links 2, respectively, UE is the horizontal displacement of the crosshead"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001626_0094-114x(81)90040-9-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001626_0094-114x(81)90040-9-Figure3-1.png",
        "caption": "Figure 3.",
        "texts": [
            " We locate the robot hand at the end of offset $33 (Fig. 2). If in practice the hand is located at the end of a link, an additional offset of zero length is inserted between them. The actuator for each joint could be located anywhere along an offset, but for convenience will be considered at the far end of each offset. The maximum reach will be independent of 01 since whatever the configuration, the reach defines a circle centered around and in a plane normal to axis $1. Therefore, 01 can be set to an arbitrary position (Fig. 3). The angle 03 is located near the hand and does not affect the reach. This leaves 02 as the independent variable. The vector pairs a12S22 and a23S33 can be replaced by their respective vector sums, VI2 and V23. The reach as a function of 02 will be made up of the vector sum V12 and V23, V13. The cone of revolution of possible postions of V23 is about the axis $2. Letting d~ equal the angle between vectors VI2 and V23 (Fig. 4) defined in the plane of these two vectors, the maximum reach will be found where ~ is a maximum. This occurs when vector V23 is at position 1 (Fig. 3), in the plane defined by $22 and the base point. No other vector in the cone can have a greater angle d~. In this position all of the vectors V12, V23, V13 and S22 are in the same plane, and V13 must intersect the axis $2. The reach V~3 can also be defined by the chain a12a12 + $22S2 -t- a23a23 + $33S3 = VI3. (1) ~ 3 The direction cosines for these vectors are al2(1,0, 0) Sd0, - s12, c ,9 a23(c2, U*I, U21) S3(X2, I\"2, Z2) as defined in the Appendix. The distance between vectors V~3 and $2 is zero when X2--Xl Y2--Yl Z2--Zl al bl cl =0 a2 b2 c2 where x y z refer to any respective points on each vector and a b c to their respective direction numbers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002627_cdc.2005.1583353-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002627_cdc.2005.1583353-Figure3-1.png",
        "caption": "Fig. 3. Total mass functions",
        "texts": [
            " From (6) it is clear that the computation of the control requires knowledge of the disturbance d. In the next section we show that, for the particular problem at hand, the control depends linearly on d, and standard adaptive control techniques can be used to estimate the disturbance. V. APPLICATION TO A FLOTATION CIRCUIT The basic idea is to shape the total mass functions associated to each tank. For smooth outlet flow a flat energy function around a nominal level, Hd1, will be required, as illustrated in Fig. 3. However, to keep a tight control around the set point, a energy function,like function Hd2, which penalizes big errors should be designed. In our application we will use the first tank to damp the inflow disturbances; i.e. we will allow its level to move within certain boundaries. However, the levels of the downstream tanks must be kept constant to obtain a desired concentrate grade. Towards this end, the following desired total mass function is proposed: Hd(x) = H(x) + Ha(x) = 3\u2211 i=1 xi + \u03c6i(xi, xi\u2217), (7) where the functions \u03c6i(xi, xi\u2217) must assign the equilibrium point to the closed loop system and capture the objectives described above"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001667_robot.2004.1307171-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001667_robot.2004.1307171-Figure10-1.png",
        "caption": "Fig. 10 Sets of variables. a) four temporary variablq b) Morala variables.",
        "texts": [],
        "surrounding_texts": [
            "configurations. Relevant to the computation of possible grasps are the abduction motion of the two fingers and the geometric dimensions of the hand.\nThe grasp problem involves finding a set of four grasp parameters X=[x y 8 A], where x and y are the Cartesian coordinates of the palm center, 8 i s the orientation ofthe wrist and A is the abduction ofthe opposite fingers (Fig. 8). We also define the finger extensions dl , d2 and d3 which are dependent on the previous variables and cannot be controlled independently.\nWe proceed to determine finger placement points (which is equivalent to determining X ) to optimize the criteria proposed by Morales et al. In particular, the criterion for finger extension (FE) can be defined with:\nFE=(d, -d , )2+ (d , -d3 )2+(d2-d3)2 (2)\nMinimizing the above will minimize the torque on the object in its plane. This torque results when finger contractions are different and hence, the depths of the contact points on the object are different. . Here we define a force line criterion (FL) that takes into consideration the different fliction coefficients for object surfaces. The new FL criterion is based on the following general form:\nFL = k p , = wherep, /4 (3) t i l\n.where angles rjl are shown at Fig. 8. This criterion is important because the stability of a grasp depends on the orientation of the actual force with respect to the surface normal [3].\nFinally, the centroid distance criterion (CD) is the distance between the palm g t e r and the object centroid. This measure is also meant to minimize the torque.\n\u2019\n, B. Two-fingerGrasp~ . .\nWe present the theory for the two-finger grasp first, followed by analysis of the three-finger case. In the real two-\nfinger grasp, FE and FL have only two terms while all three terms are included for optimizing the virtual two-finger grasp because it uses three fingers.\nThe FE criterion is less important in the two-finger grasp because it always takes on either small values (virtual grasp) or 0 (real grasp). The two other criteria are more important and they can be optimized simultaneously. In the two-finger case, the optimization can be done analytically which yields an action line at angle 8, defining the orientation of the hand\nC. Three-finger Grasp The following method for spthesizing three-finger grasps has been inspired by the work of Morales et al. [3], but brings two major improvements as discussed below.\nOur problem is still to find the four parameters X = [x y 8 A], but we use a temporary set X, = [ I , G 13 s] (see Fig. loa) because the constraints on the latter are more easily expressed: li E [0, I.,] and 8 E [0, 2 4 . Here, the lengths I , measure the distance !?om the grasping zone boundary to the placement point of finger i and L, is the grasping zone length. For a given X there exists a unique solution for X and therefore the hand parameters are fully specified. The fact that we maintain the four dimensions instead of lowering the dimension of the search space to one will result in more computation, but it will allow us to find all possible grasps. Moreover, it will allow us to combine two criteria for optimality, namely FE and FL. This constitutes the main innovation of o w work.\nHere we first optimize the FL criterion. The cost function is (3) and the four search directions are the variables in the set X,. The 4 for the cost function are computed using the equations derived.in 131. These are recalled here (see Fig. lob and (5)).\nc",
            "where a, a\u2019 and h are real values known kom the object geometry and the orientation of the hand (9. The cost function is optimized using linear programming with the constraints on 1, and B. Once FL is optimized, the grasp parameters contained in X are computed using a, b and other known values like X, and the hand dimensions. The parameters X=[x y 6 A] found so far minimize the FL criterion. It is important to note that only 6 and 1 will affect the value of FL The other two variables, x and y, are not constrained yet, and can be varied to optimize FE without changing the value of FL. This second optimization step is implemented using linear programming with a new set of inequality constraints to ensure that the placement points remain on the grasping zones.\nThe result of the two-step approach described above is a set of grasp parameters with the best FL possible for the given segment lines. The value of FE is the best for the given Band A. Note that all variables are now constrained and it is not possible to optimize the centroid distance.\nThis optimization process must be repeated three times, with the thumb placed on the three lines and the band configuration with the lowest quality measure, presented in the next section, taken as the best one.\nD. Quality Measure It is necessary to establish a measure Q in order to compare the different grasps obtained with the previous methodologies. Here we follow the traditional approach of summing two normalized criteria E and E :\nwhere FEm=2(d--d~)2 and FL-=3. The quality measure Q=FE+FL used to order the grasps can be used to compare two- and three-finger grasps. If several grasps have a perfect Q (=a), the distance criterion CD is used to choose the best grasp. Note that perfea quality is often obtained for objects with symmetry. _ _\nv. RESULTS FOR SARAH\nResults are presented for SARAH in two parts: 1) the synthesis of grasp parameters according to the methodology described in the previous sections and 2) the execution of several grasps with SARAH mounted on a seven-dof robotic arm. Grasp synthesis was implemented in a Matlab program, the input to which is the object model and the output is all possible grasps ordered according to our quality measure Q.\nTo evaluate our grasp synthesis methodology, 20 revolute and extruded objects were used. Results are presented here for six of these objects chosen to demonstrate the different grasp types and to illustrate the advantages of the method. The first object is a pentagon and it was selected for comparison of the present method with that described in [3] (see Fig. 11). The top windows of Fig. 11 show the two best grasps synthesized by our program while the bottom windows show the grasps obtained employing Morales methodology using the same set of lines. It is worth noticing that four grasps were generated on that particular object (two are not shown). Our results for both and are generally better than those in [3], but they can be equal in rare cases. The reason for this is that the set ofpossible solutions obtained with the methodology in 131 is a subset of our possible solutions.\nThe best grasps synthesized for a set of three representative objects are shown in Fig. 12. They are all complex curved objects found in real life. The first two objects, cup and pitcher (Fig. 12a and b), are revolute while the third one, a brick, is planar with holes. Note that the best grasp for this last object is a two-finger grasp.\nThe last set of objects was meant to show the execution of the grasps with SARAH. The experimental evaluation was conducted at the Canadian Space Agency (CSA) with SARAH mounted on a seven-dof manipulator. The experiment consisted of picking up an object placed in the robot\u2019s workspace. The pose of the object was known and fed to the manipulator along with one of the grasps to be tested. The grasp was then qualified as \u201csuccess\u201d or \u201cfailure\u201d. Over the set of tested objects, almost every grasp was executed successfi~lly. In case of failure the synthesis program parameters (e.g., & or the limit separating the groups of lines) could be corrected.\nSARAH grasping two objects is shown in Figuresl3a and b. The object in Fig. 13a was adapted kom [3] and our best grasp, unlike most other methodologies, uses the sharp comers of this part. Finally, Fig. 13b shows a three-finger grasp of a revolute object.",
            ". . . ~\n.W. Conclusion\nThis paper addressed the problem of combining different criteria to optimize the quality of two-finger and three-finger . grasps for planar and revolute objects. The methodology developed proved efficient for optimizing simultaneously the previously mentioned criteria of finger extension, line of force direction and distance to object centroid and it achieves good results for practical applications. Although flexible and robust, the number of steps needed to account for all scenarios makes\n~. its implementation \u2018somewhat complicated. In the future, we plan to-extend the methodolo& to general 3D objects and usevision for object pose identification. Combining FL and FE with \u201cmaximal object segments\u201d [ 1,6] would ensure high\nquality grasp (using a specific hand) executable with low tolerance to errors in finger positioning.\nACKNOWLEDGMFNT\nWe gratefully acknowledge the use of-facilities and technical support received fiom the Canadian Space Agency.\nREFERENCES\n[I] I. Ponce and B. FaVejoq \u201cOn camputhg t b n e - 6 ~ ~ ~ forcbelowe grasps of polygonal objecir,\u201d BEE frammtiom on robotics and ouromorion, vol. 1 I, pp. 868381, 1995. [2] V.-D. Nguym, \u2018%onstrucbhg f o r c e z l o ~ grasps,\u201dlnt. J. Robotics Rer., vol. 1, no. 3,pp. 3-16. June 1988. . [3] A Morals, P.J. Sans AP. del Pohil, and AH. Fa=, \u2019\u2019 An w e n t is\nI E E ~ L I I . Conf On Inlelligenr Robots and System, vol. 2, pp. 1693 - 1698,202 [4] 7. Lalibae and CM. Oosselis \u2018Wundcrarmation in space rbbolic hands,\u201d Proceeding of the Inl. Symposium on AItifrciol Inl. and Robotics & Avlmnation in Space. 2001 [5] L. B. GaaU, \u201d C A D W graaq synthesis utiliing poIygor~%\u2019\u2019 hoe. IEEE Inl. Conf RobtiesondAulomotion, pp. 184-189, 1989. [6] C.-P. k g aod AC. Kak, \u201cFm Conmudion of Forceclosun Gmqx,\u201d IEEERobotiesandAvlom~ti~\u201c, vol. 12, pp. 615426,1996. [\u2019I] N. S. Pollard, \u201cSynL-g Grarps 6w Gmmlircd pmlorypcq\u201d I\u20ac\u20ac\u20ac Inl. Con$ Robotics andAulomotion. vol. 3,pp. 2124-2130.1996. [8] A T. Miller, S. kq, H. I: Chrin- P. K Allm, \u201cAutomatic Grasp P l e g Using Shapc Rimitiveg\u201d IEEE Inr. Conf Robotics ond Aubmation, \u201c013, pp. 221-232.2003.\nVkbo-bawd h g R Conact r C l d O n with @ippCr gmmmy,\u201d"
        ]
    },
    {
        "image_filename": "designv11_28_0000880_ijcat.2002.000288-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000880_ijcat.2002.000288-Figure1-1.png",
        "caption": "Figure 1 Misalignment nomenclature.",
        "texts": [
            " Only the work carried in [3] presented a reasonably sound procedure to evaluate the nature of load distribution in spline teeth and the associated misalignment loads. In this paper, a method is developed for calculating tooth load distribution in light weight couplings and accounts for the effect of such parameters as tooth and shaft stiffnesses as well as misalignment angle on spline tooth load distribution. The unbalance loads associated with the misalignment and friction moments are also considered in calculating the tooth load distribution. Copyright # 2002 Inderscience Enterprises Ltd. To illustrate the spline tooth load distribution, let us consider Figure 1 in which the driving shaft I transmits a torque T to the driven shaft II through the spline coupling as shown. The centerlines of the two shafts are assumed parallel, and an angle of misalignment will therefore take place between the spline and each shaft, separately. To simplify the analysis initially, let us consider the case of in\u00aenitely rigid teeth, rim and shaft. In this case, only two diametrically opposite teeth will transmit the torque for any value of misalignment as shown in the Figure",
            " Thus far, the misaligned tooth loads have been assumed, symmetrical about the plane of misalignment, i.e. all teeth on one side of the plane of misalignment carry identical loads as their counterparts on the other side. With re-distribution, an uneven tooth load distribution such as that shown in Figure 7 would be present, and the net reactions generated are approximately given by: P1 P M1 L P2 P M2 L 15 which will result in the additional reacting forces at the shaft bearings R as shown previously in Figure 1. Up to now, the misalignment moments calculated have been based on a \u00aexed angle of misalignment, i.e. the angle of misalignment is assumed unchanged throughout the spline coupling and is equal to the angle of misalignment between the shafts connected to the coupling. However, under the misalignment moments generated at the splines, the coupling will undergo elastic deformation as a simply supported beam subjected to externally applied moments. The deformation would effectively reduce the slopes (or angles of misalignment) at the two end splines, see Figure 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001669_03093247v204217-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001669_03093247v204217-Figure6-1.png",
        "caption": "Fig. 6 . Comparison of surface stress distribution program with that obtained from photoelastic testing",
        "texts": [
            " The JOURNAL OF STRAIN ANALYSIS VOL 20 NO 4 1985 0 IMechE 1985 -_ 0 0 0 : I The dimensions of the lug and the finite element mesh, which was used in the analysis are shown in Fig. 4. The thickness of the lug is 0.31 in, the pin diameter is 1.25 in with a diametral clearance of 0.001 in between the lug and the pin, and Young\u2019s Modulus and Poisson\u2019s Ratio for the lug material are 26.5 lbf/in2 and 0.3, respectively. The stresses obtained from the photoelastic and finite element analyses at the inner and outer surfaces of the lug are shown in Fig. 6 with the finite element results being indicated by a full line and the photoelastic results by a dotted line. These stresses were calculated for a total pin load of 16000 lbf but as only a symmetrical half of the lug was considered, a value of 8000 Ibf was used in the analysis. Maximum stress occurs on the surface of the bore at 108 degrees measured from the positive x axis. From the photoelastic analysis, this stress had a value of 80.5 Tf/inz and from the finite element calculations its 221 at Eindhoven Univ of Technology on July 2, 2014sdj.sagepub.comDownloaded from value was found to be 79.6 Tf/in2. The agreement between the program and photoelastic results is particularly good in this region of maximum stress and, considering the stress distribution as shown in Fig. 6, the general shape and magnitude of the finite element results show good agreement with the photoelastic results. A comparison of photoelastic and calculated results is shown in Fig. 7 for the stress variation across the critical 222 JOURNAL OF STRAIN ANALYSIS VOL 20 N O 4 1985 (((- IMechE 1985 at Eindhoven Univ of Technology on July 2, 2014sdj.sagepub.comDownloaded from section. The diagram shows the variation in principal stress difference, which is the value measured directly in photoelastic tests and agreement between the two sets of results is again shown to be good. On examination of the results which are shown in Fig. 6, it is clear that there is a high tensile stress on the hole boundary. Figure 7 indicates the stress distribution across the critical section of the lug. It was clear from the photoelastic results that the stress distribution in the lug is complicated and a simple analysis is likely to yield unreliable results. For that reason it was decided that a finite element analysis, which took account of the complex load distribution, would have to be used if the complicated stress distribution was to be calculated with adequate accuracy",
            " The load distribution which was obtained for a total pin load of 16000 lbf is shown in Fig. 5. Using that distribution, with the assumption of a rigid pin and negligible friction between the surface of the pin and the lug, the stresses in the lug at its bore and outer surface were calculated using the finite element model shown in Fig. 4 and using the boundary conditions described earlier. When these calculated results are compared with the values obtained from the photoelastic study, good agreement, as shown in Fig. 6, was found. The photoelastic results in Fig. 7 show a fairly non-linear stress distribution across the critical section, and although only four elements were used across the section, the photoelastic and finite element results match closely. Although only the results for one load case are presented in the paper, they indicate that the technique described for the determination of load distribution, and the finite model used in the analysis are satisfactory. The JOURNAL OF STRAIN ANALYSIS VOL 20 NO 4 1985 c, IMechE 1985 223 at Eindhoven Univ of Technology on July 2, 2014sdj"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001192_memsys.1994.555614-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001192_memsys.1994.555614-Figure4-1.png",
        "caption": "Fig. 4. Structure and dimensions of microflight mechanism.",
        "texts": [
            " In order to get drag by flapping, there should be a difference between the upstroke and downstroke. Real insects create this difference by changing the wing's angle of attack against the air, or by deforming their wings, causing a difference in C,. The former is well-known as the Clap-and-Fling mechanism. A complicated structure like a Clap-and-Fling mechanism, however, cannot be easily fabricated for a micromachine. Instead, we used simple wing deformation by applying elasticity to a micromachine, as shown in Fig.4. It has been pointed out that the electrostatic force, or Coulomb's law, is of great advantage because it is independent of scale under geometric similarity. However, it requires either an onboard battery or an electric power supply, with or without a connecting wire. In addition, induction requires a large antenna compared to the machine body. Since we are mainly interested in the dynamics of microflight, one of the simplest ways for power supply is used, interaction between a magnet and an alternating magnetic field",
            " This calculation indicates that a magnetic material such as Pt-CO or nickel can drive a wing with an alternating magnetic field of under O.l[TI. Table 1. Simulation results for flapping by magnetic material The structure shown in Fig.3 creates a difference between the upstroke and downstroke through the rear wings, which are more flexible than the fore wings. During the downstroke the fore wings and the rear wings move together, but during the upstroke the rear wings move a little bit behind the fore wings. Fig.4 shows a microfligh Nickel is sandwiched by two polyimide 1 spin-coated to 1[pm] in 0.1 [p] in thickness. vs. the surface flux Fig.7 shows the freq by a laser moire instrument. Typical values used in the experiment were i=O.l[A], B= 0.01[T], w=300[Hzl, and tip deformationdo [pm]. Although our measurement system cannot measure more than 80 pm, several hundred pm deformation was observed by using a television microscope. Frequency of altemating magnetic field [Hz] Fig.7. Frequency response of wing as measured by a laser moire"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000545_rob.4620060405-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000545_rob.4620060405-Figure7-1.png",
        "caption": "Figure 7. Five bar manipulator and applied torques.",
        "texts": [
            "'' Figure 5 illustrates a single-link robotic manipulator consisting of one elastic member attached to a rigid hub. Two linear finite elements with cubic shape functions are used to generate an elastic model with 9 degrees of freedom. The Serna and Bayo: Forward Dynamics of Elastic Robots 375 prescribed torque shown in the same figure is applied, and the resulting tip displacements are shown in Figure 6 where they are compared to the nominal displacements. These results coincide with those obtained by Bayo.\" The five-bar linkage robotic manipulator depicted in Figure 7 is composed of three rigid links and an elastic one. In order to prove the ability of the new formulation to deal with the constraints, each link was considered as a free body attached to the adjacent through the appropriate constraint conditions. The total number of coordinates is 18 with 10 constraint equations. The elastic link was discretized using three cubic beam elements. Figure 7 shows the values of the applied torques during 10 seconds of simulation. Figures 8 and 9 illustrate the motions of the system during the application of the torque, and after the torque is removed, respectively. Finally, Figure 10 represents the tip vibration of the elastic link. In this article, the authors have presented, firstly, a general procedure to define and discretize the kinetic and potential energy of a robot that is composed of elastic members, and secondly, a modified Lagrangian formulation that leads to the differential equations of motion of the system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003935_s0263574709990506-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003935_s0263574709990506-Figure2-1.png",
        "caption": "Fig. 2. A schematic view of the RCID mechanical structure.",
        "texts": [
            " Parallel manipulators are well known for their high dynamic performances and low positioning errors.24,25 In the last few years parallel manipulators have attracted great attention from researchers involved with robot manipulators, robotic end effectors, robotic devices for high-precision robotic tasks, machine-tools, simulators and haptic devices.26\u201330 The mechanical structure of the RCID comprises a (fixed) base platform and a moving (payload) platform, linked together by six independent, identical, open kinematic chains (Fig. 2). Each chain comprises two links: the first link (linear actuator) is always normal to the base and has a variable length li with one of its ends fixed to the base and the other one attached, by a universal joint, to the second link; the second link (fixed-length link) has a fixed length L and is attached to the payload platform by a spherical joint. Points Bi and Pi are the connecting points to the base and payload platforms. They are located at the vertices of two semi-regular hexagons, inscribed in circumferences of radius rB and rP , that are coplanar with the base and payload platforms (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003868_s10015-008-0557-x-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003868_s10015-008-0557-x-Figure4-1.png",
        "caption": "Fig. 4. Structure of joint",
        "texts": [
            " The manipulator has many passive joints that have lock mechanism. Two wires are installed around both sides of the manipulator, and a hose is installed in its center (Fig. 2a). A rail is installed on a side of the manipulator. Two manipulators are connected by the rail. They can be moved along the rail each other (Fig. 2b). 3.2 Mechanism of changing direction Wire is fi xed on top rink and tube is fi xed on the end rink. By pulling the wire, we can change head direction, and then lock the joints at the state (Fig. 3). 3.3 Lock mechanism Figure 4 shows structure of each joint. Each joint have two frictional materials.And, hose passed through the center. By putting water into the hose, the hose expands, and the expanded hose pushes inside friction materials, then, inside friction materials engages with outside friction materials. As a result, the joint is locked to the position (Fig. 5). The amount of the injected water into the hose is adjusted with the piston that is installed to the end part (Fig. 6). As described in subsection II-1, conventional robots have motors, sensors and controllers to operate the robot, and, require space for loading with them"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002947_robot.2005.1570219-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002947_robot.2005.1570219-Figure5-1.png",
        "caption": "Fig. 5. Point contact between micro-part and saw-tooth",
        "texts": [
            " 2 shows the surface profile of a 2012-type ceramic chip capacitor. It was the electrodes of the micro-part that contacted the feeder surface as they were about 40 m higher than the conductor. The electrode surface exhibited concavities and convexities. the electrode surface are perfectly spherical with radius (Fig. 3) and the feeder surface is saw-toothed (Fig. 4). Let be the elevation angle of a saw tooth, as illustrated in 0-7803-8914-X/05/$20.00 \u00a92005 IEEE. 825 the figure. A saw-tooth contacts an electrode in one of two ways: point contact (Fig. 5) and slope contact (Fig. 6). A micro-part moves in the desired direction if it stops during point contact but slips during slope contact. We will analyse point- and slope-contact to derive a set of conditions for unidirectional feeding. Let us formulate the point-contact illustrated in Fig.5. Let be the force vector generated by the vibration of a parts feeder. Let be the angle between a horizontal line (parallel to the electrode surface) and one connecting the contact point and the center of a concavity or a convexity. The driving force on a capacitor can be represented as the sum of a tangent component and a normal conponent defined as: = cos (1) = sin (2) Assuming that the weight of a micro-part is negligible, the micro-part stops when the inequality = sin cos 0 (3) is satisfied",
            " = sin (4) = cos (5) Then, the slip condition during slope contact is expressible as: = cos sin 0 (6) where is the coefficient of friction at slope contact. Combining Eqs. (3) and (6) yields the following inequalities as conditions for the unidirectional motion of a micropart: tan (7) cos sin (8) Next, we investigate the case of feeding without directionality. When Eq.(3) is not satisfied, i.e., when the following inequality holds, slipping occurs at the contact point. tan (9) When a micro-part slips at the point contact of the concavity illustrated in Fig. 5(a), the micro-part moves in the desired direction, satisfying the condition given in Eq.(3). This implies that a micro-part stops even when its concavity begins to slip. When a micro-part slips at the point contact of the convexity shown in Fig. 5(b), increases as contact point moves in the right direction and the saw-tooth is separated from the micro-part when exceeds 90 . Then, the next saw-tooth contacts the micropart at around = 0 , and the micro-part stops at the point contact. On the other hand, the contact condition rarely changes from stopping to slipping when the amplitude of parts feeder vibration is small, which makes unidirectional motion difficult. tan 1 1 (10) In the following sections, we describe the actual friction of a saw-tooth surface by measuring the angle of friction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001788_135065005x9772-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001788_135065005x9772-Figure1-1.png",
        "caption": "Fig. 1 Schematic diagram of journal bearing",
        "texts": [
            " To take this into account, the governing equations, Reynolds, energy and heat conduction, are first solved by the inverse method, satisfying the appropriate pressure and temperature boundary conditions using the finite difference method with successive over relaxation (SOR) scheme under steady-state condition to create a data bank. The details of these equations are given in Appendix 2. The steady-state pressure distribution p0 considering thermal effects is obtained by setting _1 and _f equal to zero in equation (11). This is done by solving equations (11), (17), (19), (20), and (21) satisfying the boundary conditions given by equations (22) to (29). The pressures thus determined are integrated using Simpson\u2019s 1/3 rule to get the non-dimensional load W , which is given by (Fig. 1) W \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fr2 \u00fe Ff2 q (1) where F r \u00bc 2 \u00f01=2 0 \u00f0u2 0 p0 cos udud z (2) and Ff \u00bc 2 \u00f01=2 0 \u00f0u2 0 p0 sin udud z (3) where u2 is the angular coordinate where the film cavitates. Non-dimensional load ( W ) is given by W \u00bc WC2 h0vR 3L and attitude angle is given by f0 \u00bc tan 1 Ff Fr The coefficient of friction is found from R C m \u00bc F s W (4) Proc. IMechE Vol. 219 Part J: J. Engineering Tribology J00904 # IMechE 2005 at NATIONAL SUN YAT-SEN UNIV on August 23, 2014pij"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003259_cjce.5450490111-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003259_cjce.5450490111-Figure3-1.png",
        "caption": "Figure 3 -Movement of the reaction surface and expected concentration profiles within a circulating drop.",
        "texts": [
            " On a comparb les schtmas dbcoulement mesurt et la position de la surface de rtaction avec les prkdictions de solutions d\u2019tquation de transport et trouvk qu\u2019il y avait une concordance dans les limites d\u2019erreur exptrimentale. Figure 2d the conversion of base is completed and the entire drop is clear and colorless. The reaction shell\u2019s radius is equal to zero. Molecular diffusion without reaction follows. Figure 2e indicates a typical dependence on time of the reaction shell\u2019s radius, the concentration profiles, and the change of the concentration of base in the centre of the drop. Similarly for the case of a circulating drop Figure 3 is typical. In Figures 3b, 3c i t is seen that a ring or \u201ctorus\u201d of color is expected if the normal patterns are introduced for a circulating drop. The process is very complex but one might expect the profiles shown in Figure 3e for a circulating sphere. Mathematical analysis in this study involved solving transport phenomena equations to predict the position of the reaction shell as a function of time for a stagnant drop and position of the stagnation ring for a circulating drop. A brief summary may be found in the Appendix. Experimental work The object of the experimental work was to develop the aforementioned techniquec4\u2019 to measure the position of the reaction shell as a function of time. Equipment used A sketch of the experimental equipment is presented schematically in Figure 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003230_14644193jmbd103-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003230_14644193jmbd103-Figure2-1.png",
        "caption": "Fig. 2 Surface parameters",
        "texts": [
            " Using these vectors, the tangents t\u0304i 1 and t\u0304i 2, and the normal n\u0304i to the surface at the contact point are defined, respectively, in the body coordinate system as t\u0304i 1 = \u2202u\u0304i P \u2202si 1 , t\u0304i 2 = \u2202u\u0304i P \u2202si 2 , n\u0304i = t\u0304i 1 \u00d7 t\u0304i 2 (2) This parameterization can be used to describe the wheel and rail surfaces. For example, the surface geometry of the rail r can be described in the most general form using the two surface parameters sr 1 and sr 2, where sr 1 represents the rail arc length and sr 2 is the surface parameter that defines the rail profile, as shown in Fig. 2. The surface parameter sr 1 is defined in the rail body coordinate system, whereas the surface parameter sr 2 is defined in a profile coordinate system X rpY rpZ rp shown in Fig. 3. The location of the origin and the orientation of the profile coordinate system, defined, respectively, by the vector Rrp, and the transformation matrix Arp, can be uniquely determined using the surface parameter sr 1. Using this description, the global position vector of an arbitrary point on the surface of the rail r can be written as follows rr = Rr + Ar(Rrp + Arpu\u0304rp) (3) where Rr is the global position vector of the origin of the rail coordinate system X r Y r Z r , Ar is the transformation matrix that defines the orientation of the rail coordinate system, and u\u0304rpis the local position vector that defines the location of the arbitrary point on the rail surface with respect to the profile coordinate system",
            " The location and orientation of the rail profile coordinate system depends only on the distance travelled along the track sr 1, while the local position of an arbitrary point on the rail surface at any section depends on the value of sr 2, that is Rrp = Rrp(sr 1), Arp = Arp(sr 1), u\u0304rp = [0 sr 2 f (sr 2)]T (4) where f is the function that defines the rail profile. Similarly, the geometry of the wheel surface can be described using the two surface parameters sw 1 and sw 2 . These surface parameters can be defined in a wheel set coordinate system X wY wZ w . The surface parameter sw 1 defines the wheel profile, and sw 2 represents the angular coordinate of the contact point, as shown in Fig. 2. The location of the origin and the orientation of the wheel set coordinate system are defined, respectively, by the vector Rw and the transformation matrix Aw . Using this description, the global position vector of an arbitrary point on the surface of the wheel w can be written as follows rw = Rw + Awu\u0304w (5) where u\u0304w is the local position vector that defines the location of the arbitrary point on the wheel surface with respect to the wheel set coordinate system and can be written as u\u0304w = [ g(sw 1 ) sin sw 2 \u2212 L + sw 1 g(sw 1 ) cos sw 2 ]T (6) where g is the function that defines the wheel profile, and L is the distance between the origin of the wheel set coordinate system and point Q on the wheel, as shown in Figs 2 and 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003554_978-3-540-30301-5_4-Figure3.21-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003554_978-3-540-30301-5_4-Figure3.21-1.png",
        "caption": "Fig. 3.21 The harmonic drive",
        "texts": [],
        "surrounding_texts": [
            "The purpose of a transmission or drive mechanism is to transfer mechanical power from a source to a load. The design and selection of a robot drive mechanism requires consideration of motion, load, and power requirements and the placement of the actuator with respect to the joint. The primary considerations in transmission design are stiffness, efficiency, and cost. Backlash and windup impact drive stiffness especially in robot applications where motion is constantly reversing and loading is highly variable. High transmission stiffness and low or no backlash result in increased friction losses. Most robot transmission elements have good efficiencies when they are operating at or near their rated power levels but not necessarily when lightly loaded. Larger than necessary drives add weight, inertia and friction loss to the system. Underdesigned drives have lower stiffness, can wear rapidly in continuous or in high duty cycle operation or fail due to accidental overloads. Joint actuation in robots is generally performed by drive mechanisms which interface the actuator (mechanical work source) to the robot links through the joints in an energy-efficient manner. A variety of drive mechanisms are incorporated in practical robots. The transmission ratio of the drive mechanism sets the torque, speed, and inertia relationship of the actuator to the link. Proper placement, sizing, and design of the drive mechanisms set the stiffness, mass, and overall operational performance of the robot. Most modern robots incorporate efficient, overload damage resistant, back-driveable drives. Direct Drives The direct drive is kinematically the simplest drive mechanism. In the case of pneumatic or hydraulic actuated robots, the actuator is directly connected between the links. Electric direct-drive robots employ hightorque, low-speed motors directly interfaced to the links. The complete elimination of free play and smooth torque transmission are features of a direct drive. However, there is often a poor dynamic (inertia ratio) match of the actuator to the link requiring a larger, less energy efficient, actuator. Part A 3 .7 Band Drives A variant of direct drive is band drive. A thin alloy steel or titanium band is fixed between the actuator shaft and the driven link to produce limited rotary or linear motion. Drive ratios in the order of up to 10 : 1 (10 actuator revolutions for 1 revolution of the joint) can be obtained. Actuator mass is also moved away from the joint \u2013 usually toward the base, to reduce robot inertia and gravity loading. It is a smoother and generally stiffer drive than a cable or belt drive. Belt Drives Synchronous (toothed) belts are often employed in drive mechanisms of smaller robots and some axes of larger robots. These function much the same as band drives, but have the ability to drive continuously. Multiple stages (two or three) of belts are occasionally used to produce large drive ratios (up to 100 : 1). Tension is controlled with idlers or center adjustment. The elasticity and mass of long belts can cause drive instability and thus increased robot settling time. Gear Drives Spur or helical gear drives provide reliable, sealed, low-maintenance power transmission in robots. They are used in robot wrists where multiple axes intersect and compact drive arrangements are required. Largediameter, turntable, gears are used in the base joints of larger robots to handle high torques with high stiffness. Gears are often used in stages and often with long drive shafts, enabling large physical separation between ac- tuator and driven joint. For example, the actuator and one stage of reduction may be located near the elbow driving another stage of gearing or differential in a wrist through a long hollow drive shaft (Fig. 3.1). Planetary gear drives are often integrated into compact gearmotors (Fig. 3.20). Minimizing backlash (free play) in a joint gear drive requires careful design, high-precision and rigid support to produce a drive mechanism which does not sacrifice stiffness, efficiency and accuracy for low backlash. Backlash in robots is controlled by a number of methods including selective assembly, gear center adjustment, and proprietary anti-backlash designs. Worm Gear Drives Worm gear drives are occasionally used in low-speed robot manipulator applications. They feature rightangle and offset drive capability, high ratios, simplicity, good stiffness and load capacity. They also have poor efficiency which makes them non-back-driveable at high ratios. This causes the joints to hold their position when unpowered but also makes them prone to damage by attempts to manually reposition the robot. Part A 3 .7 Proprietary Drives Proprietary drives are widely used in standard industrial manipulators. The harmonic drive and the rotary vector (RV) drive are two examples of compact, low-backlash, high-torque-capability drives using special gears, cams, and bearings (see Figs. 3.21 and 3.22). Harmonic drives are frequently used in very small to medium-sized robots. These drives have low backlash, but the flexspline allows elastic windup and low stiffness during small reversing movements. RV drives are usually used in larger robots, especially those subject to overloads and shock loading. Linear Drives Direct-drive linear actuators incorporate a linear motor with a linkage to a linear axis. This linkage is often merely a rigid or flexure connection between the actuator forcer and the robot link. Alternatively, a packaged linear motor with its own guideways is mechanically connected directly to a linear axis. Direct linear electromagnetic drives feature zero backlash, high stiffness, high speeds, and excellent performance but are heavy, have poor energy efficiency, and cost more than other types of linear drives. Ball Screws Ball\u2013screw-based linear drives efficiently and smoothly convert rotary actuator motion into linear motion. Typically, a recirculating ball nut mates with a ground and hardened alloy steel screw to convert rotary motion into linear motion. Ball screws can be easily integrated into linear axes. Compact actuator/drive packages are available, as well as components for custom integration. Stiffness is good for short and medium travel, however it is lower for long motions because the screw can only be supported at its ends. Low or zero backlash can be obtained with precision-ground screws. Speeds are limited by screw dynamic stability so rotating nuts enable higher speeds. Low-cost robots may employ plain screw drives featuring thermoplastic nuts on smooth rolled thread screws. Rack-and-Pinion Drives These traditional components are useful for long motions where the guideways are straight or even curved. Stiffness is determined by the gear/rack interface and independent of length of travel. Backlash can be difficult to control as rack-to-pinion center tolerances must be held over the entire length of travel. Dual pinion drives are sometimes employed to deal with backlash by providing active preload. Forces are generally lower than with screws due to lower ratios. Small-diameter (low teeth count) pinions have poor contact ratios, resulting in vibration. Sliding involute tooth contact requires lubrication to minimize wear. These catalog stock drive components are often used on large gantry robots and track-mounted manipulators (Fig. 3.23). Other Drive Components Splined shafts, kinematic linkages (four-bar, slidercrank mechanisms, etc.) chains, cables, flex couplings, clutches, brakes, and limit stops are some examples of other mechanical components used in robot drive mechanisms (Fig. 3.8). The Yaskawa RobotWorld assembly and process automation robots are magnetically suspended, translate on air a planar (two-DOF) bearing, and are powered by a direct electromagnetic drive planar motor with no internal moving parts (Fig. 3.12)."
        ]
    },
    {
        "image_filename": "designv11_28_0003977_s12213-008-0010-1-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003977_s12213-008-0010-1-Figure5-1.png",
        "caption": "Fig. 5 Structure of the orthogonal microrobot",
        "texts": [
            " We also have to compensate for the versatile microrobot's motion even if we need only orthogonal motions [18, 19] although the versatile microrobot can move in an XY direction and rotate independently. We have concluded that we need a simple orthogonal positioning device that can remain stably on a surface even when no current is applied to the electromagnets. To satisfy these requirements, a simple locomotion mechanism composed of one piezoelectric actuator and two electromagnets have been developed. Here two electromagnets guided by a pair of v-grooves are connected by one piezoelectric actuator so that it can move precisely in one axis as depicted in Fig. 5. We use permanent magnets on the electromagnets so that this one-axis microrobot requires no current for remaining stably on a steel surface. The magnetic flux when no voltage is applied to the electromagnet is explained in Fig. 6. FL is a magnetic force of the left shaft and FR is that of the right shaft when no voltage is applied. The magnetic flux when a voltage is applied to the electromagnet is explained in Fig. 7. FL' is a magnetic force of the left shaft and FR' is that of the right shaft when a voltage is applied"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001583_j.ndteint.2004.11.002-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001583_j.ndteint.2004.11.002-Figure1-1.png",
        "caption": "Fig. 1. Structure of shells in a nuclear fuel container designed for train shipment.",
        "texts": [
            " They establish the shipping routes and a rigorous standard for certifications of used nuclear fuel container. 0963-8695/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ndteint.2004.11.002 * Corresponding author. Tel.: C34 942 200 879; fax: C34 942 200 877. E-mail address: madruga@teisa.unican.es (F.J. Madruga). These specially designed containers are composed of multiple shields of steel, lead and other materials to confine the radiation from the used nuclear fuel. Just to illustrate the device in Fig. 1, the composition of a typical container for used nuclear fuel is shown. The used nuclear fuel is enclosed in a cylindrical container whose walls consist of the lead shield enclosed by two stainless steel shells (inner and outer). A solid neutron absorbent material (neutron shield) covers completely the cylindrical form and an impact absorber cap is used to limit the impact force in the container. The fabrication process of container starts to build the stainless steel structure with the gap for the lead shield and it continues stuffing the gap with liquid lead"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002903_0010-4485(75)90135-9-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002903_0010-4485(75)90135-9-Figure7-1.png",
        "caption": "FIGURE 7. Balanced linkage (diagrammatic) correspond ing to Figure 6(b)",
        "texts": [
            " EXAMPL E The use of the program is illustrated here with an example showing how a linkage is force-balancedby two methods. Current data is tabulated upon request from the user (step a, Figure 6). This lists kinematic and dynamic properties of the linkage. It is not necessary to alter the position of the centre of mass of the coupler, so the co-ordinates are re-entered unaltered. The dynamic properties of the balanced linkage are next calculated and tabulated together with required locations for the counterweights (step b). (The resulting linkage is shown in Figure 7). In certain instances, it may be desirable to move the centre of mass of the coupler in which case the program will calculate the required size and location of a counterweight of minimized inertia. In this example, it is assumed that the coupler must be balanced at the crank pin. Step c makes the necessary alteration and the next table of values specifies the new counterweights for this case (step d). Figure 8 shows the corresponding linkage. The effects of this force-balancing upon the pin forces within the mechanism may be examined using the analytical facility of the program"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002027_1.2179460-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002027_1.2179460-Figure1-1.png",
        "caption": "Fig. 1 Schematic structure of the toroidal drive",
        "texts": [
            " It consists of a central input sun-worm, planet worm-gears, a stationary internal gear with toroidal shaped teeth, and a central output planet carrier. The contact between the sun-worm and the planet worm-gears and that between the worm-gears and the internal gear are in the form of rolling consisting of meshing rollers. The rollers are distributed uniformly around the reference circle of the planet worm-gears for meshing with the sun-worm and with the stationary internal gear. The rollers in this paper are in the form of balls. The schematic structure of the toroidal drive is illustrated in Fig. 1. Journal of Mechanical Design rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/27/201 To analyze the meshing contact, the coordinate frame between the meshing roller and the planet worm-gear is introduced. Figure 2 illustrates the sun-worm meshing with a planet worm-gear via a meshing roller to demonstrate the relationship between a roller and the planet worm-gear. The roller coordinate frame S o , i , j ,k of a meshing roller is fixed at the center of the roller, the planet worm-gear rotatable coordinate frame S2 o2 , i2 , j2 ,k2 is fixed at the center of the worm-gear and rotates with the worm-gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000475_irds.2002.1043911-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000475_irds.2002.1043911-Figure4-1.png",
        "caption": "Figure 4 : Control Variables",
        "texts": [
            " Especially, differential wheel velocity type mobile robot is adopted as an agent of the ISpace in current system, it is almost impossible to use human\u2019s movement as input of robot control. To trace human who walks freely, a control strategy that absorbs limitation of non-holonomic constraint is needed. The proposed virtual spring model is able to absorb the gap between motion of human and a mobile robot. Since the point of application of elastic force differ from rotation center of a mobile robot as shown in Fig.4, non-holonomic restriction is overcome. 3.2 Derivation of control law In Fig.4.(2h1 ?Jh, eh) is world coordinate of joint, which connects the mobile robot to the virtual spring. Here, Oh represents the direction which human walks and it is the direction of human\u2019s velocity vector. (x,., y,., e,.) is the position and direction of the mobile robot. These both coordinates are measured by the ISpace. The angle between the virtual springs connected to human and human\u2019s facing direction is expressed as 0,h. This parameter is adjustable and when it is set to esh = 180\u00b0, a robot follows a man from right behind"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002932_j.bioelechem.2006.03.037-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002932_j.bioelechem.2006.03.037-Figure2-1.png",
        "caption": "Fig. 2. Schematic representation of the experimental set-up showing the inverted m attached dual-barrel electrode and the electrochemical cell with a 300 \u03bcl droplet as bu 5 \u03bcm from the adherently growing C6-glioma cell layer.",
        "texts": [
            " We already have shown earlier that in the case of C6-glioma cells K+-stimulated glutamate release did not affect NO-release, while NO bradykinin stimulated release did not induce glutamate release [15]. A cover slip with adherently growing C6-glioma cells was located on the platform of an inverted microscope and covered with a droplet of 300 \u03bcl buffer. Under visual control, the tip of the dual electrode was moved towards the cells until a contact between the microelectrode and the cell layer was seen. This distance is referred to as relative distance zero. Using the z-micromanipulator the dual-barrel electrode was retracted to a position of 5 \u03bcm apart from the cells. Fig. 2 shows a schematic representation of the used set-up and an image of the dual electrode positioned at a distance of 5 \u03bcm to the cells. After positioning of the tip of the dual electrode at the predefined distance from the cell population the working potentials were applied to both sensors. After a stable background current was attained, 35 \u03bcl of a mixture of the stimulants, namely bradykinin and K+, were carefully injected in close proximity to the electrodes into the 300 \u03bcl buffer solution on top of the cell layer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003762_026635108785260588-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003762_026635108785260588-Figure9-1.png",
        "caption": "Figure 9. Discrete model and Continuum model.",
        "texts": [
            " We then tried to evaluate the influence of the initial selfstress on the equivalent rigidities of the quadruplex, keeping the same variation of the selfstress coefficient. Here too, figure 10 shows that the evolution of the axial rigidity EA in function of the selfstress is almost nonlinear. In the other three figures, by contrast, (Fig.11, 12 and 13), the evolution of GJ, EI and of GA in function of the evolution of the initial selfstress are linear. These figures also show that the quadruplex (Fig. 9), in its reference configuration, i.e. at zero selfstress, has neither axial rigidity nor torsional rigidity. This result can also be explained, in the same way, by the fact that International Journal of Space Structures Vol. 23 No. 2 2008 111 Table 4. Equivalent rigidities of the vertical quadruplex Quadruplex Energy method F.E.M. EA 6339 6355 EIy=EIz 319 916 942 285 714 285 GAy=GAz 26.188 24 183 GJ 4 000 023 4 000 000 6,00x107 5,00x107 4,00x107 3,00x107 2,00x107 1,00x107 0.00 \u22122 0 2 4 6 8 10 12 14 16 G J (d aN "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003998_iros.2009.5353991-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003998_iros.2009.5353991-Figure1-1.png",
        "caption": "Fig. 1. A manipulator carrying a heavy payload.",
        "texts": [
            " Using the robust control theory [16], [17], we also show that the control algorithm can overcome the modeling uncertainty. Stability and convergence of the robot impedance to the target impedance under the proposed impedance control scheme have been analyzed. This paper is organized as follows: Section II introduces the impedance control law for manipulators carrying a heavy payload. The impedance controller is further developed in Section III using an inner/outer control scheme. Finally, Section IV presents some experimental results. II. IMPEDANCE CONTROL Fig. 1 shows a manipulator carrying a payload with nonnegligible mass. Denote q \u2208 R n as the vector of the manipulator joint angles. Without loss of generality, we assume that n = 6 and that no kinematic singularities are encountered meaning that the robot can always operate in the 6-dimensional task space. A 6-axis force/moment sensor installed at the manipulator wrist to measure the external force applied to the payload. However due to the payload mass, the force sensor signal f \u2032 s contains the component of the generalized external force f \u2032 ext superimposed by the gravitational and inertial forces of the payload"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001231_robot.1986.1087722-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001231_robot.1986.1087722-Figure2-1.png",
        "caption": "Figure 2. ?he f i n i t e element model of the mixed-loop robot used i n the numerical example.",
        "texts": [
            " To find the positions and velocities at the next time step, the system accelerations vector is integrated through the time step. The following equations are used to perform this integration: P {Y] = { Y o } + {$,}*At + g{YO}*(Atl2 {G} = [to} + {Yo}*At where { Y o } and { io} are the position and velocity vectors at the beginning of the Previous time step. NUMERICAL EXAMPLE : To demonstrate the use of this analysis method, the following example is presented. Consider th m x d-loop c nfiguration manipulator shown on Figure 2. The end effector of the manipulator is to trace a straight line performing a fast cutting operation. The motion program of the end effector along the straight line is cycloidal motion given by X = L(- t 1 - - sin -) 2nt B 2* B where X is the distance along the line, L is the length of the line, and B is the duration of the motion. The cutting force is given as P,7 = Fci The dimension and properties of the manipulator are as shown on Figure 2. The manipulator was analyzed in forward and in inverse dynamics. For the specified end effector motion the driving torques T1, T2, and T3 where obtained via forward analysis. The driving torques obtained are approximated by a function of time and then used to perform inverse dynamic analysis trying to produce the same motion program of the end effector. In this example, we try to illustrate how we can use the forward dynamic analysis in predicting the driving torques. The predicted driving torques can be fed to the manipulator without the need for feed-back control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001970_0301-679x(78)90179-2-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001970_0301-679x(78)90179-2-Figure3-1.png",
        "caption": "Fig 3 Optical path through equipment",
        "texts": [
            " In some cases the modulus was altered by adding oil or carbon black to the mix. In this way the softest specimens had a Youngs modulus of 2 x 10 5 N/m 2 and the hardest, a modulus of 2 x l0 6 N/m 2 . The surface of the rubber was specular over the greatest part of its area but it proved 0310-679X/78/1104-0219 $03.00 \u00a9 1978 IPC Business Press TRIBOLOGY international August 1978 219 impossible to avoid defects at various isolated regions. The refractive index of the unfilled rubber was 1.53. Optical system The general arrangement of the optical system is shown in Fig 3. Since the interference takes place between the rubber and the glass this is essentially two-beam interferometry. In the presence of a lubricant f'dm between the rubber and glass only 0.4% of the incident intensity is reflected from the contact, while 4% is reflected from the lower surface of the glass disc. To overcome this difficulty a stationary glass plate was placed beneath the disc and the space was filled with a thin silicone oil of refractive index 1.51 which provided a good optical match with the refractive index of glass"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002633_02678290512331324039-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002633_02678290512331324039-Figure5-1.png",
        "caption": "Figure 5. Strength of effective anchoring p/b(eff) as a function of p/b2 for a single substrate possessing an alternating stripe pattern of planar and homeotropic anchoring. The widths of the stripes are equal. U0\u2013NT or Up/2\u2013NT phase transitions correspond to p/b(eff)50.",
        "texts": [
            " Since y(x, z) tends exponentially to a constant, for zR\u2018, h has the same asymptotic form as for homogeneous substrates, i.e. h(x, z),C(z+b(eff)), for large z. The effective extrapolation length, defined as b(eff)5limzR\u2018y(x, z), characterizes the patterned substrate as a whole and it should be distinguished from the local extrapolation lengths of the homeotropic and planar regions. To find b(eff) we solve the Laplace equation with the two boundary conditions for y(x, z) (see appendix). Having determined b(eff) we can obtain the effective anchoring strength coefficient from the relationship w(eff)5K/b(eff). In figure 5 the ratio p/b(eff), which is proportional to w(eff), is plotted against p/b2, for two values of p/b1. For p/b152, on increasing the ratio p/b2 we first cross the U0\u2013NT phase bounadry and then the NT\u2013Up/2 phase Figure 4. Phase diagrams of a NLC confined by two different flat substrates with alternating stripe patterns of planar and homeotropic anchoring (p 0\u00f0 \u00de 1 ~p D\u00f0 \u00de 1 ~p=2) as a function of the extrapolation length of the planar anchoring stripes on the upper substrate, b D\u00f0 \u00de 2 , and the substrate separation D",
            " The solid and dashed lines show first order and continuous transitions, respectively, and the black circles mark the tricritical points. D ow nl oa de d by [ U ni ve rs ity o f So ut h Fl or id a] a t 0 8: 16 1 4 O ct ob er 2 01 4 fact that in our model the surface free energy of the interface between the NLC and the effective homogeneous substrate, ca, deviates from the Rapini\u2013Papoular form. (3) The effective anchoring strength of a single periodically patterned and flat substrate vanishes at U0\u2013NT and Up/2\u2013NT phase transitions (figure 5). Using this effective anchoring strength, a hybrid nematic cell (HNC) model can be used to describe the phase behaviour of the confined NLC for substrate separations D larger than the periodicity of the stripe pattern p (figure 4). (4) Rich phase diagrams, involving the NT, home- otropic (H) and planar (P) textures are found for a HNC with a 4th order polynominal form for the surface free energy (figure 6). The transitions between the phases can be either first or second order. Finally, it would be interesting to consider the effect of surface roughness, superimposed on the stripe pattern, on the phase transition between a uniform and a nonuniform texture"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001801_1.1995769-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001801_1.1995769-Figure1-1.png",
        "caption": "Fig. 1 Schematic of the bearing chamber with the rear and front nozzles, the endoscope, the thermocouple positions adjacent to the bearing, and the immersed vent",
        "texts": [
            " The generated heat is caused by friction in the contact areas and by churning and windage as a result of dissipation of Euler work acceleration to circumferential speed . Within the scope of the ATOS program the impact of the operating parameters affecting power losses in the bearing chamber were investigated 1 . These were the oil and sealing air flow, the temperature, the axial load, the rotor speed, and the bearing chamber pressure. Power losses in bearings have been investigated by several authors. Specifically 2\u20136 can be highlighted. The bearing chamber is shown in Fig. 1, and the schematic of the test facility is depicted in Fig. 2. The bearing chamber is a vented chamber with the vent being at top position 12 o\u2019clock and the scavenge port at the bottom position. Two vent configurations were tested; the first introduced a vent that was protruding 15 mm into the chamber, and the second, a flush vent. The chamber was sealed by a straight labyrinth seal. The ball bearing shown in Fig. 1 has an inner land riding cage with a split inner ring and under-race lubrication. Each half of the inner ring has 18 1 mm holes, which centrifugally direct the oil to the cage scoop and from there to the rolling elements Figs. 1 and 3, rear-half design . Two additional 1 mm holes on each half of the inner ring are used to guide the cage Figs. 1 and 3, front-half design . The cage guiding holes are at a circumferential distance of 180 deg to each other and are placed toward the edge of the inner ring so that they face the cage land",
            " The condition of the bearing was monitored by accelerometers, Contributed by the IGTI Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received April 2, 2004; final manuscript received May 1, 2005. Assoc. Editor: W. Miglietti. 178 / Vol. 128, JANUARY 2006 Copyright \u00a9 rom: http://gasturbinespower.asmedigitalcollection.asme.org/ on 01/28/20 chip detectors, and thermocouples. The latter recorded the temperature of the outer ring at different circumferential locations Fig. 1, TOR . The heat rejection of the bearing was monitored by thermocouples, which recorded the temperature of the oil leaving the bearing. A row of three thermocouples was placed adjacent to the bearing on each side Fig. 1, positions A and B . These recorded the temperature of the oil leaving the bearing through the gap between the outer ring and the cage. Two additional rows of thermocouples were installed at a distance of 1 cm on either side of the bearing for additional monitoring. In order to visualize the bearing, an endoscope was used, which could be connected to a high-speed camera Fig. 4 . In order to avoid the oil droplets that smear the lens of the endoscope during operation, a tube was placed around it and purge air was conducted through the tube. The purge air pressure was regulated. A pressure of about 3 KPa above chamber pressure was adequate to maintain a clean lens. Also Plexiglas windows were introduced into the bearing chamber front cover Fig. 1 , which enabled additional view of the interior. Pressure transducers were used to monitor the chamber pressure. Additionally, the torque on the bearing shaft was measured. Torque measurements were used to assess the power consumption of the bearing and, therefore, enable comparisons among different operating conditions. The estimated power consumption values were nondimensionalized by the parameter P0. This equals 7.0 KW of power consumption and corresponds to an operating condition at 15,000 rpm, 14"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000873_j.geomphys.2003.08.005-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000873_j.geomphys.2003.08.005-Figure1-1.png",
        "caption": "Fig. 1. A servomechanism.",
        "texts": [
            " Let M = R 2 and denote by x = (x1, x2) \u2208 R 2 the Cartesian coordinates of the point x \u2208 R 2 and by v = (v1, v2) \u2208 R 2 the corresponding velocity vector. Then, we define f : TM\u2192 RM by fx(v1, v2) = v2 \u2212 \u221a 1+ v2 1 and apply Proposition 2. (c) (Marle\u2019s [36] servomechanism). This example can be viewed as the model of a control system formed by a rod on a vertical plane and an actuator which communicates motion to its lower extremity along a fixed horizontal line, in order to manipulate the rod in a certain way\u2014see Fig. 1. We put M = R\u00d7S1 and f : TM \u2261 R 2 M \u2192 RM given by f(x, \u03b8, x\u0307, \u03b8\u0307) = x\u0307\u2212h(x, \u03b8, \u03b8\u0307), whereh : RM \u2192 R is a smooth function. Then, applying Proposition 2,C := f\u22121[ORM ] is a constraint. (d) (Isokinetic dynamics). Let e > 0. We define the constraint applying Proposition 2, with f : TM\u2192 RM given by f(vq) = (1/2)\u3008vq, vq\u3009 \u2212 e, see [19,23,45,56]. (e) (Benenti\u2019s example). In [17] a non-linear, quadratic homogeneous constraint in the velocities is proposed. It requires that two points in the plane have parallel velocities to each other"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003499_j.1934-6093.2007.tb00417.x-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003499_j.1934-6093.2007.tb00417.x-Figure3-1.png",
        "caption": "Fig. 3 Cart-Pendulum system simplified model.",
        "texts": [
            " Also, the input signal and the sliding trajectory converge faster. Therefore, the system with the algorithm in this paper possesses stronger robustness, faster convergence, and chatter elimination. Although the input signal in Fig. 1 is a bit larger than that in Fig. 2 at the very start, the proposed algorithm in this paper is better on the whole. Case 2. Here, we apply the algorithm to a Cart-Pendulum experiment system. Assume there is no friction in the system, the simplified model of the system is shown in Fig. 3, and system parameters are shown in Table 2. Suppose the cart moving to the right side is the positive direction and the pendulum rotating clockwise has a positive angle, then when the pendulum is at vertical down position, the following linear model holds: 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 p c c p c c pc p T x x m Kg u m mx x m m K g m lm l x x \u23a1 \u23a4 \u23a1 \u23a4 \u23a2 \u23a5 \u23a2 \u23a5\u23a1 \u23a4 \u23a1 \u23a4\u23a2 \u23a5 \u23a2 \u23a5\u23a2 \u23a5 \u23a2 \u23a5\u23a2 \u23a5 \u23a2 \u23a5\u03b8 \u03b8\u23a2 \u23a5 \u23a2 \u23a5\u23a2 \u23a5\u2212= + \u23a2 \u23a5 ,\u23a2 \u23a5 \u23a2 \u23a5\u23a2 \u23a5 \u23a2 \u23a5\u23a2 \u23a5 \u23a2 \u23a5\u23a2 \u23a5 \u23a2 \u23a5+\u03b8 \u03b8\u23a2 \u23a5 \u23a2 \u23a5\u23a3 \u23a6 \u23a3 \u23a6\u23a2 \u23a5 \u23a2 \u23a5\u2212\u23a2 \u23a5 \u23a2 \u23a5\u23a3 \u23a6\u23a3 \u23a6 \u23a1 \u23a4 \u23a1 \u23a4= \u03b8 \u03b8\u23a2 \u23a5 \u23a3 \u23a6 \u23a3 \u23a6 y where x is cart displacement, \u03b8 is pendulum angle, x is cart velocity, \u03b8 is pendulum angle velocity, x is cart accelera- tion, \u03b8 is pendulum angle acceleration, u is the input voltage, y is the system output"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003049_bfb0109974-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003049_bfb0109974-Figure1-1.png",
        "caption": "Fig. 1. Decomposition of drift vector field along span {g(x)}, onto T~S",
        "texts": [
            " In other words the system is minimum phase with respect to the output y = a(x). According to the results in [2], the sliding surface function is a passive ontput. For each x E X, we define a projection operator, along the span of the control vector field g(x) onto the tangent space to the constant level sets of the sliding surface function a(x), as the matrix M(x) given by M(x) = [I-- Lgl(x)g(x) ~-~T] (3) The following proposition points out some properties of the matr ix M(x) which further justify the given name of \"projection operator\" (see Figure 1) 126 P r o p o s i t i o n 1. The matrix M (x) enjoys the following properties: g(x) E Ker M(x ) Oa a---x E ICer MT(x) M ( x ) ( I - M(x)) -= 0 (4) P r o o f The first property establishes that, locally, M(x)g(x) = O. Indeed, using the definition of M(x) one has I 1 O a 1 L,;(x) g(z)a-~j g(x) 1 Oa = g(x) Lga(x~g(x ) g j g ( x ) 1 = g(x) Lga(x)g(x)Lga(x) = g(x) - g(x) = 0 (5) The second property is equivalent to Oa/OxTM (x) = O. Oa [i 1 0 0 ] ax T L90(x) g(x)-O----x T 00 1 Oo 00 Ox T Lga(x) ~xTg(X) OxT 00 Oa OX T OX T = 0 (6) The last property follows immediately from tile fact that the columns of the matrix (I - M(x)) are all in the subspace span {g(x)}"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002998_robio.2006.340097-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002998_robio.2006.340097-Figure4-1.png",
        "caption": "Fig. 4. Surfaces (solid-drawn circles) on snake robot that constitute the contact between the robot and the ground.",
        "texts": [
            " Hence, it holds that rHjSi = { rHjSF i , front part of link i is closest, rHjSRi , rear part of link i is closest, (9) where rHjSF i = Axy (rGi + rGiSF i ) \u2212 rHj , (10) rHjSRi = Axy (rGi + rGiSRi ) \u2212 rHj , (11) with rGiSF i = LGSi eBi z , rGiSRi = \u2212LGSi eBi z , and Axy = diag ([1, 1, 0]). 3) Vector of Gap functions for Contact with External Objects: We now gather the gap functions gHij for all n links and \u03bd obstacles in the vector gH = [ gH11 \u00b7 \u00b7 \u00b7 gHn1 gH12 \u00b7 \u00b7 \u00b7 gHn2 \u00b7 \u00b7 \u00b7 gH1\u03bd \u00b7 \u00b7 \u00b7 gHn\u03bd ]T (12) where the elements gHij are found from either (7) or (8) depending on which part of link i is closest to obstacle j. The gap functions for the distance between the ground and the front and rear end-sphere surfaces are illustrated in Fig. 4 and are written as (see [10] for a more thorough description) gNF i = (rSF i ) T eI z \u2212LSC , gNRi = (rSRi ) T eI z \u2212 LSC , (13) where rSF i = rGi + LGSi eBi z , rSRi = rGi \u2212 LGSi eBi z . The gap functions are gathered in the vector gN = [ gNF1 \u00b7 \u00b7 \u00b7 gNFn gNR1 \u00b7 \u00b7 \u00b7 gNRn ]T . (14) In this section we calculate the relative velocities between the snake robot, and the obstacles and the ground, by taking the time-derivative (when it exists) of the appurtenant gap functions. The relative velocities are needed to set up the set-valued contact forces for the closed contacts [15]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003522_6.2007-5738-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003522_6.2007-5738-Figure1-1.png",
        "caption": "Figure 1. Isometric drawing of the high-speed brush seal test rig, the C5R.",
        "texts": [
            " The rotors are assembled onto a high-speed brush seal test rig that operates within the Performance Technologies Laboratory Seals\u2019 Test Cell at GE Global Research. The high-speed brush seal test rig, known as the C5R, is capable of spinning up to 20K rpm and can accommodate rotors up to 150 mm in diameter. The rig can be pressurized with either nitrogen (up to 345 kPa) or air (up to 3450 kPa). However, in the current experiment, the brush seal was not pressurized in order to focus the analysis on the conductive heat transfer characteristics of the seal. The C5R is shown in Figure 1. American Institute of Aeronautics and Astronautics 4 For a given test, the prototype Kevlar\u00ae fiber brush seal was secured to a static mechanical housing that surrounds the C5R spindle. The seal was held in place axially by six lead screws through a front plate bolted securely to the mechanical housing. The C5R has two degrees of freedom\u2014through two precision lead screws, the test engineer can adjust either the axial position or radial position of the rotor. In the current tests, the radial degree of freedom was locked at the concentric position between the centerline of the mechanical housing and the centerline of the rotor, and the axial position was marked and repeated for each new test"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000809_s0003-2670(01)01291-0-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000809_s0003-2670(01)01291-0-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the system for oxalate determination.",
        "texts": [
            " The enzymes were immobilised onto the support material by employing glutaraldehyde, a widely used homo-bifunctional reagent. This reagent possesses two reactive carbonyl groups, allowing the formation of inter-molecular cross-linked bonding between the support and the enzyme, through its carbonyl group, which reacts with the amine groups of the enzymes and the support [44]. The system used in this work was based on those described by Fernandes et al. [46], by replacing the CO2 selective electrode by the optode covered by a PTFE membrane (Black Swan MFG Co.) permeable to this gaseous species. Fig. 1 shows a schematic representation of the system. The stirring bar reactor was filled with 0.5 g of the support material, containing the immobilised enzymes, which was hold in the interior of the reactor with the use of a 390 mesh Nylon\u00ae grid. Measurements were carried out in a cell maintained at 25\u25e6C with a thermostatic bath (Quimis Q.214.D2). Each set of measurements was carried out by pipetting 10.00 ml of succinate buffer solution (in adequate pH) into the cell shown in Fig. 1. A preliminary spectrum was initially run, in order to determine the wavelength of maximum sensitivity (530 nm at pH 4.0). After the proper wavelength had been set, air was bubbled into the solution for 10 min, in order to saturate it with oxygen, and the reflectance was continuously monitored until a steady state was obtained. Then, aliquots of an oxalic acid reference solution were added to the buffer solution and the variation in the diffuse reflectance was monitored. The additions of the solutions were made every 3 min, as soon as a steady state was reached, due to the permeation of carbon dioxide through the membrane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002971_robot.2006.1642273-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002971_robot.2006.1642273-Figure5-1.png",
        "caption": "Fig. 5. The position and the shape of the unloading platform have been changed compared to the map of the environment. The unloading platform has been shifted to the right and it has been enlarged by 0.2 meters. The docking configuration is computed as the configuration where the docking pattern best fits the unloading platform.",
        "texts": [
            " In this experiment the landmarks are segments. The docking pattern L can be composed of any number of segments li. In order to be robust to occlusions, the matching algorithm of section IIIB treat segments as straight lines. In this experiment, the docking pattern represents the shape of the unloading platform as perceived by the sensor when the trailer is parked. It is represented in figure 2. Thus the inputs of the docking task are: \u2022 a planned trajectory for the robot towards a goal config- uration \u2022 the docking pattern L. Figure 5 illustrates the case where the unloading platform has been moved and the map has not been updated. Moreover, the shape of the unloading platform has changed: it is larger than the docking pattern. The matching between the perception and the docking pattern is robust to these perturbations and the docking configuration is still defined relatively to the unloading platform. Quantitative results are very good in these experiments. The error between the theoretical trailer position at the unloading platform and the experimental position is about 5 centimeters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002768_9780470116883.ch2-Figure2.13-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002768_9780470116883.ch2-Figure2.13-1.png",
        "caption": "Figure 2.13 Closed surface surrounding the wire.",
        "texts": [
            "263) yields dV\u00f0x\u00de dx \u00fe joL0I\u00f0x\u00de \u00bc V 0S1\u00f0x\u00de \u00f02:266\u00de where the distributed voltage source along the line is given by V 0S1\u00f0x\u00de \u00bc jom0 Zd 0 Hinc y \u00f0x; z\u00dedz \u00f02:267\u00de Equation (2.266) is the first telegrapher\u2019s equation for the case of a distributed field excitation along the transmission line. 2.17.2.2 Second Telegrapher\u2019s Equation Second Telegrapher\u2019s equation can be derived starting from the Maxwell equation, rx~H \u00bc~J \u00fe joe~E \u00f02:268\u00de whose integral form is: Z S rx~Hd~S \u00bc Z S ~J \u00fe jo~E d~S \u00f02:269\u00de For the case of a closed surface S, surrounding one of the conductors as shown in Figure 2.13 left-hand side of eqn (2.269) vanishes, that,Z S rx~Hd~S \u00bc 0 \u00f02:270\u00de Rearranging eqn (2.269) yields I\u00f0x\u00fe x\u00de I\u00f0x\u00de \u00fe joe ZZ S1 Errd dx \u00bc 0 \u00f02:271\u00de where Er is the total radial field in the vicinity of the wire. The total electric field can be represented as a sum of the incident and scattered component. Dividing eqn (2.271) with x and taking the limits r ! a and x! 0 results in the following equation: dI\u00f0x\u00de dx \u00fe joe Z2p 0 Esct r \u00f0x\u00dead \u00fe joe Z2p 0 Einc r \u00f0x\u00dead \u00bc 0 \u00f02:272\u00de Assuming a d, the first integral at the left-hand side in eqn (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001776_j.jbiotec.2005.09.001-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001776_j.jbiotec.2005.09.001-Figure2-1.png",
        "caption": "Fig. 2. Cross-section of a multiplayer membrane glucose sensor, 1 of 82 glucose sensors fabricated on the 4 in. diameter glass substrate.",
        "texts": [
            ", 1998, 2001, 2002). The electrode sets formed a matrix of 11 columns (columns A\u2013K) and 8 lines (lines 1\u20138) on the substrate. For example, the electrode sets of column A were located at substrate positions A1\u2013A8, and those of line 1 were at A1, B1, C1, D1, E1, F1, G1, H1 and I1. The J2 electrode set, which is shown in detail, was located at the crossing of column J and line 2 on the substrate. The electrode sets were covered by a multilayer membrane consisting of five layers to form the glucose sensors. Fig. 2 shows one of the 82 glucose sensors. The multilayer membrane glucose sensors were fabricated by spin-coating a -APTES solution, a Nafion\u00ae solution, a BSA solution containing GA and GOX (to form the enzyme layer), the -APTES solution and a PFCP solution (in that order) onto the 82 electrode sets. The first -APTES layer was an adhesion layer that adhered to the electrodes and the Nafion\u00ae layer. The second - APTES layer was an adhesion layer that adhered to the enzyme layer and the PFCP layer. After fabrication, the substrate was divided into 82 10 mm \u00d7 6 mm electrode sets"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002968_cdc.2005.1582957-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002968_cdc.2005.1582957-Figure1-1.png",
        "caption": "Fig. 1. Inverted pendulum",
        "texts": [
            " Indeed, using (29) we have that \u00b5(\u03b3k+1,Wk+1) \u2264 \u00b5(\u03b3k,Wk) \u00d7 exp(\u03b8k(\u03b3k+1,Wk+1) \u2212 2) (32) from which it is seen that its right hand side is an upper bound of the current cost value attained by the feasible solution provided by (31) at iteration k + 1 for all k = 0, 1, \u00b7 \u00b7 \u00b7 . In several examples solved, it has been verified that the proposed algorithm performed well and provided a solution in a few number of iterations. In addition, for N = 1 in all these cases the global optimum has always been attained. Figure 1 shows an inverted pendulum mounted on a small car moving horizontally due the action of an external force u(t). The inverted pendulum is constituted by a bar with uniformly distributed mass. The goal is to determine the control action u(t) in order to bring the pendulum to the vertical position \u03b8 = \u03c6 \u2212 \u03c0/2 = 0 from any initial small deviation. Assuming that the friction coefficient between the air and the car fc and the air and the bar fb are not exactly known but belong to the box (fc, fb) = [0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002974_robot.2005.1570241-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002974_robot.2005.1570241-Figure1-1.png",
        "caption": "Fig. 1. Modelling a link as a set of points with some fixed distances between them.",
        "texts": [
            " Since the first and last links ar mutually fixed, the problem is equivalent to that of finding the valid configurations of a closed loop of six pairwise articulated links. The translation of each link into distance constraints depends on the type of joints it connects, either prismatic or revolute, and on whether the axes of these joints are skew or concurrent. A link connecting two skew revolute axes can be modelled by taking two points on each of these axes, and by connecting them all with rigid bars to form a tetrahedron (Fig. 1-a). In this way, for example, a 6R linkage can be modelled as a ring of six pairwise-articulated tetrahedra, as indicated in Fig. 5. If the two axes of the link are not skew but intersecting, we can economize points and simply model the link as a triangle of fixed distances (Fig. 1-b), thus reducing the number of unknown entries in D. Note that the case of parallel revolute axes can be seen as a specialization of the previous one, where the point of intersection is an improper point at infinity in the direction of the axes, instead of a common proper point (Fig. 1-c). This will cause no trouble in our analyis below, as a point at infinity can always be approximated by a proper point, sufficiently far away in some direction. Similar transformations are applied to a link with one or two prismatic joints: since a translation along direction v can always be seen as a rotation about the line at infinity of any plane orthogonal to v, we can model a prismatic joint as a revolute joint infinitely far away on this plane. Computationally, we will represent such joint by designating two points on , placed sufficiently far away along different directions (points p2 and p4 in Fig. 1-d). On the other hand, an in-parallel robot is formed by two rigid bodies, the base and the platform, joined by six legs. Each leg is a linear actuator linked to the base and the platform by spherical joints. The direct kinematics problem is to compute all platform poses that are compatible with some specified leg-lengths. The translation of this goal into a set of distance constraints is trivial. We simply put a point on each leg attachment point and specify the fact that all leg lengths are known, and that the distances between any pair of points lying both on the base, or both on the platform, is also known"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002167_1-4020-4611-1_8-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002167_1-4020-4611-1_8-Figure7-1.png",
        "caption": "Figure 7. (a) Flow diagram of the optical fibre continuous-flow system for bioluminescence and chemiluminescence measurements: S, sample; C, carrier stream; PP, peristaltic pump; IV, injection valve; W, waste; FO, optical fibre; FC, flow-cell. (b) Details of the optical fibre biosensor/flow-cell interface: a, optical fibre; b, sensing layer; c, light-tight flow-cell; d, stirring bar.",
        "texts": [],
        "surrounding_texts": [
            "As mentioned above, in order to extend the potentialities of the luminescence-based optical fibre biosensors to other analytes, auxiliary enzymes can be used. The classical approaches consist either of the coimmobilization of all the necessary enzymes on the same membrane or of the use of microreactors including immobilized auxiliary enzymes and L.J. Blum and C.A. Marquette 167 placed in a FIA system, upstream from the luminescence-based optical fibre sensor."
        ]
    },
    {
        "image_filename": "designv11_28_0002110_2005-01-1927-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002110_2005-01-1927-Figure5-1.png",
        "caption": "Figure 5. Control direction of AGCS",
        "texts": [],
        "surrounding_texts": [
            "(AGCS) System Sangho Lee, Hyun Sung and Unkoo Lee Hyundai Motor Company Copyright \u00a9 2005 SAE International"
        ]
    },
    {
        "image_filename": "designv11_28_0000652_0470867906-Figure6.7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000652_0470867906-Figure6.7-1.png",
        "caption": "Figure 6.7 Selection of finite elements from structural mechanics: (a) Shear-resistant 1-D beam, two nodes, two degrees of freedom per node (uy, rz) (b) Non shear-resistant 1-D, two nodes, two degrees of freedom per node (uy, rz) (c) Plane element, four nodes, two degrees of freedom per nodes (ux, uy) (d) Plate element, four nodes, four degrees of freedom per node (uy, rx, ry, rz)",
        "texts": [
            " Overall, this opens up a simpler, faster and more secure way of modelling mechanical continua that is compatible with hardware description languages and thus also with circuit simulation. 6.3 CONTINUUM MECHANICS 117 In principle, finite elements can be used in many fields of engineering science. Our discussion is based upon the field of structural mechanics. Thus the following quantities have to be linked together: displacements, forces, strain, and applied loads, which act as a trigger here. Depending upon the application, different finite elements are used, which vary in structure, number of nodes and degrees of freedom. Figure 6.7 shows a selection of finite elements of structural mechanics. The degrees of freedom of the finite elements can be of both a translational (ux, uy, uz) and a rotational (rx, ry, rz) nature. The numerical complexity of the calculation increases with their number. Fundamentally, the element selected should fulfil the question formulated with as few superfluous degrees of freedom as possible. In addition, symmetry considerations are used to keep the number of finite elements as low as possible. In the following, an approach will be presented that allows the finite elements of structural mechanics to be represented in hardware description languages"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000685_ecc.2001.7076312-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000685_ecc.2001.7076312-Figure1-1.png",
        "caption": "Figure 1: The reaction wheel pendulum",
        "texts": [],
        "surrounding_texts": [
            "The reaction wheel pendulum is one of the simplest nonlinear underactuated systems. It is a pendulum with a rotating wheel at the end which is free to spin about an axis parallel to the axis of rotation of the pendulum (see Figure (1)). The wheel is actuated by a DC-motor, while the pendulum is unactuated. The coupling torque generated by the angular acceleration of the disk can be used to actively control the system. This mechanical system was introduced and studied in [7] where a partial-feedback linearization control law has been presented. The control objective here will also be to swing the pendulum up and balance it about its unstable inverted position. We will focus our study on the swinging-up control law. The nonlinear swinging-up controller will be based on the total energy of the system. The control design will exploit the passivity property of the complete Lagrangian system dynamics. Similar control strategies have been used to control other underactuated mechanical systems in [8] for the cart and pole system, in [9] for the pendubot and in [10] for planar manipulators with springs. In this paper we present two approaches based on the total energy stored in the system. We make use of LaSalle theorem to prove that the system trajectories asymptotically converge to a homoclinic orbit in both approaches. Therefore, asymptotically, after every swing of the pendulum, the system state gets successively closer to the origin. The first approach proposed here is such that the wheel\u2019s angular velocity converges to zero but does not necessarily bring In Section (2), we develop the equations of motion of the reaction wheel pendulum. In Section (3) and (4), two different energy-based control algorithms are presented. Simulation results are given in Section (5). The concluding remarks are presented in Section (6)."
        ]
    },
    {
        "image_filename": "designv11_28_0001001_0921-8890(89)90052-3-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001001_0921-8890(89)90052-3-Figure6-1.png",
        "caption": "Fig. 6.",
        "texts": [
            " This section presented an algorithm to obtain the time schedule of the positions, velocities and accelerations of the joint variables of a manipulator along some specified points. The constraints on the velocities and accelerations of the joint are taken into account. The obtained motion is continuous with respect to the positions and velocities. 4 . S i m u l a t i o n R e s u l t s To demonstrate the applicability of the proposed trajectory generation, digital simulation of the Stanford arm (cf. Fig. 6) is used. To simulate the robot behaviour, a computer program was written, which carries out the following functions: - solving the inverse kinematical problem for a number of points along the desired end-effector trajectory - generating the desired joint trajectories qia(t), i = 1 . . . . , n, by means of the above presented algorithm - computing the corresponding control with the hierarchical control scheme proposed in [8]. - integrating the non-linear system equation, describing the actual robot dynamics, when external disturbances and computer control is applied"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003789_j.jsv.2008.03.072-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003789_j.jsv.2008.03.072-Figure9-1.png",
        "caption": "Fig. 9. System with rubber impedance and beam impedance.",
        "texts": [],
        "surrounding_texts": [
            "For harmonic motion one can assume that w\u00f0x; t\u00de \u00bcW \u00f0x\u00de exp\u00f0ift\u00de (27) Then the inertia force p has the form p \u00bc mq2w\u00f0x; t\u00de=qt2 \u00bc mWf 2 exp\u00f0ift\u00de (28) Substitution of w and p from Eqs. (27) and (28) into Eq. (26) gives d6W dx6 g\u00bd1\u00fe \u00f0Y 1 \u00fe Y 2\u00de d4W dx4 \u00fe g2\u00bd\u00f0Y 1 \u00fe Y 2\u00de 2Y 1 d1 Y 2 d2 \u00f0d1 \u00fe d2\u00de d2W dx2 s d2W dx2 \u00fe sgW \u00bc 0 (29) which is a simple linear differential equation of the sixth order. Hence a solution of the form W \u00f0x\u00de \u00bc A exp\u00f0sx\u00de (30) can be assumed. Substitution of Eq. (30) into Eq. (29) yields the characteristic equation s6 g\u00bd1\u00fe \u00f0Y 1 \u00fe Y 2\u00de s4 \u00fe g2\u00bd\u00f0Y 1 \u00fe Y 2\u00de 2Y 1 d1 Y 2 d2 \u00f0d1 \u00fe d2\u00de s2 ss2 \u00fe sgW \u00bc 0 (31) which is cubic in s2. The roots can be exactly determined [14]. The method of finding roots is described in Appendix A. The complete solution of differential equation (29) can then be expressed as W \u00f0x\u00de \u00bc X6 j\u00bc1 Aj exp\u00f0sjx\u00de (32) The constants Aj, j \u00bc 1, 2,y, 6, are to be obtained by application of the boundary conditions of the beam. 4.1. Boundary conditions The beam can be imagined to be comprised of identical halves, each of which is acted upon by one-half of the applied force F0 at the junction point (Fig. 7). The center of the beam can now conveniently be taken as the origin (Fig. 8). The expressions for P1, M, S and u1 in terms of w and its derivatives are obtained as follows. Since there can be no longitudinal force on both the face plates, i.e., the first face plate and the third face plate. Hence; P1 \u00fe P3 \u00bc 0 or P1 \u00bc P3 or Eh1b qu1 qx \u00bc Eh1b qu3 qx (33) ARTICLE IN PRESS B.P. Yadav / Journal of Sound and Vibration 317 (2008) 576\u2013590584 Eqs. (15), (16) and (33) can readily be manipulated to show that P1 \u00bc Dt g\u00f02d1 d2\u00de q4w qx4 g\u00f0Y 1 \u00fe Y 2\u00de q2w qx2 Ws (34) The total bending moment, M, acting on the section can be split into four components analogous to those of the shear force. (a) and (b) moments M1 and M3 associated with the flexural stiffness D1 and D3 of the top and bottom face plates, i.e. M1 \u00bc D1 q2w qx2 ; M3 \u00bc D3 q2w qx2 (35a, b) ARTICLE IN PRESS B.P. Yadav / Journal of Sound and Vibration 317 (2008) 576\u2013590 585 (c) Moment M2 associated with the equal and opposite forces, P1 and P3 which act along the mid-planes of the face plates, i.e. M2 \u00bc P3d1 \u00bc Dt g\u00f02d1 d2\u00de q4w qx4 g\u00f0Y 1 \u00fe Y 2\u00de q2w qx2 Ws d1 (35c) (d) Moment M4 associated with the force P3 which act along the mid-plane of the face plate, i.e. M4 \u00bc P3d2 \u00bc Dt g\u00f02d1 d2\u00de q4w qx4 g\u00f0Y 1 \u00fe Y 2\u00de q2w qx2 Ws d2 (35d) Then M \u00bcM1 \u00feM2 \u00feM3 \u00feM4 \u00bc Dt\u00f0d1 d2\u00de g\u00f02d1 d2\u00de q4w qx4 \u00fe g \u00f0Y 1 \u00fe Y 2\u00de\u00f0d1 d2\u00de \u00fe \u00f02d1 d2\u00de \u00f0d1 d2\u00de q2w qx2 \u00feWs (36) Since the total shear force, S, is given by qM/qx, it follows that S \u00bc Dt\u00f0d1 d2\u00de g\u00f02d1 d2\u00de q5w qx5 \u00fe g \u00f0Y 1 \u00fe Y 2\u00de\u00f0d1 d2\u00de \u00fe \u00f02d1 d2\u00de \u00f0d1 d2\u00de q3w qx3 \u00fe qW qx s (37) Now, P1 \u00bc Eh1b(qu1/qx) hence from Eq. (34), Dt g\u00f02d1 d2\u00de q4w qx4 g\u00f0Y 1 \u00fe Y 2\u00de q2w qx2 Ws \u00bc Eh1b qu1 qx or qu1 qx \u00bc Dt g2\u00f02d1 d2\u00deEh1b g q4w qx4 g2\u00f0Y 1 \u00fe Y 2\u00de q2w qx2 gWs (38) Eqs. (29) and (38) can readily be manipulated to show that u1 \u00bc Dt g2Eh1b\u00f02d1 d2\u00de q5w qx5 g\u00f0Y 1 \u00fe Y 2\u00de q3w qx3 g2s\u00fe 2g2Y 1 d1 \u00fe d2 d1 g2Y 2 d1 \u00fe d2 d2 qw qx (39) The possible boundary conditions for a sandwich beam free at one end and simply supported at the other end are as follows: at x \u00bc 0 (at center) (i) shear force \u00bc F0/2, (ii) slope \u00bc dW/dx \u00bc 0, (iii) u1 \u00bc 0; at x \u00bc l/2 (at right end) (iv) deflection \u00bcW \u00bc 0, (v) bending moment \u00bc 0, (vi) P1 \u00bc P3 \u00bc 0. Applying the above six boundary conditions, with the help of Eqs. (34) and (36)\u2013(39), one obtains finally a matrix equation of the form \u00bdC fBg \u00bc fHg (40) where [C] is a square matrix of dimension 6 6. {B} and {H} are column matrices. The elements of these matrices are, for j \u00bc 1, 2,y, 6, C1j \u00bc s5j \u00fe g \u00f0Y 1 \u00fe Y 2\u00de\u00f0d1 d2\u00de \u00fe \u00f02d1 d2\u00de \u00f0d1 d2\u00de s3j C2j \u00bc sj ARTICLE IN PRESS B.P. Yadav / Journal of Sound and Vibration 317 (2008) 576\u2013590586 C3j \u00bc sj5 g\u00f0Y 1 \u00fe Y 2\u00des3j C4j \u00bc exp sj l 2 C5j \u00bc s2j exp sj l 2 C6j \u00bc s4j exp sj l 2 Bj \u00bc Aj=F0; Hj \u00bc g\u00f02d1 d2\u00de 2Dt\u00f0d1 d2\u00de ; j \u00bc 1 \u00bc 0; ja1 Eq. (40) can be solved for B1, B2,y,B6. The beam solution then can be written as W \u00f0x\u00de F 0 \u00bc X6 j\u00bc1 Bj exp\u00f0sjx\u00de 4.2. Response of primary system With the solution for the beam thus obtained, the primary system with its spring and damper can now be considered as attached to the center of the beam (see Figs. 1 and 2). In Fig. 1 the beam can be replaced by its dynamic stiffness as shown in Figs. 9 and 10. The dynamic stiffness of the beam at the junction point, which may be defined as the ratio of force to displacement is given by Z \u00bc F 0=W \u00f00\u00de \u00bc 1 ,X6 j\u00bc1 Bj (41) The equivalent dynamic stiffness of the system (see Fig. 10) is given by Zeq \u00bc 1 , X6 j\u00bc1 Bj \u00fe 1 K\u00f01\u00fe id\u00de ( ) (42) The equation of motion for the system as shown in Fig. 10 is m \u20acy1 \u00fe Zeqy1 \u00bc F exp\u00f0ift\u00de (43) Since the motion is harmonic, y1 may be assumed to be of the form y1 \u00bc Y 1 exp\u00f0ift\u00de (44) ARTICLE IN PRESS B.P. Yadav / Journal of Sound and Vibration 317 (2008) 576\u2013590 587 Substituting Eq. (44) in Eq. (42) gives Y 1=F \u00bc 1=\u00f0 mf 2 \u00fe Zeq\u00de (45) Combining Eqs. (42) and (45) then yields Y 1=F \u00bc X6 j\u00bc1 Bj \u00fe 1 K\u00f01\u00fe id\u00de ( ), mf 2 X6 j\u00bc1 Bj mf 2 K\u00f01\u00fe id\u00de \u00fe 1 ( ) (46) which is the response of the primary system to an exciting force of unit amplitude. 4.3. Transmissibility With reference to Fig. 10 the exciting force at the junction of the beam and the primary system can be expressed in the form F 0=F \u00bc Zeq=\u00f0 mf 2 \u00fe Zeq\u00de (47) From Eq. (37) for the shear force at any section of the beam, the right-hand support force F1 can be obtained by substituting Eq. (32) into it and putting x \u00bc l/2. This gives F1 F0 \u00bc Dt\u00f0d1 d2\u00de g\u00f02d1 d2\u00de X6 j\u00bc1 s5j \u00fe g \u00f0Y 1 \u00fe Y 2\u00de\u00f0d1 d2\u00de \u00fe \u00f02d1 d2\u00de \u00f0d1 d2\u00de s3j \u00fe \u00f0mf 2=Dt\u00desj Bj exp\u00f0sj l=2\u00de (48) The transmissibility, which may be defined as the ratio of the total dynamic force transmitted at the end support to the impressed force [15], is given by T \u00bc 2F1=F (49) Combining Eqs. (47)\u2013(49), and simplifying, finally yields T \u00bc 2 Dt\u00f0d1 d2\u00de g\u00f02d1 d2\u00de P6 j\u00bc1 s5j \u00fe g \u00f0Y 1 \u00fe Y 2\u00de\u00f0d1 d2\u00de \u00fe \u00f02d1 d2\u00de \u00f0d1 d2\u00de s3j \u00fe mf 2 Dt sj Bj exp\u00f0sj l=2\u00de mf 2P6 j\u00bc1 Bj mf 2 K\u00f01\u00fe id\u00de \u00fe 1 \" # (50)"
        ]
    },
    {
        "image_filename": "designv11_28_0000418_095440603767764426-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000418_095440603767764426-Figure6-1.png",
        "caption": "Fig. 6 A constraint wrench when the linkage drive angle y1 \u02c6 308",
        "texts": [],
        "surrounding_texts": [
            "A new approach of analysing con guration changes of the Schatz linkage has been proposed by examining the reciprocal screw and the relationship between the reciprocal screw and the stem-screw system in which the reciprocal screw was obtained using the cofactor approach. This generated an algebraic surface formed by the trajectory of the reciprocal screw. The relationship between the reciprocal screw and the stem-screw system has been examined. There are four intersections when the reciprocal screw has zero pitch in which the reciprocal screw becomes a subset of the stemscrew system. On these occasions, the reciprocal screw is a combination of joint screws $1 and $5 when the drive angle is 08 and p, and a combination of joint screws $2 and $6 when the drive angle is 908 and 2708. The corresponding four special con gurations were then presented. Apart from these four con gurations, there are no other intersections between the reciprocal screw and the stem-screw system. The reciprocal screw and the stemscrew system are hence disjoined. The study helped the analysis of the constraint wrench, which acts along the reciprocal screw and does no work to the linkage. This presented a change of con gurations with a ruled surface of the trajectory of the constraint wrench."
        ]
    },
    {
        "image_filename": "designv11_28_0000567_robot.1992.220303-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000567_robot.1992.220303-Figure2-1.png",
        "caption": "Figure 2: Two onclink manipulators holding an object.",
        "texts": [
            " If Ni is not zero (C11 is not empty), the object velocity corresponding to a given joint velocity is not uniquely determined by the quasi-static analysis. In fact, from (9), U = c1ac&i + CllY, vq E R(C,,), (12) where y E RNi is a free coefficient vector. The apparent physical non-sense of such indeterminacy is due to the assumed quasi-static model of the system, and can be readily solved by taking into account the object dynamics. Case Studies In the following, two case studies are presented in order to illustrate the application of the above technique. The first case refers to the example of fig.2, i.e. %owever, some of these \u201c!&\u201d motions can be indirectly controlled in iome CMCS via exploitation of the dynamic couplings the object might have. For a related d i r d o n , see e.g. (Jab and Rodrigues, 19911. two onolink arms holding a common object. The m e bility and kinematic analysis of the system is presented in mme different h potheses about contact constraints. The seeond exampe refers to two cooperating SCAMlike robots, together manipulating an object: the cases of completoconstraint contacts and hard-finger contacts are considered. 4.1 Case Study 1 Consider the simple example shown in fig. 2, for which the matrices G, D, and the matrices H corresponding to different contact models have been presented previously. The mobility and kinematic analysis of the mechanisms proceeds accordingly. If both contacts are modeled as hard-finger, at eech contact point the object is free to rotate about any direction in the space. Obviously, we expect that some of these rotations will be inhibited by the other contact constraint. In fact, by applying the mobility analysis algorithm, we obtain Accordingly, the mobility and connectivity of the system are Nm = Ne = 2, being the redundancy N, = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002768_9780470116883.ch2-Figure2.2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002768_9780470116883.ch2-Figure2.2-1.png",
        "caption": "Figure 2.2 Geometry of a moving medium.",
        "texts": [
            " The third and fourth Maxwell equations are not affected by the motion of the medium. On the contrary, the extension of the law of induction expressed by the first Maxwell equation, to take into account the motion of the medium, requires considerable care. In other words, the first Maxwell equation must contain the total time rate of magnetic flux density change rx~E \u00bc d~B dt \u00f02:25\u00de The total time rate of flux changes across a given surface, when the surface itself across which the flux is evaluated is in motion, as shown in Figure 2.2 (The velocity of a moving medium is~v) is given by df dt \u00bc d dt Z S ~Bd~S \u00f02:26\u00de where the time rate of magnetic flux density variation in Cartesian coordinates can be expressed as d~B dt \u00bc q~B qx dx dt \u00fe q~B qy dy dt \u00fe q~B qz dz dt \u00fe q~B qt \u00f02:27\u00de which can also be written in the form d~B dt \u00bc \u00f0~v r\u00de~B\u00fe q~B qt \u00f02:28\u00de As the first term on the right-hand side of eqn (2.28) can be written as \u00f0~v r\u00de ~B \u00bc rx\u00f0~vx~B\u00de \u00f02:29\u00de it follows rx~E \u00bc q~B qt \u00ferx\u00f0~vx~B\u00de \u00f02:30\u00de and the first Maxwell equation is then given by rx\u00f0~E ~vx~B\u00de \u00bc q~B qt \u00f02:31\u00de and represents the differential form of the Faraday\u2019s law in a moving medium",
            " Finally, the medium is isotropic if s, m, and e are independent of direction or anisotropic otherwise. The boundary conditions at the interface separating two different media 1 and 2 with parameters s1, m1, e1 and s2, m2, and e2, respectively, as shown in Figure 2.3, can be easily derived from the Maxwell\u2019s equations in their integral form. A relation for the tangential components of the electric field may be found by taking a line integral along a closed path of length l on one side of the boundary and returning on the other side as it is indicated in Figure 2.2. The general conservative property of the electric field implies that any closed line of electrostatic field must be zero, that is,I c ~Ed~s \u00bc 0 \u00f02:93\u00de The sides normal to the boundary are assumed to be small enough that their contributions to the line integral vanish when compared with those of the sides parallel to the surface. Therefore, one hasI c ~Ed~s \u00bc Et1 l Et2 l \u00f02:94\u00de The subscript t denotes component tangential to the interface. The length of the tangential loop sides is small enough to take Et as constant over the length"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003717_08ias.2008.78-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003717_08ias.2008.78-Figure8-1.png",
        "caption": "Fig. 8. Cut view of an HSUB machine.",
        "texts": [
            " 7b shows that to enhance the main air gap flux, a PM is placed between the upper and lower ferrous rotor pieces or around a pole, as shown in Fig. 5. The PM in the rotor produces flux in the main air gap and also prevents magnetic flux diffusion between the poles. Thus it enhances the usable main air gap flux density. Fig. 7c shows that reversing the current direction in the excitation coil can reduce the main air gap flux. This provides a simple field-weakening feature in the main air gap of this new machine. The HSUB machine can be built as an axial-gap or a radial-gap machine. Fig. 8 shows the cut view of an axialgap HSUB prototype machine. It is brushless and consists of an armature, a rotor, and a dc-excitation stator. These three components are separated by air gaps. The armature has a set of polyphase windings and a magnetic core. When phase currents energize the polyphase windings, they produce a rotating magnetic wave in the main air gap. The rotor has two sides. One side faces the armature; the other side faces the dc-excitation stator. Rotor torque on the dcexcitation side, which is the derivative of the flux linkage of the dc-excitation coil with respect to the rotor angular displacement, is zero because of the unchanging dc flux"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003357_piee.1971.0105-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003357_piee.1971.0105-Figure10-1.png",
        "caption": "Fig. 10 Inclusion of insulating sections to provide nontracking flush surface for fibre brushes",
        "texts": [
            "ccupied by the micas, it has been found possible to build up a rather low-resistance carbon track. As the object of the fibre-brush addition is to raise output, and thus inherently to increase the bar-bar voltages, it is undesirable to have a tracking tendency established by the fibre brushes. With this in mind, the most sensible modification to be made to a conventional commutator is that shown in Fig. 10. Small sections of each commutator segment are removed and replaced by insulating material, and these sections are staggered from one segment to the next. When the segments are put together to form the commutator, there will be a smooth surface on which the fibre brushes can run, but very ample insulation between positive and negative brush arms, in spite of the tendency of the fibre brushes to lay down a relatively low-resistance carbon film. Conclusion Fibre brushes have great promise when applied to improvements in commutation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000652_0470867906-Figure7.12-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000652_0470867906-Figure7.12-1.png",
        "caption": "Figure 7.12 Hard disk drive overview",
        "texts": [
            " Moreover, this section details the resulting electronics design methodology. For instance, it will be shown how key system properties, e.g. seek time, can be determined by means of the mixed simulation of mechanics, electronics and firmware. In addition, the same simulation environment is used to realistically verify analogue and digital circuitry as well as firmware. The following section details some typical configurations of a disk drive and discusses how these translate into requirements for the associated electronics, see also Figure 7.12. A drive normally contains up to five rotating disks. This disk (stack of disks) is driven by the spindle motor, which is a brushless DC motor. The rotational velocity varies between 4200 and 15 000 revolutions per minute.2 The RW-head flies on an air cushion 10\u201350 nm above the disk surface. It is supported by the load-beam, which can be moved about its pivot by the so-called voice coil motor. This consists of a coil that lies in a fixed magnetic field provided by permanent magnets, see Figure 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002350_1.2199559-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002350_1.2199559-Figure1-1.png",
        "caption": "Fig. 1 Coordinate systems",
        "texts": [
            " The following dynamic model governs the low-frequency horizontal motions of a vessel: M + M11 x\u03081 \u2212 M + M22 x\u03072x\u03076 \u2212 M26x\u03076 2 + C11x\u03071 = F1E + F1T M + M22 x\u03082 + M26x\u03086 + M + M11 x\u03071x\u03076 + C22x\u03072 = F2E + F2T 1 IZ + M66 x\u03086 + M26x\u03082 + M26x\u03071x\u03076 + C66x\u03076 = F6E + F6T where Iz is the moment of inertia about the vertical axis; M is the vessel total mass, Cij are damping coefficients, Mij are added mass matrix terms, F1E, F2E, F6E are surge, sway, and yaw environmental loads current, wind, and waves and F1T, F2T, F6T are forces and moment delivered by the propulsion system. The vari- 204 / Vol. 128, AUGUST 2006 rom: http://offshoremechanics.asmedigitalcollection.asme.org/ on 01/29/20 ables x\u03071, x\u03072 are the absolute1 surge and sway velocities of a central point at midship and x\u03076 is the yaw absolute rate of rotation Fig. 1 , all expressed in the ship\u2019s moving reference frame. Current induced forces are determined via a heuristic model based on a low aspect ratio wing theory with experimental validation 6 . Wind forces are calculated employing coefficients suggested by OCIMF 7 and wind gusts are also considered. Wave drift forces are evaluated using the hull drift-coefficients worked out by means of a standard second-order potential flow analysis performed by a computer software Wamit . The interaction between current and waves wave-drift damping is also taken into account 8 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003740_1.2975154-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003740_1.2975154-Figure3-1.png",
        "caption": "FIG. 3. a Components of n along the straight directions n\u2212n and g\u2212g; b computation of the n components along the axes X, Y, and Z for a left handed helicoidal magnet.",
        "texts": [
            " Here t\u2212 t and n\u2212n are the tangent and the normal straight lines to in P, respectively. The straight line g\u2212g represents the generatrix of the cylinder9 whose radius is indicated as r. The curve belongs to this cylinder. We observe that the normal n\u2212n is inclined with the helix angle with respect to the generatrix g\u2212g. The value of is always the same whatever the position of P belonging to is. We can also define the unit vector n applied in P along the normal n\u2212n. Then the n components along n\u2212n and g\u2212g are equal to n cos and n sin , respectively Fig. 3 a . The components nx, ny, and nz of n along the axes X, Y, and Z Fig. 3 b are nx = n cos , 11 ny = \u2212 n sin sin \u2212 , 12 nz = \u2212 n sin cos \u2212 , 13 where n= n =1 is the magnitude of n. Now we consider the magnetization of the helicoidal sector by applying to the generic point P of the magnet, a magnetization vector M characterized by a constant magnitude. This M is oriented as the correspondent unit vector n Fig. 2 b . The vector M just defined therefore is of a helicoidal kind. In Fig. 4 the distribution of M along a generic cylindrical helix with starting and ending points A and B, respectively, is illustrated by a qualitative picture",
            " Now, since the orientation of M is the same one of n we straightaway obtain the components Mx, My, and Mz of M. In fact, with reference to O X ,Y ,Z and Eqs. 11 \u2013 13 , it follows that Fig. 5 a Mx = M cos , 14 My = \u2212 M sin sin \u2212 , 15 Mz = \u2212 M sin cos \u2212 . 16 Substituting Eqs. 9 and 10 in Eqs. 11 \u2013 16 , we obtain in each point P of the magnet the volume and surface charge density M P and M P , respectively. In particular, in order to compute M P by Eq. 9 , it is convenient to write Mx, My, and Mz as a function of the Cartesian coordinates x, y, and z of P, that is the point where M is applied. Observing Fig. 3 b we find that r = y2 + z2, 17 where y and z are just the two coordinates of P in the frame of reference O X ,Y ,Z . Because cos \u2212 = \u2212 y r , 18 sin \u2212 = z r , 19 from Eq. 17 it follows that [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: 131.230.73.202 On: Thu, 18 Dec 2014 07:41:10 cos \u2212 = \u2212 y y2 + z2 20 and sin \u2212 = z y2 + z2 . 21 Moreover, if we denote by p the pitch of the cylindrical helix shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003007_6.2006-6147-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003007_6.2006-6147-Figure2-1.png",
        "caption": "Figure 2. Rotor system response to thrust control.",
        "texts": [
            " Methodology The system iden ed in this project is the cy-Response Method is well suited to the acc The control movements are mixed to give the correct lateral cyclic and collective pitch motions to the rotors through the dual UBAs under each swashplate. The helicopter is controlled vertically with the thrust control lever. Thrust control inputs yield an equal and simultaneous increase or decrease in the pitch of all blades on both rotors, thereby causing the helicopter to ascend or descend vertically. Thrust control movements are illustrated in Figure 2. Directional control is achieved with the directional pedals by imparting equal but opposite (i.e., differential) lateral cyclic pitch to the forward and rear rotor blades respectively; thus causing the Tip Path Plane (TPP) of each rotor to tilt in opposite directions. For example, moving the right pedal forward causes the forward rotor TPP to tilt to the right, whereas the rear rotor TPP will tilt to the left, resulting in a clockwise directional moment about the center of gravity as illustrated in Figure 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002741_cca.2006.286027-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002741_cca.2006.286027-Figure2-1.png",
        "caption": "Fig. 2. SEM images of the components of the \u03bc-LDV: (a) the glass substrate and (b) the Si substrate.",
        "texts": [
            " In this research, we successfully used our highly integrated \u03bc-LDV to measure the velocity of various scattering surfaces (aluminum, cardboard, and plastic) directly, without any attachment like a grating scale, by applying fast Fourier transform (FFT) analysis to the output of the device, and processing the resulting power spectra from the FFT analysis. We also confirmed characteristics of the measurement distance and tilt installation error corresponded to its allowable alignment error. Fig. 1 shows a picture of the \u03bc-LDV. It consists of two elements, a pyrex glass substrate (Fig. 2(a)) and a Si substrate (Fig. 2(b)). Electrodes are formed on the back surface of the Pyrex glass substrate by depositing Au, and the InGaAs PIN PD (size: 280 \u00d7 460 \u00d7 150 \u03bcm; active diameter: 70 \u03bcm) is bonded onto the electrode. The electrode pad and light-receiving area of the PD are formed on the back surface. Micro aspherical lenses for collimating the laser can be formed by inductively coupled plasma (ICP) etching with a gray-scale-patterned photoresist structure [25], [26]. The Si substrate has a wet-etched cavity defined by (1 1 1) crystal planes [27], and this is used to build a free space and tilt surface for Au mirrors",
            "1 nm/\u00b0C) was used to avoid using a beam splitter and to maintain the temperature stability of the wavelength. A DFB-LD was bonded onto the bottom of the Si cavity. The optical components are bonded by Au-Au surface-activated bonding [28], [29]. This method allows bonding in low-temperature conditions (150 \u00b0C), which is effective for preventing thermal damage to the LD and PD, and for precise alignment. Both substrates also can be bonded to become airtight by a bonding method using an Au pattern for substrate bonding (Fig. 2(a) and (b)). The electrodes on the Pyrex glass substrate are connected to electrodes on the Si substrate, and all electrodes are connected by through-hole electrodes from the sensor bottom to outside the sensor. This design enables the sensor to be fabricated with wafer-level packaging and to have an extremely small size (2.8 \u00d7 2.8 mm \u00d7 1.0 mm). Fig. 3 shows a schematic of the A\u2013A\u2032 cross-section shown in Fig. 1. Two laser beams are simultaneously emitted from the LD, reflected by the Au mirrors, collimated by the refractive micro aspherical lenses, and impact the moving object"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003759_jst.84-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003759_jst.84-Figure3-1.png",
        "caption": "Figure 3. Configuration of the ski jumper and l in flight.",
        "texts": [
            " The virtual ski jumper had a mass, including equipment, of 70 kg and a height of 1.76m [10], and used commercially available skis of 2.57m length (146% of athlete\u2019s height), 11.5 cm width, and ski bindings (boot tip to ski tip distance of 57% of ski length). The equipment complied with Fe\u0301de\u0301ration Internationale de Ski [17] specifications. The following angles determine the posture of the ski jumper (based upon Meile et al. [8], Schwameder [9], and Mu\u0308ller et al. [14,15]). The ski opening angle (l) (Figure 3) was set at 201, 251 and 301. The forward leaning angle (y) was sampled from 0 to 401 at 101 intervals. Hip angle (b) was held at 01 (based on the wind tunnel database of Seo et al. [10]), and the arm abduction angle was constant at 101 (arms held to the sides of the body). Simulation of competition levels incorporated freestream air velocities (Va) of 20m/s (typical at takeoff in medium jumping hills), 25m/s (large hills) and 30m/s (ski flying hills) [15\u201317]. Air density (r) was assumed to be 1",
            " Inertial properties of the helmet, boots, and skis (five additional segments) were included using equations for symmetric objects of uniform composition (Equations 2 and 3 [19]). The ski tips were assumed to bend upward during flight [10] creating negatively cambered profiles. The coordinates for the Planica K185 jumping hill [17] were plotted using CAD for the computation of flight trajectory, flight time (tf) and jump length (\u2018j). The direction of flight path (j) is expressed by the projectile velocity (V) vector (Figure 3). Va is opposite in direction to V. a is the angle between the skis and Va [15]. a0 represents equilibrium for longitudinal oscillatory motion [10], and the stall angle (aST) is the angle beyond which lift declines (based on Kermode [1] and Bertin [12]). M is the net rotational effect of aerodynamic forces around the y axis [7]. Nose-up M is defined as positive [2]. Angular acceleration (\u20aca) around a0 is induced by aerodynamic moments during out-of-trim flight [3]. The CP is an abstract theoretical concept that signifies the nomadic point of application of resultant aerodynamic pressure forces [4]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003906_868425-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003906_868425-Figure3-1.png",
        "caption": "Figure 3: Visualization of sets used in the proof of Theorem 4.1.",
        "texts": [
            "20) yields \u0394Ve ( ex(k), ez(k), W\u0303(k) ) \u2264 \u2212 \u03bc1 \u2225\u2225P 1/2ex(k) \u2225\u2225 2 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 + c\u03bc2 \u2225\u2225P 1/2ex(k) \u2225\u2225 2 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 + c\u22121 \u2225\u2225P 1/2e\u0303(k) \u2225\u2225 2 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 + (\u03b1/a) \u2225\u2225P 1/2ex(k) \u2225\u2225 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 + a \u2225\u2225P 1/2e\u0303(k) \u2225\u2225 2\u2225\u2225P 1/2ex(k) \u2225\u2225 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 + \u03b2 \u2225\u2225P 1/2ex(k) \u2225\u2225 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 \u2212 ( 2 \u2225\u2225P 1/2ex(k) \u2225\u2225 \u2212 1 )\u2225\u2225P 1/2e\u0303(k) \u2225\u2225 2 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 + \u03be \u2225\u2225P 1/2e\u0303(k) \u2225\u2225 2\u2225\u2225P 1/2ex(k) \u2225\u2225 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 \u2212 nx\u2211 i=1 pibi\u03b3i \u2225\u2225W\u0303i(k) \u2225\u2225 2\u2225\u2225P 1/2ex(k) \u2225\u2225 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 \u2212 nx\u2211 i=1 pibi\u03b3i \u2225\u2225W\u0302i(k) \u2225\u2225 2\u2225\u2225P 1/2ex(k) \u2225\u2225 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 ( 1 \u2212 2qi\u03b3i \u2225\u2225P 1/2ex(k) \u2225\u2225 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 ) \u2264 \u2212 \u2225\u2225P 1/2ex(k) \u2225\u2225 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 [( \u03bc1 \u2212 c\u03bc2 )\u2225\u2225P 1/2ex(k) \u2225\u2225 \u2212 \u03b2 \u2212 \u03b1a\u22121] \u2212 \u2225\u2225P 1/2e\u0303(k) \u2225\u2225 2 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 [ (2 \u2212 a \u2212 \u03be) \u2225\u2225P 1/2ex(k) \u2225\u2225 \u2212 1 \u2212 c\u22121] \u2212 nx\u2211 i=1 pibi\u03b3i \u2225\u2225W\u0303i(k) \u2225\u2225 2\u2225\u2225P 1/2ex(k) \u2225\u2225 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 \u2212 nx\u2211 i=1 pibi\u03b3i \u2225\u2225W\u0302i(k) \u2225\u2225 2\u2225\u2225P 1/2ex(k) \u2225\u2225 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 ( 1 \u2212 2qi\u03b3i \u2225\u2225P 1/2ex(k) \u2225\u2225 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 ) \u2264 \u2212 \u2225\u2225P 1/2ex(k) \u2225\u2225 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 [( \u03bc1 \u2212 c\u03bc2 )\u2225\u2225P 1/2ex(k) \u2225\u2225 \u2212 \u03b2 \u2212 \u03b1a\u22121] \u2212 \u2225\u2225P 1/2e\u0303(k) \u2225\u2225 2 1 + \u2225\u2225P 1/2ex(k) \u2225\u2225 2 [ (2 \u2212 a \u2212 \u03be) \u2225\u2225P 1/2ex(k) \u2225\u2225 \u2212 1 \u2212 c\u22121]. (A.22) Now, for \u2225\u2225P 1/2ex(k) \u2225\u2225 > max { a\u03b2 + \u03b1 a ( \u03bc1 \u2212 c\u03bc2 ) , 1 + c c(2 \u2212 a \u2212 \u03be) } \u03b1x, (A.23) it follows that \u0394Ve(ex(k), ez(k), W\u0303(k)) \u2264 \u2212W(ex(k)) for all k \u2208 Z+, where W ( ex ) \u2225\u2225P 1/2ex \u2225\u2225 1 + \u2225\u2225P 1/2ex \u2225\u2225 2 [( \u03bc1 \u2212 c\u03bc2 )\u2225\u2225P 1/2ex \u2225\u2225 \u2212 \u03b2 \u2212 \u03b1a\u22121], (A.24) or, equivalently, \u0394Ve(ex(k), ez(k), W\u0303(k)) \u2264 \u2212W(ex(k)) for all (ex(k), ez(k), W\u0303(k)) \u2208 D\u0303 e \\ D\u0303 er, k \u2208 Z+, where (see Figure 3) D\u0303 e {( ex, ez, W\u0303 ) \u2208 R nx \u00d7 R nz \u00d7 R nx\u00d7s : x \u2208 Dx } , (A.25) D\u0303 er {( ex, ez, W\u0303 ) \u2208 R nx \u00d7 R nz \u00d7 R nx\u00d7s : \u2225\u2225P 1/2ex \u2225\u2225 \u2264 \u03b1x}. (A.26) Next, we show that \u2016x1(k)\u2016 < \u03b5e, k \u2208 Z+. Since \u2016x2(k)\u2016 2 \u2264 \u03b5w for all k \u2208 Z+, it follows that, for x1(k) \u2208 B\u03b1x(0), k \u2208 Z+, Ve ( x1(k), x2(k), x3(k) ) + \u0394Ve ( x1(k), x2(k), x3(k) ) \u2264 \u03b1 2 x + \u03b5w + \u0394Ve ( x1(k), x2(k), x3(k) ) \u2264 \u03b1 2 x + \u03b5w + 1 2 ( \u03b1 a + \u03b2 ) + ( 1 + 1 c )\u2225\u2225P 1/2e\u0303(k) \u2225\u2225 2 \u2264 \u03b1 2 x + \u03b5w + 1 2 ( \u03b1 a + \u03b2 ) + ( 1 + 1 c )( 2\u03b1 + 2\u03be\u03b5w ) \u03b7. (A.27) Now, let \u03b4 \u2208 (0, \u03b1x] and assume \u2016x10\u2016 \u2264 \u03b4",
            " Hence, if x10 \u2208 B\u03b4(0), then \u2225\u2225x1(k) \u2225\u2225 \u2264 \u03b1\u22121 ( max { \u03b7, \u03b2 (\u221a \u03b4 2 + \u03b5w )}) \u03b5e, k \u2208 Z+. (A.30) Finally, repeating the above arguments with \u2016x2(k)\u2016 2 \u2264 \u03b5w, k \u2208 Z+, replaced by \u2016x2(k)\u2016 2 \u2264 \u03b7w, k \u2265 K > 0, it can be shown that \u2016x1(k)\u2016 < \u03b5, k \u2265 K, where \u03b5 = \u221a e\u03b7 \u2212 1. Next, define D\u0303\u03b1 {( ex, ez, W\u0303 ) \u2208 R nx \u00d7 R nz \u00d7 R nx\u00d7s : Ve ( ex, ez, W\u0303 ) \u2264 \u03b1 } , (A.31) where \u03b1 is the maximum value such that D\u0303\u03b1 \u2286 D\u0303 e, and define D\u0303 \u03b7 {( ex, ez, W\u0303 ) \u2208 R nx \u00d7 R nz \u00d7 R nx\u00d7s : Ve ( ex, ez, W\u0303 ) \u2264 \u03b5 2 e } , (A.32) where \u03b5e is given by (A.30). Assume that D\u0303 \u03b7 \u2282 D\u0303\u03b1 (see Figure 3) (this assumption is standard in the neural network literature and ensures that in the error space D\u0303 e there exists at least one Lyapunov level set D\u0303 \u03b7 \u2282 D\u0303\u03b1. In the case where the neural network approximation holds in R nx \u00d7R nz , this assumption is automatically satisfied. See Remark A.1 for further details). Now, for all (ex, ez, W\u0303) \u2208 D\u0303 \u03b7 \u2229 (D\u0303 e \\ D\u0303 er), \u0394Ve(ex, ez, W\u0303) \u2264 0. Alternatively, for all (ex, ez, W\u0303) \u2208 D\u0303 \u03b7 \u2229 D\u0303 er, Ve(ex, ez, W\u0303) + \u0394Ve(ex, ez, W\u0303) \u2264 \u03b7 \u2264 \u03b5 2 e . Hence, it follows that D\u0303 \u03b7 is positively invariant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002667_acc.2006.1657387-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002667_acc.2006.1657387-Figure1-1.png",
        "caption": "Fig. 1. l \u2013 \u03c8 control configuration",
        "texts": [
            " Note that when a vehicle is constrained by more than one neighbor in the formation, a second feedback controller is needed to control the distances of the vehicle from two neighboring vehicles. This controller is called the l \u2013 l controller. These two local controllers are necessary to define a general formation. Usually the vehicles at an edge of the formation geometry control their distance with their immediate front vehicle using the l \u2013 \u03c8 controller. The other vehicles control their distances to their immediate front and side vehicles using the l \u2013 l controller. In Fig. 1, a system of two neighboring vehicles in the formation is shown. The vehicles are separated by a distance l12 between the center of mass of vehicle 1 and an arbitrary point, p, on vehicle 2. The arbitrary point has a distance d with the center of mass. A feedback control law for control inputs F2 and T2 must be determined to control vehicle 2 such that the desired distance ld12 and view angle \u03c8d 12 to vehicle 1 are maintained. Therefore the outputs of the control system are: [l12, \u03c812]. The variables that define the configuration of vehicle 2 are: [x2, y2, \u03b82]",
            " In this method, two asymptotically stable first order surfaces are assumed (\u03bb1,2 > 0): s = [ s1 s2 ] = [ (\u03c8\u030712 \u2212 \u03c8\u0307d 12) + \u03bb1(\u03c812 \u2212 \u03c8d 12) (l\u030712 \u2212 l\u0307d12) + \u03bb2(l12 \u2212 ld12) ] (12) s = z\u0307 \u2212 [ \u03c8\u0307d 12 \u2212 \u03bb1(\u03c812 \u2212 \u03c8d 12) l\u0307d12 \u2212 \u03bb2(l12 \u2212 ld12) ] (13) The following control law stabilizes the outputs in the presence of parameter uncertainty and disturbance: u = b\u0302\u22121(\u2212f\u0302 \u2212 w\u0302 + s\u0307r \u2212 [ k1 sat(s1/\u03c61) k2 sat(s2/\u03c62) ] ) (14) where sr is the second term of (13) and (\u0302.) indicates that the matrices in (11) are evaluated for the nominal values of the system parameters and wave disturbances. \u03c61 and \u03c62 are the boundary layer of the surfaces, and k1 and k2 are the controller\u2019s nonlinearity gains. Note that the determinant of b\u0302 in (14) is nonzero at all times except when l12 = 0, which is avoided by defining proper desired value (Fig. 1). Therefore, the system is controllable. The following bounds are assumed for the parameter uncertainties and disturbances in order to determine the controller nonlinearity gains: |f \u2212 f\u0302 | \u2264 F (15) |w \u2212 w\u0302| \u2264 W (16) b = (I + \u03b4)b\u0302 |\u03b4ij | \u2264 \u0394ij i, j = 1..2 (17) Based on these bounds, one must determine the nonlinearity gains such that the reaching condition si.s\u0307i \u2264 \u2212\u03b7i|si| \u03b7i > 0 i = 1, 2 (18) is satisfied, where \u03b7i > 0 determines the reaching speed. This is done by substituting the first order derivative of components of (13) in (18) and using (10) and (14) in the results",
            " After some algebraic manipulation, rearranging in terms of k1 and k2, and applying inequalities (15) to (17), one obtains the following condition [10]: (1 \u2212 \u0394ii)ki + \u22112 j =i \u0394ijkj = Fi + Wi +\u03b7i + \u22112 j=1 \u0394ij | \u2212 f\u0302j + s\u0307rj | i, j = 1..2 (19) When ki\u2019s satisfy (19), it is guaranteed that the outputs reach the surfaces despite the existence of parameter uncertainties and disturbances defined in (15) to (17). After the outputs are on their corresponding surfaces, s1 and s2 are zero. Therefore, the outputs slide to their desired values as is observed from (12). Note that although the distance l12 and view angle \u03c812 in the l \u2013 \u03c8 configuration, shown in Fig. 1, converge to their corresponding desired values, \u03b82, the orientation of vehicle 2, is not directly controlled. The dynamics of this degree of freedom when others have been stabilized is referred to as the zero dynamics of the system and its stability has to be investigated separately. In this section, the stability of the zero dynamics is proven by considering the relation between the controlled outputs and the orientation of vehicle 2. This relation is obtained by the velocity analysis of the l \u2013 \u03c8 configuration shown in Fig. 1 as: \u03c8\u030712 = 1 l12 [(y\u03072 \u2212 y\u03071) c\u03b10 \u2212 (x\u03072 \u2212 x\u03071) s\u03b10 + d\u03b8\u03072 c\u03b31 \u2212l12\u03b8\u03071] (20) l\u030712 = [(y\u03072 \u2212 y\u03071) s\u03b10 + (x\u03072 \u2212 x\u03071) c\u03b10 + d\u03b8\u03072 s\u03b31] (21) Note that l12 = ld12, \u03c812 = \u03c8d 12, l\u030712 = 0, and \u03c8\u030712 = 0, after the controlled outputs have reached the steady state. These conditions are applied to (20) and (21) and the results are solved for \u03b8\u03072: \u03b8\u03072 = 1 d ( y\u03071 c\u03b82 \u2212 x\u03071 s\u03b82 + ld12\u03b8\u03071 c\u03b31 \u2212 v2 ) (22) where v2 = y\u03072 c\u03b82 \u2212 x\u03072 s\u03b82 is the lateral velocity of vehicle 2. Equation (22) describes the zero dynamics of the l \u2013 \u03c8 controller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002522_jmes_jour_1975_017_003_02-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002522_jmes_jour_1975_017_003_02-Figure1-1.png",
        "caption": "Fig. 1. Oilfilm and bearing geometry",
        "texts": [],
        "surrounding_texts": [
            "The use of the finite-element method in problems of heat conduction in solids has been studied by Visser (21), and Emery and Carson (22), and convective heat transfer between parallel planes has been investigated by Tay and Davis (23). The application of the finite-element method to solve the energy equation for oil-film temperatures in thrust bearings without side leakage, taking into account heat convection and viscous dissipation, has been considered by Tieu (1).\nIn this paper, the method is extended to tapered and parallel finite-width thrust pads. The results obtained from the simulated models are compared with those for infinitely wide bearings. The correctness of the model is also verified by correlating the computed results with experimental observations. Factors affecting the pad performance such as oil inlet temperature, hot oil carryover, rotor surface temperature and pad radial tilting are also investigated. This paper extends the work reported by the author in (24).\nT, (theoretical)\nU 21, 1) V VISM (experimental)\nVISM (theoretical)\nVISTM\nx, XI W\nY , Y l\nBearing width Specific heat of oil Local potential Thickness of oil film Minimum film thickness Thermal conductivity of oil Pad length in direction of motion Pressure Heat flux Pad mean, inner and outer radii Radius Temperature\nMean temperature (- 1 y ) Rotor sliding velocity Fluid velocity Volume Oil viscosity at inlet -~ S?dV\nV Oil, viscosity at temperature T, Pad thickness Co-ordinates in direction of mo-\ntion Co-ordinates perpendicular to x\nand z Co-ordinates in direction of oil\nfilm thickness Coefficients of linear viscosity-\ntemperature relationship Pressure-viscosity coefficient Oil viscosity Oil viscosity at reference temper-\nature Angular position of pivot or\ncomputed centre of pressure pad inlet\nSector angle\nP Oil density V a\nax* -, where i = 1 ,2 or 3\nNon-dimensional IF Denotes oil film thickness configuration (= 1,2, 3 or 4, see equations in Table 2) kL E\nIs\nPC, UOh; ph, V O UO\nT\n- U U -\nUO\n..\nY L - J\n- Z Z -\nh2\n? ?O - r\n2 THEORY 2.1 Assumptions The oil-film temperature distribution is determined from the energy equation, based on the assumptions that :\n(i) steady-state conditions exist; (ii) flow is laminar with no slip at the bearing-oil\ninterface; (iii) oil is Newtonian and incompressible; (iv) oil density, thermal conductivity and specific heat\nare constant (v) the velocity in the direction of oil-film thickness is\nnegligible. In support of the last two assumptions, it should be noted that Dowson and Hudson (7) reported that oil density has little effect on the performance of the plane inclined slider bearing. Moreover, for the cases where the oil properties were treated as variables, the effect of the transverse velocity across the oil-film thickness was said to be small.\n2.2 Generalized Reynolds equation The steady-state, two-dimensional continuity equation for incompressible flow in a thin film. incorporating a reduced form of the three-dimensional Navier-Stokes equation, has been derived by Dowson (25), and it can be written in non-dimensional form as:\nJournal Mechanical Engineering Science OIMechE 1975 Vol 17 No 1 1975\nat UNIV OF VIRGINIA on October 3, 2012jms.sagepub.comDownloaded from",
            ". . . . (1)\n- z(z - 2') F , = s,\" dZ\nii The pressure distribution, p , satisfying the differential equation (l), and subject to atmospheric pressure at the boundary, can be obtained by minimizing an equivalent functional similar to that obtained in (13):\nThe finite-element formulation in the minimization of functional (2) is of standard form, and a detailed description can be found in (26).\n2.3 The oil-film energy equation The energy equation for viscous incompressible flow in a thin film, taking account of viscous dissipation as well as conduction and convection, takes the conventional form:\n+ fl[(gy + (y . . . . . . . (3) az Equation (3) is subject to\n. . . . . . . . . . (4) T = To - k v T = i j\non appropriate boundaries. Based on the variational analogue to the differential equation (3), a finite-element method is developed to approximate the oil-film temperature field. Detailed descriptions of the variational principle and the application of the finite-element method in infinitely wide bearings are given by the author in (1).\nThe corresponding functional of equation (3) to be minimized can be written from (1):\nwhere I/ is the total volume of the oil film and A is the boundary area where heat flux is prescribed.\nThe oil-film volume, as shown in Fig. 2, is divided into\n488 tetrahedral elements for the tapered oil film, or 320 elements for the parallel oil film. Assuming a linear interpolation function within an element, one can specify the temperature, viscosity and velocity distributions in terms of their corresponding nodal values. Details of the finite-element formulation for the minimization of expression (5) can be found in 27).\nIn the minimizing procedure for E*, .c' superposition\nof the contributions. 4, of the e elrients adjacent to\nnode i is obtained:\nl?E* aq\nand this will result ina set of simultaneous linear equations written as:\nCSTI (TI = (R) where [ST] is an asymmetric banded matrix of the coefficients. [ST], with half band width of 31 including the diagonal, is a (175 x 175) matrix for the tapered oil film, and (125 x 125) for the parallel oil film. (T} is a vector of unknown temperature. (R} is a vector of constants on the right-hand side.\n2.4 Numerical procedure The mesh'lengths in the 2, j and Z directions of the pressure and temperature models are allowed to vary independently to suit changes in the function gradients. The oil viscosity-temperature characteristic is approximated by a linear relationship similar to that shown in (1). The\nJournal Mechanical Engineering Science OIMechE I975 Vol 17 No 1 1975\nat UNIV OF VIRGINIA on October 3, 2012jms.sagepub.comDownloaded from",
            "following exponential relationship is used after the first iteration :\nr = exp [ Y P - P'(T - TJI The computation of the temperature fields requires solving the system of simultaneous linear equations, the coefficient matrix of which is unsymmetrical and banded. The Gauss-Seidel iterative method has been found unstable in the high-speed cases: for average duty with small h,, the method needs from 8 to 15 iterative cycles to produce successive solutions that do not differ by more than 0.1 per cent. However, the thicker the oil film at high speed, the more iterative cycles within the Gauss-Seidel method are required, and, at a certain film thickness, the solution diverges. The film thicknesses at which instability of the method occurs were found to vary with different bearing geometries. The mesh length, prescribed boundary conditions and viscosity-temperature relationship did not affect the convergence significantly, and the source of the method instability was found to be the convective term\n( E g + g). The direct Gaussian elimination method was used successfully with the system of equations for all bearing geometries and operating conditions.\nFrom the computed oil-film temperature, the oil viscosity field is evaluated and used in the next temperature iteration until successive differ by less than 0.1 per cent. For the model considered here, the temperature distribution for the isoviscous oil film is to be iterated 3 to 4 times, and for the varying viscosity field, 2 to 3 cycles of iterations are required. The resulting viscosity field is used in the pressure iteration until the successive pi agree to less than 0.5 per cent, which is obtained in 4 to 5 cycles of computation for the cases of the tapered slider bearing.\nThe boundary conditions prescribed for the oil-film volume are expected to affect significantly the oil-film temperature distribution: the main considerations are the temperature of the inlet oil and of the solid surfaces. The oil inlet temperature is unlikely to be uniform from the rotor to the bearing surface due to the effect of hot oil carry-over. The effects of the oil inlet temperature and the hot oil carry-over on the bearing performance have been reported by Hahn (9), Ettles (28) and Neal (12). As mentioned elsewhere, the hot oil carry-over relates specifically to the individual type of bearing and its operating conditions. The same argument is applied to the prescribed temperature at the rotor and bearing surfaces which is governed by different mounting arrangements and different modes of lubrication, i.e. localized directed or flooded lubrication. The correctness of the oil inlet temperature can be verified by applying the heat balance to the oilfilm volume where the inlet temperature is corrected by a factor of hot oil carry-over varying between 0 to 0.5 for directed lubrication, and the prescribed temperature of the solid surfaces is consistent with experimental observations. The rotor surface temperature is assumed constant, as has been justified theoretically (9).\n3 COMPUTED RESULTS FOR FINITE-WIDTH BEARINGS\nFor the three-dimensional cases considered in Table 1, a\nR , = 1.524m; 0, = 6.87'; N = 191 rev/min; 'lo = 137.8cP; h, = 91.4 x 10-4cm; h,/h, = 2. Boundary condition type A : temperature prescribed on surfaces A,, A,, A,, A, and A, of Fig. 2. Boundary condition type B: temperature prescribed on surfaces A,,, A, and A, as shown in Fig. 2. Convergence factor E = 0.005 for all cases except case 3, when E = 0.04 (iteration of pressure).\nbearing width-to-length ratio, B/L, of 5 is chosen so that the computed pressures and temperatures along the mid-circumference are comparable to those for the infinitely wide bearing (9-04) as plotted in Fig. 3. The prersure curves of isoviscous cases 1 and 4 agree with the\nisoviscous curve HZ of Hunter and Zienkiewicz (6). The varying mesh lengths in the %-direction in these two cases do not have any effect on the resulting pressure distributions. The non-isoviscous pressure of case 2 (boundary condition type A) is lower than that of case 3 (boundary condition type B) at inlet, but is higher at outlet. Thus, for large BIL ratios, different types of boundary condition of the oil-film volume do not affect significantly the bearing load-carrying capacity.\nCompared with the non-isoviscous curve I, from (7),\nJournal Mechanical Engineering Science OIMechE 1975 Vol 17 No 1 1975\nat UNIV OF VIRGINIA on October 3, 2012jms.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv11_28_0002776_3-540-26415-9_88-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002776_3-540-26415-9_88-Figure1-1.png",
        "caption": "Fig. 1. Quadruped robot model and control architecture",
        "texts": [
            " This study intends to generalize previous work [9] through the formulation of two indices measuring the average energy consumption and the hip trajectory errors during forward straight line walking at different velocities. Bearing these facts in mind, the paper is organized as follows. Section two introduces the robot model and control architecture and section three presents the optimizing indices. Section four develops a set of experiments that reveal the influence of the locomotion parameters and robot gaits on the performance measures, as a function of robot body velocity. Finally, section five outlines the main conclusions. We consider a quadruped walking system (Fig. 1) with n = 4 legs, equally distributed along both sides of the robot body, having each two rotational joints (i.e., j = {1, 2} {hip, knee}). Motion is described by means of a world coordinate system. The kinematic model comprises: the cycle time T, the duty factor , the transference time tT = (1 )T, the support time tS = T, the step length LS, the stroke pitch SP, the body height HB, the maximum foot clearance FC, the i th leg lengths Li1 and Li2 and the foot trajectory offset Oi (i = 1, \u2026, n). The forward motion planning algorithm accepts, as inputs, the desired cartesian trajectories of the legs hips pHd(t) = [xiHd(t), yiHd(t)] T (horizontal movement with a constant forward speed VF = LS / T) and feet pFd(t) = [xiFd(t), yiFd(t)] T (periodic trajectory for each foot, being the trajectory of the swing leg foot computed through a cycloid function [7]) and, by means of an inverse kinematics algorithm, generates the related joint trajectories d(t) = [ i1d(t), i2d(t)] T , selecting the solution corresponding to a forward knee [7]. Concerning the dynamic model, the robot body is divided in n identical segments (each with mass Mbn 1 ) and a linear spring-damper system is adopted to implement the intra-body compliance (Fig. 1) [7], being its parameters defined so that the body behaviour is similar to the one expected to occur on an animal (Table 1). The contact of the i th robot foot with the ground is modelled through a non-linear system [7] with linear stiffness and non-linear damping (Fig. 1). The values for the parameters are based on the studies of soil mechanics (Table 1). The robot inverse dynamic model is formulated as: ( ) T RH RFH c , g F J F (1) where = [fix, fiy, i1, i2] T (i = 1, \u2026, n) is the vector of forces / torques, = [xiH, yiH, i1, i2] T is the vector of position coordinates, H( ) is the inertia matrix and ,c and g( ) are the vectors of centrifu- gal / Coriolis and gravitational forces / torques, respectively. The (m+2) 2 (m = 2) matrix J T ( ) is the transpose of the robot Jacobian matrix, FRH is the (m+2) 1 vector of the body inter-segment forces and FRF is the 2 1 vector of the reaction forces that the ground exerts on the robot feet. These forces are null during the foot transfer phase. Furthermore, we consider that the joint actuators are not ideal, exhibit- ing saturation, being ijC the controller demanded torque, ijMax the maximum torque that the actuator can supply and ijm the motor effective torque. The general control architecture of the multi-legged locomotion system is presented in Fig. 1. The control algorithm considers an external position and velocity feedback and an internal feedback loop with information of foot-ground interaction force [10]. For Gc1(s) we adopt a PD controller and for Gc2 a simple P controller. For the PD algorithm we have: 1 , 1 C j j j G s Kp Kd s j ,2 (2) being Kpj and Kdj the proportional and derivative gains. Table 1. System parameters Robot model parameters Locomotion parameters SP 1 m LS 1 m Lij 0.5 m HB 0.9 m Oi 0 m FC 0.1 m Mb 88.0 kg Mij 1 kg Ground parameters KxH 10 5 Nm 1 KxF 1302152"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003913_s12555-009-0520-1-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003913_s12555-009-0520-1-Figure2-1.png",
        "caption": "Fig. 2. Three real solutions for the Forward kinematics.",
        "texts": [
            " From the three real roots, corresponding ,x ,y ,z and \u03b1 are calculated (see Table 2). When T = 0.0448256, the traveling plate is located out of the workspace. And Hee-Byoung Choi, Atsushi Konno, and Masaru Uchiyama 862 when T = 1.2282071, the solution is also infeasible because of collisions between central bar and lateral bar and swing angle\u2019s limitation of ball joints. Therefore, finally the only acceptable solution is when T = 0.4134581. The three forward kinematics solutions are illustrated in Fig. 2. 5. CONCLUSION In this paper, the closed-form forward kinematics solution of the 4-DOF parallel robot H4 is derived. It is shown that the solutions of the forward kinematics can be obtained by solving a 16th order polynomial in a single variable. A numerical example is presented to validate the proposed method. The real configurations are illustrated which correspond to the real roots of the polynomial equation. APPENDIX A Coefficients for the polynomial equation: 1 4 4 2 3 2 2 3 4 3 3 4 2 4{( )( ) ( )( ) ( )( )} n b Q p p b Q p p b Q p p = \u2212 \u2212 + \u2212 \u2212 + \u2212 \u2212 2 4 2 3 3 2 4 2 3 4 4{ ( ) ( ) ( )}n a p p a p p a p p= \u2212 + + \u2212 + \u2212 + 3 4 2 3 2 3 3 2 4 2 4 2 3 4 3 4 4{ ( ) ( ) ( )} n a b b Q Q a b b Q Q a b b Q Q = \u2212 \u2212 + + \u2212 + + \u2212 + \u2212 \u2212 + 4 4 2 3 2 3 4 3 2 4 4{ ( ) ( ) ( )}n c p p c p p c p p= \u2212 + \u2212 + \u2212 + 5 3 4 2 2 2 4 3 3 2 3 4 4 4{( )( ) ( )( ) ( )( )} n c c b Q c c b Q c c b Q = \u2212 \u2212 + \u2212 \u2212 + + \u2212 \u2212 6 4 2 3 2 3 4 3 2 4 4{ ( ) ( ) ( )}n c p p c p p c p p= \u2212 \u2212 + \u2212 + \u2212 + 7 4 2 3 2 3 4 3 2 4 4{ ( ) ( ) ( )}n a c c a c c a c c= \u2212 \u2212 + \u2212 + \u2212 + 8 2 3 4 2 2 3 2 4 3 3 2 3 4 4 4 4{ ( )( ) ( )( ) ( ) ( ) n p p p b Q p p p b Q p p p b Q = \u2212 \u2212 + \u2212 \u2212 + + \u2212 \u2212 9 4 4 2 3 2 3 3 3 2 4 2 4 2 2 3 4 3 4 4{ ( ) ( ) ( )} n a p b b Q Q a p b b Q Q a p b b Q Q = \u2212 \u2212 \u2212 + + \u2212 + + \u2212 + \u2212 \u2212 + 2 2 2 2 2 2 10 3 4 2 3 3 2 4 4 3 4 2 2 2 2 2 2 2 2 2 4 2 2 3 3 4 4 2 4 2 3 2 2 2 2 2 2 3 2 3 2 3 2 4 3 4 2 2 2 2 2 2 3 2 3 4 2 4 3 2 4 2 4 2 4 4 2 3 3 2 4 3 4 ( 2 2 ) ( 2 2 ) ( 2 2 ) ( ) 2( ) 2( )( ) 2( )( n a a b b b b b b c c p a a b b b b b b c c p p p p a a b b b b b b c c p p p p p Q p p Q Q b b p Q p Q p Q b b = \u2212 \u2212 + + \u2212 + \u2212 \u2212 \u2212 + \u2212 + \u2212 + \u2212 + + + \u2212 + \u2212 \u2212 + + \u2212 + \u2212 + \u2212 + \u2212 \u2212 \u2212 + + + \u2212 2 2 4 3 3 4 2 3 3 2 2 3 4 4 2 2 2 3 4 2 3 4 2 3 4 2 3 4 ) 2( )( ) ( )( 2 ) ( )( 2 ) p Q p Q p Q b b p Q p Q p Q p p Q Q Q p p p Q Q Q + + + \u2212 + + \u2212 \u2212 + \u2212 \u2212 + + 11 2 2 3 4 4 2 3 4 3 3 2 4 4( ( ) ( ) ( ))n a p p p a p p p a p p p= \u2212 + \u2212 + \u2212 + 2 2 2 2 2 2 2 2 12 3 4 2 2 4 2 3 2 3 2 3 2( ( ) ( ) (n a a b a a b b b b a a= \u2212 \u2212 + \u2212 + \u2212 \u2212 \u2212 2 2 2 2 2 2 3 4 2 3 4 3 4 2 2 4 3 ) ( ) ( ) ( )b b b b b b b b c b b c+ \u2212 + \u2212 + \u2212 \u2212 \u2212 2 2 2 2 2 3 4 3 4 2 2 4 3 2 3 4 2 2 2 2 2 2 2 3 4 2 3 3 2 4 4 3 4 3 2 2 2 2 2 4 2 3 4 2 2 4 2 2 3 3 4 2 2 2 2 2 2 4 2 4 2 4 2 2 3 2 2 3 ( ) ( ) ( ) ( ) ( 2 2 ) ( ) ( 2 2 2 2 ) b b c b b p b b p b b p a a b b b b b b c c p p Q b b Q a a b b b b b b c c p p b Q b Q Q Q + \u2212 + \u2212 \u2212 \u2212 + \u2212 + \u2212 \u2212 + + \u2212 + \u2212 + \u2212 + \u2212 \u2212 \u2212 + \u2212 + \u2212 + \u2212 + \u2212 \u2212 + + 2 2 2 2 2 4 2 3 2 3 3 2 4 2 2 ( ) ( 2b b Q Q a a b b b b+ \u2212 + + + \u2212 + \u2212 \u2212 2 2 2 2 2 3 4 2 3 2 3 2 2 4 2 2 2 2 2b b c c p p b Q b Q Q+ + \u2212 + \u2212 \u2212 + + 2 2 3 3 4 3 3 4 2 3 2 3 4 2 2 ) ( ) )b Q b Q Q Q b b Q Q Q+ \u2212 \u2212 + \u2212 \u2212 + )2 3 4 2 2 3 2 4 3 34 ( )( ) ( ( ){p p p b Q p p p b Q\u2212 \u2212 \u2212 + \u2212 \u2212 + 2 3 4 4 4 ( ) ( )p p p b Q }+ \u2212 \u2212 13 2 2 3 4 4 2 3 4 3 3 2 4 4( ( ) ( ) ( ))n a p p p a p p p a p p p= \u2212 \u2212 + \u2212 + \u2212 + 2 2 2 2 2 2 14 3 2 3 4 4 3 4 3 4 2 2{( 2 ( ) )n a a a a a b b c c p= \u2212 + \u2212 + \u2212 + \u2212 + 2 2 2 2 2 2 2 2 3 3 4 4 2 4 2 4 ( 2 2a a a a a a b b c c+ \u2212 + \u2212 + \u2212 + \u2212 2 2 2 2 2 2 3 2 3 2 3 2 4 3 4 2 2 2 2 2 2 2 3 2 3 2 3 4 2 3 4 2 2 3 4 2 3 4 2 3 2 4 3 2 2 2 4 3 4 2 3 4 2 3 4 ) ( 2 2 ) ( ) 2 ( ) ( ) 2 ( ) ( ) 2 ( ) ( ) } p p p p a a a a a a b b c c p p p p p p b p p Q p p Q b p p Q p p Q b p p Q p p Q + \u2212 \u2212 \u2212 \u2212 + + \u2212 + \u2212 + \u2212 + \u2212 + \u2212 + + \u2212 + \u2212 \u2212 \u2212 + \u2212 + + \u2212 15 4 2 2 3 3 2 2 3 3 2 3 3 4 4 3 3 4 4 3 2 2 4 4 2 2 4 4 4{ ( } ( ) ( )) n a b p b p p Q p Q a b p b p p Q p Q a b p b p p Q p Q = \u2212 + + \u2212 + \u2212 + + \u2212 + \u2212 \u2212 + 16 2 3 4 2 2 3 2 4 3 3 2 3 4 4 4 4{ ( )( ) ( )( ) ( ) ( )} n p p p b Q p p p b Q p p p b Q = \u2212 \u2212 \u2212 + \u2212 \u2212 \u2212 \u2212 \u2212 2 2 2 2 17 3 4 2 2 2 2 2 2 ( )( 2 2 2 4 2 )n a a b c p b Q Q= \u2212 \u2212 \u2212 \u2212 + \u2212 2 2 2 2 2 4 3 3 3 3 3 3 ( )(2 2 2 4 2 )a a b c p b Q Q+ \u2212 + + \u2212 + 2 2 2 3 2 3 2 3 4 4 4 ( ) 2 2( ) 2 2a a { a a a a a a b+ \u2212 \u2212 + + \u2212 \u2212 2 2 2 4 4 4 4 4 2 2 4 2c p b Q Q }\u2212 \u2212 + \u2212 2 2 2 2 1 1 6 2 4 m n n n n= + \u2212 \u2212 2 1 3 6 7 2 2 ,m n n n n= + 3 2 3 4 5 2 2 ,m n n n n= + 4 1 2 2m n n= 2 2 2 2 2 5 2 3 4 5 7 ,m n n n n n= + + + + 2 2 6 1 2 ,m n n= \u2212 7 1 3 2m n n= 8 2 3 2 ,m n n= 9 1 2 2 ,m n n= 2 2 10 2 3 ,m n n= + 11 6 13 2m n n= 2 12 2 1 2 1 6 14 6 13 7 5 8 2 2 2m C n B n n n n n n n n= + + + + 13 4 8 16 6 2 2m n n n n= + 14 2 1 2 2 1 4 15 6 2 2 6 4 9 11 5 16 7 2 2 2 2 2 m C n n A n n n n B n n n n n n n n = + + + + + + 15 2 1 3 2 1 5 17 6 2 3 6 2 1 7 14 7 5 9 2 2 2 2 m C n n A n n n n B n n B n n n n n n = + + + + + + 16 2 2 3 12 4 2 3 4 10 5 2 2 5 15 7 2 2 7 2 2 2 2 m C n n n n A n n n n A n n n n B n n = + + + + + + 17 11 4 2m n n= 2 18 2 3 12 5 2 3 5 17 7 2 3 7 2 2m C n n n A n n n n B n n= + + + + 2 19 2 2 10 4 2 2 4 2m C n n n A n n= + + 2 2 20 13 8 m n n= + 21 2 1 13 13 14 2 1 8 8 9 2 2m B n n n n A n n n n= + + + 22 13 16 11 8 2 2m n n n n= + 2 2 23 2 1 2 1 14 14 13 17 2 13 3 12 8 2 2 3 8 2 1 9 9 2 2m D n B n n n n n B n n n n A n n A n n n = + + + + + + + + 24 13 15 2 13 2 10 8 2 2 8 2 1 11 2 2m n n B n n n n A n n A n n= + + + + Closed-Form Forward Kinematics Solutions of a 4-DOF Parallel Robot 863 2 1 16 14 16 11 9 2 2B n n n n n n+ + + 2 2 25 11 16 m n n= + 26 2 1 12 2 1 17 14 17 2 1 3 2 14 3 12 9 2 3 9 2 2 2 m A n n B n n n n D n n B n n n n A n n = + + + + + + 2 2 2 27 10 15 2 10 2 2 15 2 2 2 m n n A n n B n n D n= + + + + 28 10 12 15 17 2 12 2 2 17 2 2 10 3 2 15 3 2 2 3 2 2 2 m n n n n A n n B n n A n n B n n D n n = + + + + + + 10 11 15 16 2 11 2 2 16 229 2 2m n n n n A n n B n n= + + + 30 11 12 16 17 2 11 3 2 16 3 2 1 10 1 15 14 15 2 1 2 2 14 2 10 9 2 2 9 2 2 2 2 2 2 m n n n n A n n B n n A n n B n n n n D n n B n n n n A n n = + + + + + + + + + + 2 2 2 31 12 17 2 12 3 2 17 3 2 3 m n n A n n B n n D n= + + + + 32 13 6 2m n n= 2 33 1 1 1 1 6 14 6 13 7 5 8 2 2 2m C n B n n n n n n n n= + + + + 34 4 8 16 6 2 2m n n n n= + 35 11 5 16 7 1 1 2 1 1 4 15 6 1 2 6 4 9 2 2 2 2 2 m n n n n C n n A n n n n B n n n n = + + + + + + 36 11 4 2m n n= 37 1 1 3 1 1 5 17 6 1 3 6 1 1 7 14 7 5 9 2 2 2 2 m C n n A n n n n B n n B n n n n n n = + + + + + + 38 1 2 3 12 4 1 3 4 10 5 1 2 5 15 7 1 2 7 2 2 2 2 m C n n n n A n n n n A n n n n B n n = + + + + + + 2 39 1 2 10 4 1 2 4 2m C n n n A n n= + + 2 40 1 3 12 5 1 3 5 17 7 1 3 7 2 2m C n n n A n n n n B n n= + + + + 2 2 41 13 8 ,m n n= + 42 1 1 13 13 14 1 1 8 8 9 2 2m B n n n n A n n n n= + + + 43 13 16 11 8 2 2m n n n n= + 2 2 44 1 1 1 1 14 14 13 17 1 13 3 12 8 2 1 3 8 1 1 9 9 2 2m D n B n n n n n B n n n n A n n A n n n = + + + + + + + + 2 2 45 11 16 m n n= + 46 13 15 1 13 2 10 8 1 2 8 1 1 11 1 1 16 14 16 11 9 2 2 2 2 m n n B n n n n A n n A n n B n n n n n n = + + + + + + + 47 10 11 15 16 1 11 2 1 16 2 2 2m n n n n A n n B n n= + + + 48 1 1 12 1 1 17 14 17 1 1 3 1 14 3 12 9 1 3 9 2 2 2 m A n n B n n n n D n n B n n n n A n n = + + + + + + 2 2 2 49 10 15 1 10 2 1 15 2 1 2 m n n A n n B n n D n= + + + + 50 10 12 15 17 1 12 2 1 17 2 1 10 3 1 15 3 1 2 3 2 2 2 m n n n n A n n B n n A n n B n n D n n = + + + + + + 51 11 12 16 17 1 11 3 1 16 3 1 1 10 1 1 15 2 2m n n n n A n n B n n A n n B n n= + + + + + 14 15 1 1 2 1 14 2 10 9 1 2 9 2 2 2n n D n n B n n n n A n n+ + + + + 2 2 2 52 12 17 1 12 3 1 17 3 1 3 m n n A n n B n n D n= + + + + )53 1 2 1 1 6 2 6 5 1 5 2 6 1 6 2 (2 2 2 2 2 2 2 2 m c c n b n b n n p n p n Q n Q = \u2212 + \u2212 \u2212 + \u2212 + 54 1 2 2 4 4 7 1 7 2 (2 2 ) 2 1 2 2 2 2m c c n a n a n n p n p= \u2212 + \u2212 \u2212 + 55 4 1 6 1 4 2 6 2 2 2 2 2m n p n p n p n p= \u2212 \u2212 + + 56 1 2 3 5 5 1 7 2 7 7 1 7 2 (2 2 ) 2 1 2 2 2 2 2 2 m c c n a n a n b n b n n Q n Q = \u2212 + \u2212 + \u2212 \u2212 + 57 8 1 8 2 16 1 16 2 2 2 2 2m n p n p n p n p= \u2212 + + \u2212 58 8 8 1 13 2 13 1 1 9 1 2 1 2 2 2 2 2 1 2m a n a n b n b n a n p n p= \u2212 + \u2212 + \u2212 1 2 9 2 13 1 13 2 1 2 1 2 2 2 2 2 (2a n p n p n Q n Q b n p\u2212 + \u2212 + \u2212 15 1 2 2 2 15 2 2 1 1 2 2 2 2 2 2 2 2 )n p b n p n p n p Q n p Q\u2212 \u2212 + \u2212 + 59 11 1 13 1 11 2 13 2 2 2 2 2m n p n p n p n p= \u2212 \u2212 + + 2 2 2 2 2 60 16 1 16 2 1 1 2 1 1 1 2 1 1 1 2 2m n p n p a n a n b n b n c n= \u2212 + \u2212 + \u2212 + \u2212 2 2 1 1 9 2 9 1 14 2 14 1 3 1 2 2 2 2 2c n a n a n b n b n a n p+ + \u2212 + \u2212 + 2 2 12 1 1 1 2 3 2 12 2 1 2 1 1 1 2 2 2 2n p n p a n p n p n p b n Q\u2212 \u2212 \u2212 + + + 2 2 14 1 1 1 2 1 2 14 2 1 2 2 2 2n Q n Q b n Q n Q n Q\u2212 \u2212 \u2212 + + 61 9 9 3 12 1 3 12 2 2 1 2 2 2( 1 ) ( 2 2 2 )m a n a n a n n p a n n p= \u2212 + \u2212 + \u2212 + 2 2 2 2 14 1 2 1 2 1 1 2 2 ( ) ( 1 2n b b Q Q n a a b b+ \u2212 \u2212 + + \u2212 + \u2212 + 2 2 2 2 2 2 1 2 1 2 1 1 1 2 2 2 2 2 )c c p p b Q Q b Q Q\u2212 + \u2212 + + \u2212 \u2212 + 16 1 2 2 ( )n p p+ \u2212 + 62 10 1 1 3 17 3 1 15 1 2 1 2 2 2 3 17 3 2 2 2 2 2 2 2 2 1 2 1 2 2 2 2 2 1 2 1 1 1 2 2 2 2( 1 2) 2 ( ) 2 ( ) 2 ( ) ( 1 2 2 2 ) m a a n p b n n n Q n b b Q Q p b n n n Q n a a b b c c p p bQ Q b Q Q = \u2212 + \u2212 \u2212 + \u2212 \u2212 + + \u2212 + + + \u2212 + \u2212 + \u2212 + \u2212 + + \u2212 \u2212 + 2 2 2 2 2 2 63 3 3 1 3 2 3 1 3 2 3 12 2 2 12 1 17 2 17 3 1 3 2 1 3 1 1 2 2 1 2 2 2 2 2 m a n a n b n b n c n c n a n a n b n b n n p n p b n Q = \u2212 + \u2212 + \u2212 + + \u2212 + \u2212 \u2212 + + 2 2 17 1 3 1 2 3 2 17 2 3 2 1 2 1 15 1 2 2 2 15 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 "
        ],
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        "image_filename": "designv11_28_0003057_ecc.2007.7068615-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003057_ecc.2007.7068615-Figure1-1.png",
        "caption": "Fig. 1. The drone helicopter benchmark.",
        "texts": [
            " Simulations without network constitute the reference for the subsequent analysis. Section III presents some simulation studies of the main faults related to sensors and actuators. Section IV proposes a preliminary analysis of the faults induced by the network. M 4332ISBN 978-3-9524173-8-6 A drone with 4 rotors is regarded as a composition of two PVTOL (Planar Vertical Take off Landing) problems whose axes are orthogonal allowing a movement of six degrees of freedom [6]. The four electric motors, driving the four blades, provide the thrust for the movement of the drone (Fig. 1). To develop the dynamic equations, two frames are considered, an inertial frame (or reference) R (position) and a frame B attached to the drone (orientation). The dynamic model is described by the fundamental equations of dynamics, linking accelerations and torques. The orientation (or attitude) of the drone is given by three rotation angles with respect to frame B: yaw (\u03c8), pitch (\u03b8) and roll (\u03c6). \u03d6 is the angular velocity of the drone measured by the rate gyros in frame B. The drone attitude is represented by a quaternion q which is a 4 dimensions vector [7]"
        ],
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    },
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        "image_filename": "designv11_28_0000485_robot.2002.1014296-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000485_robot.2002.1014296-Figure4-1.png",
        "caption": "Figure 4 Convex set formed by 2 and 3 boundary hyperplanes",
        "texts": [],
        "surrounding_texts": [
            "must be satisfied, where ri E R2 is the position vector of ith finger, d l of ki l , hi2 will not become 0 at the same time, and 8 denotes the cross product of vectors. 2.2 Selecting Edge Candidates\nWe select candidates for the successful grasp from all combinations of the object edges by using the force equilibrium condition eq. (2), that can be rewritten as\nE1 k = 0 E R2, k 2 0, (4) A\nA El=[eii e12 e21 e22 en1 enz] ERzXZ\", ( 5 )\nk=[k i i kiz k21 kzz ... knl knzlT E R2\". (6) The solution set of k in eq.(4) can be represented by a convex polyhedral cone [7], that is\nk = H l a = [hu, hla, . a - , hlm]a, Q 2 0, (7)\n(8)\nwhere hlj, j = 1,2,. . . , m are span vectors of the polyhedral cone. a is a coefficient vector representing the component of hl, , j = 1,2,. . . , m. If IC does not exist, the combination of edges can be excluded. If IC exists, the combination of edges will be one of graspable candidates. 3 Graspable Finger Posit ion Regions 3.1\n~ y = [ a 1 A a2 a m I T E R m ,\nBoundary Hyperplanes of Finger Position Region\nThe fingertip position vector on ith edge can be described as\nwhere roi E R2 is a vertex position vector of ith edge, ti E Ra the direction vector of the edge, and l i the position variable (see Fig.1). When the length of i th edge is L,, the bound of l i is 0 5 li 5 L;.\nFor n edges touched by n fingers, let\nr; = rgi f l i t ; , i = 1,2,..* ,n, (9)\n(10)\n0 5 l I L , (11)\n(12)\nA Z = [ I 1 12 ... lnIT E R\"\nrefer to a Finger Position Vector, whose bounds are\nA L = [Li L2 - * * LnIT E R\".\nIn this paper, the permissible region of 1 is called as Graspable Finger Position Region (GFPR hereafter) that meets the force closure grasp, the force and the moment equilibrium, and the edge length bounds for the stable grasp of a object.\nSubstituting eqs.(7) and (9) into eq.(3), the equation of variables 1 and a can be obtained as\n(lTA + b)k = (ZTA + b)Hla = 0, a 1 0, (13)\nwhere A and b are denoted its\n(14)\n[tl@l 0 1 x 2 *. . 01x2\ne12 Om1 Ozxl 02x1 Ozxi OzXl e21 e22 02x1 Ozxi GR2nxzn , (15) 1 . . . . . . . . . . . . . . . . ., . . . .\nA b = [ [ ~ 0 1 @ ) 1 [ ~ o z B ] ... TO^@]] EzE RlXZn, (16)\n(17)\n(18)\n[ti 8 ] = [-Gy tiS] E RlX2<\n[Toi 8 1 = [ - T N ~ ~ O i r ] E R\"'.\nEq.(13 shows a nonlinear problem with respect to the\nintroduce boundary hyperplanes of 1 corresponding to the span vectors of polyhedral cone of eq.(7). Then, we derive an algorithm to determine the GFPR using the boundary hyperplanes.\nEq.(13) represents a hyperplane of 1 for a given a. From eq.(7), the solution set of IC is a convex polyhedral expressed by m span vectors hlj, j = 1,2,...,m . For one span vector hlj where crj = 1, as = 0, s = 1,2, .- . ,m, s # j, we can obtain one hyperplane Pj. For n span vectors of I C , we CM obtain m hyperplanes\nP,={ZI(ZTA+b)hl, =O}, j=1 ,2 , . . . ,m . (19)\nEach Pj for span vector hlj is a boundary hyperplane of the GFPR and divides the finger position configuration space R\" into two hemi-spaces\nPT = {ZI(ZTA+b)hlj 2 01, j = 1,2,...,m, (20) PJT ={ll(ZrA+b)hlj SO), j = l , 2 , . . - , m . (21)\nvariabes i Z and a. To solve the problem linearly, we\n3.2\nAccording to eq.(13), the graspable finger position vector 1 corresponding two span vectors hl, and hl, of IC exists in the following set (see Fig.2)\nGFPR Formed by Two Hyperplanes\nWqr={Z I (Z*A + b) h ~ q * q + ( lTA+ b) hlr a r d , - a q , ~ ~ ~ 2 0 ) . (22\nEy(22) shows that Wqr is the linear combination of (1 A+b)hl, and (Z%fb)hl, depending on a, and a,. Because of a,, ar 2 0, the set of 1 satisfying eq.(22) can be obtained by the following proposition.\nProposition 1: Corresponding to the region between the two span vectors h, and h, of k , the set Wqr can be represented using the set of U,, between the boundary hyperplanes P , and Pr, where U,, is expressed as follows (which has been proved in [SI)\nU,, = CJiruu:r 3 (23) u& =P:nP;, u;, = p p np,'. (24)\nFrom the length bounds of object edge, 0 5 1 5 L,",
            "U,, will be divided into 2 convex polyhedrons(shown in Fig.3) as the following:\nV~,=(ZI(Z%+b)hi,>O, (lTA+b)hi,lO, 051<L}, (25) V:,={ZI(Z?4+b)hiq~0, (l?4+b)hlr 20, O<l<L}. (26)\nThus, the GFPR can be represented by Vqr = V:r U Vir, (27)\nand Vi, or V:, can be represented such as D D\nl = x l v d P d , P d Z 0 , x P d = I r (28) d=l d= 1\nwhere, lvd, d = 1,2, -. 1 , D are the vertexes, p d is the barycentric coordinates. The GFPRs are located in the union set of the all of the Vir and Vi,. Generally the union set is a polyhedron but not a convex. 3.3 GFPR Formed by m Hyperplanes\nNow, we give a method for obtaining GFPR formed by m hyperplanes. According to eq.(13), for the set of k formed by m span vectors, the set of 1 can be represented by\nWI= l)x(ZTA+b)hij~j=O, aj20, j = l , 2 , . * * ,m . (29)\nFrom m span vectors of I C , m hyperplanes of Pj , j = 1,2, . . ., m are obtained.\nProposition 2: For the set of k formed by m span vectors, the set W [ can be expressed by the union set U1 of all of the set U,, { m j = 1 1 m\nU I = U uqr = 9 (u&U U&), (30) p,r=l,q#r q,r=l,q#v\nwhere U,, is formed by 2 arbitrary hyperplanes P , and P,, q, r = 1,2 , . . . , m, q # r (which has been proved in the literature [SI).\nMoreover, by considering the length bounds of object edges, from proposition 2 and eq.(27), the GFPR can be expressed as\n(31)\n4 Determining Stable GFPR In the previous section, the GFPR has been obtained as an union set of convex polyhedrons, but is not a convex polyhedron. In general, the stabler grasp can be achieved at these h g e r configuration points where the distances between the points and each hyperplane\nof GFPR polyhedron are farther. If we can iind the biggest inscribed hypersphere of the GFPR polyhedron, the grasp near to the center of the hypersphere will be stabler, when a few errors of the contact points on the actual object exist. In addition, if the volume of a convex polyhedron of GFPR containing the hypersphere is larger, the stable finger position region is larger.\nFrom what has been said above, for the obtained GFPR polyhedron, the Stable GFPR is defined as the convex polyhedron that contains the biggest inscribed hypersphere of the GFPR, and has larger volume. 4.1 Convex Polyhedron of Containing\nIn fact, for a GFPR formed by a boundary hyperplanes, the convex polyhedrons in the GFPR are encircled by the plural boundary hyperplanes from 2 to m and object edge length bounds. In this paper, we give a proposition for considering what convex polyhedron the biggest inscribed hypersphere may lie in. For the finger position set formed by m boundary hyperplanes, the convex set U:, is enclosed by the 2 arbitrary boundary hyperplanes P z and P; , and the U:, is enclosed by Pp and P:. The convex sets, that are enclosed by plural boundary hyperplanes including P: and P; , belong to U:,. The convex sets, that are enclosed by plural boundary hyperplanes including P i and P:, belong to U:,. At first, we consider the convex sets formed by 3 boundary hyperplanes. A hyperplane P , is chosen from m hyperplanes arbitrarily. Because P a does not pardel to P , or P,, the 2 convex sets that are enclosed by P:, P; and Pa(q # r # s) are represented as\nu:f = (p,+np; nP$) c (P:nP;) = U:,, uif = (p,+np; np;) c (P,+np;) = U:,.\nBiggest Hypersphere of GFPR\nproposition 3:\nproof\n(32) (33)\nSimilarly, the 2 convex sets that are enclosed by P i , P,' and P,(q # T # 8 ) are represented as\nU:: = (P;nPf nPt) c (P;nPf) = U:,, U:? = (P;nP: nP;) c (PpnPf) = U&\n(34) (35)\nFrom eqs. 32 - 35), we have U::CU!,, )&cU:,, tJ::CU:,, U:?CU&. (36)\nThus, the convex sets enclosed by P;, P; and P, (q # r # s) belong to the convex set U,, enclosed by P;, P ; . The convex sets enclosed by P; , P$ and P . (q # T # s) belong to the convex set U$ enclosed by Pi, P:.",
            "By the same way, we can also draw the conclusion that the convex sets enclosed by dural hvmmlanes including P i , P; (or P; , P:J defong to the convex sets U!, (or U!-). v , .\nFrom $;position 3, taking the object edge length limits 0 5 1 5 L into account, for the GFPR formed by m hyperplanes, the convex sets that are encircled by more than 2 hyperplanes including P,, P,, and object edge length bounds, belong to the convex polyhedrons ~ & o r V $ . ( q , r = 1 , 2 , . . . , m, q + r ) .\nTherefore, the biggest inscribed hypersphere of the convex polyhedron, that is enclosed by more than 2 hyperplanes including P,, P , and edge length bounds, belongs to the convex polyhedron V& or Vir. It can be seen that the biggest inscribed hypersphere of the GFPR lies in the convex polyhedrons Vt, or V& (q, T = 1, 2 , - . * , m , 42'). 4.2 Distances from One Point to Hyper-\nplanes of Convex Polyhedron The radius of an inscribed hypersphere i s the distance from the hypersphere center to the tangent hyperplane of the convex polyhedron. To find the biggest inscribed hypersphere of a convex polyhedron, we consider the distances from one point to the hyperplanes.\nAs shown in Fig.5, each convex polyhedron Vi, or V:, of GFPR is formed by the boundary hyperplanes\n(ZTA+b)hy=O, j = q , r , q#r, 9 , ~ = 1 , 2 , . . * , m , (37)\nand the edge bound hyperplanes l i = 0, li = Li, i = 1 ,2 , . - . , n. (38)\n(a j , I!) = bj , j = 1,2, ., J, (39) We can rewrite these hyperplanes as - 1\nwhere, J is the number of the hyperplanes forming the convex polyhedron. a; is the normal vector (inward the convex polyhedron shown in Fig.5) of the hyperplane P j . aj and 6; for eq.(37) can be obtained as\n(40) a; = Ahlj, 3 = -bhl j , if (ITA + b)hlj 2 0,\na; = -Ahij, 83 = bhlj , if (ITA+ b)hlj 5 0, (41)\nfor eq.(38), aj and b; can be obtained as a;=@ O...O]T~Rnxt &j=O, i f Z i = O , (42)\n3 -\naj=p . . .p -2 o . . . o l T ~ W X 1 , &=-L;, i f ~ i = ~ i ( 4 3 )\nAs shown in Fig& 1; is the intersection of the hy-\nj\nperplane Pi and the normd line lC1; of P;. distance from the point 1, to Pi . We have\nis the\n(44)\n(45)\n(46)\n1, - 1' - tc.a:. 3 - 3 3\nSince the point 1; is on Pj , from eq.(39) we have (at, J 1:) J =5- j'\nt! I J = (a- , lc) - 3, 3 = 1,2, - a , J. Eqs.(44) and (45) give the distance t: as\n4.3 Biggest Inscribed Hypersphere of Convex Polyhedron\nLet us consider the biggest inscribed hypersphere for each convex polyhedron Vi, or V& (q, r = 1 ,2 , . ... m, q # r ) . Then, we will determine the biggest inscribed hypersphere of GFPR.\nAs shown in Fig.G(a), for a 2D polyhedron, the center of an inscribed hypersphere is determined by 2 bisectors of 2 interior angles formed by 3 hyperplanes. In the same way, for an nD polyhedron, the center of an inscribed hypersphere is determined by n bisectors of n interior angles formed by (n + 1) hyperplanes.\nNow, we consider the method for determining the inscribed hyperspheres of an nD convex polyhedron formed by J ( J 2 (n + 1)) hyperplanes. At first, (n + 1) hyperplanes are chosen arbitrarily from J hyperplanes. The inscribed hypersphere for these (n+ 1) hyperplanes can be solved. Since the distances from the center of the inscribed hypersphere to the tangent hyperplanes are radiuses and meet\n...... t; = t; = tin+1] = ~ c . (47)\n(al, z,) - 81 = (az, le) - 82, (48)\n(al, - Sr = (a3, lc) - 83 , (49)\n=\nFrom eq.(46), we rewrite the above equation as\n.............................. (a19 l c ) - 61 = (a(n+i), lc) - b(n+l)* (50)\nThe inscribed hypersphere satisfying eqs.(48) N (50 is one hypersphere inscribed the (n + 1) hyperplanes dosen from J hyperplanes of the nD convex polyhedron. But it may not be an inscribed hypersphere of the convex polyhedron (reference Fig.G(c)).\nThen, according to eq.( 46), the coefficient of the distance t!. from 1, to hyperplanes forming convex polyhedron and radius rc can be obtained. If 3\nr c < t ; , ;= 1 ,2 , . . . , J (51)"
        ]
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        "image_filename": "designv11_28_0000570_095440802760075021-Figure5-1.png",
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        "caption": "Fig. 5 Geometrical interpretation of the synthesis of pitch circles H1 and H2",
        "texts": [
            " Since the Helicon gear is disc shaped, its backlash control is performed by gear displacement along its axis. This is why these gear pairs are successfully applied when the accurate work of the mechanism requires meshing without backlash. A synthesis model using a pitch contact point solves the following two basic problems: (a) synthesis of the pitch circles; (b) synthesis of the tooth surfaces. Let the skewed axes 1\u20131, axis of the Spiroid pinion \u2026i \u02c6 1\u2020, and 2\u20132, axis of the Spiroid gear \u2026i \u02c6 2\u2020, be given. Their mutual position (shown in Fig. 5) is completely determined by the angle d 2 \u20260; p=2\u0160 and centre distance, offset aw. Let P be a contact point of the pair of conjugate surfaces S1 and S2. Pitch circles H1 and H2 are displaced in different half-spaces, with respect to the plane Tm which contains the tangents to these circles at point P. Pitch circle planes are perpendicular to the axes 1\u20131 and 2\u20132 respectively. Radii r1 and r2 of both circles, together with eight other parameters d; aw, ri; ai, yi; di \u2026i \u02c6 1; 2\u2020, uniquelydetermine the pitch circles in space"
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    {
        "image_filename": "designv11_28_0003276_s00158-008-0298-4-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003276_s00158-008-0298-4-Figure2-1.png",
        "caption": "Fig. 2 A body coming into contact with a surface. a Definition of initial gap h and displacement u. b Lagrange multiplier \u03bb as reaction force preventing penetration. c Contact penalty as spring with stiffness kg, allowing penetration",
        "texts": [
            " Alternatively, Raous et al. (1999) and Wriggers (2002) introduce adhesion forces only when the gap becomes zero. These forces are a function of the viscosity of the bond material and are rate dependent. This formulation is more appropriate for macro-scale adhesive problems such as those involving the delamination of composite materials and is not explored in this paper. 2.1 Contact model To illustrate the penalty contact formulation, consider a one-dimensional one degree of freedom (DOF) contact example, shown in Fig. 2. For an elastic body subject to conservative external forces, the potential energy of the system can be expressed as = U \u2212 W + a(g) (1) g = h \u2212 u \u2265 0 (2) Here U is the internal strain energy, W is the external work and a is the adhesive energy in the system, defined as a function of the gap, g. Contact occurs when g is reduced to zero. To account for this, the energy minimization problem that arises in seeking the equilibrium displacement field is constrained by the inequality (2), where h is the initial distance between (a) (b) (c) the points closest to each other on the surfaces coming into contact and u is the relative displacement of these points"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000264_s0022-460x(02)01392-5-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000264_s0022-460x(02)01392-5-Figure3-1.png",
        "caption": "Fig. 3. Support configuration between flexible shaft and flexible basis.",
        "texts": [
            " In this section, a relationship for h is derived as a function of the generalized co-ordinates of the supporting structure (Eq. (4)) and the shaft (Eq. (5)). The shaft deformation is governed by its elastic curve (deformation of its centerline). Due to the high local rigidity of the shaft, its cross-sectional geometry is assumed to stay circular before and after deformation. Since the length of each support is relatively short, the deformation e of the shaft centerline along each support (see Fig. 3) is considered to be quadratic. For each support, the deformations e1; e2 and e3 at the left end, middle and right end locations are used to define the shaft deformation distribution e\u00f0z\u00de along the support length as e\u00f0z\u00de \u00bc c1z 2 \u00fe c2z \u00fe c3: \u00f011\u00de The constants c1; c2 and c3 can be expressed in terms of e1; e2 and e3: Therefore, Eq. (11) can be rewritten as e\u00f0z\u00de \u00bc A1\u00f0z\u00dee1 \u00fe A2\u00f0z\u00dee2 \u00fe A3\u00f0z\u00dee3; \u00f012\u00de where A1\u00f0z\u00de \u00bc 2 z Lb 2 3 z Lb \u00fe 1; A2\u00f0z\u00de \u00bc 4 z Lb 2 \u00fe4 z Lb ; A3\u00f0z\u00de \u00bc 2 z Lb 2 z Lb ; \u00f013\u00de where Lb is the length of the support. Assuming temporarily that the support structure is undeformed, the clearance distribution between the outer surface of the shaft and the inner surface of the support can be expressed as [26] hr \u00bc c ex cosj ey sin j; \u00f014\u00de where, as shown in Fig. 3, j \u00bc tan 1\u00f0ey=ex\u00de: \u00f015\u00de The quantity c represents the original radial clearance at the undeformed state, and ex and ey represent the shaft deformations in the x and y directions, respectively. Substitution of Eq. (12) into Eq. (14) yields hr \u00bc c \u00bdA1\u00f0z\u00de A2\u00f0z\u00de A3\u00f0z\u00de cosj ex1 ex2 ex3 8>< >: 9>= >; \u00bdA1\u00f0z\u00de A2\u00f0z\u00de A3\u00f0z\u00de sin j ey1 ey2 ey3 8>< >: 9>= >; \u00bc c \u00bdTc fxcg; \u00f016\u00de where exi and eyi ; i \u00bc 1; 2; 3 are the shaft deformations at node i in the x and y directions, respectively (see Fig. 3). The transformation matrix \u00bdTc in Eq. (16) is \u00bdTc \u00bc \u00bdA1\u00f0z\u00decosj A1\u00f0z\u00desinj A2\u00f0z\u00decosj A2\u00f0z\u00desin j A3\u00f0z\u00decosj A3\u00f0z\u00desin j \u00f017\u00de and fxcg \u00bc f ex1 ey1 ex2 ey2 ex3 ey3 g T: \u00f018\u00de The above vector fxcg is a part of the retained d.o.f. vector fxc rg of the shaft (see Eq. (6)). A large number of non-linear spring elements are used in the circumferential direction (Fig. 4). Each non-linear spring element connects a node on the axis of the shaft with a point on the inner surface of the support. The force\u2013displacement relationship of the spring element depends on the clearance between the inner surface of the support and the outer surface of the shaft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001211_robot.2001.933067-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001211_robot.2001.933067-Figure5-1.png",
        "caption": "Figure 5: A sketch of the experimental setup",
        "texts": [
            " 5 Experiments The mobile robot is equipped with a CCD color Toshiba camera (focal length is 7.5 mm) that acquires images about the local environment. At present, we use a LP-310 Plus laser pointer (wavelength is 635 nm, power output is 2 mW) that provides a red light. In order to direct the laser beam onto the the desired positions on the floor, this laser is mounted onto a pan-tilt mechanism equipped with two step motors of a Canon communication camera VC-C1, as it is shown in Fig. 4. The experimental setup is sketched in Fig. 5, where the robot\u2019s camera is in the inclined position relative to the ground. The laser light beacon is seen in the image as a bright spot of the size of a few pixels, as illustrated in Fig. 6 and Fig. 7 . The projected laser light on the ground has a blur contour and the shape of the beacon is elliptical, shown in Fig. 7 . The central part of the beacon in the image is white-colored that shows saturation of the camera. The pixels indicated by bold contours in Fig. 7 illustrate the horizontal and vertical differencing applied in order to find the pixels where the intensity change of the red color is maximal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003094_j.mechmachtheory.2007.12.001-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003094_j.mechmachtheory.2007.12.001-Figure5-1.png",
        "caption": "Fig. 5. RR-PR-PP Assur group.",
        "texts": [
            " 4), the internal revolute joint C lies on the fourth order curve of the A1BEF four-bar mechanism of the PRPR type [5,12]. Also C belongs to the straight line parallel to the sliding direction of the external prismatic joint D1 and located at distance d4. The point C is the intersection point of the fourth order curve with a straight line and four real intersection points exist at most. Therefore the maximum number of the assembly modes of the PR-PR-RP triad with one internal and two external prismatic joints is four. In Fig. 5 the RR-PR-PP triad with one internal and two external prismatic joints is illustrated. The coordinates of the external joint A (0,0) and of the auxiliary points D (d,0) and F (xF, yF) situated on the sliding direction of the corresponding external prismatic joint are known, as well as the length of links lAB, lBC and the angles h1, h2 and a. The distances d1 d2, d3 and d4 are also given. The position of the triad links can be described by the coordinates of the internal joint B (x,y) and the displacement s3",
            " Finally, the displacements s1 and s2 can be evaluated from the ABEFA loop: x d1 cos\u00f0a h2\u00de \u00bc xF \u00fe s1 cos h2 d3 sin h2 \u00f0s2 \u00fe r\u00de sin\u00f0a h2\u00de \u00f071\u00de y \u00fe d1 sin\u00f0a h2\u00de \u00bc yF \u00fe s1 sin h2 \u00fe d3 cos h2 \u00f0s2 \u00fe r\u00de cos\u00f0a h2\u00de \u00f072\u00de From Eqs. (71) and (72), after transformations, yields a system of two linear equations in s1 and s2. Solving this system the displacements s1 and s2 are calculated. The maximum number of the assembly modes of triad is two and this is confirmed by the following consideration: For a given position of the external joints A, D1 and F1 (see Fig. 5), the internal joint C lies on the second order curve (circle) of the ABEF1 four-bar mechanism of the RRPP type [5,12]. Also C belongs to the straight line parallel to the sliding direction of the external prismatic joint D1 and located at distance d4. The point C 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 this triad is two. In this section the proposed procedures are applied to corresponding numerical examples",
            " The solving of the final fourth order polynomial equation (65) leads to two real roots and two complex roots (see Table 4) for the input data here considered. For each real value of the displacement s1, using back substitution, the displacement s2, s3 and the coordinates of the internal revolute joints B, C and E are calculated. The corresponding two assembly modes of the PR-PR-RP triad are illustrated in Fig. 9. Example 5. The geometrical data and the coordinates of the points A, D and F of the RR-PR-PP triad (see Fig. 5) are inserted in the upper part of Table 5. The solving of the final second order polynomial leads to two real roots (see Table 5) for the input data here considered. For each real value of the displacement s3, using back substitution, the coordinates of the internal revolute joint B and the displacements s1 and s2 are calculated. The corresponding two assembly modes of the RR-PR-PP triad are illustrated in Fig. 10. Table 5 Data and solutions of the RR-PR-PP Assur group Data lAB = 45, lBC = 49, xF = 116"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000567_robot.1992.220303-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000567_robot.1992.220303-Figure3-1.png",
        "caption": "Figure 3: Two SCARA robots cooperating to manipulate an object.",
        "texts": [
            " In this case, only the coordinate movement of joints displacing the object along the 2-direction is possible for the system. Note that the same result is obtained if any single contact is modeled as soft-finger. If any of the contacts are complete-constraint, all the C<j block matrices result empty, and hence Nm = Ne = Ni = N. = 0. There are no possible motions for the mechwm, as can be easily understood from direct inspection of the system. 4.2 Case study 2 In this example, we will consider two four-degreesof-freedom, SCAM-type robots manipulating an object, M shown in fig. 3. Contact points are located at cl = (L L L)T, and c2 = ( 3 L L L)T; the corro sponding normal unit vectors are nl = (1 0 O)', and PI = (-1 0 O)T. The origin of the link reference frames are at 01 = (0 2~ o ) ~ , 0 2 = ( L 2~ o ) ~ , 0 8 = (L L o)', 07 = ( 4 L L 2L)*, and 0 8 = (4L 0 2L)T, respectively. The joint axes are q = s2 = = s4 = (0 0 l)T, and SS = S6 = s7 = sg = (1 0 O)T. Note that joints 4 and 5 are prismatic. Accordingly, the G and D matrices are: 0 4 = ( L L o )T , 0 5 = ( 4 5 L L)T , 0 6 = (4& L G= 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 - 1 1 0 - 1 1 1 0 0 1 0 0 -1 1 0 - 1 8 0 0 0 1 0 0 1 1 0 - 1 1 0 - 8 0 1 0 0 1 0 DT = 0 0 0 1 0 0 0 0 0 0 0 0 ' r l l 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 o o ~ ~ o o o o o o o o 0 0 0 0 0 0 0 0 0 1 0 0 o o ~ o i o o o o i o o r 0 0 0 0 1 1 0 0 0 1 0 0 I If two complete-constraint contacts are used to model the grip on the object, we obtain / ; - ; -1 0 0 \\ 0 0 1 1 The system in this configuration has connectivity Ne = 3, no redundancy nor indeterminacy. The feasible motions for the object are all pure translations (the last three rows of C11 are zeroes), achieved by moving the joints with suitable combinations of the columns of c22. On the other hand, if two hard-finger contacts are assumed to be in effect (which can be imagined if the grippers in fig. 3 are substituted with two sticks), we have: C = 0 1 -1 1 0 0 0 0 0 0 0 0 0 0 - L O 0 0 0 0 L 0 0 0 O O L O O 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 L - L 0 L 0 0 L - L 0 0 0 0 0 0 0 1 - 3 0 1 -1 0 1 - a 0 1 - 1 a a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 - In this case, the mechanism has full connectivity (Ne = 6), although one of the movements of the object is quasi-statically indeterminate (Ni = 1). The system also exhibits redundant degrees of freedom in this configuration (N, = 2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001324_6.2002-4565-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001324_6.2002-4565-Figure1-1.png",
        "caption": "Fig. 1. Two-Link Flexible Robot",
        "texts": [
            " They include; inverse dynamics (IDC), linear quadratic regulator (LQR), linear quadratic Gaussian (LQG) with linearized Kalman filter, extended Kalman filter (EKF) and fuzzy logic adaptive extended Kalman filter (FLAEKF), fuzzy logic (FLC) and, repeated learning (RL). A description of a command shaping, inverse kinematics technique for tracking a square trajectory studied by Banerjee and Singhose is included for comparison.3, 4 Their work stimulated the studies reviewed in this paper and is alluded to in previous papers.6, 7, 8, 9, 10 The two-link flexible robot, in Fig. 1, has a shoulder joint revolute 2\u03c0 rad and an elbow joint oscillating ~3/2\u03c0 rad. Robot motion and vibration modes are planar and its physical parameters taken from Banerjee and Singhose.3, 4 Accurate control of end-effector trajectory tracking for a two-link flexible robot shown in Fig. 1, is restricted by three major difficulties; (i) non-minimum phase behaviour due to finite speed propagation of mechanical waves along the links, (ii) flexural vibrations induced by motion of the flexible links and (iii) nonlinearity of the robot dynamics. To satisfy the requirements for minimal vibration and precise control of long reach flexible robots deployed in spacecraft operations, a control scheme is required that will ensure minimum-phase response, dampening of flexural vibrations and correct modeling of the nonlinear dynamics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000817_s0007-8506(07)60577-0-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000817_s0007-8506(07)60577-0-Figure4-1.png",
        "caption": "Figure 4: a - 3 0 CAD model of die, holder and punch",
        "texts": [],
        "surrounding_texts": [
            "Traditional metal stamping processes involve relevant ms ts linked to the equipments to be utilized and to the required set-up times. The industrial application of traditional metal stamping tech- is therefore e m c a l t y suitable only for large scale produdion (mass produdion). where the m s t s linked to die manufadure and set-up are distributed over a very large n u m e r of starrped parts. On the other hand in the last few decades new relevant and irrpellent needs have arisen such as the produdion of small batches of sheet metal m r q m e n t s . the inaeasing demand of process Rexibillty and finally the necesslty to reduce the time to market of the produds. The m e n t h e d needs are inmsistent Mh the traditional metal stamping processes. As a msequence two major adions are followed: first of all new forming processes Mich do not require expansive mventional equipments and time m s u m n g set-up operations have been recently proposed [MI; f u r t h e m e rapld tooling techniques have been recently introduced mainly to reduce the time to market of new produds [66]. It should be observed that the -em layer manufaduring technokgies saentmmlty support the mncept of \u2018Rapld Produd Development\u2019. The former applications of rapld tooling for plastic parts manufaduring have been successful and the efforts are ongang irproving materials productrvlty and quallty. On the other hand. when rapd tooling is aimed to the produdion of tools for sheet metal stamping no rapld t d i n g first choice technokgy is evident. T w approaches can be r e q n k e d : thredimensional printing m or seledive laser sintering [KIO] optrons. Layer CNC mt ro l l ed 9 D printing machines are in development for medium and big sized parts. Small sized parts may be mt effedivety produced using other rapld tooling options such as Seledive Laser Sintering. The research here addressed a i m to explore the use of SLS (Seledive Laser Sintering) tech- for this applimtion a m d i n g to the adual state of the art and identny M u r e research diredions."
        ]
    },
    {
        "image_filename": "designv11_28_0002195_3-540-27168-6_4-Figure4.1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002195_3-540-27168-6_4-Figure4.1-1.png",
        "caption": "Fig. 4.1. Principle of using high pressures to accelerate projectile or plates",
        "texts": [
            " The technique uses smoothly increasing \u223c300\u2013400 GPa magnetic pressure pulses to launch plates \u223c200\u2013 300 \u00b5m in thickness to velocities approaching 30 km/s. The absence of shocks in the magnetic loading drive is the key in achieving the enormously high flyer plate velocities while keeping the plate cool. Successful launches of aluminum to \u223c27 km/s and titanium to \u223c22 km/s have been demonstrated. The principle of gun operation is primarily based on using the energy release from highly compressed gases to propel projectiles to high velocities. This technique is schematically depicted in Fig. 4.1. If P (t) is the time dependent driving pressure used to propel a projectile or a plate of mass M in a gun barrel having a cross sectional area A, then it can be shown that the velocity of the projectile at time t, V (t), is given by V (t) = A M \u222b t 0 P (t) dt . (4.1) This principle of gun operation is applicable in the operations of smoothbore gun launchers developed for controlled impact studies. Specifically, in a 100-mm bore single-stage compressed-gas gun a 0.04 GPa gas pressure is used to drive a projectile weighing approximately 1 kg to a terminal velocity of \u223c1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002443_s0007-8506(07)60041-9-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002443_s0007-8506(07)60041-9-Figure8-1.png",
        "caption": "Figure 8: Modular structure of the feeder: the prototype of a linear module.",
        "texts": [
            " Therefore the components move from an electrode to the next one along a straight line and at the same time align their axes with the electrode projection on the working plane. Typical results are shown in the Figure 7: the part (a microgear) moves step by step under the electrodes V-tips. In order to allow the component alignment, the switching period T has necessarily to be increased. The results of preliminary tests have been transferred in an engineered version of the feeder based on modular elements (Figure 8) which can be assembled in a reconfigurable system when required by production needs. By rapid set up changes it is possible to obtain the desired path by assembling straight and angular modules. Each module can be fitted to new requirements (part dimensions, materials and shapes) through the adjustment of mechanical (5 and 6 in Figure 8) and electrical elements (1, 3, 4). In particular vibration amplitude and frequency can be chosen among those sustaining a random Brownian motion of the component. The horizontal position of each platform has to be adjusted (6) in order to avoid a systematic drift of the component towards the borders of the platform. Also the switching period T depends on the component shape and mass, on the pitch of the electrodes and the supply voltage, on the environmental and tribological conditions. The junction between adjacent modules may be critical since the parts tend to remain trapped in the contact zone"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001295_tmag.2003.816258-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001295_tmag.2003.816258-Figure1-1.png",
        "caption": "Fig. 1. General 3-D view of the planar actuator under study.",
        "texts": [
            "ndex Terms\u2014Analytical model of the air gap magnetic field, planar actuator, static forces. I. INTRODUCTION AN ANALYTICAL method for predicting the three-dimensional (3-D) flux density distribution in the air gap of an electromagnetic planar actuator and its propulsion planar force, was developed. Fig. 1 shows a perspective of the prototype under study. The stator has multiphase armature windings placed in such a way that two orthogonal windings are produced: one is assembled to form the coil phases and the other, the coil phases. The armature core is a slotless iron slab. The wireless mover has two NdFeB-type permanent magnets. The mover is attached to a suspension structure with linear bearings that enable bidirectional motion. This results in an actuator with two degrees of freedom. The movement can take place along the axis and axis simultaneously"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002724_978-1-4684-1033-4_13-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002724_978-1-4684-1033-4_13-Figure7-1.png",
        "caption": "FIGURE 7 WIDE COLUMN GEOMETRY SELECTION",
        "texts": [
            " a SK I N = 33,200 PSI a RIB = 83,000 PSI TABLE 3. BUCKLING PREDICTIONS FOR THE CYLINDRICAL SHELL 225 226 L. W. REHFIELD, R. B. DEO AND G. D. RENIERI A wide column design was selected having the same isogrid triangle geometry, stiffener and skin thickness and the same critical strain levels as the 20 inch diameter cylinder. Rib depth was increased to obtain a reasonable longitudinal buckle half wave length. The resulting design is shown in Figure 6. A trade study which led to the selection of rib depth is summarized in Figure 7. General instability load is plotted versus rib depth (d) for various half wave lengths (A). A half wave length of 5.25 inches and rib depth of 0.31 inch were selected which result in the same skin and rib strains (E) at the time of general instability for the wide column as for the cylinder (Ecolumn/Ecyl inder = 1.0). The 5.25 inch buckle half wave length was to be achieved in test by properly restraining the panel. Predicted buckling loads are summarized in Table 4. 228 L. W. REHFIELD, R. B. OED AND G"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003891_s0263574709990683-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003891_s0263574709990683-Figure1-1.png",
        "caption": "Fig. 1. The 3-RRUR spherical parallel manipulator.",
        "texts": [
            " Besides, it was decided that the equivalent planar joint was formed only by R pairs in order to avoid friction phenomena and inaccuracies of the P pairs. In addition, the equivalent planar pair was placed at the beginning of the leg. In so doing the intersection of the axes of the two R joints of each leg coincide with the center of the spherical motion of the moving platform. The kinematic analysis of such type of tripods looks simple since the analysis can exploit the planar nature of each leg and the intersecting condition of their two R joints axes. Figure 1 illustrates the 3-RRUR. The manipulator consists of a fixed base and a moving platform (M) connected to each other by three legs, each with a RRUR kinematic chain. The R pairs connected to the frame are to be considered actuated. As can be observed in Fig. 1, at the nominal pose (zero rotation of the moving platform), each manipulator\u2019s leg belongs to a face of a cube, i.e., the nominal cube. From Fig. 1 it can be seen that the actuated R pairs coincide with three vertices of the nominal cube and that, due to the symmetry, the moving platform is a tetrahedron. The following reference frames are defined in studying the kinematics of the manipulator (Fig. 2). A fixed reference frame OX0Y0Z0, hereafter {0}, with origin O coincident with a vertex of the nominal cube and axes which are pointing along the edges of the nominal cube. A reference frame PXGYGZG, hereafter {G}, attached to the moving platform and with P coincident with a vertex of the tetrahedron"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000545_rob.4620060405-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000545_rob.4620060405-Figure4-1.png",
        "caption": "Figure 4. Prismatic joint.",
        "texts": [
            " Let us first consider two different links with origins Oi and Oi, respectively, that arc interconnected by a revolute joint as illustrated in Figure 3. If ul: is the axial elastic displacement at the end of link i (whose position coincides with the origin of link j ) the constraint conditions can be expressed as xi +(Li + u!) cos@, - xi = 0 yi + (Li + 1.4:) sin Qi - = 0 where Li is the length of the link i in its undeformed configuration. If axial deformations are neglected Eq. (30) can be used to eliminate the Cartesian coordinates of the joints as generalized coordinates. On the other hand Figure 4 illustrates a typical case of prismatic joint. The constraint condition is defined in this case as X i + ( Li + uci) cos Oi = Xi + ( x + N . ( X ) U ; ~ ) cos Oi - C N , ( X ) U ; ~ sin Qi ( 3 I ) a 374 and Journal of Robotic Systems-I989 where the variable x defines the position of the prismatic joint. As indicated above these constraint equations are introduced i n the differential equations of motion by means of the penalty formulation. The corresponding penalty terms impose the necessary coupling between the links"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003319_iet-epa:20060321-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003319_iet-epa:20060321-Figure6-1.png",
        "caption": "Fig. 6 Photo of the micromotor and load",
        "texts": [
            " The parameter of the proportional controller is 60. Then, the d\u2013q axis to a\u2013b\u2013c axis transformation is executed. Finally, a PWM generator outputs the triggering signals, T\u00fe a , T a , T\u00fe b , T b , T \u00fe c and T c , to the inverter. The inverter switches IET Electr. Power Appl., Vol. 2, No. 1, January 2008 to make the micromotor rotate. A closed-loop system is thus obtained. A micropermanent-magnet synchronous motor of diameter 6 mm is used. The motor is manufactured by a Swiss company Maxon with a type EC 6-215551, which is shown in Fig. 6. The input DC voltage of the inverter is 12 V. The sampling interval of the DSP is 100 ms. The parameters of the motor are shown in Table 3. Fig. 7 shows the Bode diagram of W1 21(s) W3 21(s), S(s) and T(s). According to Fig. 7, S(s) is always below W1 21(s) and T(s) is always below W3 21(s). Figs. 8a and b show the measured step input responses of the micropermanent-magnet motor control system. Fig. 8a compares the position responses of the H1 controller and the PI controller. The rise time of the H1 controller is 200 ms; however, it is 500 ms when the PI controller is used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003658_13506501jet540-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003658_13506501jet540-Figure1-1.png",
        "caption": "Fig. 1 Direct acting cam/follower with defined geometry",
        "texts": [
            " In this article, a simple valve train friction model developed by Ball [4], a sub-model of FLAME (Friction and Lubrication Analytical Model for Engines) [5] software, is modified to incorporate the chemical sensitivity of the additives in the engine lubricant. The model is based on the kinematics\u2013dynamics at the geometrical contact surface and includes several important factors to predict minimum oil film thickness, Hertzian stress, friction force, and frictional torque loss around the cam cycle [4]. Although the valve train friction model is capable of analysing all types of cam/follower, in this paper the analysis is confined to a Direct Acting Tappet (DAT) cam/follower as shown in Fig. 1. The cam rotates about its centre \u2018O\u2019 on the camshaft, with \u2018R\u2019 as the instantaneous radius of curvature at the point of contact between the cam and the follower as shown in Fig. 1(b). The kinematic analyses at the point of contact of cam acting against a flat-faced follower [4, 12] provide us with information about the velocity of the contact point relative to the cam and the follower. Thus, the lubricant entrainment speed \u2018Ve\u2019 and the sliding speed \u2018VS\u2019 between the two tribological sliding surfaces are given by equations (1) and (2), respectively, as Ve = 1 2 (Vc + Vf ) (1) Vs = Vc \u2212 Vf (2) where \u2018Vc\u2019 and \u2018Vf \u2019 are the velocities of the point of contact relative to the cam and follower, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000629_a:1004853828657-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000629_a:1004853828657-Figure1-1.png",
        "caption": "Figure 1. A rigid body undergoing a spherical motion with respect to another.",
        "texts": [
            " Further, if Euler\u2019s parameters are arranged as g(t) = cos [ 1 2\u03b8(t) ]+ ux(t) sin [ 1 2\u03b8(t) ] i + uy(t) sin [ 1 2\u03b8(t) ] j + uz(t) sin [ 1 2\u03b8(t) ] k, (2) the resulting quaternion satisfies g(t)[g(t)]\u2212 = cos2 [ 1 2\u03b8(t) ]+ sin2 [ 1 2\u03b8(t) ] [ ux(t) 2 + uy(t)2 + uz(t)2 ] = 1, (3) where [g(t)]\u2212 represents the conjugate of g(t). Thus, g(t) belongs to the group of unit quaternions, a well-known representation of the rotation group, SO(3), see Porteous [6]. PROBLEM STATEMENT. Consider a rigid body m subjected to a spherical motion around a fixed point O, with respect to another rigid body j , see Figure 1. Assume that the spherical motion is represented by a unit quaternion g(t) = cos [ 1 2\u03b8(t) ]+ ux(t) sin [ 1 2\u03b8(t) ] i + uy(t) sin [ 1 2\u03b8(t) ] j + uz(t) sin [ 1 2\u03b8(t) ] k. Determine, for each instant of time, the angular velocity and acceleration, \u03c9(t) and \u03b1(t), of the spherical motion. Before proceeding to solve the problem, it is important to note that although this contribution employs the quaternion representation of the rotation group, the results can be easily extended to any other representation, most notably the orthogonal matrix representation via the corresponding isomorphism. Let \u03b2 a constant vector function in a reference frame or rigid body m, that is subjected to a rotation around a fixed point O, see Figure 1. Then, choosing a coordinate system whose origin is at point O, there is a one-to-one relationship between the constant vector \u03b2 an the point P fixed in the rigid body m. More precisely, the relationship is given by rP/O = \u03c1O = \u03b2, (4) where \u03c1O is the position vector of point P at t = 0. If the rigid body m is subjected to a spherical motion, with respect to the reference system, j , represented by g(t), it is well known, see Brand [7], that the position vector \u03c1(t) of point P at time t is given by \u03c1(t) = g(t)\u03c1O [g(t)]\u2212 , (5) where [g(t)]\u2212 = [g(t)]\u22121 is the conjugate of the unit quaternion g(t), and it is also its inverse under the quaternion product; namely, [g(t)] [g(t)]\u2212 = 1 = [g(t)]\u2212 [g(t)] ",
            " Therefore, since conjugation is an anti-automorphism, see proposition A4, \u03c1\u0307 = g\u0307(g\u2212\u03c1g)g\u2212 + g (g\u2212\u03c1g) (g\u0307)\u2212 = g\u0307g\u2212\u03c1 + \u03c1g(g\u0307)\u2212 = (g\u0307g\u2212)\u03c1 + \u03c1(g\u0307g\u2212)\u2212. (8) By proposition A6, it is known that g\u0307g\u2212 = 1 2 {\u03b8\u0307 u\u0302(t)+ \u02d9\u0302u(t) sin [\u03b8(t)]+ (1\u2212 cos [\u03b8(t)]) u\u0302(t)\u00d7 \u02d9\u0302u(t)}, (9) namely a quaternion with zero real part. Further, by proposition A3, it follows that \u03c1\u0307 (t) = {\u03b8\u0307 u\u0302(t)+ \u02d9\u0302u(t) sin [\u03b8(t)]+ (1\u2212 cos [\u03b8(t)])u\u0302(t)\u00d7 \u02d9\u0302u(t)} \u00d7 \u03c1(t). (10) Thus, the following result has been proved. PROPOSITION 1. Consider a rigid body m subjected to a spherical motion around a fixed point O, with respect to another rigid body j , see Figure 1. Assume that the spherical motion is represented by the quaternion function g(t) = cos [ 1 2\u03b8(t)]+ u\u0302(t) sin [ 1 2\u03b8(t)], where |u\u0302(t)| = 1. Then, the velocity of a point P, \u03c1\u0307 (t), fixed in the rigid body m is given by \u03c1\u0307 (t) = {\u03b8\u0307 u\u0302(t)+ \u02d9\u0302u(t) sin [\u03b8(t)]+ (1\u2212 cos [\u03b8(t)])u\u0302(t)\u00d7 \u02d9\u0302u(t)} \u00d7 \u03c1(t). In order to find the angular velocity, \u03c9, of body m with respect to body j . It is necessary to resort to the following result. PROPOSITION 2. Let m and j be a pair of rigid bodies, then \u03c9 is the angular velocity of body m with respect to body j if, and only if, for any vector \u03b2 , fixed in the rigid body m, it follows that d\u03b2 dt = \u03c9 \u00d7 \u03b2, (11) where d\u03b2/dt represents the time derivative with respect to the reference frame j . Proof. See Kane and Levinson [8] or Rico and Duffy [9]. 2 Now, one can prove the main result of this contribution. PROPOSITION 3. Consider a rigid body m subjected to a spherical motion around a fixed point O, with respect to another rigid body j , see Figure 1. Assume that the spherical motion is represented by the quaternion function g(t) = cos [ 1 2\u03b8(t)]+ u\u0302(t) sin [ 1 2\u03b8(t)], where |u\u0302(t)| = 1. Then, the angular velocity, \u03c9, of body m, with respect to body j , is given by \u03c9 = \u03b8\u0307 (t)u\u0302(t)+ \u02d9\u0302u sin [\u03b8(t)]+ u\u0302(t)\u00d7 \u02d9\u0302u(t){1\u2212 cos [\u03b8(t)]}. (12) Proof. By Proposition 1, the velocity of any point fixed in the rigid body m and therefore the velocity rate of any constant vector in the reference frame m, with respect to the reference frame j , is given by equation (10). By comparing the right hand sides of equations (10) and (11), for arbitrary values of \u03c1(t) or \u03b2 , it follows that \u03c9 = \u03b8\u0307 (t)u\u0302(t)+ \u02d9\u0302u sin [\u03b8(t)]+ u\u0302(t)\u00d7 \u02d9\u0302u(t){1\u2212 cos[\u03b8(t)]}. 2 The result of Proposition 3 can be easily extended to angular acceleration. PROPOSITION 4. Consider a rigid body m subjected to a spherical motion around a fixed point O, with respect to another rigid body j , see Figure 1. Assume that the spherical motion is represented by the quaternion function g(t) = cos [ 1 2\u03b8(t)]+ u\u0302(t) sin [ 1 2\u03b8(t)], where |u\u0302(t)| = 1. Then, the angular acceleration, \u03b1 , of body m, with respect to body j , is given by \u03b1 = \u03b8\u0308 (t)u\u0302(t)+ \u03b8\u0307 (t) \u02d9\u0302u(t) {1+ cos [\u03b8(t)]} + \u00a8\u0302u(t) sin [\u03b8(t)]+ + \u03b8\u0307 (t)u\u0302(t)\u00d7 \u02d9\u0302u(t) sin [\u03b8(t)]+ u\u0302(t)\u00d7 \u00a8\u0302u(t) {1\u2212 cos [\u03b8(t)]} . (13) Proof. It is well known, see Kane and Levinson [8], that \u03b1 = d\u03c9 dt . (14) By direct computation, the reference to the independent variable will be dropped for compactness sake \u03b1 = d dt {\u03b8\u0307 u\u0302+ \u02d9\u0302u sin \u03b8 + u\u0302\u00d7 \u02d9\u0302u (1\u2212 cos \u03b8)} = \u03b8\u0308 u\u0302+ \u03b8\u0307 \u02d9\u0302u+ \u00a8\u0302u sin \u03b8 + \u02d9\u0302u\u03b8\u0307 cos \u03b8 + \u02d9\u0302u\u00d7 \u02d9\u0302u (1\u2212 cos \u03b8)+ + u\u0302\u00d7 \u00a8\u0302u (1\u2212 cos \u03b8)+ u\u0302\u00d7 \u02d9\u0302u\u03b8\u0307 sin \u03b8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002950_6.2006-4369-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002950_6.2006-4369-Figure6-1.png",
        "caption": "Figure 6. Validation of CFX manifold model (left) and VOLSOL conjugated channel model (right) to sub scale test data.",
        "texts": [
            " o The in-house developed 1 D tool TCCOOL is used as a design tool during the concept design of the cooling system layout. This include both using the TCCOOL results in order to compare concepts and also to use TCCOOL values (pressure and temperature) as input for more detailed aero-thermal studies such as the one using CFX. The second purpose of TCCOOL is to make internal load files describing wall and coolant temperatures to be used for mechanical analysis. o For the sandwich channel wall, the in-house flow solver VOLSOL has been used as a conjugated 3 D tool to compare to the TCCOOL tool, see Figure 6. Moreover, the flame side calculations are performed with VOLSOL since the code has been extensively validated for this purpose in previous nozzle extension programs. Flame side calculation includes ISP calculation and contour deformation as well as outlet manifold flow interaction with main jet. o The commercial CFD code CFX has been used for simulation of the complete cooling system. The VOLSOL code is more suited to high Reynolds calculations, while CFX is also valid for low Reynolds. The second advantage of CFX for channel wall calculation is the possibility to export 3D loads to the ANSYS tool for mechanical analysis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002559_tmag.2005.846213-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002559_tmag.2005.846213-Figure5-1.png",
        "caption": "Fig. 5. Distributions of force vectors. (a) x\u2013y plane (z = 58 mm). (b) Birdseye view.",
        "texts": [
            " 4 shows the calculated waveforms of torque and electromagnetic force acting on the rotor when the parameter of is 0.0 and 0.4 mm using the Maxwell stress tensor method and the nodal force method. From Fig. 4(a), although the torque of the nodal force method is larger than that of the Maxwell stress tensor method, it is found that they agree well with each other, and the average torque is almost the same in the state of off-center too. From Fig. 4(b), it is found that the component of force is about 350 N, which is very large when the rotor is off-centered. Fig. 5 shows the distributions of force vectors calculated by the nodal force method [6]. The vectors shown in Fig. 5 are the force vectors which are divided by the total volume of elements including the node so that the size of the vector is not affected by the mesh size. It is found that the force in the right part of the rotor is larger than the left part of that when the rotor is off-centered. Fig. 6 shows the characteristics of nodal force of radial direction and rotation direction on the node A. The fundamental frequency is 240 Hz. The cycle of waveform of nodal force is 90 . Fig. 7 shows the characteristics of nodal force of radial direction and rotation direction on the node B"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001244_ijcnn.2002.1007507-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001244_ijcnn.2002.1007507-Figure1-1.png",
        "caption": "Figure 1 -The mobile robot",
        "texts": [
            " THE MOBILE ROBOT A mobile robot is assumed to contain 37 obstacle sensors arranged around the robot, so that each one measures the distance from the robot to the closest obstacle in its direction (angle a), 36 target sensors, also arranged around the robot and each one being an antenna which takes the target emitted signal and determines an error signal concerning the current heading direction (angle p), collision sensors, capture sensors that informs when the robot reached the target and a velocity sensor. Figure 1 shows the robot. The presence of multiple obstacle and target sensors improves the robustness against noise and allows the construction of sensor patterns which provide punctual information (related to each sensor) and relational information (related to the ordered vector of sensors). At each navigation step, after the sensor input, the controller applies a modification in the robot's direction and velocity. This characterizes the controller as being reactive. The robot and the environment are both part of a simulation system which considers a significant amount of restrictions that are found in the real world"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001667_robot.2004.1307171-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001667_robot.2004.1307171-Figure4-1.png",
        "caption": "Fig. 4 A M b l e lines on revolute objeas. a) Grasp I to 5 would be generated for this profile ifthc objed was m U y planar. Only grasps I and 2 are legal on revolute objmcts. Grasps 3 and 4 are infeasible since p a p 3 U- WO differmt group5 of lims and the thumb of grasp 4 d o s not clme towards the axis Grasp 5 wuld be feasible, but it would require 3D analysis. b) Accessible ku The thick liner above the separating points form gmup I and the other thick liner form",
        "texts": [
            " This definition reflects the fact that revolute objects (considered as planar) can only be grasped with fingers closing towards the axis of revolution. Here we suggest that revolute objects can be treated similarly to planarobjects. This is true if the following rules are respected: 1) all contact points and the axis of revolution must lie in a common plane and, 2) all three contact points must be on three lines belonging to the same group. Points located outside a certain limit separate groups of lines. This limit is dependent on the hand dimensions and it ensures that the fingers will reach the common plane. Fig. 4a shows examples of legal and illegal grasps. The first step in the procedure is to locate the points outside the limit. Second we separate the lines in different groups and we can then find the accessible segments for each group separately. Third, and differently from extruded objects, we project the points horizontally and not necessarily normal to the contact line. Fig. 4b shows the two groups of lines and the resulting accessible. lines. It is worth noting that the object model has only one set of lines, but it can accommodate objects with holes. The only effect is that the model will cpntain one extra line per hole linking the inside with the outside (see Fig. I2c). This extra line will not affect the line conditioning algorithm described above because it will be discarded as non-accessible. . poup 2. 111. IDENTIFYING GRASPING ZONES We begin by finding maximal object, segments, referred to as grasping zones, where at least one solution exists for force closure grasp"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000243_1.1537264-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000243_1.1537264-Figure1-1.png",
        "caption": "Fig. 1 Test linear bearing",
        "texts": [
            " The results in this study will be useful for noise reduction of linear bearings. Contributed by the Tribology Division for publication in the ASME JOURNAL OF TRIBOLOGY. Manuscript received by the Tribology Division January 20, 2002; revised manuscript received October 22, 2002. Associate Editor: M. D. Bryant. 480 \u00d5 Vol. 125, JULY 2003 Copyright \u00a9 2 rom: http://tribology.asmedigitalcollection.asme.org/pdfaccess.ashx?url= 2.1 Test Linear Bearings. The test linear bearings used in the experiments are linear bearings shown in Fig. 1. One test linear bearing consists of one profile rail and one carriage with recirculating balls. Table 1 shows the basic specifications of the test linear bearings. The specifications of the balls in the test linear bearings are shown in Table 2. The steel ball linear bearing and the ceramic (Si3N4) ball linear bearing were used as test bearings. The steel balls and ceramic balls have the same diameter, the same grade, and almost the same roughness. Table 3 shows the material constants of the balls and the carriage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000438_0379-6779(91)91787-b-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000438_0379-6779(91)91787-b-Figure7-1.png",
        "caption": "Fig. 7. (a) Cyclic voltammograms for PPP in 95% H2SO4 (1) and in the presence of 2 \u00d7 10 -a M Br2 (2) at potential sweel rate v= 100 mV/s. (b) Voltammograms for PPP (1) and Pt (2) in 2 \u00d7 10 -a M Br2+H2SO 4 (95%) at rotation rate f = 2 3 5 0 rpm (curve (1) is corrected for the values of dedoping currents of PPP for the same potential sweep rate).",
        "texts": [
            " The r edox p r o c e s s in PPP in tha t m e d i u m is sufficiently revers ib le . B romine reduc t ion was s tudied by s t eady-s t a t e and nons t eady - s t a t e v o l t a m m e t r y . The hal f -wave po ten t i a l o f the r eac t i on of b r o m i n e a t PPP is by severa l t en ths of mV m o r e pos i t ive than the c o r r e s p o n d i n g va lues at u n c o v e r e d Pt, and the l imit ing r educ t ion cur ren ts , even tak ing into a c c o u n t the p o l y m e r dop ing cur ren t s , are s o m e w h a t l a rge r than those at Pt (Fig. 7). The resu l t s on the d e p e n d e n c e of cu r r en t va lue on po ten t ia l sweep ra te and on e l ec t rode ro ta t ion ra te t aken t o g e t h e r are exp la ined by m a s s t r a n s p o r t con t ro l in a s y s t e m with a s l ight r eac t i on p r o d u c t a d s o r p t i o n at PPP. P r e s e n c e of b r o m i n e in the solut ion af fec ts the k ine t ics of PPP dop ing and d e d o p i n g p r o c e s s e s . Addi t ional comp l i ca t i ons involved in the in te rp re ta t ion of the b r o m i n e reduc t ion p r o c e s s in c o n c e n t r a t e d HeSO4 are a s s o c i a t e d with its ca ta ly t ic m e c h a n i s m (EC' r eac t ion) [11 ]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002624_1-4020-3393-1_7-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002624_1-4020-3393-1_7-Figure6-1.png",
        "caption": "Fig. 6. Muscle actuator defined between points n and m of rigid bodies i and j.",
        "texts": [
            " The semimembranosus is a two-point muscle, the origin and insertion points, and the tensor fasciae latea is a muscle defined by multiple points for an accurate characterization of its curvature. A constraint equation that specifies the muscle action during the analysis period is associated to each muscle actuator. These kinematic relations constrain the distance between two generic points of different rigid bodies to change in agreement with a specified length history previously calculated from the motion reconstruction. Considering a two-point muscle actuator, with an origin located in point n of rigid body i, and an insertion located in point m of rigid body j, as depicted by Figure 6, the mathematical expression used to define the constraint is ( ,1) 2 ( , ) ( ) 0 TMA m n m n nmt L tq r r r r (5) where rm and rn are respectively the global position vectors of the origin and insertion points and Lnm(t) is the muscle total length, calculated for each time step of the analysis. The two generic points n and m of rigid bodies i and j that are used to define the muscle actuator do not belong to the set of basic points and unit vectors used in the construction of the rigid bodies to which they are attached"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002346_00368790510601716-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002346_00368790510601716-Figure3-1.png",
        "caption": "Figure 3 Variation of p with x for different values of permeability parameter c with b \u00bc 0:3 and t \u00bc 5:0",
        "texts": [
            " The effect of couple stresses on the porous slider bearing characteristics is evaluated by the relative difference coefficients Rw, RF and Rf, where, Rw \u00bc \u00f0 wcouplestress 2 wNewtonian= wNewtonian\u00de100; RF \u00bc \u00f0Fcouplestress 2 FNewtonian=FNewtonian\u00de100 and Rf \u00bc \u00f0 fcouplestress 2 fNewtonian= fNewtonian\u00de100: the variation of nondimensional pressure p with x is shown in Figure 2 for different values of tfor both slip \u00f0 s \u00bc 0:5\u00de andno slip \u00f0 s \u00bc 1\u00de cases. It is observed that, the effect of couple stresses is to increase p as compared to the corresponding Newtonian case\u00f0t \u00bc 1\u00de: Further it is also observed that, the effect of velocity slip on the porous interface reduces p significantly as compared to the no-slip case \u00f0 s \u00bc 1\u00de: The effect permeability parameter c on the variation of p with x is shown in Figure 3. The dotted curves in the figure represent the no slipcase \u00f0 s \u00bc 1\u00de: The decrease in p is observed for increasing values of c. It is also interesting to note that the point of maximum pressure xmax shifts towards the inlet edge for increasing values of c. Figure 4 shows the variation of non-dimensional load carrying capacity w with t for different values of c for both slip \u00f0 s \u00bc 0:5\u00de and no slip \u00f0 s \u00bc 1\u00de: A significant increase in w is observed for smaller values of t and this increase in w is more pronounced for smaller values of c"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002047_j.jelechem.2004.02.008-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002047_j.jelechem.2004.02.008-Figure1-1.png",
        "caption": "Fig. 1. The EQCM-fluorescence setup (a) and its spectroelectrochemical cell (b) (not to scale). WE, the working electrode; RE: the SCE reference electrode; AE, the auxiliary electrode; OE1, oscillation electrode 1 (Au, contacting solution); OE2, oscillation electrode 2 (Au, in air); 1, 1 1 cm quartz cell; 2, OE1 (WE); 3, OE2; 4, RE; 5, AE, and 6, Teflon base.",
        "texts": [
            " In this work, a simultaneous QCM\u2013fluorescence\u2013 electrochemistry method has been developed as a novel and informative tool to monitor the electrooxidation process of pyridoxol on a polycrystalline Au electrode in alkaline aqueous solutions, by which the simultaneous recording of QCM frequency and resistance, fluorescence and electrochemistry data is feasible. In addition, the voltammetrically electrogenerated fluorescence is proposed as a new protocol for assay of pyridoxol. The experimental setup is illustrated schematically in Fig. 1. Electrochemical experiments were performed on a CHI660A electrochemical workstation (CH Instruments Co., USA) controlled by the CHI660A software. Fluorescence measurements were carried out on an F-4500 fluorescence spectrophotometer (Hitachi Co., Japan) controlled by Hitachi FL Solutions software. A research quartz crystal microbalance (Maxtek Inc., USA) controlled by Maxtek RQCM software was used to record QCM frequency and resistance data. The research quartz crystal microbalance (RQCM) is able to record the resonant frequency (f0) and the motional resistance (R1) of the crystal accurately via its high performance phase lock oscillator circuit, as given in the operation manual provided by the manufacturer",
            " UV\u2013Vis spectra were collected on a TU-1221 UV\u2013Vis spectrophotometer (PUXI General Co., China). AT-cut piezoelectric quartz crystals (PQCs) with a nominal frequency of 9 MHz and Au electrodes of 0.6 cm diameter were used. The PQC of 1.25 cm crystal diameter was adapted and then sealed into the edge of a hole at a Teflon base using 704 silicon rubber adhesive. One PQC gold electrode (OE1) was in contact with the solution and served as the working electrode (WE), while the PQC gold electrode on the other side (OE2) was located in the waterproof air compartment, as shown in Fig. 1(b). The reference electrode (RE) was a saturated KCl calomel electrode (SCE) and all potentials are reported versus the SCE in this work. The auxiliary electrode (AE) was a platinum sheet. Pyridoxol hydrochloride was purchased from Sigma and used as received. All other reagents were of analytical grade or better. All solutions were prepared fresh prior to use, and twicedistilled water was used throughout. All experiments were carried out at room temperature (20 2 C). To remove possible surface contamination, the Au working electrode was carefully treated prior to use",
            " The HNO3 treatment was repeated three times, followed by a similar concentrated H2SO4 treatment for three times. The acid-treated Au electrode was then subject to potential cycling between 0 and 1.5 V (50 mV s 1) in 0.2 mol l 1 HClO4 for sufficient cycles to obtain reproducible cyclic voltammograms and also QCM frequency and resistance responses [21,22]. The electrode was rinsed with twice-distilled water after completion of potential cycling. The WE, RE and AE were placed in the spectroelectrochemical cell which was inserted into the 1 cm cuvette holder of the F-4500, as shown in Fig. 1, then a test solution was injected into the cell to immerse the electrode surfaces. Electrochemistry, fluorescence, frequency, and resistance responses were monitored simultaneously during multi-mode experiments. The sample drug solution for assay of pyridoxol was prepared by dissolving one tablet of pyridoxol in 0.10 M KOH aqueous solution and then filtering, followed by further dilution with 0.10 M KOH solution. The Au-electrode surface roughness was estimated from values of the transition time in the galvanostatic oxidation process of 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003717_08ias.2008.78-Figure24-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003717_08ias.2008.78-Figure24-1.png",
        "caption": "Fig. 24. Flux density vector distributions at maximum torque position (stator current amplitude = 200 A and field excitation = 3000 At).",
        "texts": [
            ", and the stator core outer diameter is 10.6in. The PM properties used in the simulation are Br = 4 kG, and Hc = 16 kOe. The low Br value indicates a relatively low-cost permanent magnet. Fig. 22 shows that under the no-load condition, the airgap flux density can be changed significantly by changing the excitation ampere-turns. This indicates the field weakening and enhancement capabilities of the HSUB machine. The corresponding flux density vector distribution with 3000 ampere-turns field excitation is shown in Fig. 23. Fig. 24 shows the flux density vector distribution at maximum torque position with stator current magnitude of 200 A and field excitation of 3000 ampere-turns. Fig. 25 shows the comparison of output torque versus various excitation ampere-turn values. A torque increase over 60% can be achieved by flux enhancement. . VI CONCLUSIONS \u2022 An HSUB machine is introduced. It can be built as an axial-gap or a radial-gap machine. \u2022 The dc flux produced by an excitation coil is delivered to the rotor through an undiffused magnetic path without brushes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003035_haptic.2006.1627069-Figure18-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003035_haptic.2006.1627069-Figure18-1.png",
        "caption": "Figure 18: (a) Closeup top view of fabricated CMOS LSI chip. The size of the chip is 5 x 5 sq mm. (b) CMOS LSI chip after bonding (right) and molding (left).",
        "texts": [
            " The divided voltages are represented as Vout(OFF) = C2 C1 +C2 Vdd (9) Vout(ON) = C2 C1 +C2 +Cre f Vdd (10) where Vout (OFF) and Vout (ON) mean the voltages of the junction when the switch SW is off and on, respectively. The chip sends the values of Vout (OFF) and Vout (ON) after coding them by an A/D converter on the chip. We can know C1 and C2 by solving Eq.(9) and (10). The chip has initialization process before the measurement of Vout (OFF) and Vout (ON) in which the charges in C1, C2 and Cre f are all released. At the present stage, we have completed fabrication of the first prototype of CMOS LSI chip based on the 0.35 \u00b5m rule for the sensor/communication chip (Fig.18). While the size of the LSI chip is 5\u00d75 mm2, the total area of the analog-digital mixed circuits is within 1.5 mm2. The operating frequency is 50 MHz. Each chip measures Vout with an 8-bit A/D converter and it has a function to transmit the data to the neighboring sensing chip. We verified the chip could measure the capacitances of the sensor element and transmit data to a PC successfully. The data packets from the chip were received by a FPGA, and the data decoded by the FPGA were transferred to the PC via USB"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001297_iros.1991.174423-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001297_iros.1991.174423-Figure6-1.png",
        "caption": "Fig. 6: Compliant motions of the triangular prism",
        "texts": [
            " Figure 3 shows case seldom occurs in the real world, but it shows the generality ofour algorithm that the same algorithm can be applied to the case with no modification. The algorithm for the analysis of constraint is implemented in C. There are six differential motions that correspond to (vZ - v,) in the equation (17) for the triangular prism on the table shown in Fig.3. An arbitrary motion that main. the constraints on a triangular prism on a table. In the figure, tains the contact c a n be represented by a nonnegative linear combination of them. Three of them are shown in Fig.6. 0 _,_.'. ,. : .._ -.. ..... contact with a hole. Figure 5 shows an example of the contact between the vertices and between a vert,ex and an edge. At least one of four conditions must hold a t the contact point between the vertices, and a t least one of two ones must hold at t h e point between the vertex and the edge. Though such a Figure 7 shows three differential motions of the triangular prism that correspond t o V I E l , VIE, , VIE , in the equation (17) respectively. A n arbitrary motion that breaks the con- tact can be represented by a nonnegahe linear combination of them"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003955_tsmcc.2009.2030668-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003955_tsmcc.2009.2030668-Figure1-1.png",
        "caption": "Fig. 1. Three-link sagittal biped is composed of three rigid links and a massless foot. The term ki for i = 1, 2, or 3 is the distance from the bottom of link i to the center of mass of link i. The term li is the length of link i. Angles are measured clockwise from the vertical with \u03b8i \u2208 (\u2212\u03c0, \u03c0).",
        "texts": [
            " GVS may be useful for resolving cue conflicts, such as those experienced during visually enhanced control of remote automata [23] or virtual reality simulations. Our purpose, here, is to develop an analytical and quantitative model of a biped on a support surface that undergoes a sudden backwards translational disturbance. Such a model could be used for testing hypotheses related to control strategies for maintaining balance. Our model is composed of three rigid links that are restricted to lie in the sagittal plane, shown in Fig. 1. This model is similar to that used in [24] and [25]. Model parameters are provided in Appendix A. Bilateral symmetry is assumed, with link 1 representing both of the calves, link 2 both of the thighs, and link 3 the head, both of the arms, and the torso. Hyperextension at the hip and knees is prevented, as discussed in Appendix E. The model also has a massless link representing the feet, used to estimate horizontal excursions of the center of pressure, as discussed in Appendix F. Reasonable foot length should be approximately 20 cm [26]",
            ", the head does not rotate relative to the torso, so that the position of the vestibular system can be estimated from torso position and vice versa. Furthermore, we assume the location of the vestibular system and the head are the same, and both are located at the top of link 1. For each simulation, position of the CoG and the CoP along the x-axis are plotted versus time. At equilibrium, these should be 0 m; thus, these values are excursions from the equilibrium, with positive values representing movement forward. Calculation of the CoP is derived in Appendix F and assumes the model has a massless link representing the feet as shown in Fig. 1. The feet are connected to the soleus\u2013tibialis and gastrocnemius\u2013 antagonist group muscle pairs and are assumed to be approximately 20 cm in length. In the first experiment, we assume the muscles are at their nominal activity level, i.e., \u03b1 and \u03b2 are as given in (2), and there is no vestibular input or modulation. Excursions of the CoG and CoP versus time due to the disturbance of the support surface are plotted in Fig. 3. In this case, there are forward excursions of the CoG and CoP, with a maximum CoP excursion of 19",
            ", Fm = \u2212\u03b1m m \u2212 \u03b2m \u0307m (11) where m = rm \u03b8\u0302m , rm is the radius of the spring, \u03b8\u0302m is the angle between corresponding body segments, \u03b1m is a proportional gain, and \u03b2m is a derivative gain. For simplicity, we will choose rm = 1 for each muscle pair. In this case, F1 corresponds to the soleus\u2013tibialis anterior, F2 to the short heads of the quadriceps\u2013 hamstrings, F3 to the paraspinal\u2013abdominal muscles, F4 to the quadriceps\u2013hamstrings, and F5 to the gastrocnemius, as shown in Fig. 2. Thus 1 = \u03b8\u03021 = \u03b81 2 = \u03b8\u03022 = \u03b82 \u2212 \u03b81 3 = \u03b8\u03023 = \u03b83 \u2212 \u03b82 4 = \u03b8\u03024 = \u03b81 \u2212 \u03b83 5 = \u03b8\u03025 = \u03b82 (12) with \u03b81 , \u03b82 , and \u03b83 as shown in Fig. 1. Nominal gains for the muscle pairs are as given in Section III, i.e., \u03b1 = [\u03b11 , \u03b12 , \u03b13 , \u03b14 , \u03b15 ]T = [500, 300, 300, 300, 300]T and \u03b2 = [\u03b21 , \u03b22 , \u03b23 , \u03b24 , \u03b25 ]T = 0.25\u03b1. We can now derive the form of the muscle input to the system by writing the generalized torques in the \u03b8 space. Let F = [F1 , F2 , F3 , F4 , F5 ]T = [ 1 , 2 , 3 , 4 , 5 ]T and \u03b8 = [\u03b81 , \u03b82 , \u03b83 ]T . The generalized torques are then written as \u03c4 = \u2202 \u2202\u03b8 T F (13) where \u03c4 = [\u03c41 , \u03c42 , \u03c43 ]T . Using (12) \u2202 \u2202\u03b8 T =   1 \u22121 0 1 0 0 1 \u22121 0 1 0 0 1 \u22121 0   ",
            "5 \u03b4(t) m/s2 . Thus, for an initial position \u03b8(0) = [0.1,\u22120.1, 0.1]T rad by (18) and using the value of \u03b8\u0307 at time t = 0+ for time t = 0, \u03b8\u0307(0) = [2.5580,\u22120.0654, 0.0027]T rad/s. PREVENTING HYPEREXTENSION The model used here incorporates protections against hyperextension at the knee and hip. This is done by applying a Dirac delta or impulse torque resulting from forces opposing the hyperextension at the corresponding joint. As a simplification, we define hyperextension at the knee as \u03b82 > \u03b81 in Fig. 1 and hyperextension at the hip as \u03b82 > \u03b83 . First, consider the case of hyperextension at the knee. Let \u03b8i(th) be the value of \u03b8i at time t = th . During simulation, if \u03b81(th) \u2212 \u03b82(th) < 0.001 and \u03b8\u03072(th) \u2212 \u03b8\u03071(th) > 0.001, hyperextension at the knee is about to occur. Thus, additional equal and opposite impulse torques of magnitude \u03c4\u0302 \u03b4(t \u2212 th) should be applied to links 1 and 2. Similar to the derivation of Section D, the equations of motion for the system become J(\u03b8)\u03b8\u0308 + C(\u03b8, \u03b8\u0307)\u03b8\u0307 + G(\u03b8) = [1,\u22121, 0]T \u03c4\u0302 \u03b4(t \u2212 th) + \u03c4",
            " Using values at time t = t+h for time t = th results in an a change in total torque at time th and \u03b8\u03071(th) = 0 and \u03b8\u03072(th) = 0. When \u03b83(th) \u2212 \u03b82(th) < 0.001 and \u03b8\u03072(th) \u2212 \u03b8\u03073(th) > 0.001, hyperextension at the hip is about to occur. A similar derivation can be used to show that the counteracting torque in this case should be \u03c4\u0302 = ([0,\u22121, 1]J\u22121(\u03b8(th))[0,\u22121, 1]T )\u22121 [\u03b8\u03072(t\u2212h ) \u2212 \u03b8\u03073(t\u2212h )]. CALCULATING CENTER OF PRESSURE With a flat, massless link representing the feet connected to link 1, as shown in Fig. 1, we can estimate the CoP during movement using a method similar to that described in [30]. This method equates ankle torque to the ground reaction force applied at some distance from the ankle joint. This distance is the CoP. Note that the only muscle pairs connected to the feet are the soleus/tibialis anterior pairs and the gastrocnemius\u2013antagonist group pairs. Thus, torque at the ankle is equal to u1 + u5 as in (15). Assuming as an approximation that the foot has no height, the torque provided by Fg is 0 N\u00b7m"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000478_tec.2003.816601-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000478_tec.2003.816601-Figure3-1.png",
        "caption": "Fig. 3. Constant torque curves with fixed and T variable.",
        "texts": [
            " In the general case, the inductance matrix of the stator of the SyRM contains nonsinusoidal functions of and are, respectively, the self- and the mutual inductances from the three phases of the stator. The electromagnetic torque may be expressed (1) with the stator current vector and with . The Concordia\u2019s transformation is defined by , with the two-phase current in Concordia\u2019s reference frame and the Concordia\u2019s matrix After Concordia\u2019s transformation, a new expression of the electromagnetic torque is obtained (2) Let (3) In expanded form, (2) becomes (4) This quadratic equation denotes a hyperbola of centre O and vertex S, (Fig. 3). The trajectory of a point , such as the torque is constant, is shown (Fig. 3) for some values of . The focal axis is rotated by an angle as regards axis (Fig. 3). All M points sited on a hyperbola give a constant torque and indicates the cooper losses. OM is minimal when , then the S point corresponds to the minimal cooper losses. We notice that the angle between the two asymptotes only depends on . So, if is constant, the focal axis does not change when the torque changes. We deduce that the torque curves family, with constant, is given by hyperbolas, which have the same asymptotes and the same focal axis. The S points are all on the same line . First, we calculate the electromagnetic torque in the reference frame ( denotes the focal axis, Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002507_robio.2006.340096-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002507_robio.2006.340096-Figure2-1.png",
        "caption": "Fig. 2. Surfaces (solid-drawn circles) on snake robot that constitute the contact between the robot and the ground.",
        "texts": [
            " The time-derivative of the rotation matrix is found from [9] as (4) The coordinates (positions and orientation) and velocities of all links are gathered in the vectors q =[qT*qT .qTT and U [UT TU]T. B. Gap Functions for Unilateral Constraints The gap functions for the unilateral constraints (i.e. the floor) give the minimal distance between the floor and the front and rear part of each link. The contact surfaces between a link and the ground are modeled as two spheres at the ends of the link as illustrated for a three-link robot in Fig. 2. We denote the distance between the centre of the two spheres that belong to link i by 2LGs, and the radius of the spheres by Lsc. The position of the centre of the front and rear spheres are denoted by rSF, and rSRi, respectively. The shortest distance between the ground and the points on the front and rear spheres closest to the ground are denoted by gNFi and gNRi, respectively. The distances are found from gNFi (rsFi) ez gNRi (rsRi) z (5) where rSFi = rGi -GSiLez i, rSRi = rGi LGSiez The gap functions are gathered in the vector T gN = [gNF "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000462_s0263574701003691-Figure20-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000462_s0263574701003691-Figure20-1.png",
        "caption": "Fig. 20. Oriented fluid source.",
        "texts": [
            " New global equations are then defined: div + F= 0 (30) div v=0 (31) With the following additional constraint: v || v || < max where Kmax is the upper bound of the curvature. By this method, roads with a bounded curvature radius are obtained (Figure 18), to be compared with the classical simplest Stokes\u2019 equation (Figure 17). http://journals.cambridge.org Downloaded: 03 Jun 2014 IP address: 150.216.68.200 A non-holonomic robot is only able to start in a limited range of directions (Figure 19). In order to model this constraint, we limit the fluid direction around the starting and arrival points. Our solution is to build a virtual wall all around these points (Figure 20). Figure 21 shows a safe path planning with a lower bound of the radius of curvature. Imposing a bounded radius, the problem may have no solution. In such cases, the velocity vectors are null all over the domain. So we can easily predict the existence or nonexistence of a feasible solution. http://journals.cambridge.org Downloaded: 03 Jun 2014 IP address: 150.216.68.200 In this paper we have presented an original incompressible viscous fluid method for generating safe paths between two points in a complex environment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003505_robot.2007.363143-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003505_robot.2007.363143-Figure2-1.png",
        "caption": "Fig. 2. The acceleration of the center of mass",
        "texts": [
            " Once x2 is known, the vehicle\u2019s center of mass x, and orientation \u03b8 are easily found. The path constraint leaves the vehicle only one degree of freedom in the plane, which can be represented by the arc length, s, along the path followed by the center of mass. The vehicle\u2019s linear and angular acceleration are thus expressed in terms of the speed s\u0307 and acceleration s\u0308 along the path. The vehicle acceleration x\u0308 is decomposed into its tangent and normal components to the path, s\u0308t and s\u03072/\u03c1n, as shown in Figure 2, where n points toward the instantaneous center of curvature, and \u03c1 is the radius of curvature. Substituting \u03ba for (1/\u03c1)n, this transformation to path coordinates is expressed in matrix form: x\u0308 = [ tx \u03bax ty \u03bay ][ s\u0308 s\u03072 ] = K(s) [ s\u0308 s\u03072 ] (2) The angular acceleration may be similarly expressed as: \u03b8\u0308 = \u03b8ss\u0308+\u03b8sss\u0307 2 (3) where \u03b8s and \u03b8ss are the 1st and 2nd derivatives of \u03b8 with respect to s. The forces developed between the wheel and ground when moving on a horizontal surface are shown in Figure 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002525_1.2429700-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002525_1.2429700-Figure3-1.png",
        "caption": "Fig. 3 Nonlinear joint diagram d",
        "texts": [
            " Hence, in order to avoid joint separation, the separating force must remain less than Fe max, which is obtained by setting the clamping force equal to zero in Eq. 1b , which yields Fe max = Kb + Kc Kc Fi 4 If a purely separating action of the external force Fe is harmonic, as is the case of head bolts in an internal combustion engine, both the increase in the fastener tension and the corresponding reduction in the clamping force, given by Eqs. 1a and 1b , will be harmonic as well. Nonlinear Behavior During the Separating Half Cycle Figure 3 shows the joint diagram; at initial tightening both the joint and the fastener were yielded. Line segment AB C and ABC show the load\u2013deflection curves for the yielded joint and fastener, respectively. In the nonlinear joint diagram ACA , point C represents the initial tightening condition at which the fastener tension and the joint clamp load are both equal to some initial value Fi. Point C is represented by its coordinates Xi and Fi as follows Transactions of the ASME x?url=/data/journals/jmdedb/27846/ on 02/16/2017 Terms of Use: http://www",
            " As the force Fe tries to separate the joint during the first half ycle, the fastener tension is increased by F, while the clamping orce is decreased by FClamp. The fastener tension increases noninearly along curve CD to point D, while the clamp load Fc ecreases linearly along its new elastic line CO. Point D is repreented by its coordinates as follows D xi + x Fi + F 6 here x=increase in the fastener elongation due to the external eparating force Fe; and F=increase in the fastener tension due o the external separating force Fe. Because the fastener is well into the plastic region at D Fig. 3 , he reduction of the external separating force Fe will cause the astener tension to decrease along a new elastic line DH, which is arallel to the original elastic line AB. Simultaneously, the clampng force will increase along its new elastic line OC. When the alue of Fe goes to zero, the system achieves a new equilibrium at oint H, which is lower than the initial equilibrium point C. At the ew equilibrium point H, the residual value of the fastener tension nd joint clamping force are reduced from their initial value of Fi o a lower value FH"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002721_oceans.2004.1406351-FigureI-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002721_oceans.2004.1406351-FigureI-1.png",
        "caption": "Fig. I . Two UVMS holding a common object",
        "texts": [],
        "surrounding_texts": [
            "I. INTRODUCTION Recently, many research efforts have heen devoted to the development of underwater robotics [1]-[5] as the need for exploring and preserving the oceanic environments has gained significant momentum. An underwater vehicle equipped with manipulator systems, usually called underwater vehicle-manipulator systems ( W M S ) , is particularly useful and plays an important role in most of the underwater manipulation tasks, such as underwater pipeline welding, mining, drilling, underwater cable burial, and military applications. Its applications has intensify the research interest on the development of the control systems for W M S . However, the presence of hydrodynamics effects makes the control problem of W M S a challenging task.\nModelling of the UVMS can he found in [31,[61,[71,[81,t91. In [IO], a control law for tracking of a desired motion trajectory for an UVMS has been proposed, where an observer has been designed to provide estimation of velocities used by the control law. Several force control schemes for W M S have been presented in [11],[121,[13]. In [141, a solution to the problem of redundancy resolution and motion coordination between vehicle and manipulator hy using fuzzy technique has been presented. In [6],[8],[15], feedback linearization control has been proposed for an underwater vehicle-manipulator systems, where the exact dynamic model is assumed to he known. In [ 161, the underwater vehicle-manipulator systems has been partially decouple and the control scheme compensates only part of the nonlinear coupling effects. Although the control complexity was reduced, partial knowledge of dynamics model is still required. To overcome parametric uncertainties on the UVMS, adaptive controllers have been introduced in [171,[18]. However, these controllers require a regressor of the dynamics model which include the inertia matrix, Coriolis and centripetal force, hydrodynamic damping, gravity and\nbuoyancy force. In underwater applications, the number of the dynamic parameters of the W M S to he updated by the adaptive law is very large and hence is too complex to he implemented.\nBesides the single W M S , cooperative manipulation is another new and important capability for extending the domain of underwater robotics application. We will enjoy great benefits and advantages when multiple W M S are used in performing cooperative tasks. For example, multiple cooperative W M S can he used to move objects easily and conveniently which cannot he performed hy a single W M S due to the object\u2019s size and weight constraint; they can also he used in various underwater assembly tasks such as underwater structures construction and maintenance; underwater pipeline and cable transportation and replacement can be easily done by multiple cooperative W M S ; underwater search and rescue work will he more efficient and effective if multiple UVMS are used as rescue vessel. However, besides the work on the modelling of two cooperative W M S [19], there is no result heing proposed for the modelling and control of the multiple cooperative UVMS holding a common object. In this paper, we propose two simple setpoint controllers for the coordinated control of multiple cooperative W M S holding a common object. First, we propose a saturated proportional-derivative (SP-D) controller with exact gravitational and buoyancy force compensation. Next, in order to compensate the uncertainties in gravitational and buoyancy force, we propose another saturated proportional-derivative (SP-D) controller using gravity regressor. The proposed controllers do not require the knowledge of the inertia matrix, Coriolis and centripetal matrix and hydrodynamic damping matrix. Lyapunov-like functions are propose for the stability analysis. Sufficient\n0-78O3-8669-8/04/%20.00 02004 IEEE. ~ 1542 -",
            "conditions for choosing the feedback gains to guarantee the stability of the multiple cooperative UVMS holding a common object are presented.\nThe remaining of this paper is organized as follows. Section Il summarizes the multiple UVMS kinematic constraint and dynamics models and its main properties. Section Ill proposes a saturated proportional-derivative (SP-D) controller with gravitational and buoyancy force compensation and provides conditions on the controller gains to ensure the system stability. Section N proposes a saturated proportional-derivative (SP-D) controller with gravity regressor. Finally, Section V concludes this paper.\n11. PROBLEM FORMULATION\nWe consider k cooperative UVMS holding a common load rigidly in a 6 degree of freedom space as illustrated in Fig. 2 and Fig. 3. Let vi E R6 denotes the ith vehicle velocity vector in body fixed frame; qi E Rn' denotes the joint position vector of the ith manipulator where ni is the number of joints and pe , E R6 denotes the position and orientation of the ith end effector in the earth fixed frame. The kinematic relations between velocities can be written in a compact form as ~11,[21,[31,~91,[191:\nWhen multiple W M S cooperate to manipulate a common load, the motions in the whole systems are coupled due to the fact that the velocities of the end effectors are related via the rigid load. The kinematic constraint is obtained by expressing the common load velocity in terms of the velocities of each W M S . The common load\nvelocity can be expressed in the terms of the end effector velocity as [19]:\nx = J,:'p,, , (2 )\nwhere 1 E R6 denotes the linear and angular velocity of the load in the earth fixed frame; J;' E RGx6 denotes the velocity transformation matrixes between the load velocity and end effector velocity of the ith manipulator. Hence, the kinematic constraint can be obtained by combining (1) and (2). such that\nJX = J,<> (3)\nwhere J = [JT,...,JZlT, J, = diag{Jz ,..., J:} and From (3) , it follows that c = E,. ., <:IT.\n(4)\nThe dynamic equation of the ith W M S in the body\nn j: = J+ J,S = J ~ C\nwhere J+ = ( J T J ) - I J T is the pseudo-inverse of J . '\nfixed frame can be written as [3],[61,[91,[191:\nMi ( q i ) t + Ci (q i , Ci)C + Di(q,, Ci )Ci + gi hi, q i )\n= ri - J 2 f e , , i = 1, ..., k (3 where Mi(q;) E R(G+\"')x(6+n,) is the mass matrix, Ci(qi;<;)ci E R6+n. is the vector of Coriolis and centripetal terms. Di(qi, E R6+\"* is the vector of friction and hydrodynamic damping terms, gi(qi,qz) E RG+n* is the vector of gravitational and buoyant generalized forces, ri E RGfn. is the vector of forces and moments acting on the i th vehicle as well as of the joint torque of the manipulator, f,; E R6 is the vector of forceslmoments applied by the ith manipulator on the object at the ith point of contact.\nUsing (3, the equation of motion of the k UVMSs can now be described in a unified way as follows:\nM(di + C(q, C)C + D(q, C)C + s ( v 9)\n= r - J T f e , (6)\nwhere M ( d = d i a g { W ( q l ) , . . . ,M&)}. diagICl(q1, cl), . ' ' :Ck(Pkr Ck)}r c(q> I) - D(q,<) = diagCDi(4i,Ci),...,Dk(qk,Ck)}. C = ~ = [ ~ T ; . . , r ~ ] ~ a n d f , = [ f , ~ ; . . , f , ~ ] . [cT,'\">c:l', 9 ( % d = [ sT~ol ,P l ) ,~ .TISkT(vk,Yk) lT ,\nThe equation of motion of the object can be written in\n(7)\nthe earth fixed frame as\nMO? + C&,x)x + D,(z,f)j: + g&) = F,\nwhere x E R6 denotes the position and orientation vector of the object coordinate frame in the earth fixed frame, MO E R6w6 is the inertia matrix of the object including added mass terms, C,(z,i) E R6x6 is the vector of Coriolis and centripetal terms, D,(x, x) E R6xG is the vector of friction and hydrodynamic damping terms, g,(z) E R6 is the vector of gravity and buoyancy effects. Here F E R6 is the total force exerted by the UVMSs on the object:\nF = E:==, J?fe, = J T f e , (8)\n- 1543"
        ]
    },
    {
        "image_filename": "designv11_28_0002530_epepemc.2006.4778540-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002530_epepemc.2006.4778540-Figure8-1.png",
        "caption": "Fig. 8. Interconnection of stator and rotor reluctance networks.",
        "texts": [
            " fep fe into two independent parts e (0 ) and e (0 ) respectively s s r s attached to the stator and the rotor. The total airgap length function is then given by: e(0)= e (0 )+e (0 ). s s s r s (3) generally too low to cause saturation. Only the d-axis flux path is saturated. The thickness of the ferromagnetic segments was chosen so that both motors have the same direct inductance L of l2mH. d F. Interconnection Network For any rotor position, the interconnection network modeling the airgap connects the rotor and stator reluctance networks to form one global network. Fig.8 explains the principle of the interconnection network elaboration. Fig.5 to 7 represent the interconnection nodes (thick nodes) with the associated angular zones of effect. The stator and rotor nodes of respective numbers \u00ab i >> and <<j >> are connected if their zones of effect overlap. The value of the permeance A connecting them is i, I calculated by integrating the inverse of the total airgap length function e (0 ) over the overlapping angular zone. s dO A = II +e) i,j f ooutp2 ze(0 ) overlapping zone s (4) E"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002764_11866565_70-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002764_11866565_70-Figure6-1.png",
        "caption": "Fig. 6. Three-link manipulator with double Fig. 7. Insertion of an instrument into a port actuator mechanism",
        "texts": [
            " This translation without rotation prevents the jamming and galling, which can generate excessive contact force. Since conventional RCC devices employ passive mechanical compliance, the compliance center is fixed at the tip of the part to be inserted and moves further into the hole after the part is inserted. By implementing three double-actuator units on a three-link manipulator, the position of the compliance center can be controlled in two-dimensional space so that the compliance center is maintained near the insertion point during the whole insertion operation (Fig. 6). This adaptive control of RCC, when applied to MIS, can be advantageous, since it prevents excessive force at the port site where the surgical instrument or endoscope is inserted. Fig. 7 illustrates the insertion of a surgical instrument into a port. The position of the endpoint of the robot manipulator (point B) with respect to the insertion point (point A) is represented by vector r ( T yx rr ),(=r ). Using the double-actuator mechanism, the compliance center can be placed at the insertion point (point A), and the compliance matrix described at point A is given as: \u23a5 \u23a6 \u23a4 \u23a2 \u23a3 \u23a1 = \u23a5 \u23a5 \u23a5 \u23a6 \u23a4 \u23a2 \u23a2 \u23a2 \u23a3 \u23a1 = \u03b8 \u03b8\u03b8 C C CC CC r yyyx xyxx A 0 0C C 00 0 0 (3) The compliance matrix is transformed by Jacobian matrix J between point A and point B to yield the compliance matrix at the endpoint of the manipulator (point B)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002916_jphyscol:1975138-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002916_jphyscol:1975138-Figure3-1.png",
        "caption": "FIG. 3. - The four possible distortions in the Poiseuille flow geometry referred to in the text as solutions 1 and 2.",
        "texts": [
            " the molecules fixed by the boundaries is again perpen- Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1975138 dicular to the velocity and velocity gradient. The velocity profile is parabolic and the pressure drop along y over the length L is The shear rate s is maximum near the limiting plates and the instability can be understood qualitatively as in the shear flow problem if we assume that, near the linear threshold, the distortions near the two plates are independent. Two types of solutions are expected (Fig. 3). Solution 1. This solution involves a finite average twist over the thickness. Solution 2. This one has an associated average splay. Clearly one also has two other mirror solutions obtained by reflection through a yz plane.. Thus we have four possible distorted states. In fact, above the threshold, nonlinear effects resulting in an interaction between the upper- and lower-half distorted structures are expected. These effects are beyond the present description. The linear problem was first discussed by de Gennes [3]",
            " - At very low frequencies the instability is a uniform distortion in domains limited by boundaries perpendicular to the flow and visible on the photograph of figure 4. The spacing between the domains clearly decreases with the cell width. In the narrowest cell, where the width is of the order of the wall thickness, no domains are obtained. This distortion corresponds to the homogeneous shear flow instability : In a given domain the conoscopic image indicates an average twist but no splay as for solution 1 of figure 3. Figure 6 gives a top view of the We describe here the results of microscopic visua observations. The wavelength of the roll instabilities was measured from the very regular diffraction pattern of a monochromatic laser beam going through the cell. All observations reported were done after a long enough time was allowed to let the structure stabilize. P correspond to instability states discussed in the text. lines) separating the domains has yet to be studied. configuration in different domains and points towards the most likely mechanism : As soon as the distortion is present, a transverse force appears, due to the effect A, which deflects the velocity along X"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003697_memsys.2008.4443589-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003697_memsys.2008.4443589-Figure1-1.png",
        "caption": "Figure 1: Sketches of the out-of-plane actuator: a) traditional two-layer bimorph actuator b) novel actuator with a combined material top actuation block, where both effective CTE and Young\u2019s modulus are improved.",
        "texts": [
            " The actuator stiffness is measured to be 75 N/m, thus the corresponding calculated out-of-plane force is 2.3 mN. The maximum actuation temperature during the measurement is 100 \u00baC (80 \u00baC change). A 25 Hz response frequency is measured by monitoring the resistance change due to the temperature variation. Out-of-plane actuators are essential elements in micropumps, micromirrors and other MEMS devices, where both large displacement and force are needed. The commonly used electrothermal bimorph actuators, consisting of an actuation layer on the top of a suspended bottom layer (Fig. 1a), can generate a downward out-of-plane motion. The performance of the actuator depends highly on the properties of the working material. Metal and doped silicon layers can only provide limited displacements and require high actuation temperature [1]. Polymeric bimorph actuators [2, 3] due to their high coefficient of thermal expansion (CTE) can overcome these limitations. However, the generated force is weak because of the low stiffness due to the small Young\u2019s modulus. To enhance the out-of-plane force, a thick layer of polymer could be employed, but the poor thermal conductivity still has to be overcome. Thus, an actuation material with large CTE, large Young\u2019s modulus and reasonable thermal conductivity is needed to comply with the out-of-plane displacement, force and response time requirements. A new concept (Fig. 1b) of bimorph actuator is proposed in this paper, offering an effective solution to the above challenge. In this actuator, the original top actuation layer is replaced by a combined material block consisting of polymer layers constrained vertically between stiff plates. This device is capable of generating both large bending displacements and forces with a reasonable response time. The basic principle, fabrication process and experimental validation of the concept will be illustrated and discussed in the following sections. The proposed bimorph structure is schematically depicted in Fig. 1b and Fig. 2. Figure 2: A cross-section sketch of the bimorph actuator with combined material block. The combined material block consists of polymer layers and stiff plates placed in parallel after each other. When a thin polymer layer is bonded between two stiff plates, it is constrained at the interface. Therefore, when heated up, instead of expanding in all three dimensions, volumetric expansion of the polymer is directed mainly perpendicular to the bond interface. Consequently, the bonded polymer exhibits more perpendicular thermal expansion than an unconstrained polymer alone [4, 5] Assuming the polymer layers and the plates are infinitely wide in the parallel direction, a lamellar model [5] is used to express the CTE (\u03b1con) and Young\u2019s Modulus (Econ) of the constrained polymer as: ( ) ( ) 2 1 1 polymer polymer plate con polymer polymer plate \u03c5 \u03b1 \u03b1 \u03b1 \u03b1 \u03c5 \u03b3 \u03c5 \u2212 = + +\u2212 \u2212 (1) ( ) ( ) 2 1 1 1 polymer polymer plate con polymer polymer plate E E \u03c5 \u03c5 \u03b7\u03c5 \u03c5 \u03b3 \u03c5=          \u2212 \u2212 \u2212 + \u2212 (2) in which \u03b7=Epolymer/Eplate and \u03b3=tpolymerEpolymer/tplateEplate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000516_tpcg.2003.1206940-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000516_tpcg.2003.1206940-Figure5-1.png",
        "caption": "Figure 5: V2 boid vectors and angles.",
        "texts": [
            " In this model the boids are assumed to have global perception and thus all other boids are considered in the calculation of each boid\u2019s load factor. A boid i is located at position Xi. The flock has a cohesion centroid C located at XC. Each boid has its own cohesion vector, Bi, (XC \u2013 Xi) oriented at an angle i. The flock also has an alignment vector A, which is common for all boids and oriented at an angle . The way in which the cohesion centroid and alignment vectors are calculated is dependent on the flocking type selected and is described shortly. Figure 5 illustrates the state of a boid i in terms of the vectors and angles associated with it. The load factor for a given boid is calculated by finding the differences between the boids current heading angle and the alignment angle , and the cohesion angle i. These values represent the heading angle errors i and i (i.e. the angles the boid must turn through to be heading in the direction of the alignment angle and cohesion angle respectively). They are defined as: ii \u03c8\u03b1\u03c8\u03b1 \u2212= , \u03c0\u03c8\u03c0 \u03b1 <<\u2212 i (8) iii \u03c8\u03b2\u03c8 \u03b2 \u2212= , \u03c0\u03c8\u03c0 \u03b2 <<\u2212 i (9) To find the load factor these values are first multiplied by the cohesion and alignment rule weights W\u03b1 and W\u03b2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000035_a:1008965826397-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000035_a:1008965826397-Figure1-1.png",
        "caption": "Figure 1 Graphical cross-section of the percutaneous device used in the experiment.",
        "texts": [
            " The objective of this study is to investigate whether the previously developed animal model can be used for in vivo measurements with subcutaneously implantable glucose sensors. A percutaneous device containing a subcutaneous tissue chamber was implanted in rabbits. Glucose kinetics in subcutaneous tissue \u00afuid were *Author to whom correspondence should be sent. 0957\u00b14530 # 2001 Kluwer Academic Publishers 129 determined after aspiration of tissue \u00afuid from the chamber and with implantable amperometric glucose sensors. Implantable percutaneous devices as shown in Fig. 1 were used. The devices consisted of a KEL-F body ( poly-chloride-tri\u00afuoro-ethylene) in which a subcutaneous chamber was formed with a volume of 500 ml connected with a percutaneous part that penetrated the skin. The access to the subcutaneous chamber was closed with a stainless steel screw. A sintered titanium \u00aeber mesh sheet (volumetric porosity 80%, \u00aeber mesh weight 600 g/m2, \u00aeber diameter 50 mm, Bekaert Fiber Technologies, Belgium) was used for subcutaneous anchorage of the device. In previous experiments, this material showed good biocompatibility and anchorage in soft tissue [9, 10]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000550_robot.2000.844843-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000550_robot.2000.844843-Figure6-1.png",
        "caption": "Fig. 6: Desired trajectory and initial configuration of Manipulator",
        "texts": [
            " The null desired velocity, which is to optimize a scalar potential function m(q), is assigned by gradient projection method type [8] as follows: '#id = nVm(q), (25) where rc denotes the rate of convergence factor. It is difficult to evaluate our proposed index to compare with others, because most impact performance index assumes the knowledge of environment. Here, we compare the performance of the proposed index with the manipulability index which is generally used for the control of manipulators. As shown in Fig.6, simulation is executed for the task of tracking a line trajectory. Initial point is given by p(0 ) = (0.0, 0.15)m, and the initial configuration represents the maximum values of each performance index. And, the wall is modeled by (tancu)~ - y + 0.611 = 0, so the normal vector of the wall is n = [sin a, -cos aIT. The total execution time is 1.4s. We executed for several values of a to investigate the effect of unknown environment. For all cases, the pre-impact velocity is about 0.15m/s. The task control system is simulated with position and velocity feedback gain matrix K, = diag(l50, 150) and K d = diag(30, 30}, respectively, and, the null velocity feedback gain constant is used as Kn = 100"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000338_10402000108982460-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000338_10402000108982460-Figure5-1.png",
        "caption": "Fig. 5--Schematic of the strip drawing simulation.",
        "texts": [
            " The evolution of the surface roughness amplitude and the contact ratio a under these conditions is shown in Fig. 4. Although the inlet zone is very short, it accounts for most of the surface flattening. Further flattening takes place in the transition zone where there is bulk deformation. No significant flattening occurs in the work zone. A Semi-Empirical Friction Model for Cold Metal Rolling Pas, a=2.2x10\" pa:. SlMLlLATlON OF BOUNDARY FRICTION The schematic of the strip drawing rig used for this simulation is shown in Fig. 5. A more detailed description is given by Ahmed and Sutcliffe (12). The simplicity of the set-up and the ease with which process and die conditions can be varied makes strip drawing a much more attractive laboratory test of boundary lubrication mechanisms than corresponding rolling tests. The drawing dies used in the tests are made from heat-treated tool steel. Half dieangles @ of 3 ,5 , 10 and 20 degrees are used to vary the lubricant film thickness, which is characterized using the smooth film thickness h,, Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002603_3-540-29461-9_77-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002603_3-540-29461-9_77-Figure4-1.png",
        "caption": "Fig. 4. (a) 7-link simulation model with ankle joints and flat feet. (b) Foot geometry indicating design parameters that are investigated in this research",
        "texts": [
            "4 K n ee a n g le \u03c6 k ( ra d ) Absolute body angle \u03c6 (simulation only) Inner swing Outer swing Inner swing Outer swing Step 1 Step 2 knee strike prototype heel strike prototype knee strike simulation Fig. 3. Comparison of the walking motion of the real prototype and the 5- link simulation model, indicating that this simulation model gives a satisfactory description of the robot\u2019s dynamics. This figure is taken from Wisse et al. 2004 [10] with flat feet and ankle joints. The arced feet in the model were replaced by ankle joints and flat feet, while all other model parameters (including actuation) remained the same. The resulting 7-link model is depicted in Fig. 4a. Figure 4b. gives a detailed view of the foot and the design parameters that are investigated in this paper. The ankle joint is aligned with the hip and knee joint when the leg is fully stretched. The heel and toe radius were chosen to be equal. There is a spring-damper combination in the ankle joint with variable stiffness k, damping d and equilibrium position \u03c6a0. The simulations have resulted in knowledge on how the performance of the walker changes due to variations in the new foot design parameters. This relation is presented in the next section by showing how the performance measures change when the design parameters are varied around a typical working point in the parameter space"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000099_icsmc.1999.812539-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000099_icsmc.1999.812539-Figure4-1.png",
        "caption": "Figure 4: Coordinate Frames of WABIAN-RII.",
        "texts": [
            " In this section the modeling of the robot is described, and emotional walking control strategy is discussed on the basis of the Zero Moment Point (ZMP) criterion. 3.1 Modeling In order to define mathematical quantities, a world coordinate frame Fo is fixed on the floor where the robot can walk. Also, a moving coordinate frame .Fo is attached on the center of the waist relative to the world frame FO to consider the relative motion of each part. Q(z,y, zq) is defined as the origin of the moving frame Fo relative to Fo. Figure 4 shows coordinate frames. For modeling the walking machine, four assumption are defined as follows: 1. The walking robot consists of a set of particles. 2. The foothold of the robot is rigid and not moved by any force and moment. 3. The contact region between the foot and the floor surface is a set of contact points. 4. The coefficients of friction for rotation around the X, Y and Z-axes are nearly zero at the contact point between the foot and the floor surface. 5. The foot of the robot does not slide on the contact surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003363_isorc.2007.32-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003363_isorc.2007.32-Figure6-1.png",
        "caption": "Figure 6. Number of active sensors.",
        "texts": [
            "acki := \u3008sj , SEQj\u3009; h := CTj ; } else{send(a, m); return:} send(a, m); } We have to reduce the energy consumption of each sensor node in a wireless sensor-actuator network (WSAN). Various types of technologies have been so far discussed [13, 12]. A sensor node mainly consumes the energy to send and receive messages. Multiple sensor nodes sense an event and generate messages to deliver the sensed value to an actuator node because they are closely located [2]. There are multiple sensor nodes in a collision area. If every sensor node which senses an event transmits a message, the collision occurs and lost messages are retransmitted as shown in Figure 6a). Hence, the more number of sensor nodes send messages, the more amount of energy is consumed. Only a limited number of sensor nodes which sense an event send messages to reduce the total energy consumption of sensor nodes as shown in Figure 6b). Clustering techniques have been so far proposed to limit the number of sensor nodes which transmit messages. However, some devices like the beacon [15] and GPS [10] device Proceedings of the 10th IEEE International Symposium on Object and Component-Oriented Real-Time Distributed Computing (ISORC'07) 0-7695-2765-5/07 $20.00 \u00a9 2007 are required in these approaches. In the beacon systems, it is necessary to set up the base station to send out a beacon or sensor node must send out a beacon itself"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000752_bf03179258-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000752_bf03179258-Figure8-1.png",
        "caption": "Fig. 8. Schematic of VAR furnace for Ti alloy casting with centrifugal turntable.",
        "texts": [
            " The investment casting method developed in the mid-1960s was used primarily for high-quality aerospace components of various sizes. Table 3 lists the casting methods and their maximum poured weight. 5.1.1. Cast part production Because of the high reactivity of liquid titanium, Ti alloy electrodes are arc-melted in a vacuum furnace and then placed into a water-cooled copper crucible which forms the protective skull. A melting apparatus with a melt chamber connected to a centrifugal table mold chamber is shown in Fig. 8. As will be discussed later, the centrifugal table assists in filling the mold to the maximum possible density and is especially important in large component casting. The oxygen level of the castings is controlled primarily by the melt stock. Therefore, the preferred practice is to carefully control the blend of revert (properly recycled scrap) with virgin ingot to the desired chemical composition, and directly cast. To illustrate the typical stages involved in the process of producing Ti cast parts, a manufacturing sequence for the investment casting method is shown in Fig",
            " This is repeated several times to build a ceramic shell with enough strength to sustain the molten metal pressure after being hardened by firing. The patterned wax is then removed in a steam autoclave, which leaves the mold cavity ready for casting after firing. The minimum practical wall thickness is 1.0 mm. To improve productivity, many duplicate components can be cast in a cluster pattern which is manufactured in an automated line. The casting tree is placed on a centrifugal table inside the mold chamber of the vacuum arc furnace (Fig. 8) in order to assist the metal flow. Investment casting provides very good dimensional accuracy and is suitable for production of highquality aerospace engine components. As indicated in Table 3, components up to 650 kg can presently be produced by this method. The typical flow chart for the method is given in Fig. 9. 5.1.5. Sand casting Sand casting is the lowest cost casting practice and a device to coat sand layers with ZrO2 was recently developed by the U.S. Bureau of Mines. Sand casting has the potential of lower cost components and is primarily aimed at marine and chemical applications"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003168_1.23613-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003168_1.23613-Figure2-1.png",
        "caption": "Fig. 2 Relative dimensions of a SOCBT projectile [4].",
        "texts": [
            " In our study, the porosity strength on both suction and blowing will be studied individually. This has been carried out by changing the maximum porosity factor over the suction and blowing parts. The maximum porosity factors that have been used are 0.01, 0.03, 0.05, and 0.1 to 0.8 by an increment equal to 0.1. Our numerical study on the SOCBT projectile was carried out by applying a Navier\u2013Stokes equation using the commercial code Fluent. The relative dimensions in terms of projectile caliber are shown in Fig. 2. The two-dimensionalNavier\u2013Stokes equationswere discretized by using the second-order upwind method for the spatial dependent properties. A coupled implicit scheme was applied to solve the system of differential equations. The Spalart\u2013Allmaras [7] turbulencemodel was used in this study. This model was developed for aerodynamic applications and gave good results in the present case. It was used with both solid and porous projectiles. The transpiration velocity is used in the interface between the inner and outer flows"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000880_ijcat.2002.000288-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000880_ijcat.2002.000288-Figure9-1.png",
        "caption": "Figure 9 Case study\u00d0spline geometry.",
        "texts": [
            " In this study, the equivalent stiffness of both the spline teeth and shaft was determined by considering the teeth and shaft as two springs connected in series. The equilibrium misalignment moments and unbalance loads are used to calculate the bearing reaction. Each shaft is treated as a free body under static equilibrium and the reactions at the bearings are readily calculated. A spline coupling which is commonly used in the Aviation industry is analyzed in this study under normal operating conditions. The main dimensions of the spline, which is made from a hardened alloy steel AMS 6265, is outlined in Figure 9. The spline data for the coupling is given in Table 1. The coupling is subjected to a rated torque of 1080 N.m. The angle of misalignment, due to assembly and cumulative manufacturing errors, between the driving and driven shafts that are connected by the coupling is 0.1468; or 0.00255 rad. The coupling stiffness was \u00aerst calculated considering the teeth de\u00afection only as a \u00aerst approximation. The results yielded a stiffness of 1:05 10 9 N=m and only ten teeth, out of a total of 38 teeth of the entire spline, were to share the transmitted load; the rest of the teeth were unloaded"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000778_s0045-7949(02)00294-8-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000778_s0045-7949(02)00294-8-Figure1-1.png",
        "caption": "Fig. 1. Structure of cam-type engine shafting system.",
        "texts": [
            " The inner shaft assemble and the outer shaft assemble revolve in opposite directions via interaction between pistons and cam-disc. The rotation direction of front propeller installed on outer shaft is also opposite to that of rear propeller installed on inner shaft. The piston assemble undergoes reciprocating movement inside the cylinder, at the same time they rotate around axis of engine output shaft together with the cylinder. The model of the cam-type engine shafting system s structure is shown in Fig. 1. Because of the special feature of the cam-type engine shafting system and the existence of interaction between the inner and outer shaft assembles, they must be considered as a whole system in vibration analysis. If the vibration of inner and outer shaft is studied respectively [4], the vibration characteristics of the whole system cannot be obtained. Thus, in this paper, the whole system is divided into two first-class substructures connected by a \u2018\u2018flexible substructure\u2019\u2019. The combination of cylinder-body, outer shaft, front propeller, and enginedriven auxiliary machinery is defined as first-class substructure a"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001259_robot.1986.1087707-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001259_robot.1986.1087707-Figure3-1.png",
        "caption": "Figure 3. Definition of geometric parameters of the links and the joint angles.",
        "texts": [
            " f o r t h i s t y p e L of singularity to occur without the reference point being on the workspace boundary [6]. Also, as will be seen in the next section, its kinematic equations are manageable and, in fact, it lends itself to exceedingly simple, and operationally useful, coordination strategies. DEVELOPMENT OF JACOBIAN The Jacobian matrix for the configuration of Figure 2b will be developed using the notation of reference [13]. The geometric parameters of the links and the joint angles are defined as shown in Figure 3. For the chosen configuration, the parameters are listed in Table I. A s was noted in reference [131, the form of the Jacobian is greatly simplified by transforming to a new fixed frame which is instantaneously coincident with one of the intermediate link reference frames. We choose to work in a frame coincident with frame 5 since, although the expressions for the positions of the inboard ioints will be relatively complex, this choice will produce a quadrant of zeros in the Jacobian matrix. A s defined in Figure 3 , reference frame 5 is located with its origin on joint axis 6 and its 2, axis lying along that axis. It's x axis lies along the common normal of axes 5 and 6. That is, its origin lies at the point of concurrence of axes 5, 6 and 7, its y axis is along joint axis 5, and its z axis along joint axis 6. If the velocity state of the hand is given by the vector pair (w_, 11) where W, is the hand angular velocity, and is the velocity of the point in the hand which is instantaneously coincident with the fixed reference frame, it is necessary to transform w_ and g into the intermediate reference frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002177_760369-Figure58-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002177_760369-Figure58-1.png",
        "caption": "Fig. 58, entitled \"Hendrickson SR Series Tandem Rear Axle Shear Ride Suspension,\" illustrates the basic design provided in this suspension.",
        "texts": [],
        "surrounding_texts": [
            "1384 E. R. STERNBERG\nence should be made to Fig. 31, entitled \"Ridewell Trailing Arm Type Single Rear Axle Air Suspension.\" 7. Western Unit Air Suspensions Western Unit provides air suspensions with both overslung and underslung spring con struction, with the spring serving as the trailing arm. In the case of tandem axle air suspensions, the Western Unit suspensions are generally similar to the single axle air sus pensions, except that two suspensions are re quired for each tandem rear axle unit. In\nthe case of both the overslung and underslung spring units, the design of the tandem axle installation therefore simply results in using two of the basic single rear axle suspensions with the exception of the drive pinion angles which are varied to suit tandem axle operation by changing the spring seats and clips to properly line up the axles from the standpoint of drive pinion angles. Reference should be made to Fig. 33, entitled \"Western Unit Underslung Spring Single Rear Axle Air Suspension,\" and to Fig. 34, entitled \"Western Unit Overslung Spring Single Rear Axle Air Suspension,\" for further details on the Western Unit tandem rear axle air suspensions. Torsion Bar Suspensions Kenworth TBB Torsion Bar Suspension The Kenworth TBB torsion bar suspension for tandem rear axles is similar in design principles to the Kenworth TBS series single rear axle torsion bar suspensions, but the tandem axle suspension uses two torsion bar springs twisted by opposed crank assemblies. All springing is taken in torsion and there is no bending of the bars which are pre stressed to twist in one direction only and must be installed in pairs. Capacities range from 34,000 to 44,000 pounds at the ground with 1-1/2\" diameter bars provided for the 34,000 to 38,000 pound capacity and 1-5/8\" diameter bars provided for the 44,000 pound capacity. Two lengths\nof bars are provided, one being 66\" long and available only in the 1-5/8\" diameter and which is normally specified when maximum stability is required. The 108\" bar is available in either 1-1/2\" or 1-5/8\" diameter. The larger diameter bar provides greater stability than provided with the 1-1/2\" diameter bar. This suspension is suggested for all operations where good riding quali ties are required except in mixer operations and where high center of gravity loads are involved. Fig. 55,\nentitled \"Kenworth TBB Torsion Bar Tandem Rear Axle Suspension,\" illustrates the basic design of this suspension which incorporates a single torsion bar located at each side of the frame. Rubber Suspensions A variety of suspensions incorporating rubber as the suspension means are avail able. Rubber can be used in compression, in shear, or in torsion providing a rather wide variety of rubber suspension systems. 1. Chalmers\nRubberSuspension - The Chalmers tandem rear axle rubber suspension (15) uses variable rate hollow rubber springs as the suspension means. Fig. 56, entitled \"Chalmers Rubber Tandem Rear Axle Suspension,' illustrates the design provided in this sus pension, which is similar to the Chalmers single rear axle suspension. Rubber springs to cover a nominal capacity range of from 34,000 to 44,000 pounds can be provided(16). Because f the variable rate feature, this type\nof suspension, with the proper selection of the rubber springs, is suitable for use in on-highway operations, including tractor service, and for use in on and off highway operations. 2. Hendrickson RSSeries Rubber Load Cushion Suspensions - The basic design of the Hendrickson RS series suspension is similar to the Hendrickson spring and ex tended spring suspensions except that the leaf springs are eliminated and rubber load cushions are located between frame brackets anda saddle generally similar to the type used on the Hendrickson AR series air suspension. Vertical drive pins are pro vided with rubber bushings to trasmit the drive between the axles and the frame.",
            "HEAVY-DUTY TRUCK SUSPENSIONS 1385\nDeflection is relatively limited and therefore the suspension is primarily intended for operations where stability and resistance to rollover are primary considera tions. However, because of the relatively light weight and durability of these suspen sions, a number of them are also used in tractor applications. In such cases, special care must be taken in selecting the rubber load cushions which are available in a variety of durometers and also in a variety of designs from the standpoint of the amount of rubber provided within the overall con figuration of the load cushion. The 34,000 and 38,000 pound suspensions use two load cushions per side, while the 44,000, 50,000 and 65,000 pound capacity suspensions use three load cushions per side. A third load cushion can be provided on the 34,000 and 38,000 pound suspensions when increased stability is required.\nFig. 57, entitled \"Hendrickson RS Series Tandem Rear Axle Rubber Load Cushion Suspension,\" illustrates the basic design provided in a suspension of this type having a capacity of 38,000 pounds\n3.Hendrickson SR Series Shear Ride\nSuspensions - The Hendrickson SR series suspension is generally similar in appear ance to the RS suspension except that the rubber load cushions used in compression are replaced with rubber springs in shear. These springs are of the two-stage type and are located at the ends of the saddles. Under light load, both stages are in shear to provide a lower load rate, but at rated load, a flange on the vertical drive pin cushions out the first stage, increasing the rate of the rubber springs and thereby providing for reduced deflection as the rated load capacity is reached. Vertical drive pins are used to pro vide the drive between the axles and the frame. The same basic walking beam con struction as provided in other Hendrickson suspensions is incorporated in this design. Shear ride suspensions are available in the 34,000 and 38,000 pound capacity only.\nelastomer type rubber springs with, in effect, divided walking beam. Fig. 59, entitled \"Ridewell Dynalastic Tandem Rear Axle Suspension,\" illustrates the basic design of this suspension. Trunnion type frame brackets are pro vided with a through cross tube on which a compensator assembly is mounted. Elastomer type rubber springs are mounted to the com pensator assembly at each end and are also attached to torque beam assemblies at the lower end of the springs. The torque beam assemblies are pivoted in the compensator assembly and therefore instead of a single beam, two separate \"half beams\" are provided so that each elastomer type spring is free to deflect independently f the other springs used in the suspension. Upper torque rods are provided so that the axles are held in alignment by a parallelogram type arrange ment. This suspension is normally used with drive axles of the 34,000 and 38,000 pound capacity range and is primarily used in highway operations, particularly of the tractor type. 5. White Velvet Ride Rubber Torsion Suspension - The White Velvet Ride suspension (developed under a license from Elwood Willitts) is a premium type suspension using rubber in torsion as the suspension means. Static spring deflection at rated load is approximately 2-5/8\" providinga frequency of approximately 115 cycles per minute; The suspension consists of an integral cross member and frame brackets supporting canti lever type pivot tubes on which two indepen dent spring arm assemblies are attached. Two rubber springs in torsion are provided with the secondary spring supporting the full chassis weight and undergoing both torsional and vertical static deflection. The main spring is pressed into one of the arms and subject to torsional loading. Attachment of the arms to the axles is similar to the installation provided on the Hendrickson suspensions and upper tor que rods are provided to maintain the proper drive pinion angles. Shock absorbers are provided to dampen excessive movement under resonant conditions, due to the fact that there is no inherent friction other than the hystersis in the rubber. Further details on this suspension are provided in the SAE paper listed in the reference section (17). The basic suspension is illustrated i Fig.",
            "1386 E. R. STERNBERG\n60, entitled \"White Velvet Ride Tandem Rear Axle Rubber Torsion Suspension.\" Solid Mount Suspensions\nSolid mount suspensions are limited to certain restricted applications in which they should be used, particularly due to the fact that the ride provided is not satisfactory for on-highway operations but in mixer applications where maximum stabil ity and resistance to rollover is of primary importance, the use of solid mount suspen sions is increasing in popularity. As a result, a variety of solid mount suspensions, which eliminate the springing means between the frame and the axles but still permit the axles to articulate in relation to each other and to the frame as uneven terrain is nego tiated, are being provided. 1.Hendrickson R Series Walking Beam Suspensions - The Hendrickson R Series solid mount walking beam suspensions are basically similar to the Hendrickson leaf spring sus pensions except that the leaf spring and attaching brackets are eliminated completely and a centrally located trunnion bracket is attached to the frame with the walking beam pivoting about the trunnion tube. The upper torque rods are retained to provide a parallelogram effect in conjunction with the walking beams. The basic design of this suspension is illustrated in Fig. 61, entitled \"Hendrickson R Series Tandem Rear Axle Solid Mount Suspension.\" Suspensions of this type are available in a capacity range of 34,000 through 65,000 pounds and are recommended for on and off highway use where stability is a prime consideration. Operations in which this type of suspension is used include trucks intended for oil field use and for concrete mixer service. 2.Mack Walking Beam Suspensions The Mack suspensions of the walking beam type are basically similar in design to the Mack spring suspensions except that the springs are eliminated and a steel walking beam is mounted on the trunnion tube. Frame brackets support the trunnion tube, with the beams replacing the spring saddle mounted on the ends of the tube. The\nends of the beams are held in place by rubber shock insulators and by the spring seat caps similar to the manner in which the Mack\nsprings are held. Upper torque rods provide a parallelogram arrangement in conjunction with the beams. Suspensions of this type are available in a capacity range of 34,000 through 80,000 pounds. A typical suspension of this type is illustrated in Fig. 62, entitled \"Mack Walking Beam Tandem Rear Axle Solid Mount Suspension.\" 3.\nRockwell Walking Beam InstallationThe Rockwell two overslung spring suspen sions can be converted t solid mount sus pensions by eliminating the springs and substituting cast or fabricated walking beams. Such installations have been provided in both the 4\" and 5\" wide spring suspensions, but specific walking beams for such suspen sions have been provided by certain vehicle manufacturers. Fig.\n63, entitled \"Rockwell Tandem Rear Axle Suspension Modified to Provide Solid Mount,\" illustrates the general appear ance of a suspension f the basic Rockwell design in which springs have been eliminated and walking beams substituted. Tandem Axle Spacings- The standard tandem axle spacing provided varies with the type of suspension and with the capacity of the suspension. Generally, highway type suspensions i the 34,000 and 38,000 pound capacity are provided with a standard spac ing of 50\", while four spring suspensions which are sometimes limited as to the mini mum spacing which can be provided by virtue of the necessity of providinga reasonable length of spring have standard spacings of 50\" to 52\". Heavier suspensions from 44,000 pound capacity and up are normally pro vided with tandem axle spacings ranging from 54\" to 58\". The\nbridge formula approach to estab lishing gross weight limitations on every group of two or more axles and various state laws (7) make it desirable to increase the tandem axle spacing. In Michigan, if the spacing between two axles exceeds 108\", the axles are considered as individual axles. As a result, there have been a num ber of walking beam suspensions provided with 109\" tandem axle spacing. In other states, higher weight limits are permitted on various spacings from 54\" on up and as a result, optional spacings of 54\", 60\", 72\", 96\" and 109\" have been provided from"
        ]
    },
    {
        "image_filename": "designv11_28_0000550_robot.2000.844843-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000550_robot.2000.844843-Figure1-1.png",
        "caption": "Fig. 1: Normalized task velocity",
        "texts": [],
        "surrounding_texts": [
            "the operational space like below\nf c = 4 q ) B + q(q, 4 ) - f, (3)\nwhere f , E 92\" is the fictitious force vector applied to the end-effector of the manipulator, A = (JM-'JT)- ' E Rmxm is the pseudo-inertia matrix [3] , and q E 3tm is the non-linear force vector.\n2.2 Modeling of impulsive contact\nWe can derive the model of impact dynamics from the basic assumption, that is, impact occurs at time t and lasts for an infinitesimal period, 6t , of time [ll]. Under this assumption, we integrate both sides of Eq. (2) over 6t as follows\nt+6t Tcdt = 4 [Mij + Cq - J T f ] d t . (4)\nThen, because all linear and angular velocities remain finite, and there are no changes in positions or orientations of any bodies in the system as 6t + 0, the integrals involving rc and C(q, q)q in Eq. (4) become zero. So we can rewrite Eq. (4) as the following equivalent equation.\nM-' JTFimp = lim [q(t + bt) - q(t)] = Aq (6) 6t-0\nJ M - ~ J ~ F ~ ~ ~ = J A ~ = f i (7)\nFimp = (JM-'JT)-lAfi = A(q)Afi. (8)\nThe discontinuity of velocity will happen at the moment of impact between the robot and the environment has infinite or sufficiently large mass. The jump in velocity has to be specified through a so-called restitution rule which relates post- and pre-impact velocities. This rule is expressed as:\n( p + Ap)Tn = -epTn, (9)\nwhere n is the unit vector normal to the plane of contact between the end-effector and the environment, and e is the constant coefficient of restitution denoting the type of collision taking place. Finally, we note that the impulsive force is generated only in the direction of normal to the contact plane. Therefore, we can write\nFimp = Fimpn. (10)\nFrom Eqs.(8), (9), and (lo), the following equation can be easily derived:\nThis equation defines the magnitude of the impulsive force in terms of three controllable parameters, i.e., the manipulator's configuration(q) at impact, the pre-impact velocity(fi) of end-effector, and the unit vector(n) normal to the plane of collision impact [SI.\n3 Normalized impact geometry\nWe can easily visualize the characteristics of manipulator kinematics and dynamics through some geometrical representation, for example, many kinds of ellipsoid structures [1,7,9, lo].\n3.1 Dynamic and Generalized impact ellipsoid\nIn 1994, Walker [?] proposed the dynamic impact ellipsoid which represents relative magnitudes of the impulsive impact forces corresponding to the unit ball of changes in joint velocities of the robot. Also, he proposed the generalized impact ellipsoid and explained it from the viewpoint of the change of kinetic energy. Based on Eq.(6), the dynamic impact ellipsoid and the generalized impact ellipsoid in Rm are described respectively by Eqs. (12) and (13).\nRecalling Eq. (6) again, the dynamic impact ellipsoid is formed by those contact impulse force Fimp that corresponds to instantaneous changes in the joint velocities Aq with unit norm or less, i.e., IIAqlr = AqTAq 5 1. Also, the quantity Fimp (JM-'JT)Fimp L. 1, for a given force Fimp, is the change in kinetic energy, AqTMAq, of the robot due to the collision. However, there are two limitations in those ellipsoids. Firstly, the magnitude and direction of task velocity, which play an important role in the magnitude of impulsive force as Eq. ( l l ) , are not considered. And, secondly, the magnitude of those ellipsoid does not directly represent the impact force. From Eq. (lo),",
            "Eqs. (12) and (13) may be represented as follows:\nFimp = 1/JnT(JMW2JT)n,\nIf these are compared with Eq. ( l l ) , we can easily find that these do not represent exactly impact forces. Next, let's consider the generalized impact ellipsoid with the following relations:\n2AEk = 2(&, - Eki) = qTMqf - qTMqi (15)\n= AqTMAq + 2AqTMqi,\nwhere Ek means the kinetic energy of the robot manipulator. As shown in Eq. (15 ) , the generalized impact ellipsoid does not mean the change of kinetic energy at all.\n3.2 Normalized impact geometry\nLet n be the unit normal vector to the environment. Then, we define the normalized impact geometry in SE\" based on nT$:\nI - nTp,I 5 1. (16)\nThen,\nnT(JM-'JT)nFt 5 1. (n E SE\"), (17)\nwhere Ft = %. This new geometry means the range of directional impact force for given n-directional task velocity like Eq. (16) . From Eqs. (10) and (13), the following equation is derived:\nwhere nTAp is the task velocity change along the normal direction of environment. And, as shown in Eq. (9), we can derive\nnTAp = nT(JM-' JT)nFimp, (18)\nnTAp = -(1+ e)nTp. (19)\nTherefore, if the magnitude is 1, the following relation is obtained:\nnT(JM-lJT)nFt = 1 (n E SE\"). (20)\nConsequently, the smallest axis in Fig. 2 is the preferable direction of impact reduction and this impact geometry has clear physical meaning as can be seen in the following examples.\n3.3 Numerical example\nAs shown in Fig.3, the end-effector is located at (O.O70.4)m and the pre-impact velocity to the normal direction of environment is about 0.24m/s.",
            "Then, for several task directions, impact forces are generated and depicted in Fig.4. Fkom this figure, we can find that the proposed normalized impact geometry agrees with physical intuition. Namely, the proposed geometry indicates the impact force when the velocity component normal to the environment is equal to 1.\n4 A new impact performance index\nMany former researchers used the denominator of Eq.(ll) as a performance index to resolve null motion of redundant manipulators for impact reduction. If we maximize this index of Eq. (21), the magnitude of impact force will be minimized.\nm(q) = nT(JM-'JT)n. (21)\nThere are, however, some assumptions that the task velocity(@) is already known and the restitution constant(e) is given. Also, the unit vector(n), which is normal to the contact plane, is supposed to be known. Therefore, the only controllable parameter is the configuration(q) of manipulator at the moment of impact. Therefore, if we don't have any information of environment, we cannot use it. However, as we already know that the impact force also has some relations with the direction of task velocity, if we use this additional characteristic of impact, then we can accomplish the impact reduction especially for the first impact, even the environment is unknown.\n4.1 Impact performance index based on velocity direction\nThe basic idea is the change of linear momentum which is equivalent to the magnitude of impulsive force:\nwhere P is a linear momentum. Therefore, if we reduce the momentum to the velocity direction using null motion of redundant manipulators, the impulsive effects are also reduced. Now, let's replace the direction vector n of Eq.(21) by the task velocity direction of manipulators as if we know the wall is lying in velocity direction like Fig. 5. Then, we define Eq. (23) as the impact performance index based on velocity direction:\nAP = A(mp), (22)\nm\"(q) = uT(JM-'JT)u, (@d - @ = 0) (23)\nwhere v = is the task velocity direction of manipulators. We will use above U instead of U = &, assuming good velocity servo performance. This simple strategy will reduce the first impact even for uncertain environment. After the first impact, however, the geometry information of environment can be obtained from a forcetorque sensor. So, we can use the same impact performance index with others from the second impact. IlPdll\n4.2 Simulation study\nHere, we illustrate the impact reduction property of the proposed impact performance index by presenting some simulations results. The simulated manipulator is a rigid three-link planar redundant manipulator without gravity. The surface of environment is modeled as a spring with stiffness KB = 2 x 105N/m to represent a hard surface. For simulations and experiments in this article, a systematic decomposition method is used, that is, the kinematically decomposed joint space decomposition(KD-JSD) method by Park [5]. The controller based on KD-JSD is Eq. (24), which is composed of PD-type task motion controller and null motion damping controller.\n+ ZW#( i iw) ,d + K n t n - (iw + Zfi )qd)} + Cq, (24)\nwhere the weighted matrix W is selected as the joint inertia matrix M , Z is the null bases matrix, ni denotes null state, e is @d - p , e is pd - p , and en is n W 3 , d - n W 4 -\n1 7.1 7"
        ]
    },
    {
        "image_filename": "designv11_28_0002507_robio.2006.340096-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002507_robio.2006.340096-Figure1-1.png",
        "caption": "Fig. 1. Reference frames.",
        "texts": [
            " This section will first give an overview of the coordinates used to describe the position and orientation of the snake robot. Subsequently, the gap functions will be presented. 1-4244-0571-8/06/$20.00 C)2006 IEEE 1181 A. Coordinates and Reference Frames The snake robot consists of n cylindrical links that are connected by n -1 cardan joints, each having two degrees of freedom (DOF). The distance Li between two adjacent cardan joints equals the length of link i, and the radius of each link is Lsc. We denote the earth-fixed coordinate frame I = (0, ex, el, el), see Fig. 1, as an approximation to an inertial frame where its centre 0 is fixed to the ground surface and the el-axis is pointing in the opposite direction of the acceleration of gravity vector g. The position and orientation of link i are described by the non-minimal absolute coordinates q Pirj (1) where IrGi (E R3 is the position of the centre of gravity of link iandthevectorpi= [eio eT]T,whereeT= [eC ei2e,31, contains the four Euler parameters used to describe the rotation. The Euler parameters form a unit quatemion vector with the constraint pTPi = 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000687_robot.2002.1014792-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000687_robot.2002.1014792-Figure1-1.png",
        "caption": "Figure 1: Coordinate variables for RRR planar robot",
        "texts": [
            " One of the last n - 2 joints is passive, say the kth joint, k E (3,. . . ,n). In this case, the proximal joints 3 to k - 1 and the distal joints I C + 1 to n, all actuated, can be steered to their desired positions and then blocked, so as to reduce robot motion to that of three rigid bodies. The system reflects then the control properties of an RRR robot. In the remaining analysis, carried out in the next sections for n = 3 and m = 2 actuated joints, we shall make use of two different sets of generalized coordinates (see Fig. 1): the set { q l , q 2 , q 3 ) consists of the three relative link angles (with the first one measured w.r.t. an arbitrary reference z-axis), while the set {z, y, 03) expresses the Cartesian location of the third joint and the absolute angle of the third link w.r.t. an arbitrary reference x-axis. 4.1 Actuator configuration: RRZ This system has already been found to be STLC in [7]. We will check this result with our Proposition 1. Relying on the coordinate system {z, g, &} , the inertia matrix B(q) is [17] 1 bll (z, Y) b12(z, Y) -m3d3s3 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003491_pes.2008.4596941-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003491_pes.2008.4596941-Figure3-1.png",
        "caption": "Fig. 3. Schematic diagram of a five-phase permanent magnet motor. Back emf and phase currents in the stator currents are defined under phase-a open-circuit fault condition.",
        "texts": [
            " From the symmetry of rotary machine structure and mirror symmetrical spatial distribution of phase-k and phase-m it can be seen that phase-k current at rotor position \u03b1 should be equal to the phase-m current at rotor position \u03b1\u2212 and vice versa ( 1221 , mkmk iiii == ). This can be mathematically expressed as: T mk ii )()( \u03b1\u03b1 \u2212= (1) For sinusoidal excitation, the fault tolerant current in the phases which are symmetrically located with respect to the fault axis can be defined as in (2). The symmetrical currents are shown in Fig. 2. )cos( \u03b8\u03c9 \u2212= tIik )cos()cos( \u03b8\u03c9\u03b8\u03c9 +=\u2212\u2212= tItIim (2) Consider the schematic diagram of a five phase PMM as shown in Fig. 3. If an open-circuit fault occurs at phase-a, the remaining healthy four phases has to be controlled to compen- sate the fault and produce the required torque. It can be seen, with respect to faulty phase-a, phase-b & phase-e are symmetrically located, so are phase-c and phase-d. Considering the rotor at a speed\u03c9 , the back-emf induced in the five stator phases ),,,,( edcba eeeee are defined in Fig. 3. Consider, in general, any phase with back emf )cos(. \u03b2\u03c9 += tEe and current )cos(. \u03b8\u03c9 += tIi . The instantaneous power s in the phase can be expressed as in (3): qpies +== . ( ) )2cos( 2 cos 2 \u03b8\u03b2\u03c9 \u03b8\u03b2 ++= \u2212= t EI q EI p (3) From (3) it can be found that, instantaneous power consists of two components. One is constant torque producing real component p and other is pulsating torque producing reactive component q . To achieve fault tolerant operation of the five-phase machine the summation of the real components (\u2211 p ) in the healthy phases should produce the required mechanical output",
            " As per this existing solution the values of the variables ),,,( 2211 \u03b8\u03b8 II can be found as: ( ))5cos(1)(21 \u03c0\u03c9 +=== ETIII 51 \u03c0\u03b8 = , 542 \u03c0\u03b8 = (8) But it is not verified that whether this solution is an optimal one to produce minimum stator ohmic loss. To find such optimal solution in this work the stator ohmic loss is minimized. Considering equal stator phase resistances, a loss function lw representing the equivalent total stator ohmic loss can be defined as in (9). 2 2 2 1 IIwl += (9) These emfs are known quantities. Using (2) from the previous Sec-II, the unknown fault-tolerant control currents in the four healthy phases ),,,( edcb iiii can be defines as in Fig. 3. It can be seen that due to the application of current symmetry only four variables ),,,( 2211 \u03b8\u03b8 II are to be determined. By using (6), (6) and (7), the loss function lw (9) can be expressed as a function of only 1\u03b8 as below: ( ) ( ){ } \u23a5 \u23a6 \u23a4 \u23a2 \u23a3 \u23a1 \u2212\u2212++ \u239f\u239f \u23a0 \u239e \u239c\u239c \u239d \u239b \u2212 = 2 121 2 2 tan).52sin()54cos()52cos( )54(sin 1 tan2 . )54cos()52cos(2 \u03b8\u03c0\u03c0\u03c0 \u03c0 \u03b8 \u03c0\u03c0 \u03c9 ET wl (10) The condition for minimum ohmic loss can be obtained by making 01 =\u03b8ddwl . Using this condition a closed-form optimum solution of 1\u03b8 can be obtained as in (11)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001161_s0009-2509(00)00353-5-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001161_s0009-2509(00)00353-5-Figure8-1.png",
        "caption": "Fig. 8. Di!usion in a PVA gel.",
        "texts": [
            " The growth of the maximum size cluster can be found in Table 1. The formation of the two phases can be observed from the structure factor S(k, t) (see Fig. 7a). Owing to the interrupted spinodal decomposition the maximum of the S(k, t) curve is not as high as for a complete decomposition (see Fig. 7b). The structures given in Fig. 6 and similar ones with di!erent PVA concentrations were employed as a framework for the ion di!usion processes. The di!usion of ions within the hydrogels can be visualized as in Fig. 8. The PVA gel causes a fractional decrease D/D in the rate of di!usion of a small solute. D represents the di!usivity in water. The presence of impenetrable polymer molecules leads to an increase in the path length for di!usion. The phenomenon is called obstruction e!ect. Other e!ects were reviewed by Muhr and Blanshard (1982). The obstruction e!ect is dominating in the present system. The di!usivities of the ions in diluted solutions relevant for nitrate reduction can be found in books by Mills and Lobo (1989) or Yizhak (1997)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002807_02286203.2006.11442366-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002807_02286203.2006.11442366-Figure1-1.png",
        "caption": "Figure 1. Per-phase equivalent circuit of a three-phase SEIG.",
        "texts": [
            " The other important feature of the present approach is the possibility of determining more than two unknown parameters simultaneously. Therefore, it can be used to obtain the performance characteristics of three-phase (or single-phase) self-excited induction generator feeding three-phase (or single-phase) induction motor. To confirm the validity of the proposed approach, simulation results are compared with the corresponding experimental test results. The steady-state per-phase equivalent circuit of a SEIG supplying a balanced RL-load is shown in Fig. 1. In this model, the normal assumptions [1\u20134] are considered: core losses as well as harmonic effects are ignored and all machine parameters, except the magnetizing reactance XM , are assumed constant and independent of magnetic saturation. Using the circuit of Fig. 1, the loop equation can be given by: ZT IS = 0 (1) Under steady-state self-excitation, the total impedance ZT must be zero, as the stator current IS should not be zero. ZT can be expressed by: ZT = ZLZC ZL + ZC + ZS + ZMZR ZM + ZR (2) where: ZL = RL F + jXL (3) ZC = \u2212jXC F 2 (4) ZS = RS F + jXS (5) ZM = jXM (6) ZR = RR F \u2212 \u03bd + jXR (7) Equation (2) is a nonlinear equation of four variables (F,XM , XC , \u03bd). If two of these parameters are given, a numerical technique, like Newton\u2013Raphson method [2], could be used to find the values of the two unknowns, such as XM and F"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003112_j.triboint.2008.01.007-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003112_j.triboint.2008.01.007-Figure2-1.png",
        "caption": "Fig. 2. Schematic of the ball-disk worn mode.",
        "texts": [
            " The obtained tribopolymer was subjected to various characterizations to deduce the mechanism of tribopolymerization. The rubbing experiments were conducted on a homemade pin-on-disk device. It consists of a steel disk attached to a milling machine spindle and a beam that loads a ball (the pin) against the rotating disk. A lubricant cup held the fluid to completely cover the ball and the disk surface, and the temperature of the lubricant fluid was controlled by circulating water. Fig. 1 shows a sketch of the device (Fig. 2). The ball (diameter 10mm) was made of GCr15 (AISI52100) bearing steel. The disk was made of AISI1015 steel, with a diameter of 60mm and a thickness of 5mm. BA and styrene were purified via vacuum distillation over CaH2 at a N2 atmosphere. n-Butyl alcohol, hexadecane, acetone, methanol, hydroquinone, and calcium hydroxide are all analytical reagent (AR) grade reagents used without further purification. All the reagents were purchased from Beijing Yili Chemical Reagent Co. Ltd, China. For BA- (with or without 1wt% n-butyl alcohol) and styrene-lubricated tribopolymerization tests, the experimental conditions are: 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000418_095440603767764426-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000418_095440603767764426-Figure7-1.png",
        "caption": "Fig. 7 A ruled surface by the change of the constraint wrenches when the linkage operates",
        "texts": [],
        "surrounding_texts": [
            "A new approach of analysing con guration changes of the Schatz linkage has been proposed by examining the reciprocal screw and the relationship between the reciprocal screw and the stem-screw system in which the reciprocal screw was obtained using the cofactor approach. This generated an algebraic surface formed by the trajectory of the reciprocal screw. The relationship between the reciprocal screw and the stem-screw system has been examined. There are four intersections when the reciprocal screw has zero pitch in which the reciprocal screw becomes a subset of the stemscrew system. On these occasions, the reciprocal screw is a combination of joint screws $1 and $5 when the drive angle is 08 and p, and a combination of joint screws $2 and $6 when the drive angle is 908 and 2708. The corresponding four special con gurations were then presented. Apart from these four con gurations, there are no other intersections between the reciprocal screw and the stem-screw system. The reciprocal screw and the stemscrew system are hence disjoined. The study helped the analysis of the constraint wrench, which acts along the reciprocal screw and does no work to the linkage. This presented a change of con gurations with a ruled surface of the trajectory of the constraint wrench."
        ]
    },
    {
        "image_filename": "designv11_28_0003082_1.2736431-Figure11-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003082_1.2736431-Figure11-1.png",
        "caption": "Fig. 11 Geometric relationship between stick-rotation angle and displacement increments",
        "texts": [
            " 9 reveal that the rolling-stick contact is a complex process with energy dissipation, the conventional friction coefficient, defined as the ratio between tangential resistance and normal compressive force, is not sufficient to describe the physics involved in this process. In order to characterize the adhesion-friction behavior under this situation, this paper suggests an \u201cadhesion friction coefficient\u201d for plane strain rolling contact with nonsingular adhesion that is defined by A = Q T0 2R/ 6G + P 48 where Q is the friction resistance force, parallel to the rolling/sliding direction; P is the applied force normal to the rolling direction 34,35 . ppendix A: The Boundary Condition (23) According to the geometric relation illustrated in Fig. 11, the orizontal and vertical displacements, denoted as uII and vII, re- pectively, can be expressed as ournal of Tribology om: http://tribology.asmedigitalcollection.asme.org/ on 07/01/2013 Terms JULY 2007, Vol. 129 / 491 of Use: http://asme.org/terms A a s o h t A F n m = 4 Downloaded Fr uII = 2R sin 2 cos 2 + vII = 2R sin 2 sin 2 + A1 pplying the Talyor\u2019s expansions sin = \u2212 3 3! + \u00af cos = 1 \u2212 2 2! + \u00af A2 nd = t R A3 ubstituting A2 and A3 into A1 , and leaving out the high rder small terms in the above relations one obtains: According to the geometric relation illustrated in Fig. 11, the orizontal and vertical displacements, denoted as u and v, respecively, can be expressed as u = 2R sin 2 cos 2 + v = 2R sin 2 sin 2 + A1 pplying the Talyor\u2019s expansions ig. 10 The relationship among maximum adhesion T0, total ormal compression force P, and the corresponding resultant oment M, where T\u03040=T0 / \u201e6G\u2026, P\u0304=P / \u201eRG\u2026, M\u0304=M / \u201eRbG\u2026, and b 1 for the plane strain + 1 92 / Vol. 129, JULY 2007 om: http://tribology.asmedigitalcollection.asme.org/ on 07/01/2013 Terms sin = \u2212 3 3! + \u00af cos = 1 \u2212 2 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002025_cdc.2003.1271951-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002025_cdc.2003.1271951-Figure5-1.png",
        "caption": "Fig. 5. mot& caordinate system",
        "texts": [
            " Takeda and T. Hirasa: Loss minimization control of permanent magnet synchronous motor drives, IEEE trans. on Industrial Electronics, IE41, NOS, pp.511/517 (1994) [ I 11 K. Ohyama and M. Kosaka: High efficiency control for interior permanent magnet synchronous motor, Prw. of IPEC-Tokyo 2000 (International Power Electronics Conference), pp.614/620 (2000) APPENDIX Nomenclature, subscripts and superscripts Here, nomenclature, subscripts and superscripts are de- The motor coordinate system is shown in Fig. 5. scribed. The following subscripts and superscripts are defined. .U, V, &I/ denote 3-axis stationary frame quantities[4]. .a, denote 2-axis rectangular stationary frame quantities. o denotes neutral point quantities[4]. d, q denote 2-axis rectangular synchronous frame quantitiesl41. .T denote transposed matrix. . \" denotes estimated quantities. .kJk - 1 denotes prediction step quantities. .klk denotes innovation step quantities. .* denotes reference quantities. .t means time. .W. 0 mean motor speed and rotor position, respectively, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002994_imsccs.2006.26-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002994_imsccs.2006.26-Figure1-1.png",
        "caption": "Fig. 1. Rhomb grid",
        "texts": [
            " The VRGMSD algorithm (1) can form a MCDS and the MCDS has k-robustness relative to one constructed by single node; (2) ensures that there is no \u201choles\u201d in the sensor field; (3) can select different k (the degree of coverage or connectivity) according to the demand on different applications. This flexibility allows the network to self-configure for a wide range of applications. We assume that all sensor nodes have identical capabilities for sensing, communication. Also, we assume that the initial deployment is random. Another assumption is that every node has the ability to know its own location by some method such as GPS [19] or other methods [20]- [23]. At last, we assume that each node can be mobile. To illustrate in Figure 1, each sensor associates itself with one of the vertices of a rhomb grid. The rhomb grid both makes enough use of sensing and communication range and ensures full coverage and full connectivity of sensor field. Furthermore, the minimum number of the nodes in sensor field covered fully and seamlessly is determined by the equation [24] (1) ( )23 3 2 2 2= = 1 3 3rr F F FN \u03b4 = Where F is the area of the sensor field, 3 3 2 2 r\u03b4 is the effective area of each sensor, the r is the radius of sensing or communication of sensors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001681_robot.2004.1307975-Figure13-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001681_robot.2004.1307975-Figure13-1.png",
        "caption": "Fig. 13. . Search Trajectoty on XZ Fig. 14. Plane Desired Point Reference- Point and",
        "texts": [
            " In this paper, task condition is evaluated as follows Condition A = Ivy1 > Ivydl U a~vy > 0, (3) where, V, is insertion velocity, Vyd is required insertion velocity and ay is insertion acceleration. If condition is A the manipulator continues the operation with keeping the trajectory, otherwise the manipulator behave to find the condition in which an insertion operation is available. dy is set to make the insertion force F suitable. The trajectory of gripping point on the xz plane is shown in Fig.13. In this paper, we adopt Xd,Yd,Zd at the last time when the insertion is available as xr..f, yTef, zref. We consider that inclinations of insertion direction make the jamming phenomenon. To avoid jamming, the manipulator should estimate the inclinations and revise the insertion direction. The revision method is that a,dy,,j, a,dy,,f are added to desired position of gripping point respectively. The inclinations a and a, are calculated with linear regression using the position of gripping point at the time when insertion operation is available"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002313_dia.2005.7.927-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002313_dia.2005.7.927-Figure2-1.png",
        "caption": "FIG. 2. Schematic diagram of the winged catheter with injection cap with sensor wires: 1, glucose sensor and wires; 2, winged catheter hub with apertures for suturing; 3, injection cap for sensor wire protection; 4, silicon adhesive for securing the sensor wires; 5, opening with catheter removed.",
        "texts": [
            " After the above techniques failed, the following devices were tested and found to be successful in protecting the sensors. All devices were well tolerated by the rats despite occasional minor skin infections observed by the medical staff after many days of implantation. The infection, located remotely from the sensor, did not cause a loss of sensor function and was controlled with cleaning and gentle debridement of the wound edges. A winged 22-gauge intravenous catheter hub was modified by removing the catheter, leaving a 3-mm opening at the base (Fig. 2). At the incision site a 2- 1-cm pocket was opened in the subcutaneous space by blunt dissection. Into the compartment the winged 22-gauge intravenous catheter hub was implanted with the sensor wires in the subcutaneous space threaded through the hub. Once implanted, the end of the catheter hub and sensor wires projected externally. The wires were immobilized using silicone glue placed inside the catheter hub. Injection caps were placed onto the catheter hub to protect the sensor wires. The winged catheter hub was secured using simple interrupted 3-0 Prolene sutures passing through the wings; closure of the skin was completed also using 3-0 Prolene sutures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000319_1.1519275-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000319_1.1519275-Figure4-1.png",
        "caption": "Fig. 4 Model of tooth wear: \u201ea\u2026 Modeling of wear; \u201eb\u2026 Trace of displacement caused by wear",
        "texts": [
            "/2 (5) Where I is the moment of inertia and A is the area of the tooth cross section. Both of these two parameters are related to the thickness of the tooth. From Fig. 2~b!, it is apparent that the thickness of the tooth has a significant effect on the crack area. When substituting the thickness of the tooth with a crack into Eq. ~3!, the crack will affect the deflection and bending stiffness of the tooth. 2.2.3 Modeling Wear. Wear is modeled as the removal of material across the entire width of a tooth. A pictorial of this damage type is displayed in Fig. 4~a!. Because wear typically involves the loss of material over the entire width of a tooth, the profile of a tooth is different from the perfect involute profile. To capture these changes, the distance between the undamaged involute profile and the worn profile along the undamaged line of action is calculated for each position of the mesh. These distances are denoted by d1 , d2 , etc., in Fig. 4~b!. Because d1 , d2 , etc., are rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 09/09/20 equivalent to the removal of material, they are added to the transmission error of undamaged tooth to get the transmission error of damaged tooth. It should be mentioned that because of wear, the contact point and line of action will change from those under the undamaged mesh condition. These factors are not considered since they are to be secondary effects compared with the direct effect that wearing has on transmission error"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003195_s11071-007-9275-5-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003195_s11071-007-9275-5-Figure3-1.png",
        "caption": "Fig. 3 Model of the rotor before and after body separation",
        "texts": [
            " The same result is evident for the translatory moving particle with continual mass variation where the absolute velocity of separation is zero (21) d dt (Mv) = 0. (33) The solution of the Levi-Civita equation [4] v = Q M , (34) shows that if mass decreases the velocity of motion increases. Q depends on the initial values. 4. If the motion of the whole body is translatory, the relative angular velocity and the absolute angu- lar velocity of the remainder body are equal (see Table 2). A symmetrically supported rotor, which is modeled as a shaft-disc system, is plotted in Fig. 3. Mass of the disc is M . The mass center S is in the geometric center of the disc. Mass of the shaft is negligible in comparison to the mass of the disc. The moment of inertia of the disc is IS for the axis z in mass center S. The rigidity of the shaft is c. The motion of the disc is in a plane Oxy. The differential equations which describe the motion of the rotor are Mx\u0308 + cx = 0, My\u0308 + cy = 0, IS\u03c8\u0308 + k\u03c8\u0307 = M, (35) where k is the damping coefficient and M is the torque. The steady state solution for the third differential equation (35) is \u03a9b = M k "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003758_s0020-7373(69)80012-x-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003758_s0020-7373(69)80012-x-Figure4-1.png",
        "caption": "FIG. 4. Mathetics. Mathetics training procedures often depend heavily on visual presentation. Here an overall view of the activity is presented, together with a chained sequence of behaviours (From a program written by Cambridge Consultants (Training) Ltd. for",
        "texts": [
            " Once the state of affairs constituting the solution has been specified, the next thing to consider is: 'What kind of situations could lead up to that state of affairs ?\" When designing a program a mathetics analyst seeks to find a \"master performer\" whose behaviour can serve as a model. The analyst then progresses through a series of defined stages to crystallize the master performance into a form that can be used as a basis for the program. It is in industrial training that mathematics has found its natural home. Figure 4 gives some idea of what the material looks like. British Olivetti Ltd.) Structural Communication is a technique which aims to achieve higherlevel cognitive objectures. This system has been developed by John Bennet of the Institute for the Comparative Study of History, Philosophy and the Sciences, Kingston (U.K.) and Tony Hodgeson, Director of the Centre for Structural Communication, Kingston (U.K.). To quote from their account (Bennet et al., 1967): \"In structural communication the aim is to evoke understanding, not to convey facts except as a by-product"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000880_ijcat.2002.000288-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000880_ijcat.2002.000288-Figure2-1.png",
        "caption": "Figure 2 Coupling displacement.",
        "texts": [
            " The actual tooth load distribution, however, depends on; the clearance between the mating splines (backlash), the tooth stiffness, the rim stiffness, the applied torque and the angle of misalignment. When a straight spline is misaligned, the splines rotate by the angle of misalignment g around a point midway along the spline face length. This hinge is determined by the centering action of the spline teeth. One end of the spline, therefore, moves upward and the other moves downward by a value of Imax, normal to the tooth pro\u00aele, Figure 2 Imax b=2 sin g cosf 5 which is the downward shift of the two teeth at a plane perpendicular to the plane of misalignment. The shift of the other teeth is less than Imax, and depends upon the angular position of the tooth as shown in Figure 3. The displacement at the nth tooth pair In is related to Imax as follows: In Imax cos n\u00ff 1 y 6 where y Angle between two adjacent teeth 360 N degrees N Number of spline teeth n Index number Since the teeth cannot physically overlap with those of the mating spline, the clearance between teeth varies with angular position ny, Figure 4, and the interference at the pair of teeth which is shifted by an angle f from the axis of misalignment in the direction of rotation equals zero [10]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003391_coase.2008.4626479-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003391_coase.2008.4626479-Figure10-1.png",
        "caption": "Figure 10 (a) NAS Test part for comparison of geometric tolerances (b) Faces and edges marked on NAS Test part",
        "texts": [
            " Deviations of these dimensions show a decreasing trend because of the decreasing size of the hexagon. The improvement in accuracy for these dimensions can be achieved by compensating using geometry dependant scaling factors in Y direction. Hence it is observed that dimensional accuracy improves along the scan direction due to new compensation approach. B. Case study II The second part is National Aerospace Standard (NAS 979) component which is usually used for evaluating form tolerance capabilities of machine tools. The test part is shown in Figure 10(a). The NAS test part consists of a circular shape on top of a diamond shape which is on top of a square shape. The faces are identified by the numbers and are marked from F1 to F8 and edges formed out of these faces are marked from E1 to E8 as shown in Figure 10(b). Two versions of the part are fired and process parameters are kept constant. For one of the parts, machine manufacturer suggested scaling factor is used and for other flexible shrinkage model is used. The process parameters are given in the Table I. Flatness values on the sides of the square and diamond sections are measured using a CMM and are plotted in Figure 11 (a). Faces F1 & F3 on the square section are having less flatness for flexible scaling than rigid scaling because of the compensation of non-uniform shrinkage along X direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002530_epepemc.2006.4778540-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002530_epepemc.2006.4778540-Figure9-1.png",
        "caption": "Fig. 9. Length and Section of the equivalent flux tube.",
        "texts": [
            " The value of the permeance A connecting them is i, I calculated by integrating the inverse of the total airgap length function e (0 ) over the overlapping angular zone. s dO A = II +e) i,j f ooutp2 ze(0 ) overlapping zone s (4) E. Massive and Flux Barrier Rotor Reluctance Networks Fig 6 and 7 respectively show the massive and the flux barrier rotor reluctance networks. Both rotors are longitudinally subdivided into 4 zones preliminarily defined to fit the finite element results. The q-axis flux is A. Non Linear Reluctance The flux-tube modeled by a non linear reluctance number <<j >> may have any shape. As shown in Fig.9, its permeance is calculated from its average length L m assuming its section is constant and equal to S eq We define the characteristic yo(V.) linking the flux and I J the magnetic potential of the reluctance number <<j >> with the dimensions of the equivalent flux tube and the magnetization curve of the material. B. Resolution Method The global reluctance network is built to be connex. It has N nodes and N branches. A non linear system of nd br equations is solved to compute the node magnetic potentials"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003508_978-1-84628-469-4_13-Figure13.3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003508_978-1-84628-469-4_13-Figure13.3-1.png",
        "caption": "Figure 13.3. The fuzzification of switching function for a fuzzy sliding mode controllers",
        "texts": [
            " The resulting Fuzzy Sliding Mode Controller (FSMC) is actually a Single-Input-SingleOutput fuzzy logic controller. The input to the controller is the switching function . The output from the controller is the control command . The number of rules in the rule base depends on the fuzzification level of and u ; however it is generally much less than a typical fuzzy logic controller for the same system. A typ al rule of a FSMC has the following format: u s s u s ic IF is PB (and is PB), THEN u is PB or a constant.s s How the switching function is fuzzified is illustrated in Figure 13.3. This kind of rule format effectively adds a boundary layer to the system. This boundary layer is illustrated in Figure 13.4. Figure 13.5 illustrates the relationship of control command u and switching function s s . The main drawback of an FSMC is that, before the fuzzification, the coefficients of the sliding surface have to be pre-defined carefully by an expert. That is, the value of in Equation (13.2) has to be determined first. The only advantage of an FSMC compared with a typical SMC is that in the former case, the boundary layer is nonlinear whereas in the latter case the boundary layer is linear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002697_6.2005-6408-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002697_6.2005-6408-Figure1-1.png",
        "caption": "Figure 1. Pictures of the Bunting Mini UAV",
        "texts": [
            " Therefore, robust control has been developed. This paper focuses on the design of a robust flight control system for a mini-UAV using coupled stability derivatives. Finally, the performance of the robust control system can be compared with the performance of a classical controller in order to analyse benefits of the former method. I. Introduction the Royal Military Academy of Belgium (RMA). The \u201dBunting\u201d MAV is scheduled to make its initial flight in the near future. Pictures of this aircraft can be found in fig. 1. Currently, a flight control system for this unmanned vehicle is under development in cooperation with Delft University of Technology (DUT). The ultimate aim is to make the MAV capable to fly completely independently a trajectory of pre-defined waypoints. The control system is composed of two main parts, namely a stability augmentation system (SAS) and a control augmentation system (CAS). This control system has been developed in two ways, namely by means of classical control and alternatively robust multivariable H\u221e theories"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003240_robot.2007.363872-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003240_robot.2007.363872-Figure1-1.png",
        "caption": "Fig. 1. Examples of different closed-chain systems. Each must satisfy certain closure constraints. (a) Single loop: loop must remain closed. W is the world coordinate frame. (b) Multiple loops: all loops must remain closed. (c) Multiple robot grasping: all robot end-effectors must remain in contact with the grasped object.",
        "texts": [
            "n this paper, we describe this hierarchical chain representation and give a sampling algorithm with complexity linear in the number of links. We provide the necessary motion planning primitives for most sampling-based motion planners. Our experimental results show our method is fast, making sampling closed configurations comparable to sampling open chain configurations that ignore closure constraints. Our method is general, easy to implement, and also extends to other distance-related constraints besides the ones demonstrated here. I. INTRODUCTION Closed-chain systems, as in Figure 1, are involved in many applications in robotics and beyond, such as parallel robots [12], closed molecular chains [16], animation [4], reconfigurable robots [7], [14], and grasping [6]. However, motion planning for closed-chain systems is particularly challenging due to additional constraints, called closure constraints, placed on the system. Using only the traditional joint angle representation, the probability that a random set of joint angles lies on the constraint surface is zero [9]. Instead of randomly sampling in the joint angle space to find closed configurations, we propose Planning with Reachable Distance (PRD)",
            " 2694 configurations that ignore closure constraints entirely. Our method is easy to implement and general \u2014 it can be applied to other articulated systems. It is also extendible to more distance-related constraints besides the ones here. For example, it can be used to sample configurations with the end effector in specific regions. II. PRELIMINARIES This paper focuses on closed-chain systems. A closedchain system differs from other systems in that it must also satisfy certain closure constraints. Figure 1 gives examples of different types of closed-chain systems. Each system has a different set of closure constraints to satisfy. Closed-chain systems are traditionally represented by the position and orientation of the base or a base link and one or more angles for each joint (corresponding to the joint\u2019s dof). For example, the single loop in Figure 1(a) is represented by 11 values: 6 for the position and orientation of link l0 and 5 for the angles \u03b81 . . . \u03b85. While this representation sufficiently describes a configuration, it is extremely difficult to sample these parameters randomly while satisfying the closure constraints. This is because this joint angle representation does not also encode the closure constraints \u2014 they are handled separately. In fact, it has been shown that the probability of randomly sampling a set of joint angles that satisfy the closure constraints is zero [9]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000678_irds.2002.1041739-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000678_irds.2002.1041739-Figure5-1.png",
        "caption": "Fig. 5 Search-Type Motion Primitive",
        "texts": [
            " Figure 3 shows that the search direction to the exact insertion position depends on the position at which the manipulated object is touched and uncertainty in sensing and control of the position by the robot. If the human teaching data of this kind of insertion motion is used, the robot may fail to fmd the insertion position and to achieve the insertion task (Fig. 4). In this paper, we deal with this \u201csearch-type motion\u201d as an important typical example of the motion that includes non-deterministic contact state transition. First, we compare a search-type motion primitive with a conventional skilful motion primitive (Fig. 5). Figure 5a illustrates a motion that consists of conventional skilful motion primitives. The same contact states as the contact states extracted from the motion demonstrated by a human operator are achieved by using the corresponding skilful motion primitives. After hand-eye calibration of a robot is done, the manipulated object is guaranteed to be positioned to the destination point within a certain precision in a free motion. The position of the grasped object can he regarded as \u201cvisually constrained by the calibration. Each contact state transition is detected and achieved using sensory data (i.e. force sensor) in a tine motion. Figure 5b illustrates a motion that includes a search-type motion primitive. The object is positioned \u201cvisually\u201d near the insertion position and the exact insertion position is searched. In this case, since the visually constrained state includes many contact states, the desired contact state should be searched in this visually constrained state. We need two tools in order to achieve this search-type motion as well as skillful motion primitives (Figure 6). The frst one is sensory constrained motion primitive [5] that makes a sensory constrained state (for example, a visually constrained state, Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002023_j.jnnfm.2004.02.004-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002023_j.jnnfm.2004.02.004-Figure2-1.png",
        "caption": "Fig. 2. Graphical illustration of the projection of the four-parameter general linear planar flow-liquid system (p1, p2, p3, a) onto the corresponding two-parameter simple shear flow-\u201cliquid\u201d system (Pe, a\u0304).",
        "texts": [
            " Since |a| < 1 for real aspect ratios r, 0 < r < \u221e (see (2)), a\u0304 real with |a\u0304| > 1 in a simple shear flow is equivalent to an imaginary value of r. Alternatively, this correspondence shows that application of the Doi theory with |a| > 1 in simple shear corresponds to another planar flow type of a physical aspect ratio liquid, indeed a one-parameter family of planar flows and aspect ratios linked by \u03c9a = constant! (see below for a variety of examples). This gives credence to applications of the Doi theory for |a| > 1 [23] and to the use of any real shape parameter a, as a \u201csliding parameter\u201d [7]. Fig. 2 depicts the correspondence principle graphically. Any general linear planar flow with non-zero vorticity, by (17), uniquely determines the ordered pair ((2p1)/(p2 \u2212 p3), (p2 + p3)/(p2 \u2212 p3)) (which specifies the flow type) and the Peclet number Pe (which can be considered as a third coordinate transverse to the plane of Fig. 2, parametrizing strength of that flow-type). The horizontal axis represents all four-roll mill flows (23), and the vertical axis represents all canonical flows (19). Simple shear (with rate parameter Pe = p2) (20) is the single point (0, 1). Retaining the parameter Pe transverse to Fig. 2, we want to map this entire plane onto (0, 1), retaining the correspondence between kinetic theory \u201ctriples\u201d in the process. Each point in this 2D space has \u201cpolar coordinates\u201d determined by the rotation angle \u03b4 and the renormalization \u201cradius\u201d \u03c9. (The angle in this figure is determined assuming Pe = p2 \u2212 p3 > 0. If Pe < 0, signs of all angles should be reversed.) If we rotate the x\u2013y axes by the angle \u03b4, every planar flow (17) becomes a canonical flow (33) in the rotated coordinates so that the plane in Fig. 2 is mapped onto the vertical axis. Flows with zero vorticity lie at \u221e in Fig. 2 and are handled separately in Section 4.3. After we renormalize the aspect ratio, the canonical flow then becomes the simple shear flow, i.e., the vertical axis is then mapped onto the simple point (0, 1). Since Pe was arbitrary in this two-step correspondence, one retains a flow-strength degree of freedom and a renormalized aspect ratio parameter a. We make a note here about the moments of the PDF. Since after the rotation step, m in the original coordinates becomes m\u0304 = U \u00b7 m, we have:\u222b \u2016m\u0304=1\u2016 m\u0304m\u0304f(m\u0304) dm\u0304 = U (\u222b \u2016m=1\u2016 mmf(m) dm ) UT, (34) that is, Q\u0304 = U \u00b7 Q \u00b7 UT",
            " The respective frames of directors are related by the coordinate rotation, ni = UTn\u0304i, i = 1, 2, 3, (50) where ni are directors for the triple (a, {p1, p2, p3}, f or Q), and n\u0304i the directors for the triple (a\u0304, {0,Pe, 0}, f\u0304 or Q\u0304). As a consequence, for all steady in-plane flow-aligned solutions, the Leslie alignment angle \u03c6L for (p1, p2, p3, a) is determined by: \u03c6L = \u03c6\u0304L + \u03b4, (51) where \u03c6\u0304L is the Leslie alignment angle for the simple shear with the triple (a\u0304, {0,Pe, 0}, Q\u0304), and \u03b4 is defined in (28). We emphasize that each radial line of flow types in Fig. 2 defined by \u03b4 = constant, Eq. (28), share exactly the same Leslie flow-alignment angle \u03c6L for in-plane steady states, if they exist. Whether flow-aligning (FA) steady states exist, and if they are stable, can be deduced from the simple shear problem with generalized aspect ratio a\u0304. This analysis is discussed in detail for various mesoscopic closure models in [9,24] and for the particular Doi closure in complete generality in [25]. These existence and stability features of FA states vary with both Pe and a\u0304",
            " The set of all such stable solutions for fixed a\u0304 comprises the simple shear phase diagram of monodomain attractors versus (N,Pe), provided in [27,28] for a\u0304 = 1. We now want to infer a class of planar flows and physical aspect ratio liquids that share the identical phase diagram. We can therefore conclude rheological properties for a broad class of experiments without any further calculations. If the correspondence requires a\u0304 = 1, then the same numerical code can be used instead of having to derive new Galerkin expansions. We first recall from Fig. 2 and the discussion above that any planar linear flow determined by {p1, p2, p3} for p2 = p3 can be parametrized by the ratio \u03c9 of rate-of-strain to vorticity and the rotation angle \u03b4. For any two parameters \u03c9 \u2265 |a\u0304| (so that |a| = |a\u0304/\u03c9| \u2264 1) and \u03b4 \u2208 (\u2212\u03c0/2, \u03c0/2], from (18), (26) and (28), we get an explicit parametrization:  p1 = \u22121 2 \u03c9Pe sin 2\u03b4, p2 = 1 2 (\u03c9 cos 2\u03b4+ 1)Pe, p3 = 1 2 (\u03c9 cos 2\u03b4\u2212 1)Pe, a = a\u0304 \u03c9 . (60) The correspondence principle (31) or (49) implies: for any planar flow (12), with p1, p2, p3 given by (60), and liquids with shape parameter a given by (60), all solutions, kinetic (f ) or mesoscopic (Q), their stability and flow-induced phase transitions, are in one-to-one correspondence with the solution f\u0304 or Q\u0304 of the \u201cliquid\u201d with shape parameter a\u0304 in pure shear flow with Peclet number, Pe",
            " We now vary (\u03b4, \u03c9), thereby creating a surface, Fig. 5, of linear flows (p1, p2, p3), where attached to each planar flow (p1, p2, p3) on this surface is the physical aspect ratio a = a\u0304/\u03c9 as indicated by (60). At each point on this surface, all stationary PDFs f and mesoscopic tensors Q are uniquely prescribed by f\u0304 or Q\u0304: f(m) = f\u0304 (UTm), Q = UT \u00b7 Q\u0304 \u00b7 U. (62) Note from Q(f), we immediately get \u03c6L(\u03b4, \u03c9) = \u03c6\u0304L + \u03b4. The alignment angle is independent of \u03c9, and therefore, \u03c6L is identical on the rays \u03b4 = constant in Fig. 2 or Fig. 5. For this entire two-parameter family of flows and aspect ratio liquids, no oscillatory stationary distributions exist, which is determined solely from the solution of the single triple (2, {0, 1, 0}, f\u0304 (m)). Note that on this surface (Fig. 5), we have freedom to fix \u03c9, which fixes the physical aspect ratio a, Eq. (60), i.e., we fix the nematic liquid and the ratio of rate-of-strain to vorticity. Each fixed \u03c9 \u2265 2 (circles in Fig. 2) corresponds to a curve of linear flows (p1, p2, p3)(\u03b4) of a fixed nematic liquid for which the monodomain PDFs f and tensors Q are identical up to rotation by \u03b4: the two green curves in Fig. 5 correspond to \u03c9 = 2, 2.5, equivalently to: a= 1(r = \u221e) : (p1, p2, p3)|\u03c9=2 = (\u2212 sin 2\u03b4, cos 2\u03b4+ 1 2 , cos 2\u03b4\u2212 1 2 ), (63) necessary conclusion that all of these flows induce steady flow-alignment with Leslie angle \u03c6L = \u03b4 + \u03c6\u0304L with \u03c6\u0304L = 27.5\u25e6 for a = 1, N = 6, and Pe = 2. Rather than fix both Pe and a\u0304 in the target shear flow problem, we now fix only the generalized aspect ratio parameter a\u0304 = 2 and determine the shear-phase diagram versus Pe for all triples (2, {0,Pe, 0}, f\u0304 )",
            " (66) Note our parameters (\u03c9,Pe) are related to (\u03b3,w) in [7] by \u03c9 = 1/w, Pe = 2\u03b3/(1 + w), where \u03b3 is used to measure the magnitude of the local gradient, and w the ratio of vorticity to rate of strain. The streamlines of the four-roll mill for various \u03c9 > 0 are shown in Fig. 1. For \u03c9 > 1 the streamlines are hyperbolic. For 0 \u2264 \u03c9 < 1, the streamlines form a family of ellipses. If \u03c9 = 0 (p1 = 0), the flow is purely rotational; and when \u03c9 = \u221e (p2 = 0), the flow is purely extensional. As \u03c9 varies between 0 and \u221e, the flow is a linear superposition of pure rotation and pure extension. Recall the four-roll mill is represented by the horizontal axis in Fig. 2. The rotation angle \u03b4 determined by the correspondence is always \u221245\u25e6 for p1 > 0 or 45\u25e6 for p1 < 0. The transformation matrix U, Eq. (27), is then, for p1 > 0, Umill = \u221a 2 2   1 \u22121 0 1 1 0 0 0 \u221a 2   . (67) We take \u03b4 = \u03c0/4 in formula (60), then the four-roll mill model can be parametrized by Pe and \u03c9 in the following way:  p1 = \u22121 2 \u03c9Pe, p2 = 1 2 Pe, p3 = \u22121 2 Pe, a = a\u0304 \u03c9 . (68) We now deduce various monodomain properties of four-roll mill flows of different aspect ratio nematic liquids from the target shear problem"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002835_1.3092885-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002835_1.3092885-Figure3-1.png",
        "caption": "Fig. 3. Basic kinematics of the multibody model (excluding constant velocity joint).",
        "texts": [
            " They are oriented in the beamwise, chordwise and torsion directions to represent the three fundamental natural modes of the wing. These spring-dampers also provide structural damping and their stiffness is chosen to yield the natural frequencies corresponding to the overall half wing assembly, including nacelle and rotor system, Table 2. As these are structural values, they are given for the case of a non-rotating rotor with a clamped gimbal joint. An overall view of the multibody model is given in Fig. 2. A detailed representation of the major bodies and articulations is shown in Fig. 3, although only one rotor blade is shown for clarity and the constant velocity joint is not represented. It should be noted that there is no individual flap or lead\u2013lag articulation on the rotor blades. The rotation of the swashplate is synchronized with the mast by a virtual coupler. An in-house aeroelastic wind tunnel model whose dynamic characteristics are adjustable to a large range of different dynamic configurations was used to determine open-loop stability behavior and to validate the numerical model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002234_0301-679x(76)90078-5-Figure13-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002234_0301-679x(76)90078-5-Figure13-1.png",
        "caption": "Fig 13 Damaged ball bearing resulting from inadequate high temperature properties of the lubricant",
        "texts": [
            " Component failures associated with the lubricant Component damage and failures influenced or caused directly by the lubricant may be conveniently grouped as follows: Incorrect lubricant Tiffs means the selection of a lubricant of incorrect type, quality, or viscosity. Fig 11 shows damage to a roller bearing caused by incorrect lubrication. While the extreme wear and ultimate failure of some lands of the cage possibly may not be obviously attributed to lubricant with inadequate properties, the scuffing failure on the face of the roller shown in Fig 12 is undoubtedly TRIBOLOGY international October 1976 219 the result of insufficient load carrying capacity of the lubricant used. The ball bearing shown in Fig 13 has been damaged because the lubricant selected could not resist the high temperatures occurring during the operation of the bearing. The teeth of the hypoid gear of an automotive rear axle shown in Fig 14 have been worn to a fraction of the original width within a very short time. The main reason for this failure was inadequate extreme pressure properties of the gear oil used. As a consequence of the type of damage described, it is not unusual for tooth fracture to occur when wear has reducedthe crosssectional area of the teeth to the point at which they cannot sustain the applied torque"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000027_978-94-015-9514-8_47-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000027_978-94-015-9514-8_47-Figure10-1.png",
        "caption": "Figure 10. Cylindric-and prismatic multi Sarrus-chains",
        "texts": [],
        "surrounding_texts": [
            "If in a Sarrus-chain all the vectors R Da = RNa lie in a plane (cone angle a = 90\u00b0), i.e., if the generating frame is a planar polygon in which a circle can be inscribed, the lamina-links will be unbent (y = 0), and the maximum angle will reach qJrnax = 90 degrees. So far we have alwaysassumedthat the endpoints of the vectors R Da (or RNa) lie on a sphere (with radius R) or, as in the present case, on a circle (first picture of Fig.lO). We can now abandon this condition and generalize the Sarrus-chains. As the frame can be chosen a planar polygon whose side lengths comply with a condition which depends on the number (n) of combined Sarrus-linkages. For an even number of Sarrus-linkages (or scissors) this condition reads: (10) and in one side of the polygon with the index a the distance sa or the position vector v a ( second picture of Fig.lO ) can be chosen arbitrarily. If, however, the number n is odd, then the distance sa in the polygon side with the length aa must be chosen according to : (11) If then one distance sa is chosen or determined, the n - 1 distances can be found iteratively by: (12) The conditions (lO) or (11) guarantee that all scissors in the linkage open at the same angle qJ, and, as a consequence, the projection of the linkage in the direction of the z axis shrinks at growing angles qJ in the directions x and y according to cos qJ ."
        ]
    },
    {
        "image_filename": "designv11_28_0001630_1.1640369-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001630_1.1640369-Figure1-1.png",
        "caption": "Fig. 1 Local coordinates of a pad and journal in a journal bearing",
        "texts": [
            " The journal center trajectories of nonlinear unbalance responses of a rotor-bearing system are also analyzed. Compared with the numerical solution of the Reynolds equation, the relative errors of the results by the two methods are less than 3% for all cases calculated and the CPU time used by the present method is less than one percent of the finite element method. A real journal bearing generally consists of multi-pads and each pad has partial cylindrical surface. Among these pads we need only analyze hydrodynamic forces of one pad and the bearing forces are the sum of all pads. Figure 1 shows the journal and the arc line of a pad surface in the bearing. Let R be journal radius, C be radius clearence between pad and journal, v be rotating speed of journal, g be pad arc angle, l be width to diameter ratio of the pad, and m be oil viscosity, respectively. The nondimensional fluid-film pressure distribution ~with dimensional scale 6mv2R2/C2) satisfies the nondimensional Reynolds equation: L~p !5 f in V5~0,g!3~2l ,l! (1) p50 on ]V where V is pad surface region, ]V is boundary of V, and L~p ",
            "/A# (6) where h is the film thickness, x, y are the local Cartesian coordinates of the journal center whose origin is at pad arc center, x\u0307 , y\u0307 are the velocities of the journal center, \u00ab is the essentricity ratio, and b is the polar angle of journal position. All parameters are nondimensional and the dimensional ratios are: R for z; C for x, y; and vC for x\u0307 , y\u0307 , respectively. Since pressure distribution must be non-negative in the region V. Equation ~1! is to be used in the complete film zone ~Fig. 1, V1) as well as in the cogitated zone (V0). Therefore the trial 004 by ASME MARCH 2004, Vol. 71 \u00d5 219 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: http:/ element of the accordingly functional minimization problem should be restricted in a convex set of Sobolev space H0 1(V), that is, @8#, J~p !5min qPK J~q ! (7) where K5$qPH0 1~V!uq>0 in V% (8) H0 1~V!5$qPC1~V!uq50, on ]V%. (9) The functional in Eq. ~7! is defined as J~q !5 1 2 a~q ,q !2 f ~q ! (10) where a(\u2022,\u2022) is a symitrical and bilinear functional, f (\u2022) is a linear functional, which are defined as a~p ,q ",
            " When complete film zone takes up the whole pad field ~case 2, V0 is empty!, we choose r~u ,d!5h22 \u2022sin pu g \u2022~11du! uP@0,g# . One can perform these two cases similarly. To provide a validation for the proposed method, a comparison is made with the finite element method in which the free boundary is determined by the complementary iteration, @10#. First we consider one pad case. The pad arc angle g5150 deg and length to diameter ratio l51. The local coordinates f x , f y of nondimensional fluid-film forces are shown in Fig. 1. For the unsteady case, the oil-film forces relate not only to the journal\u2019s positions but also to the journal\u2019s velocities. So we use four independent variables, A, a, \u00ab and b ~see Eqs. ~3!\u2013~6!!, to demonstrate the calculated results. Figures 2\u20135 show f x , f y versus A, a, \u00ab and b, respectively. The figures show tiny differences between the results calculated by the finite element method and the proposed method. The biggest error arises at A51, \u00ab50.6, a5260 deg and b5110 deg, where f x50.629, f y522"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002630_elan.200503292-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002630_elan.200503292-Figure1-1.png",
        "caption": "Fig. 1. Cross section of a hydrogel-based ion selective electrode. The length of each electrode is identical to the given width.",
        "texts": [
            " When the lithium ISEs were used as the reference electrodes, all solutions contained a background of 5 mM lithium acetate. Due to the unusual application of these electrodes, their design and fabrication differs significantly from conventional ISEs. The classical liquid inner filling solution was impractical due to the extreme temperature fluctuations. By substituting a poly(HEMA) hydrogel for the inner reference solution, the electrodes can be fabricated with much smaller dimensions and are far more rugged when faced with sub 0 8C temperatures [17]. Figure 1 shows a cross section view and dimensions of one of the electrodes used in the array. The individual ISEs were machined from a 3.2 mm thick PVC sheet into square housings having a length and width of 3.5 mm. The appropriate diameter wells for the silver wire and poly(HEMA) hydrogel were then milled. A silver wire (1 mm diameter, 99.999% purity) was then epoxied into the rear of the housing. The Ag/AgCl internal reference element was electrochemically generated using 0.1 M NaCl and applying a potential of \u00fe 0",
            " This master membrane was then kept in a Petri dish until needed. Individual membranes were bored from the master membrane with stainless steel tubing having a Electroanalysis 2005, 17, No. 15 \u2013 16 H 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 3 mm inner diameter. This membrane was then glued to the PVC housing with 10 mL THF and allowed to dry. All electrodes were conditioned overnight in a solution identical to the aqueous component of the hydrogel. For the chloride electrodes, the ISE housings were similar to Figure 1. However, the silver wire was extended all the way through the housing and epoxied. The face of the wire was sanded with 240 and 500 grit sandpaper to form a smooth 1 mm diameter Ag disk and then anodized to form a Ag/AgCl electrode. All individual ISEs were calibrated several times prior to incorporation into the array to ensure proper response. In the early attempts to combine the electrodes in an array format, THF was used to glue the ISEs together with no spacing between neighboring electrodes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000462_s0263574701003691-Figure19-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000462_s0263574701003691-Figure19-1.png",
        "caption": "Fig. 19. Mechanical limits of a non-holonomic vehicle.",
        "texts": [
            " To influence the particle direction, a different value of the stress coefficient k is used. New global equations are then defined: div + F= 0 (30) div v=0 (31) With the following additional constraint: v || v || < max where Kmax is the upper bound of the curvature. By this method, roads with a bounded curvature radius are obtained (Figure 18), to be compared with the classical simplest Stokes\u2019 equation (Figure 17). http://journals.cambridge.org Downloaded: 03 Jun 2014 IP address: 150.216.68.200 A non-holonomic robot is only able to start in a limited range of directions (Figure 19). In order to model this constraint, we limit the fluid direction around the starting and arrival points. Our solution is to build a virtual wall all around these points (Figure 20). Figure 21 shows a safe path planning with a lower bound of the radius of curvature. Imposing a bounded radius, the problem may have no solution. In such cases, the velocity vectors are null all over the domain. So we can easily predict the existence or nonexistence of a feasible solution. http://journals.cambridge.org Downloaded: 03 Jun 2014 IP address: 150"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001321_2002-01-2249-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001321_2002-01-2249-Figure2-1.png",
        "caption": "Figure 2b. Surface speeds of contacting solids",
        "texts": [
            " Its accuracy deteriorates when the step size is increased, thereby the acceleration in such a time step increases significantly and the condition of the linearity of acceleration variation within a step is abrogated. The following relations are from linear acceleration method: ( ) , 1 , 1 2 , 1 1 , 1 , 1 ( ) 2 1 1(2 ) 2 2 6 i j i i j i i j i i i j i i j t t t \u03d5 \u03d5 \u03d5 \u03d5 \u03d5 \u03d5 \u03d5 \u03d5 \u03d5 \u03d5 \u2212 \u2212 \u2212 \u2212 \u2212 = + + \u2206 = + + \u2206 + + \u2206 ! ! !! !! ! ! !! !! (3) SEPARATION - The contact reaction for a pair of impacting teeth for a loose set of gears can be obtained by the solution of the instantaneous contact conditions. First, the approach or separation of a pair of loose meshing teeth during the step size t\u2206 is obtained as (see figure 2a): , ,( )i j in i j out outh C r r\u03d5 \u03d5= \u2212 \u2212 (4) The term ,i jh is the film thickness, whilst the term in parenthesis is the mutual approach or separation of the impacting solids. To obtain the approach of the solids, it is necessary to calculate the angular motion of the output shaft, out\u03d5 . This is obtained as: out out t\u03d5 \u03d5= \u2206! (5) where: out\u03d5! is the angular velocity of the transmission output shaft. The iterative procedure within a time step of integration, I, is indicated by the subscript, j. This procedure must satisfy a suitable convergence criterion, before the time step of analysis is advanced",
            " As the output shaft rotates, repetitive impact is made between the mounted gear on this shaft and the conjugate loose gear on the unselected shaft. The hydrodynamic force operates in any conjunction that an approach is made between the contiguous surfaces. The force is contributed by the combined entraining and squeeze film action of the lubricant film as [9]: , , , 3 2 , , 2 3 2 i j eq eq i j i j i j i j Lu r L r h W h th \u03b7 \u03c0 \u03b7 \u2202 = \u2212 \u2202 (10) This entraining motion is the component of the velocity vector tangential to the surface of the approaching solids, ,i ju (see figure 2b). There is also a velocity of normal approach or separation of impacting teeth, normal to the surface of the contact; , , i j i j h w t \u2202 = \u2202 given by the rate of change of film in small computation steps t\u2206 . Note that the second term in equation (9) operates for negative values of squeeze velocity (i.e. approaching surfaces). The contact of a pair of teeth is represented by an equivalent roller of radius eqr against a flat, where: 1 1 1 eq in outr r r = + (11) The entraining velocity of the lubricant in the contact domain is given as the average velocity of sliding surfaces as: [ ], 1 2i j out out in inu r r\u03d5 \u03d5= +"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002584_robot.1987.1087740-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002584_robot.1987.1087740-Figure4-1.png",
        "caption": "Figure 4 : The vice to assemble.",
        "texts": [
            "This is also true for the next 2 matrices : 2 3 E and E The computation of E shows that Es,g=l ; it is to say that the exchange is possible through 3 intermediate configurations : 4 4 IGC (1,1)--(2,2)--(1,3)--(2,4)--(1,2) WGC Other examples have be n carried out.Because of the nature of exchanges matrices, this mgthod is very fast; it is also theoretically unlimited. For 5 robots and 5 gripping frames, exchanges matrices are (25 x 25) ; 7 exchanges (it is to say 7 multiplications of matrices (25 x 25) were computed in less than 2 seconds by a multi users computer. --- 2. On situ experiment The aim of this experiment is to assemble a vice of 8 parts with two 6 rotative degrees of freedom manipulators (MA-23 Societe La Calhhe) (Figure 4). To build the vice, eight assemblies are needed : four of them are performed by a single arm , the four others require the use of both manipulators (part 1 on \"base',part 4 and part 5,part 3 and part 5,part 7 and part 8 ) ; in these last cases the kinematic model is used during relative motions and for the coordination of the robots when they are carrying a part together (Figure 5). Because of inaccuracy of the robots, and lack of specialized assembly tools, the forces andtorques acting on the manipulators are m asured toc mpute correctinp;jvements making the assemblies possible The assembly parts, chosen in order to carry out various mechanical joinings (prismatic, cylindrical, multi-insertion, screwing , "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001914_05698190490439346-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001914_05698190490439346-Figure4-1.png",
        "caption": "Fig. 4\u2014Initial shape of the big-end bore and the bearings.",
        "texts": [
            " The displacement boundary conditions of the connecting rod assembly in the XYZ coordinate system are listed in the following: 1. Only half of the connecting rod assembly model is considered. Along the symmetry plane Z = 0, the symmetry displacement boundary conditions are uZ = 0. 2. A reference point is fixed at the piston pin center in the small end. There is no displacement in the Y direction at this reference point, uY = 0. 3. The connecting rod bearing center is fixed, uX = 0, uY = 0, uZ = 0. Initially, the bearing shells were pressed into the big-end bore and the bolts were pre-loaded. Figure 4 shows that this process affects the initial shape of the big-end bore and the bearing. The big-end bore is expanded because of the bearing shell press-fit. The expansion in the connecting rod axis direction is smaller than in the transverse direction. Initial clearance shapes of the big-end bore and its bearing are given in Fig. 5. Minimum diametrical expansion is 0.0007 mm and is located at 126\u25e6 where the wall is thicker because of the bolthead seat (see Fig. 1). In addition, the bolt pretension loading may have a significant effect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002835_1.3092885-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002835_1.3092885-Figure2-1.png",
        "caption": "Fig. 2. Multibody model, global view.",
        "texts": [
            " They are oriented in the beamwise, chordwise and torsion directions to represent the three fundamental natural modes of the wing. These spring-dampers also provide structural damping and their stiffness is chosen to yield the natural frequencies corresponding to the overall half wing assembly, including nacelle and rotor system, Table 2. As these are structural values, they are given for the case of a non-rotating rotor with a clamped gimbal joint. An overall view of the multibody model is given in Fig. 2. A detailed representation of the major bodies and articulations is shown in Fig. 3, although only one rotor blade is shown for clarity and the constant velocity joint is not represented. It should be noted that there is no individual flap or lead\u2013lag articulation on the rotor blades. The rotation of the swashplate is synchronized with the mast by a virtual coupler. An in-house aeroelastic wind tunnel model whose dynamic characteristics are adjustable to a large range of different dynamic configurations was used to determine open-loop stability behavior and to validate the numerical model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002525_1.2429700-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002525_1.2429700-Figure4-1.png",
        "caption": "Fig. 4 Nonlinear joint diagram",
        "texts": [
            " The difference between Fi and FH is the artial clamp load loss Fc during the separating half cycle of Fe Fc = Fi \u2212 FH 7 Solving for the vertical coordinate of point H and subtracting it rom that of point C provides the partial clamp load loss Fc uring the separating half cycle as follows Fc = Kb + Kc x \u2212 Fe 1 + Kb Kc 8 here Kb=fastener stiffness in the elastic range; and Kc=joint tiffness in the elastic range. ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ash The quantity x in Eq. 8 is yet to be solved for. Referring to line ABCD in Fig. 4, the force\u2013elongation relationship for the fastener may be written as F = f x 9 where F=clamp force; x=fastener elongation; and f x is a known function for the fastener; the slope of f x represents the fastener stiffness 2 . It must be noted that f x is determined experimentally. The strain hardening rate of the fastener material, the effective cross-sectional area of the fastener, and the fastener grip length joint thickness , as well as the material stress\u2013strain relationship, are all represented by f x ",
            " The additional fastener elongation x is equal to he amount of the joint relaxation. Thus, the clamp load Fc may be alculated as follows Fc = Fi \u2212 Kc x 13 s outlined in Ref. 9 , combining Eqs. 12 , 10 , 13 , and 3 ields Fe + Fi \u2212 Kc x = A0K Ln xi + x n 14 or a specific strain hardening rate, Eq. 14 is solved numerically or the additional fastener elongation x. The solution for x is hen substituted into Eq. 8 to obtain the corresponding partial lamp load loss during the separating half cycle. Nonlinear Behavior During the Compressive Half ycle Figure 4 depicts the nonlinear joint diagram with emphasis on he behavior of the system during the compressive half cycle. In he second half cycle, applying an external compressive force Fe 24 / Vol. 129, APRIL 2007 om: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ash to the joint will increase the clamp load further into the nonlinear region along HCD . However, the fastener behaves elastically along its new elastic line HO . Line AB C may be described by the function F=g x , which represents the joint load\u2013deflection curve",
            " For example the component of the clamp load loss due to ompression is almost four times that due to tension, for Kc /Kb 5. That suggests that the clamp load loss issue, which may lead o loosening, leakage, fatigue, etc., becomes even much more ritical as the term due to compression exists. On top of that, the endency of joint separation increases in the following tensile half ycle of the loading due to the fact that the level of the residual lamp load at the new equilibrium point H is much lower than hose of the previous equilibrium points H and C Fig. 4 . ffect of Strain Hardening Figure 10 shows the true stress versus true strain of the fastener nd joint materials for various combinations of the strain hardenng parameters K and n. The formulation presented for the clamp oad loss, in terms of the fastener and joint material strain hardning properties, makes it possible to investigate the effect of 30 / Vol. 129, APRIL 2007 om: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ash strain hardening. For stiffness ratio Kc /Kb=8, Fi /Fy =1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003740_1.2975154-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003740_1.2975154-Figure4-1.png",
        "caption": "FIG. 4. Distribution of M magnetization along a generic cylindrical helix .",
        "texts": [
            " Then the n components along n\u2212n and g\u2212g are equal to n cos and n sin , respectively Fig. 3 a . The components nx, ny, and nz of n along the axes X, Y, and Z Fig. 3 b are nx = n cos , 11 ny = \u2212 n sin sin \u2212 , 12 nz = \u2212 n sin cos \u2212 , 13 where n= n =1 is the magnitude of n. Now we consider the magnetization of the helicoidal sector by applying to the generic point P of the magnet, a magnetization vector M characterized by a constant magnitude. This M is oriented as the correspondent unit vector n Fig. 2 b . The vector M just defined therefore is of a helicoidal kind. In Fig. 4 the distribution of M along a generic cylindrical helix with starting and ending points A and B, respectively, is illustrated by a qualitative picture. In this drawing we denote the radius of by r and suppose that the extension of is almost equal to two revolutions. In Fig. 2 b is quantitatively defined by fixing the suitable value of the angle . Now, since the orientation of M is the same one of n we straightaway obtain the components Mx, My, and Mz of M. In fact, with reference to O X ,Y ,Z and Eqs",
            " In fact, by suitable geometrical operations, the real M distribution of the helicoidal cylindrical magnet can be transformed into an equivalent succession of plane rectangular distributions of M. These distributions are always characterized by a magnetization M whose orientation and magnitude are constant, that is, on each rectangular domain the divergence of M is equal to zero. With reference to this, we have already observed that, to compute M for helicoidal magnets of cylindrical kind, it is convenient to consider coaxial cylinders with radius r Fig. 4 . In this computation, M was always oriented along the normal to the cylindrical helix [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: 131.230.73.202 On: Thu, 18 Dec 2014 07:41:10 and its magnitude M was constant. Now, we can develop the generic cylinder of radius r and the relative helix in the plane. Then we obtain a rectangle whose sides are equal to 2 r and h, where h is the height of the same cylinder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003614_3.5201-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003614_3.5201-Figure2-1.png",
        "caption": "Fig. 2",
        "texts": [
            " 1, equilibrium would require a resultant at B consisting of a force equal and opposite to the follower force and a moment in such a sense as to violate any direct momentcurvature relation. With the sense of the follower force reversed, the foregoing argument is inconclusive, and although the behavior of a cantilever subjected to a tensile follower force is primarily of academic interest, it has not been discussed previously and is the subject of this Note. Consider a uniform Bernoulli-Euler beam clamped at one end and loaded at the other by a tangential tensile force of constant magnitude P (Fig. 2). Small transverse oscillations about the x axis are governed by where El and p are the bending rigidity and lineal density, respectively, of the beam. Introducing = x/l, r = t(EI/pl*Y'\\ k2 = PZ2'/El yields c)r2 0 Letting y(^r) \u2014 F(\u00a3) sincor and invoking the boundary conditions 7(0) = F'(Q) = F\"(l) = F'\"(l) = 0, we obtain the frequency equation k* + 2co2(l + coshX2 cosXi) \u2014 uk2 sinhX2 sinXi = 0 where + &4/4)1/2 - &V2]1/2 and X2 = The first three natural frequencies are shown in Fig. 3. For increasing P, the second and third frequencies increase, while the fundamental decreases asymptotically to zero",
            " but were rejected with the explanatory statement that \"such a fact as this cannot be acknowledged mechanically/' The results are not particularly surprising, however, when one recalls that for compressive follower forces (less than the critical value for flutter) the fundamental frequency increases with increasing force,1'2 a behavior which is also opposite to that for the corresponding fixed-direction loading. The results presented in Fig. 3 show that there are no adjacent equilibrium configurations; there remains, however, the possibility of bent equilibrium configurations not predictable by small-deflection theory. A large-deflection analysis which considers this possibility for an inextensible BernoulliEuler beam is outlined below. Referring again to Fig. 2, we assume a bent equilibrium configuration for which x* and y* are the coordinates of the unsupported end. The moment M at a point (x,y) is given by \u2014 P(y* \u2014 y) cosa + P(x* \u2014 x) sina where a is the inclination of the follower force P to the vertical. Setting M = -EId6/ds and again writing /b2 = P12/EI, we obtain de/ds - (k/l)24(y* ~ y) cosa - (x* - x) sina} = 0 which may be differentiated with respect to s and then recombined to yield dW/ds* - (k/l)2 sin(0 - a) = 0 An integral of this which satisfies dd/ds = 0 when 0 = a is de/ds = 2(k/l) sin[(0 - a) so that k = t cosectjcfy Since the preceding integral exists only for discrete values of a, where it vanishes, we conclude that there are no finite values of P for which the cantilever will assume a bent equilibrium configuration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002698_6.2006-4931-Figure11-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002698_6.2006-4931-Figure11-1.png",
        "caption": "Figure 11. Fluid Pressure Profiles at \u03c9= 20,000-rpm for Increasing Pressure Differentials: (a) 0-psi, Non-Compliant, (b) 0-psi, S-F Interaction, (c) 25-psi, Non-Compliant, (d) 25- psi, S-F Interaction",
        "texts": [],
        "surrounding_texts": [
            "This section discusses the solid-fluid interaction model as it was used to compare two under pad configurations: (a) a single wedge (SW) under pad with a circumferential wedge only and (b) a double wedge (DW) under pad with a combined circumferential and axial wedge. A rationale for the solid-fluid interaction model is first presented by comparing a compliant model with a rigid one of the same geometry. Then CFD-ACE+ was used to evaluate the under pad pressure generations as a function of both high-side pressure and rotor angular speed for the single and double wedge pads. Results are presented that predict under pad radial forces, overall finger lift, and fluid leakages as functions of high-side pressure and rotor angular speed. 1. Solid Fluid Interaction Rationalization A comparison was made between the single wedge solid-fluid interaction model and the exact model minus the effect of solidfluid (S-F) interaction. This was done to show the difference in fluid and finger performance results of the two. The models were run at a rotor speed of \u03c9= 20,000-rpm with pressure differentials up to 25-psi. The pressure contours of the non-complaint models as compared to the S-F interaction models, Figs. 11(a)-(d), showed that both the magnitude and the contour shapes of the under pad pressure varied significantly between the two models. This lead to an over-estimation of the non-compliant models under pad forces, Fig. 12, which became slightly worse as the pressure differential increased. The leakage showed the opposite trend, with the non-deforming model underestimating the amount of seal leakage. This of course was because there was no lift of the finger in the non-compliant model. The finger lift changes the fluid film shape which in turn changes the pressure profile which again changes the finger lift. Thus its importance is obvious in finding the steady state response of the finger to pressure differential and rotor speed inputs. 2. Under Pad Shape Comparison For both the single and double wedge pads, the radial under pad force as a function of rotor speed, Fig. 13(a), showed a slight increase in force as the rotor speed was increased. Also for any given rotor speed, the radial under pad force increased with increasing pressure differential. Graphed together, one can see that the radial under pad force was more dependent on rotor speed in the single wedge than the double wedge pad. For any constant value of high- to low-side pressure differential, the double wedge pad had greater under pad force at lower rotor speeds while the single wedge pad did at higher rotor speeds. The rotor speed at which the transition happened, however, American Institute of Aeronautics and Astronautics 12 increased with increasing pressure differential. At a pressure differential of 5-psi, the single wedge had more under pad force at rotor speeds greater than 2,000-rpm. At 15-psi, the single wedge did not have more force than the double wedge until speeds greater than 7,500- rpm; at 25-psi not until speeds greater than 18,000-rpm. From these findings, one can conclude that the single wedge design reacted more to increases in rotor speed than did the double wedge design. The maximum finger deflection as a function of rotor speed and pressure differential increased for both pad types, Fig. 13(b) with the double wedge again showing less dependency on the rotor speed. For any given pressure differential the finger lift was greater in the double wedge at lower rotor speeds and greater in the single wedge at higher rotor speeds. The speed at which the transition occurred increased for increasing pressure differential. In fact, it occurred at the same speed as the transition speed for the radial under pad force. The leakage as a function of rotor speed, Fig. 13(c), followed in line with the radial under pad force and the maximum finger deflection, with the exception that the transition speed was at a greater rpm. For a pressure differential of 25-rpm, the leakage for the double wedge pad was greater than that of the single wedge pad all the way up to a rotor speed of 30,000-rpm where the leakage for the two was about equal. This meant that there was a range of speeds where the single wedge exhibited more radial under pad force and lift yet had less leakage than the double wedge."
        ]
    },
    {
        "image_filename": "designv11_28_0003450_s00170-007-1353-9-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003450_s00170-007-1353-9-Figure3-1.png",
        "caption": "Fig. 3 Shape and dimensions of tested rods with overlays",
        "texts": [
            " It is possible to consider the cutting process according to different criteria. For the calculation, it is possible to use the following criteria: \u2013 the criterion of minimum production costs, \u2013 the criterion of maximum productivity, \u2013 the criterion of maximum profit. The criterion of minimum production costs is considered as the most important. As far as it is not necessary to use other criterion, it is used in principle this one [11]. The criterion of minimum production costs N / USD.L mm\u22121 (section length, here L=40 mm; see Fig. 3) is graphically represented in Fig. 2. Line K1/n, see Eq. (2), represents machine-tool service costs; AND decreases when cutting speed increases, . Line K2/n.T, see Eq. (3), represents tool service costs, and increases when cutting speed increases. Line K represents costs that do not depend on the cutting speed (e.g., workpiece clamping, size measuring, etc.), which have no influence on the calculation [3]. From Fig. 2 it follows that any kind of deviation from the optimum cutting speed to lower or higher values results in an increase in the machining costs of a given overlay length",
            "034, V=0.009, P=0.014 and S=0.008. The steel approximates, for example, to the steel TYPE 5 (according to the standard ISO 683/11), to the steel 16MnCr5 (EN 10084), to the steel 16MnCr5 (DIN 17 210), to the steel 16MC5 (NF A 35-551) or to the steel Gr. 5120 (ASTM A 506). This steel was chosen because it is used widely in agricultural machinery. For the tests there we used rods with overlays of 55-mm diameter and 400-mm length. The shapes and dimensions of the tested rods with overlays are evident in Fig. 3. The overlay was deposited using pulsed GMAW (gas metal arc welding) surfacing under a carbon dioxide (CO2) shield and using C 508 wire of 1.2 mm diameter. The nominal percentage composition of the wire is: C=0.3, Si=1.1, Mn=1.0, Cr=1.0 [16], the composition according to the analysis is: C=0.302, Si=1.13, Mn=1.01, Cr=1.03, Ni=0.03, Mo=0.007, V=0.005, P=0.018 and S=0.008. The material C 508 approximates, for example, to the material OK AUTROD 13.89 from ESAB or to the material FOX DUR 250 IG from B\u00f6hler [15]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003278_0022-2569(71)90371-5-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003278_0022-2569(71)90371-5-Figure2-1.png",
        "caption": "Figures 2(a)-2(d) Representation of spherical five-link mechanisms",
        "texts": [
            " The corresponding values of the third angular displacement __+ 02a can be obtained from equation (5). Alternatively we may solve equation (9) for Oa with the third offset equal to +Saa units (this gives +01a and an extraneous value of 0a), and with the third offset equal t o -Saa units (this gives -0 , a and a further extraneous value of G). We now investigate the two configurations shown in Figs. 3.1 and 3.2 which are the spatial equivalent of the spherical triangles 234 and 23'4 illustrated by Fig. 2(a). In the two spatial triangles the directions of the unit vectors S._,, a4o and S4 are the same. The first closure is t ransformed into the second closure such that:(i) The magnitudes of the common perpendiculars a2a, aa4, a4._, and the an~es c~,,:~. O~a4, \u00a3~42 are constant. (ii) The directions of the unit vectors a._,a, aa4 which define the angle O,a change to a~a and aa4 respectively which define the angle -013. (iii) The value of the third offset changes from -+-Saa to --$33 (and the unit vector Sa changes to S;) and the magnitudes of the two offsets $12, S~4 change to S",
            " It follows that for values of 0, in this range there are eight real closures of the mechanism. (ii) For other values of 0, there are two real, two imaginary values of the output 0~ and four real, four imaginary values for each of the remaining variables. Here there are four real closures of the mechanism. Corresponding sections of curves are labelled so that the various closures can be identified. For example if in Fig. 4.1 we require to obtain values of the remaining linkage variables tbr the two closures defined by 0,.~ we turn to Fig. 2(a) and write: 0,3, Or_,, 0,4, Sr,,, $1, (S:~:~ = + 2\"5) / 01.~\\ - - O ,a , 0.,_~, 0..4, S._,._,, S.,_4 (S:,3 = - 2\"5) The required values of linkage variables are defined in Figs. 4.2-4.6 by sections of curves labelled with this notation. It is interesting to note for 0, = 325 deg optimum values of the offsets labelled S,.,, S.,.,. S~4. S.,_4 are relatively large compared with other values. The corresponding values of 0,:~ are \u00b1 150 deg which are the values of 0~ closest to =~ . These results can be explained by examining infinite values for S"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000663_tia.2002.800779-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000663_tia.2002.800779-Figure6-1.png",
        "caption": "Fig. 6. Effect of inverter nonlinearity. The trajectory u represents the average stator voltage (switching harmonics excluded). (a) At motoring. (b) At regeneration.",
        "texts": [
            " The locations are determined by the respective signs of the three phase currents in (3), or, in other words, by a maximum of 30 phase displacement between the vectors and . The reference signal of the pulsewidth modulator controls the stator voltage of the machine. It follows a circular trajectory in the steady state. Owing to the forward voltages of the power devices, the average value of the stator voltage vector , taken over a switching cycle, describes trajectories that result as being distorted and discontinuous. Fig. 6 shows that the fundamental amplitude of is less than its reference value at motoring, and larger at regeneration. The voltage trajectories exhibit strong sixth harmonic components in addition. Since the threshold voltage does not vary with frequency as the stator voltage does, the distortions are more pronounced at low stator frequency where the stator voltage is low. The distortions introduced by the inverter may even exceed the commanded voltage in magnitude, which then makes correct flux estimation and stable operation of the drive impossible",
            " Accurate inverter dead-time compensation [13] is, therefore, mandatory for high-performance applications. Fig. 8 shows the same components of the reference voltage vector with a dead-time compensator implemented. The distortions are now much smaller, but complete linearity between the reference voltage vector and the stator voltage vector is not yet achieved. The remaining periodic step changes in the voltage waveforms are caused by the threshold voltages of the power devices, as described by (4) and illustrated in Fig. 6. In Fig. 6, the step changes that characterize the distorted voltage trajectory have different magnitudes, as have the projections of the step changes on the respective axes. These are proportional to the sector indicator according to (4); the locations of are shown in Fig. 4. It follows from (4) that both the larger step change and the amplitude of have the magnitude 4/3 as indicated in Fig. 9. Extracting the value of the threshold voltage from the waveform of (or ) in Fig. 8 appears quite inaccurate. A better method is subtracting the fundamental component from, e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002473_j.jmmm.2005.10.079-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002473_j.jmmm.2005.10.079-Figure1-1.png",
        "caption": "Fig. 1. Schematic drawing of a ferrovesicle under the action of field H0; notations for geometrical parameters are given. The action of the field causes elongation in the direction of the field both the outer shape and the cavity and, accordingly contraction of those in the direction across H0.",
        "texts": [
            " During this period and until now in all the theoretical papers on the subject only solid samples, i.e., simply connected domains of magnetic continuum, were considered. Meanwhile, a rich set of challenging problems arises if one considers double-connected ferrogel bodies. In reality, the latter are exemplified by the magnetic vesicles [1], i.e., fluid-filled bubbles of the outer size 100\u2013200 nm with the walls about 20 nm thick made of a magnetically sensitive membrane: a copolymer bilayer inside which magnetic nanoparticles are sandwiched, see the scheme in Fig. 1. In the present work, we model a magnetic vesicle by a hollow sphere of a homogeneous magnetizable elastic material and investigate the equilibrium deformation induced in such a sample by an external uniform magnetic field. - see front matter r 2005 Elsevier B.V. All rights reserved. /j.jmmm.2005.10.079 onding author. ddress: sov@kig.pstu.ac.ru (O.V. Stolbov). From qualitative expectations, magnetic vesicles should display a much more pronounced magneto-elongation effect in response to the applied field than their solid analogues [2,3]. Besides that, in a vesicle the \u2018\u2018outer\u2019\u2019 elongation entails the \u2018\u2018internal\u2019\u2019 elongation which may result in the change of the volume of the cavity in the deformed body. The latter effect enables one to look at magnetic vesicles as at prospective micromachines or microfluidic pumps. The geometry, the choice of coordinate axes, and the notations necessary for a full statement of the problem are shown in Fig. 1. It implies that a sphere of material (2) is embedded in a non-magnetic fluid medium (1), the cavity is filled with the same fluid (3). Two physical types of biconnectivity of a ferroelastic body are conceivable. Type 1 implies that there is a virtual hole in the membrane that keeps the inner and outer pressures equal. Type 2 corresponds to the case of impermeable membrane so that the inner volume is conserved. In below we focus on the situation of the first type, the results on the impermeable shell will be published elsewhere",
            " The symmetry of the problem complies with a cylindrical coordinated framework, and we require that urjr\u00bc0 \u00bc 0; uzjz\u00bc0 \u00bc 0, (4) and a convenient choice of dimensionless units is ~M \u00bcM= ffiffiffiffi G p ; ~T \u00bc T=G; b \u00bc l=G (5) with b being inversely proportional to the compressibility coefficient. We assume that the material obeys linear isotropic magnetization law M \u00bc wH , with w being of the order of the initial susceptibility of the composite medium. To describe elongation of a hollow sphere, we introduce the parameter uz2 \u00bc uz\u00f0r \u00bc 0; z \u00bc r2\u00de, (6) which equals the relative distance between the outer poles of the body in the direction of the Oz axis, see Fig. 1. Passing to integral formulations, one casts the elastic and magnetic problems in the formZ V\u00f0i\u00de T dedV Z G 2pM2 n \u00fe 1 2 wH2 n du dS \u00fe 1 2 Z V\u00f0i\u00de wH2I1\u00f0de\u00dedV \u00bc 0 \u00f07\u00de and \u00f01\u00fe 4pw\u00de Z V\u00f0i\u00de rc rdcdV \u00fe Z V\u00f0e\u00de rc rdcdV 4pw Z V\u00f0i\u00de H0 rdcdV \u00bc 0. \u00f08\u00de These equations are solved by finite-element method on an adaptive mesh. Relaxation scheme proved to be the most effective way to do that. Accordingly, one assumes that u u o \u00bc r T\u00fe 1 2 wr\u00f0H2\u00de, (9) c c o \u00bc r \u00f0H \u00fe 4pM\u00de, where symbol * marks the values at the preceding time step, and o is the relaxation parameter",
            " [5], performing just a one-step calculation (nonself-consistent) we have found that in a uniform field a hollow sphere elongates much more readily than a solid O.V. Stolbov, Y.L. Raikher / Journal of Magnetism and Magnetic Materials 300 (2006) e199\u2013e202 e201 one. The corresponding results obtained in a self-consistent way confirm this qualitative conclusion and as well provide a reliable quantitative data. As an illustration, in Fig. 2 we show the dimensionless \u2018\u2018external\u2019\u2019 elongation uz2 (see Eq. (6) and Fig. 1 for notations) at various radii of the cavity and for a pair of ferrogel materials whose initial magnetic susceptibilities w have reasonable magnitudes but differ each other five times. One sees that the thinner the shell surrounding the cavity the greater stretches the object. We remark that the horizontal axis in Fig. 2 is scaled in the square of the dimensionless field, defined by Eq. (5). Setting G 104 dyn/cm2 that is typical for ferrogels [6], one sees that a dimensionless value H0 5 corresponds to quite a moderate field about 200Oe"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003978_6.2009-6139-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003978_6.2009-6139-Figure1-1.png",
        "caption": "Figure 1: Flight Dynamics Model. The flight model follows simple equations of motion. Wind effects do not change the pitch angle or airspeed.",
        "texts": [
            " The following section will demonstrate how such a model is developed and later in this paper, results of a simulated flight show how well the kinematics-based model performs. For the purposes of the following discussion, it is assumed that the user is interested in modeling a fixed-wing aircraft in normal flight conditions. It is also assumed that there is a need to model climbing and descending motion, so vertical speed and pitch angle become important factors. Lastly, a steady-state wind condition is applied. A simple, kinematics-based flight performance model can approximate the behavior of most fixed-wing aircraft in normal flight modes. Figure 1(a) shows the definition of a flight condition based on two velocity values, vertical speed (Vz), and forward airspeed (u). These velocities are in different coordinate systems, Vz being an inertial-axis value, and u being a vehicle body-axis value. If these values are known, along with the aircraft pitch angle, , the total airspeed ( ) can computed as follows, (1) Note that the quantity describes the value of the dashed vertical line in Fig. 1a. Referring to Fig. 1(b), is is clear that wind ( ) can have a significant effect on the motion of the aircraft. The components of the ground velocity of an aircraft are computed using Eqns. 2 and 3. Equation 4 can then be used to compute the angle of the ground track, clockwise from North. American Institute of Aeronautics and Astronautics 3 (2) (3) (4) From the preceding process, it easy to model an aircraft in forward flight by knowing the pitch angle, airspeed, vertical velocity, and wind velocity. However, turning behavior is also a critical part of any aircraft model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001003_tmag.1984.1063164-Figure11-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001003_tmag.1984.1063164-Figure11-1.png",
        "caption": "Fig. 11. Cage-rotor.",
        "texts": [
            " 8 and 10, it was clear that the rotor flux is very large as compared with the flux induced by the primary current I and that only the gap flux distribution varies with the output power P increasing. (2) Parametric induction generator When a rotor of induction motor is rotated at the velocity over synchronous speed by an external driving motor, the induction motor operates as an induction generator. Based on this operating principle, we discussed the behavior of a parametric induction generator. We used a parametric induction motor with cagerotor shown in Fig. 11. Figure 12 shows an example of the load characteristics of the parametric induction generator. In the figure, it reveals that this motor operates as an induction generator when the slip s=-O.O6. In this case, the output power Pi6 has a maximum when the slip s=-0.21 and the maxlmum value Pmax is equal to 33 W. The efficiency qg of the induction generator is obtained as follows: -1 00 -1 \"$ 20 Fig. 12. Load characteristics of the parametric induction generator. where Plg is the output power and Pr is the input power of the external driving motor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002381_msf.505-507.631-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002381_msf.505-507.631-Figure8-1.png",
        "caption": "Figure 8 Tracing workpiece origin, tool exchange and tool path simulation",
        "texts": [
            " The embedded EONX component provided by the EON studio was adopted in the VB environment to bridge the interfacing parameters so that the components movement of the VR CNC can be controlled from the developed virtual CNC controller by VBScript connection in the developed VB program through EONX 3.0 Type Library. These parameters can be used to transfer the structured data, as shown in Figure 5. Two VR CNCs have been constructed. One is the Davinci three-axis milling machine developed by the Precision Machinery Corporation, as shown in Figure 7, and the V30 milling machine, as shown in Figure 2. The operation of the developed VR CNC was started from edge tracing of X coordinate, as shown in Figure 8(a); the edge tracing of Y coordinate is similar to X edge. The Z workpiece origin is obtained as shown in Figure 8(b). Both Figure 8(a) and Figure 8(b) were operated in MDI mode of the VR CNC. Once the workpiece edge (X,Y,Z) is obtained from the VR MDI mode, either G92 or G54~G59 can be used to set the workpiece origin before the NC tool path can be started. Coordinates settings in through the MDI mode is the easiest way to teach a novice to be familiar with the meaning of machining coordinate systems. However, it is always very dangerous in hand on practice for configuring the work piece zero origin. With the assistance of the developed VR CNC and accompanied VR CNC controller, hand on operation through VR CNC will not break anymore. The tool exchange can be operated, as shown in Figure 8(c), and the tool path simulation can also be started as well, as shown in Figure 8(d). This paper has successfully developed a VR CNC milling machine through the integration of virtual reality software and Microsoft Visual Basic programming environment. The key enabler of the VR CNC \u2013 VR controller was created to parse NC codes and to provide 3D graphic user interface to ease the operation of the VR CNC. The NC codes parser can restructure the user entered NC codes file and the tool path can be simulated afterwards. The file size of he established VR CNC were very small compared with that of CAD file size, for example, Davinci VR CNC was about 20MB (approximately 120 MB in original CAD geometry) and V30 VR CNC was about 7MB (approximately 80 MB in original CAD geometry), which is one of the major advantages of VR CNC"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000776_eej.4391030412-Figure16-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000776_eej.4391030412-Figure16-1.png",
        "caption": "Fig. 16. Brushless s e l f - e x c i t e d type synchronous motor d r iven by new c i r c u i t i n v e r t e r .",
        "texts": [
            " I n t h i s sense, t h e s a l i e n t pole-type b rush le s s s e l f - exc i t ed motor i s as p r a c t i c a l as the non-sal ient pole-type motor. 5. New I n v e r t e r C i r c u i t I f diode D i s i n s e r t e d i n t o one of t h e t h r e e s t a t o r phase windings i n Fig. 3 , t hen no cu r ren t flows through t h y r i s t o r T4 and one feedback diode. Therefore i t i s p o s s i b l e t o cons t ruc t a completely new i n v e r t e r c i r - c u i t using GTO t h y r i s t o r o r power t r a n s i s t o r as shown i n Fig. 16. Thyr i s to r T r 2 connected i n series t o diode D can be replaced by t h y r i s t o r T r 2 back-to-back connected t o a small capac i ty diode. Fu r the r , t he new c i r c u i t i n Fig. 16 works only s l i g h t l y i n feedback mode and t h e r e f o r e t h e capac i ty f o r diodes D 4 and D6 need not be so l a r g e . S imi l a r ly t o t h e c i r c u i t i n Fig. 3 , t h e new c i r c u i t i n Fig. 16 needs l a r g e c u r r e n t capaci t y t r a n s i s t o r s (Tr2, T r 4 , Tr6) and diode (D5). Voltage and c u r r e n t waveforms, ou tpu t c h a r a c t e r i s t i c s and t r a n s i e n t responses of t h e new c i r c u i t are completely t h e same as those of t h e c i r c u i t i n F ig . 3 . I f GTO t h y r i s t o r s o r power t r a n s i s t o r s are used, t hen t h e c i r c u i t can be s impl i f i ed considerably and t h e c i r c u i t r e l i a b i l i t y can b e improved [19, 2p l "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003361_detc2007-34089-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003361_detc2007-34089-Figure1-1.png",
        "caption": "Figure 1\u2014NASA Glenn Research Center gear fatigue test apparatus. (a) Cutaway view. (b) Schematic view.",
        "texts": [
            " Some qualitative results of gear wear experiments were previously reported [14]. To quantify wear rates for gears lubricated with perfluorinated polyether grade 2 grease, spur gear experiments were completed. Test Rig: The experiments were conducted using the NASA Glenn Research Center Spur Gear Fatigue Test Rigs. These test rigs have been used for more than 30 years to test oil lubricated spur gears, with emphasis on studying contact fatigue (spalling, pitting, and micropitting). The test rig, as shown in Fig. 1(a), uses the four-square (torque-regenerative) principle of applying test loads, and thus the motor needs to overcome only the frictional losses in the system. The test rig is belt driven using a variable speed electric motor. A schematic of the loading apparatus is shown in Fig. 1(b). Hydraulic oil pressure and leakage replacement flow is supplied to the load vanes through a shaft seal. As the oil pressure is increased on the load vanes located inside one of the slave gears, torque is applied to its shaft. This torque is transmitted through the test gears and back to the slave gears. In this way power is circulated, and the desired load and corresponding stress level on the test gear teeth may be obtained by adjusting the hydraulic pressure. Figure 1 depicts the spur gear rig as has been used for tests operated at 10,000 rpm for the purpose of evaluating the fatigue lives of oil lubricated gears. The test setup as used for the grease tests reported herein differed from the depiction of Figure 1 in two important ways. Figure 1 illustrates the test gears operating with faces offset. The face-offset condition is used to concentrate the Hertz contact stress as is desired for accelerated life testing of high cycle fatigue. For the grease lubricated gear testing, the gears were operated with zero offset (full faces in contact with each other). Also, Fig. 1 depicts pressurized labyrinth seals on the two shafts. For the grease testing reported herein, lip seals were used on the two shafts to prevent leakage of the slave gear lubricating oil to the grease lubricated test gear section. The lip seals have been used with much success on these rigs to maintain zero-leakage even for speeds of 10,000 rpm. For some applications, gear teeth will operate both as a driving and as a driven member depending on the motions and torques applied to the machine at any given instant",
            "10 Nickel 3.22 Chromium 1.21 Molybdenum 0.12 Copper 0.13 Manganese 0.63 Silicon 0.27 Sulfur 0.005 Phosphorous 0.005 Iron balance ot subject to copyright protection in the United States. tribution is unlimited. of Use: http://www.asme.org/about-asme/terms-of-use Test Procedure. The test gears were cleaned to remove a rust-preventative preservative, assembled on the test rig, and grease was applied. The gears were tested with the tooth faces fully engaged (the faces were not offset as depicted in Fig. 1). Tests were run at a frequency of 4 full dither cycles per second. All tests were conducted with a hydraulic pressure of 1.72 MPa (250 psi) applied to the loading device. The torque This material is declared a work of the U.S. Government a Approved for public relea Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/03/2016 T produced for such a hydraulic pressure was verified both before and after testing to be 68 N-m (51 ft-lb). The applied torque resulted in a contact condition of 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001321_2002-01-2249-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001321_2002-01-2249-Figure1-1.png",
        "caption": "Figure 1b. Schematic view of the transmission system",
        "texts": [
            " INERTIAL DYNAMICS OF A LOOSE GEAR - The equations of motion for a loose gear mounted on the third motion shaft can be written as follows (see figures 1a): , , 1 , 1i j i j in i j inJ F R W R\u03d5 \u2212 \u2212+ =!! (1) s s e fb RJ T T T\u03d5 = \u2212 \u2212!! (2) Note that for a loose gear, the applied torque is as a result of repetitive impacts between teeth of loose gear pairs. The contact load, ,i jW , is obtained in terms of the relatively lightly loaded impact of the two bodies in mutual approach, in this case a pair of teeth, one being on the driven transmission output shaft and the other on the unselected third motion shaft, which rotates at the speed of the input shaft (see figure 1b). The loose gear on this shaft is ideally held in place by the tractive action of the hydrodynamic film. However, the gear can move relative to the shaft, since the tractive force introduces a friction torque, which is insufficient to guard against the small oscillations of the loose gear. The action of the hydrodynamic traction can be considered as the restoring compliance of the system at such low applied torques. This form of lightly loaded contact is further reinforced by low speeds of entraining action, which result at low engine speeds (such as in creeping rattle at 40 67\u03d5 \u03c9 \u03c0 \u03c0= = \u2212"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000926_an9891400029-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000926_an9891400029-Figure1-1.png",
        "caption": "Fig. 1. Schematic representation of (a) the FIA apparatus and ( b ) the amperometric flow-through cell (A). (I) Enzyme working electrode; (11) auxiliary platinum electrode; (111) silver - silver chloride reference electrode; (E) silicone rubber seals; (F) plastic electrode holders; (G) potassium chloride solution; and (H) sample inlet",
        "texts": [
            " I NH2 Glutaraldehyde Glucose 1 C H=N- E n zy m e - oxidase Three of the four pre-treated platinum wires, namely A, C and D, were refluxed for 1 h with a solution of anhydrous 3-aminopropyltriethoxysilane in toluene (20% VlV), whereas wire B was refluxed for 1 h with a 10% V/V solution of anhydrous 3-aminopropyltriethoxysilane in toluene in order to observe the effect of different concentrations of silanising agent. After silanisation, each platinum wire was placed in glutaraldehyde solution (5% V/V in 100 mM phosphate buffer) in a stoppered sample tube for 1 h. To attach the enzyme to the treated wire, the electrode was dipped overnight in a solution of glucose oxidase (30 mg) in phosphate buffer (1 cm3 of 100 mM pH 7 buffer) at 4\u00b0C. The same batch of enzyme was used throughout this work. An FIA system (Fig. 1) for monitoring glucose was used to evaluate the four different electrodes. The electrode potential was controlled with, and the current monitored by, a Metrohm E 61 1 VA-detector potentiostat. A Servoscribe chart recorder was used to record the output signal. The carrier stream and sample were propelled by a four-channel Watson Marlow peristaltic pump, and an Omnifit sample injection valve was used. All connecting tubes were made from either silicone rubber or PTFE and had a nominal internal diameter of 1.27 mm. A pulse suppressor was fitted between the pump and the injection valve. The hydrogen peroxide produced by the enzymatic reaction was monitored with a three-electrode amperometric flowthrough cell system designed for FIA (Fig. 1) at 600 mV (relative to a silver - silver chloride electrode). The Perspex flow-through cell [Fig. l(b)] was laboratory-built and consisted of a platinum wire based enzyme electrode (I) as the working electrode, in addition to a platinum wire auxiliary ( a ) Servoscri be chart recorder Pump Waste Amperometric flow-through cell electrode (11) and a silver - silver chloride reference electrode (111). The cell was designed so that the auxiliary and reference electrodes were placed in a stationary solution of saturated potassium chloride and were in contact with a flowing buffer stream by means of a T junction [Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003168_1.23613-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003168_1.23613-Figure5-1.png",
        "caption": "Fig. 5 Cell geometry around the cylindrical part.",
        "texts": [
            " The momentum source term is added to the cells of this zone in the radial direction only for porosity over the cylindrical part and in both directions, radial and axial, for porosity over the boat-tail part. Thus, themomentum source for the porous surface on the cylindrical part in the radial direction will be written as Smr ivjvjSi Vi (3) where v is equal to vn. For the boat-tail, there are two components of momentum sources, Smx and Smr, Smx ivnjujSi Vi sin ; Smr ivnjvjSi Vi cos (4) where Si is illustrated as the shaded area in Fig. 5, Si 2 wi yi a 2 (5) The axial and radial velocity components can be determined in terms of the transpiration velocity by the following equations: u vn sin ; v vn cos (6) C. Interface of the Inner and the Main Flows The simulation of the flow in and out of the porous surface is difficult, because of the large numbers of holes that have a subgrid scale. To overcome this problem, the transpired velocity is used over the whole porous area. This reduces the total number of cells inside the domain and makes a robust numerical solution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000207_1.1436087-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000207_1.1436087-Figure1-1.png",
        "caption": "Fig. 1 A schematic diagram of the double butterfly linkage",
        "texts": [
            "org/about-asme/terms-of-use Downloaded F derives the polynomial equation for the Cartesian coordinates of the coupler point solely as a function of the link dimensions. The section shows that the polynomial describing the coupler curve is, at most, forty-eighth order. Finally, Section 4 presents the important conclusions of this paper and suggestions for further research. 2 Notation A schematic diagram of the single-degree-of-freedom double butterfly linkage, which is comprised of three independent fivebar loops ~denoted as I, II, and III! is shown in Fig. 1. The fixed, or ground link, is denoted as link 1 and the revolute joints connecting links 2, 5, and 8 to the ground link ~henceforth referred to as the ground pivots! are denoted as O2 , O5 and O8 , respectively. The revolute joints connecting the moving links are denoted as A, B, C, D, E, F and G and the Cartesian coordinate reference frame, denoted as XO2Y, is henceforth referred to as the fixed frame. The ternary links 3 and 7 are referred to as the coupler links and the coupler point that is used in this paper is taken to be coincident with the revolute joint B that connects the two coupler links"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003046_978-3-540-71364-7_25-Figure24.5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003046_978-3-540-71364-7_25-Figure24.5-1.png",
        "caption": "Fig. 24.5. ASIBOT robot design",
        "texts": [
            " The body has two links that contain the electronic equipment and the control unit of the arm. In this manner, the robot is self-constrained, being portable with overall weight of 11 Kg. It is important to note that the robot is symmetric, and due to this, it is possible to attach the arm at any of its ends. It is made of aluminium and carbon fiber. The actuators are torque DC motors, and the gears are flat HarmonicDrive. Power supply is taken from the connector that is placed in the centre of the docking station. The range and position of the different joints can be seen in Fig. 24.5. ASIBOT is designed to be modular and capable of fitting into any environment. This means that the robot can move accurately and reliably in between rooms and up or downstairs. It can be transfered from/to a wheelchair [9]. For this purpose the environment is equipped with serial docking stations which make the transition of the robot from one to another possible. This degree of flexibility has significant implications for the care of disabled and elderly people with special needs. Modularity makes the system able to grow as the users degree of disability changes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002477_ij-epa.1978.0019-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002477_ij-epa.1978.0019-Figure1-1.png",
        "caption": "Fig. 1 Assembly of convertor",
        "texts": [
            "he device is effectively one form of a screw thread reluctance motor described previously.1\"3 An electromagnetic convertor, based on the helical reluctance motor, has been described by Rhodes.4 A simplified diagram of the new device is given in Fig. 1. This prototype version comprises an armature which is rotated by external means. The stator is in the form of a mild steel sleeve, housed in linear bearings, and on the inside bore of which are cut orthogonal rectangular slots to give the desired saliency. The armature consists of a mild-steel cylinder section whose bore accommodates a nonmagnetic shaft and two rectangular permanent magnets bonded by Araldite. A pole shoe encasing each magnet has rectangular slots of the same pitch and dimensions as those of the stator, but cut in the form of a section of a two-start screw thread",
            " The equilibrium portion of the armature will be such that its teeth are in line with those stator threads coinciding with the magnetic poles. If, now, the axis of the magnetic field is rotated, the effect of the screw thread is to displace the stator sleeve along the longitudinal axis of the machine. Provided that the stator is not so constrained as to cause pole slipping, it will move in synchronism and will, therefore, be displaced by two screw threads per revolution of the armature. Since the field is always cyclic there are no significant end effects. The relevant dimensions of the machine are included in Fig. 1. The motor factor k included in eqn. 1 was derived in Reference 1 and was based on a computer analysis of the basic toothed structure, using conformal transformations. 2 Performance The basic helical motor machine equation1 is given by ktwrB\u00a7 sin 2(0 + <j>)dQ (1)Ft = where k = motor factor 6 = angular position of magnetic axis Be = airgap flux density as a function of 8 0 = load angle Ft = force on a complete thread Assuming a rectangular m.m.f. distribution with the permanent magnet excitation, B may be approximated as Be = B for - ^ < 6 < j and Length of armature, / = 35 mm Total area of pole shoes, Am = 2-6 X 10\"3 m2 Pitch of slots, p = 4 mm Width of teeth, tw = 2 mm Maximum travel of stator sleeve, Xm = 30 mm Paper T274 P, first received 16th May and in revised form 29th September 1978 Prof"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000569_robot.2001.932950-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000569_robot.2001.932950-Figure4-1.png",
        "caption": "Figure 4: Forces between two forces and friction angle",
        "texts": [
            " When A4 L, it is (2) Linearity: The grasp force at the vertex u k is linear for a particular solution U . A typical particular solution is Z M c 6 (A{ c:i). = A- ( -yxt ) (25) where A- is the pseudo-inverse of A. Therefore, u1i is linear for the external wrench weZt and the joint torque T and it is of the form where GI, and Dk: are appropriate matrices. 3.3 Friction angle The maximum friction angle of the forces in S is found in the vert,ices of S . Lemma 1: For any t,wo forces c1 and c2 E R\u2019, let c = (1 - s)cl+sc;?, 0 5 s 5 1 be a force along the line segment connecting them as shown in Fig. 4. Assume that the z-component of c is positive. Either c1 or c;? maximizes a friction mgle along the line segment c. Proof The proof is straightforward by focusing on the fact that a friction cone is convex. Let 81 and Q2 be the friction angles of c1 and cz: respectively and let Q = max(81,QZ). The friction cone with the friction angle B contains c1 and ca. Since it is convex, the forces c = (1 - s)cl+scz, 0 5 s 5 1 are inside the friction cone. Therefore the friction angle of c does not exceed 8 (QED)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003488_robot.2007.363548-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003488_robot.2007.363548-Figure1-1.png",
        "caption": "Fig. 1. Voltage-induction-type electrostatic motor",
        "texts": [
            " In this type, the slider is free from cables yet realizing fine positioning resolution and better output performance than the previous wirelessslider type. Since the new motor has a different electrode configuration from previously reported high-power motors, we will first analyze thrust force characteristics of the twofour-phase driving electrode configuration by ignoring the effect of electrostatic induction. Then, we discuss the effect of the induction and reveal the total performance of the newly proposed motor. II. VOLTAGE-INDUCTION TYPE ELECTROSTATIC MOTOR Fig. 1 shows a schematic diagram of the voltage-induction type electrostatic motor proposed in this paper. It consists of a pair of thin plastic films, slider and stator, made by flexible print circuit (FPC) board technology. The stator has a fourphase parallel electrode on its center, whereas the slider has 1-4244-0602-1/07/$20.00 \u00a92007 IEEE. 1572 a two-phase inter-digital electrode also on the center. Both the slider and the stator have two equally-sized induction electrodes on both sides. In slider, driving electrodes and induction electrode are united so that the induced voltages on the induction electrodes are directly applied to the driving electrodes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003094_j.mechmachtheory.2007.12.001-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003094_j.mechmachtheory.2007.12.001-Figure7-1.png",
        "caption": "Fig. 7. Assembly modes of the RR-PR-PR Assur group.",
        "texts": [
            " The two configurations of the triad corresponding to the real solutions are presented in Fig. 6. Example 2. The geometrical data and the position of the auxiliary points D and F of the RR-PR-PR triad (see Fig. 2) are given in the upper part of Table 2. For the specific geometry here considered, solving the fourth order polynomial equation (36) two real roots and two complex roots are obtained. For each real value of the displacement s1, the coordinates of the internal revolute joints B, C and E are determined. The two assembly modes of the triad are presented in Fig. 7. 1 nd solutions of the RR-RP-RP Assur group d = 40, d1 = 30, d2 = 45, d3 = 35, lAB = 75.4053, xF = 103.9025, yF = 78.9332, a = 50 . s x y s1 195.2970 32.1881 68.1901 75.0733 54.3158 34.3636 67.1201 17.6599 22.3916 4.9553i \u2013 \u2013 \u2013 22.3916 + 4.9553i \u2013 \u2013 \u2013 Example 3. The geometrical data and the position of the external joint D and of the auxiliary point F of the RR-RR-PP triad (see Fig. 3) are given in the upper part of Table 3. For the specific geometry here considered, by solving the second order polynomial equation (49) two real roots are obtained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003742_iccsit.2009.5234918-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003742_iccsit.2009.5234918-Figure6-1.png",
        "caption": "Figure 6. The outcomes of the simulation in static environment",
        "texts": [
            " Robot motion direction is determined by obstacle cells state and previous motion direction in robot neighboring. Fig. 5 shows some neighbors which cause changing in the direction of robot. VII. SIMULATION RESULTS This algorithm was simulated in an environment having a 200*200 Matrix and static obstacle in different sizes. Also, in this simulation, there were U-Shaped obstacle and the counter rate was N=100. The robot could successfully cross the entire obstacle without being trapped in any of the local minimums. The robot chooses the shortest path constantly that the outcomes are presented in the Fig. 6. The outcomes of the simulation of the moving and sudden obstacle in a dynamic environment with 20*20 matrices by using wave re-expansion are shown in Fig. 7 and 8. In moving obstacle scenario the obstacle moves vertically. The green cell shows the position of the target point, red cells show the sudden obstacle, and the blue cell shows the position of robot. Wave is expanded in each step of the robot movement. The outcomes of the simulation of the sudden obstacle in an environment with 20*20 matrices by using circling the obstacle has shown in the Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003790_elan.200704147-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003790_elan.200704147-Figure1-1.png",
        "caption": "Fig. 1. Structure of hydrotris(3-phenyl-5-methylpyrazolyl)borate cadmium complex ionophore (I1).",
        "texts": [
            " The potentials have been measured by varying the concentration of NaH2PO4 in test solution in the range 1.0 10 8 \u2013 1.0 10 2 M. The standard NaH2PO4 solutions of anion salt had been obtained by gradual dilution of 0.01 M NaH2PO4 solution. The potential measurements were carried out at 25 1 8C using saturated calomel electrodes (SCE) as reference electrodes with the following cell assembly: Hg/Hg2Cl2 jKCl (satd.) j test solution j jPVC membrane j j 0.01 M NaH2PO4 jHg/Hg2Cl2/KCl (satd.) The affinity of I1 (Fig. 1) and I2 (Fig. 2) for various anions was determined by UV\u2013visible spectroscopic method. In order to investigate the selective interaction of complex as a potential ion carrier with different anionic species, the UV\u2013visible spectral studies of the ionophores in the absence and presence of a number of common anions were obtained in acetonitrile solution. The absorption spectra of I1 and I2 (1.0 10 5 M) and their mixtures with H2PO 4 (1.0 10 4 M) in MeCN solution is shown in Figures 3 and 4. The UV-spectrum of I1 shows absorption maxima at 213"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002535_s00542-006-0317-6-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002535_s00542-006-0317-6-Figure6-1.png",
        "caption": "Fig. 6 Air bearing surface of CML femto slider",
        "texts": [
            " Air bearing shear stress on the ABS is also considered in the simulation program and its effect on the pitch and roll of the slider has been analyzed previously (unpublished). The effect of the slider\u2013disk asperity contact on the air bearing pressure is not considered due to the negligible real contact area as compared with the air bearing surface. In addition, the surface roughness effects are not included in the air bearing model. For a given ABS design the static simulation program uses the quasi-Newton method to calculate the slider static flying altitude, i.e., the equilibrium state. In the simulation we use a CML designed femto slider with the ABS shown in Fig. 6 and two types of slider\u2013disk surface roughness parameters, case 2 and case 3 in Table 1, and also a flat slider/disk interface. The asperity adhesion/contact models are applied to the first two cases and the last one uses the intermolecular force model. Figure 7 shows the relationship between the disk RPM and the slider\u2019s minimum flying height for the various cases. As the disk RPM decreases, the slider\u2019s minimum flying height also decreases. Both the original and modified intermolecular force models show significant flying height decreases due to the intermolecular adhesion stress"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003995_memsys.2008.4443786-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003995_memsys.2008.4443786-Figure1-1.png",
        "caption": "Figure 1 : Concept of transportation and self-assembly for integration of nano/micro components. (a) Components on a substrate. (b)-(d) show the time scale of a circle spot. (b) Components are around an assembly site. (c) The components are transported to the adjacent area of the site. (d) A component is assembled on the site by self-assembly.",
        "texts": [
            " In other words, contact between a component and an assembly site is necessary to proceed to the assembly process and thus the contact probability dominates the assembly performances such as yield and throughput of the assembly process. The higher contact probability resulted in higher yield and throughput. To increase the contact probability, previous works only relied on increasing in the population around the sites by increasing the quantity of components. Our newly proposed concept relies on active transportation of components to the adjacent area of the sites to increase the contact probability by increasing the components population locally around sites (Fig. 1). This method can integrate components with higher throughput by fewer components without losing the merit of self-assembly. For a technique to manipulate multiple components on a substrate with many assembly sites where the components should be assembled simultaneously, we focus on an optoelectronic tweezers (OET) technique [4]. However, the previously reported OET technique is not applicable to opaque and nonuniform conductive MEMS substrates and it is not possible to eliminate the effect of observation light on the manipulation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000956_1.572251-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000956_1.572251-Figure2-1.png",
        "caption": "FIG. 2. Hg loss from Hg'_xCdx Te asa function of temperature and compo sition, (.) x = 0.24, (e) x = 0.225, (0) x = 0.4.",
        "texts": [
            " Hg LOSS RESULTS Hg loss measurements, described in the previous section, were made as a function of several parameters: temperature, composition, and surface preparation. These results are pre sented in Figs. 2 and 3. The horizontal error bars result from the uncertainty in the temperature, estimated as 5-10 DC. The vertical error bars ( \u00b1 20%) come primarily from the curve fitting process which is limited by the system resolu tion in making the measurements. These errors only include those resulting from the measurement and curve fitting pro cesses. They do not include variations between samples. In Fig. 2 we show Hg loss rate as a function of temperature and composition. Loss rates were determined from losses by dividing by the anneal time. The compositions included in this figure are x = 0.4, x = 0.225, and x = 0.24. The best least squares fit of the data is drawn through each set of points. These lines can be represented by an equation of the form No It = Ae - .1E/kT where No It is the Hg loss rate and A and.1E are listed in Table I. Values of.1E are \u00b1 0.4 eV. There is a trend of increasing activation energy .1E and in creasing prefactorsA with increasing cadmium content. For both x = 0.4 and x = 0.23, the diffusion constants used to fit these data also obeyed Arrhenius equations. For x = 0.4, A = 1010 atoms/cm2 sand .1E = 2.7 eV. For x = 0.23, A = 10- 2 atoms/cm2 sand.1E = 1.3 eV. In Fig. 3 we examine the effect of surface preparation on Hg loss rates. This figure is similar to Fig. 2 except the pa rameter is surface preparation; con tactless, and chemime chanical polishing. For each temperature the samples for the two surface preparations were cut from the same wafer or boule in an attempt to ensure sample uniformity for the com parison. The composition of this material was Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 84.88.136.149 On: Thu, 27 Nov 2014 12:44:31 1663 Dlmlduk et al.: Annealing of Hg,_. Cd. Te No~ A exp(-"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001067_095441002760179771-Figure14-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001067_095441002760179771-Figure14-1.png",
        "caption": "Fig. 14 Close-up view of the bottom half of the submodel",
        "texts": [
            " Proc Instn Mech Engrs Vol 216 Part G: J Aerospace Engineering G01102 # IMechE 2002 at The University of Iowa Libraries on July 1, 2015pi .sagepub.comDownloaded from The ABAQUS FE package allows interpolation of the solution of a `global\u2019 model on to the relevant parts of the boundary of a submodel. This is used to study a local part of a model with a re\u00aened mesh based on interpolation of the solution from an initia l, relatively coarse, global model. This method has been used in the present analyses and the submodel can be seen in F ig. 13 with a close-up view in Fig. 14. G01102 # IMechE 2002 Proc Instn Mech Engrs Vol 216 Part G: J Aerospace Engineering at The University of Iowa Libraries on July 1, 2015pig.sagepub.comDownloaded from The results presented in Fig. 15 show the comparison of the peak stresses at the \u00aellet radius going across the facewidth from A to B obtained from the photoelastic and the FE contact analyses, with values of the coef\u00aecient of friction ranging from 0.0 to 0.2. The very low stress levels in slices 1 and 5 could have been caused by the curvature of the teeth or imperfections at the surface edges of the photoelastic specimen, which could spread the load mainly over the central part of the tooth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001159_1.1456083-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001159_1.1456083-Figure1-1.png",
        "caption": "Fig. 1 A schematic diagram of the free rotor and the supports",
        "texts": [
            " Excellent results were obtained and the approach proved itself to be a useful tool for rotor engineers in rotor analyses and design. *Professor and the President of Nan Kai College, 568 Chung Cheng Road, Tsao Tun, Nan Tou County, Taiwan. Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 2000; Revised December 2001. Associate Editor: G. T. Flowers. 296 \u00d5 Vol. 124, APRIL 2002 Copyright \u00a9 2 rom: http://vibrationacoustics.asmedigitalcollection.asme.org/pdfaccess.a Figure 1 shows a schematic diagram of a rotor system, in which the rotor system is divided into two main parts: a free rotor and the associated elastic supports. The advantage of dividing a complex rotor system into components is to simplify the analysis process, which may become very cumbersome and inaccurate if the system is treated as a whole. The authors here employed the receptance method and subsequently developed a sensitivity matrix. The sensitivity matrix is later applied in an optimization process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000969_jpsj.72.2699-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000969_jpsj.72.2699-Figure1-1.png",
        "caption": "Fig. 1. Example of the propeller-like particle. The view from the y-axis (left). The view from the z-axis (right).",
        "texts": [
            "2) The tensors a and c correspond to the translational and the rotational mobilities and the tensor b represents the translation\u2013rotation coupling. Many studies have been carried out on the relationship between the particle shape and the translation\u2013rotation coupling tensor b.2,3) However there are insufficient studies on the particle motion which results from eq. (1). In this paper, we report on the effect of the translation\u2013rotation coupling tensor on the sedimentation of a torque-free particle. We consider a propeller-like particle consisting of two orthogonal disks attached to uniaxial objects (see Fig. 1). More generally, the particle we consider has two symmetric planes of reflection orthogonal to each other. Brenner et al. showed that for such a particle, the tensors a and b are written as3) a \u00bc ax\u00f0exex \u00fe eyey\u00de \u00fe azezez \u00f02\u00de b \u00bc b\u00f0exey \u00fe eyex\u00de; \u00f03\u00de where ex, ey and ez are the three orthonormal vectors attached to the particle: ex and ey are normal to the disks and ez is parallel to the central axis. Thus our particle is characterized by three parameters ax, az and b. The effect of translation\u2013rotation coupling is represented by b"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000570_095440802760075021-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000570_095440802760075021-Figure6-1.png",
        "caption": "Fig. 6 Spiroid gear tooth geometry",
        "texts": [
            " Thus, the synthesis algorithm comprises analytical relations de ning a suf cient number of parameters of the active anks S1 by means of which the conditions for design of both the Spiroid pinion and the Spiroid hob are created. The Spiroid hob is used for Spiroid gear S2 tooth cutting. Here some of the analytical relations included in algorithms and computer programs for Spiroid and Helicon gear synthesis are presented. Expressions given below correspond to gears with right-hand pinion threads and left-hand gear teeth. The directions of angular velocity vectors w1 and w2, shown in Fig. 6, correspond to the orientation of the teeth of surfaces S1 and S2. (a) Helix angle of the pinion thread ank. This angle gives the direction of the helix of the helical ank S1 at the pitch point P. b1 is the angle between the tangent t\u2013t to the helix L1 at P and the straight line PO0 1 passing through P and concluding angle d1 with the axis 1\u20131 (see Fig. 6): b1 \u02c6 arctan i12r1 \u00a1 r2 cos m r2 sin m m \u02c6 arcsin sin y2 sin d cos d1 \u20268\u2020 Proc Instn Mech Engrs Vol 216 Part E: J Process Mechanical Engineering E0101 # IMechE 2002 at MICHIGAN STATE UNIV LIBRARIES on June 14, 2015pie.sagepub.comDownloaded from (b) Axial helical parameter and axial module. The axial helical parameter is a basic geometrical parameter of the pinion. By using it, the pinion helix pitch can be determined. Its expression is [7] ps \u02c6 r1r2 cos d1 sin m i12r1 \u00a1 r2 cos m \u20269\u2020 Assuming d \u02c6 p=2, d1 \u02c6 0 in equations (8) and (9), analytical expressions for b1 and ps corresponding to a Helicon pinion are obtained",
            " Singular points of rst order should be eliminated from the mesh region since they increase speci c friction, reduce lubrication and heat transfer, and, as a result, they decrease loading capacity of the gear pair (because of the increased relative sliding). In the case of Spiroid gear synthesis, using a pitch contact point P, the aim is to eliminate the ordinary nodes in the pitch point vicinity. To carry out this task, a limiting direction of the normal vector n1 with respect to the tooth surface S1 at point P is sought. Here it is considered that a point of S1 is an ordinary node. The analytic expression of the angle between this vector and the plane Tm (see Fig. 6) \u20307; 16; 17\u0160 is given: acr \u02c6 arctan sin b1\u2030r1 cos d1 \u2021 aw cot d\u2026cot b1\u2021 tan y1 sin d1\u2020 \u2021 a1\u2026cot b1 tan y1 \u00a1 sin d1\u2020\u0160 r1 sin d1 \u2021 a1 cos b1 \u00a1 aw cot d tan y1 cos d1 8>>>>< >>>>: 9>>>>= >>>>; \u202613\u2020 The point P will not be an ordinary node if the normal vector n1 to S1 shifts with respect to the critical normal vector ncr by the tooth standard pro le angle a. As a result, the pinion thread becomes non-symmetric in the normal section and the real pro le angles in the normal section of the thread (i.e. the pressure angles) are of the form an \u02c6 a \u00a8 jacrj \u202614\u2020 The smaller value of an determines the orientation of the surfaces S1. They belong to the pinion threads when the pinion meshes with the gear\u2019s corresponding surfaces S2 and the angular velocity vectors are those shown in Fig. 6. (d) Special force angle. The special force angle a12 is the angle between the vector of the force transferred from S1 to S2 and the circumferential velocity vector of the pitch contact point P, being a point of S2: cos a12 \u02c6 cos b2 cos an \u202615\u2020 where b2 \u02c6 b1 \u00a1 m. The value of the special force angle has a critical effect on the conditions of force transmission between the conjugated surfaces S1 and S2. It also affects the synthesized mechanical transmission ef ciency. The complex ank geometry of a Spiroid gear pair and the expensive technology of manufacturing determine a designer\u2019s approach \u203018; 19\u0160"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000329_s0263574700003908-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000329_s0263574700003908-Figure1-1.png",
        "caption": "Fig. 1. Manipulator with two links.",
        "texts": [
            " Step 10. Set 60 = 601C. If 66 > 66min, go to Step 7. Otherwise go to Step 11. Step 11. If k\u00b1m, set k = k + l and go to Step 7. Otherwise go to Step 12. Step 12. Set k = 1, i = i + l. If i<n, go to Step 5. Otherwise go to Step 13. Step 13. Compute / (0<f<fe) by equation (2). Set AJ = J- /old. If A/ > e, set /o,d = / , j = 2, k = 1 and go to Step 5. Otherwise stop. We will apply the proposed method to trajectories planning of the manipulator with two links and two degrees of freedom as shown in Figure 1. Each link has a rigid body of 10 cm in length, 10 x 10 cm2 in cross section area and 1.0 kg in mass. For simplifying calculations, suppose that the characteristics of actuators and the frictional effects are negligible. The limitations of joint velocities are 0 ^ = -0\u00a3i n = (250.0, 350.0) (deg/s), the limitations of torques are UmM= -iimin = (10.0,5.0) (N \u2022 m). The initial and terminal points in jointspace are 0r(0) = (-30.0, 0.0)(deg) and %T(te) = (-90.0, 0.0)(deg) respectively, and the specified point is 6 r = (-30"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002527_1.1828454-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002527_1.1828454-Figure3-1.png",
        "caption": "Fig. 3 Schematic diagram of herringbone grooves: \u201ea\u2026 unwrapped geometry of HGJB; \u201eb\u2026 HGTB",
        "texts": [
            " The local surface porosity obstruction can control lubricant flow at its region, and various combinations of the local obstructions might be effective to develop a wide range of hydrodynamic design options. The flanged rotating shaft surface is smooth, and herringbone grooves are formed on the stationary members only. Figure 2 is a schematic of the groove structure of the bearing system. The HGJBs are partially grooved with a central circumferential land along the bearing width, while the s of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F HGTBs are fully grooved, the inward and outward pumping grooves meet midway along the radial direction. Figure 3 describes herringbone groove configurations. 2.1 Assumptions. For modeling the bearing system, we accept the following assumptions: 1. The lubricant is an incompressible isothermal Newtonian fluid with a constant density. 2. The lubricant fills throughout the bearing structure including the porous sleeve inside. 3. The permeability inside the porous material is uniform, and Darcy\u2019s law covers the pressure gradient flow of the fluid within it. 4. The degree of the surface porosity obstruction is uniform over the entire surface of the sleeve"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003481_icelmach.2008.4800054-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003481_icelmach.2008.4800054-Figure2-1.png",
        "caption": "Fig. 2. Voltage and current waveforms of our proposed method.",
        "texts": [
            " When \u03c8(i0) is given, \u03c8(i), which is of the same order as a similar value as \u03c8(i0), is approximated by the following equation: ( ) ( ) ( )( ) ( )( )( ) \u22c5\u22c5\u22c5+\u2212+\u22c5\u22c5\u22c5+\u2212+\u2248 n n ii n iiiiii 0 0 0 0 0 !!1 ' \u03c8\u03c8\u03c8\u03c8 (2) A Taylor development is applied to this equation, which is in the x=a neighborhood of f(x), as shown below: ( ) ( ) ( ) ( ) ( )( ) ( ) \u22c5\u22c5\u22c5+\u2212+\u22c5\u22c5\u22c5+\u2212+\u2248 n n ax n afaxafafxf !!1 ' (3) TABLE I CALCULATION RULES OF \u03c8(n)(i) iDC \u03c8\u2019(i) \u03c8\u201d(i) --- \u03c8(n)(i) 0 \u03c8\u2019(0) 0 --- 0 i1 \u03c8\u2019(i1) (\u03c8\u2019(i1)-\u03c8\u2019(0))/ i1 --- (\u03c8(n\u22121)(i1)-\u03c8 (n\u22121)(0))/ i1 --- --- --- --- --- in \u03c8\u2019(in) (\u03c8\u2019(in)-\u03c8\u2019(in-1))/(in-in-1) --- (\u03c8(n\u22121)(in)-\u03c8 (n\u22121)(in-1))/(in-in-1) Figure 2 shows voltage and current waveforms of our proposed method. In equation (4), vAC is the alternating part of the supplied voltage, iAC is the alternating part of the supplied current, R is the resistance of the PMSM, and f is the frequency of the supplied current. R is calculated using the direct part of the supplied voltage and current with the following equation: DC DC i vR = (5) As shown in (4), when DC and AC superposition currents are supplied to a PMSM, \u03c8\u2019(i0) is calculated using the alternating part of the supplied voltage and current",
            " Further, any value for \u03c8(i) can be obtained from (2) as described above. \u03c8(0) means \u03c8m on the d-axis, which is given by measuring the back-EMF of the PMSM, and \u03c8(0) means zero on the q-axis. Ld is calculated from (1), and Lq is given in the same way. In this section, we compare three sets of results. The results are from measurements taken using our proposed method and a conventional method. Furthermore, there are the results from an FEM analysis. The specifications of the test PMSM are shown in Table II. Figure 2(a) and Fig. 2(b) show models of the circuit used with a conventional AC injection method [2]. The rotor is locked and AC is supplied to the PMSM. The value of AC current is varied, and Ld and Lq are calculated from the AC voltage and AC current with the following equation: ( ) AC ACAC if iRv iL \u03c02 222 \u2212 = (6) Figure 3(a) and Fig. 3(b) shows models of the circuit used with our proposed method, which uses DC and AC superposition. The rotor is locked and DC and AC superposition is supplied to the PMSM. The value of the AC component is held at about 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000418_095440603767764426-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000418_095440603767764426-Figure1-1.png",
        "caption": "Fig. 1 Schatz linkage",
        "texts": [],
        "surrounding_texts": [
            "The Schatz linkage has a special construction as shown in F ig. 1, with one pair of adjacent parallel axes, z1 and z6, and two sets of adjacent intersecting axes, z1, z2 and z5, z6. Except for the adjacent parallel axes, all joint axes are twisted with a right angle along the common normal between any two adjacent axes and all link offsets except d1 and d6 are zero. Denavit and Hartenberg kinematic notation [17] is used, with ai, ai and di representing link length, link twist angle and link offset respectively and yi representing a joint variable (i \u02c6 1,2, . . . ,6). Hence the dimensional constraints and geometric characteristics of the Schatz linkage are given as follows: a1 \u02c6 a2 \u02c6 a3 \u02c6 a4 \u02c6 a5 \u02c6 p=2 a6 \u02c6 a1 \u02c6 a5 \u02c6 d2 \u02c6 d3 \u02c6 d4 \u02c6 d5 \u02c6 0 a2 \u02c6 a3 \u02c6 a4 \u02c6 a a6 \u02c6 3 p a and d1 \u02c6 \u00a1 d6 \u02c6 d \u20261\u2020 Without loss of generality, let y1 be the input angle. Based on the 464 coordinate transformation matrix [17] and further algebraic manipulations, the closedform displacement solution of the Schatz linkage [15, 16] can be expressed as cos y2 \u02c6 \u00a1 3 p c=2 and sin y2 \u02c6 k=2 \u20262\u2020 cos y3 \u02c6 \u20261 \u00a1 3s2\u2020=k2 and sin y3 \u02c6 \u00a1 2 3 p s=k2 \u20263\u2020 Proc. Instn Mech. Engrs Vol. 217 Part C: J. Mechanical Engineering Science C14402 # IMechE 2003 at Library - Periodicals Dept on March 21, 2015pic.sagepub.comDownloaded from cos y4 \u02c6 \u20263s2 \u00a1 1\u2020=2 and sin y4 \u02c6 \u00a1 3 p ck=2 \u20264\u2020 cos y5 \u02c6 3 p s=k and sin y5 \u02c6 \u00a11=k \u20265\u2020 cos y6 \u02c6 \u00a12s=k and sin y6 \u02c6 c=k \u20266\u2020 where c \u02c6 cos y1, s \u02c6 sin y1 and k \u02c6 3s2 \u2021 1 p . These closed-form solutions can be further expressed by using trigonometric tangent functions for the convenience of computer programming on a personal computer for further investigations. Here, the rst coordinate system x 1\u2013y1\u2013z1 is taken as a global frame in F ig.1. Further, using the transformation of line and screw coordinates [15, 16, 18] and with the help of equations (2) to (6), the screw coordinates of six revolute-joint axes for the Schatz linkage with respect to the global coordinate system are obtained as follows: $1 \u02c6 \u20300, 0, 1; 0, 0, 0\u0160T \u20267\u2020 $2 \u02c6 \u2030s, \u00a1 c, 0; dc, ds, 0\u0160T \u20268\u2020 $3 \u02c6 \u2030ck=2, sk=2, 3 p c=2; \u00a1 dsk=2 \u00a1 as, dck=2 \u2021 ac, 0\u0160T \u20269\u2020 $4 \u02c6 \u20302s=k2, c=k2, \u00a1 3 p s=k; \u00a1 dc=k2 \u00a1 ac=k, 2ds=k2 \u00a1 as=k, \u00a1 3 p ac=k2\u0160T \u202610\u2020 $5 \u02c6 \u2030c=k, \u00a1 2s=k, 0; 2ds=k, dc=k, 2 3 p as=k\u0160T \u202611\u2020 $6 \u02c6 \u20300, 0, 1; 0, 3 p a:0\u0160T \u202612\u2020 These six screws constitute a screw system of order 5 with ve linearly independent screws. In matrix form, the 666 screw matrix S belonging to six revolute-joint axes of the linkage can be expressed as follows: S \u02c6 0 0 1 0 0 0 s \u00a1 c 0 dc ds 0 ck=2 sk=2 3 p c=2 \u00a1 dsk=2 \u00a1 as dck=2 \u2021 ac 0 2s=k2 c=k2 \u00a1 3 p s=k \u00a1 dc=k2 \u00a1 ac=k 2ds=k2 \u00a1 as=k \u00a1 3 p ac=k2 c=k \u00a1 2s=k 0 2ds=k dc=k 2 3 p as=k 0 0 1 0 3 p a 0 2 66666666666666664 3 77777777777777775 \u202613\u2020"
        ]
    },
    {
        "image_filename": "designv11_28_0003924_robot.2009.5152183-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003924_robot.2009.5152183-Figure1-1.png",
        "caption": "Fig. 1. Planar 2RPR/RP PKM with DOF 2.",
        "texts": [
            " Now the linear feedback acts freely on the uncertain system, in contrast to (25) and (26). Therewith the uncertainties affect the dynamics of the controlled PKM, but not the way the controls affect the system. The second and third lines in (27) and (28) embody the uncertain dynamics that is not balanced by the controller. The proposed adapted control schemes shall motivate the development of tailored model-based robust control concepts for redundantly actuated PKM. For illustration purpose the effect of geometric uncertainties of the planar RP/2RPR PKM in figure 1 is analyzed (underlines denote the actuated joints). This is a fullyparallel but not symmetric PKM. There is no moving platform, and the EE is mounted on one of the limbs. The EE is connected to the base by one RP and two RPR chains. The PKM is obtained from a non-redundant RP/RPR by adding one RPR chain. The drive units are mounted on the base at the corners of an equilateral triangle. A disturbance frequently encountered in setting up a PKM is the misplacement of joints. Now assume that one of the drive units is displaced on the ground plane as indicated in figure 1. This leads to a perturbed plant with input matrix AT . The control forces are deduced from the nominal model with AT . Consequently, the inverse dynamics solution (8) applied to the perturbed system (22) cannot perfectly reproduce the desired control forces, due to AT ( AT )+ 6= I. This leads to desired forces in the null-space of AT becoming effective, due to AT NAT 6= 0. For a quantitative analysis the drive unit has been displaced by 5% of the triangle side length, as shown in figure 2. The perfect model and the perturbed plant are evaluated along the indicated EE path"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003340_bf00705581-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003340_bf00705581-Figure7-1.png",
        "caption": "Fig. 7. The law of chords, Theorem VI, Discorsi.",
        "texts": [
            " However, an analysis of these theorems shows how far GALILEO is from attaining his goal even though his theorems, as we shall see, were instrumental in the eventual solution of the problem by HUYGENS. The law of chords and the thesis that the circle is the brachistochrone curve are given proofs in the Discorsi. We shall refer exclusively to this last work, and specifically to Theorem VI, Theorem X X I I , and the following Scholium. In the law of chords GALILEO states: \" I f from the highest or lowest point in a vertical circle there be drawn any inclined planes meeting the cicumference the times of descent along these chords are equal to the other.\" In Figure 7 the descents to A from C or D take equal times: t ~ ~ t~-~. Development of the Pendulum in the t 7 t~ Century 361 Or, as shown in Figure 8, the times of descent from rest to C along any chord, say A C or D C, are equal regardless of the amplitude of the angles subtended: t2~=t~-~. circle, a chord is drawn subtending an arc not greater than a quadrant, and if from the two ends of this chord two other chords be drawn to any point on the arc, the t ime of descent along the two latter chords will be shorter than along the first"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003978_6.2009-6139-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003978_6.2009-6139-Figure5-1.png",
        "caption": "Figure 5: Loiter Patterns. Three types of loiter patterns are discussed in this paper. (a) Orbit, (b) Figure-Eight, and (c) Racetrack. (cp denotes center point of the loiter)",
        "texts": [
            " For greater aspect angles, the aircraft is commanded to turn directly toward the waypoint. (10) A common operation for UAVs is the loiter. A loiter keeps an aircraft in a specified area. This is an important navigational feature for tasks that involve persistence. For instance, a loiter may be used to maintain sensor coverage in a particular area or to maintain a geographic location while awaiting a new mission assignment. Three types of loiters are discussed here: Orbit, racetrack, and figure-eight. Figure 5 shows each loiter type as they are described in this paper. The subsection describes the process by which each type of loiter is maintained using simple navigational techniques. Each is discussed below.  Orbit. The simplest type of loiter is the orbit. In this type of loiter, an aircraft continuously circles a given geographic point. When the aircraft is far from the loiter center-point (greater than twice the loiter radius), it is commanded to fly directly to the center of the orbit. As the aircraft gets closer, the commanded heading ( ) is computed using Eqn. 11. The aircraft will settle into a loiter around the center point at a radius of . The offset angle ( ) is the ideal value of ( ) which is for a clockwise loiter and for a counter clockwise loiter. Figure 5(a) shows the definition of angles and distances. (11)  Figure-Eight. A Figure-Eight loiter, shown in Fig. 5(b), combines two orbits of the same radius along a specified axis. The orbit tracking algorithm is used to track both sides of the figure-eight. As the aircraft approaches the center point of the loiter, the opposite orbit point is selected and the orbit direction shifts from counter-clockwise to clockwise (or vice-versa). A Figure-Eight loiter is effective for maintaining surveillance on a single geographic point using a fixed, forward-looking sensor, if it is commanded with the center point co-located with the point-of-interest. Although a fixed sensor would not be able to maintain constant surveillance, it would be able to revisit the center point at regular intervals.  Racetrack. A racetrack is defined here as a shape made up of two straight-line segments connected to two semi-circles, as shown in Fig. 5(c). Racetracks may be used to maintain a station for radio-relay or allow for persistent surveillance over a large area. When entering a racetrack, two turn-points are considered for American Institute of Aeronautics and Astronautics 7 loiter entry. (Note the four points marked in the figure.) For a clockwise orbit, points (2) and (4) are used. In a counter-clockwise orbit, points (1) and (3) are used. As the vehicle approaches the loiter shape, the closest of the two points is selected as the entry point for the loiter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001635_135065010421800202-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001635_135065010421800202-Figure1-1.png",
        "caption": "Fig. 1 Vibrations of the roller: (a) the \u00aexed coordinate system; (b) the moving coordinate system",
        "texts": [
            " However, the in\u00afuence of vibrations on the performance of EHL contacts has not received signi\u00aecant attention, although an analysis of the effect of a periodic load variation has been given by Yang and Wen [8]. The purpose of the present study was to investigate the effect of the combined vertical and longitudinal vibrations on the thermal EHL contacts. Harmonic oscillation is the basic form of the vibration phenomena. As preliminary work, in this paper the motion of the equivalent roller was assumed to be a harmonic oscillation and this oscillatory motion was further divided into a normal motion and a tangential motion with the same frequency. As shown in the \u00aexed coordinate system in Fig. 1a, the equivalent roller was assumed to vibrate both normally in the z direction and tangentially in the x direction. However, the moving coordinate system as shown in Fig. 1b was adopted for the present lubrication analysis. The time-dependent \u00aelm thickness was described as h\u2026x, t\u2020 \u02c6 h0\u2026t\u2020 \u2021 x2 2R \u00a1 2 pE0 \u2026xout xin p\u2026x0, t\u2020 ln\u2026x \u00a1 x0\u20202 dx0 \u20261\u2020 where h0\u2026t\u2020 \u02c6 h00 \u00a1 An sin\u2026ot\u2020 \u20262\u2020 where o \u02c6 2pf , f is the frequency of the vibration, An is the amplitude of the normal vibration and h00 is a constant corresponding to the steady state load w0 when vibrations are absent. The tangential vibration with the same frequency as the normal vibration was described by x0\u2026t\u2020 \u02c6 At sin\u2026ot\u2020 \u20263\u2020 where the absolute value of At is the amplitude of the Proc. Instn Mech. Engrs Vol. 218 Part J: J. Engineering Tribology J05603 # IMechE 2004 at University of Bath - The Library on July 21, 2015pij.sagepub.comDownloaded from longitudinal vibration. Since, in equation (2), An was always taken positive, so in equation (3), when At was negative, the two vibrations were called in phase; otherwise the two vibrations were out of phase. The generalized Reynolds equation for a thermal line EHL contact shown in Fig. 1b can be written as [12] q qx r Z \u00b4 e h3 qp qx \u00b5 \u00b6 \u02c6 6ua q\u2026erah\u2020 qx \u2021 6ub q\u2026erbh\u2020 qx \u2021 12 q\u2026reh\u2020 qt \u20264\u2020 where ua and ub are the instantaneous surface velocities given by ua \u02c6 ua0 \u00a1 dx0 dt , ub \u02c6 ub0 \u20265\u2020 and ua0 and ub0 are the constant surface velocities when the vibrations are absent. Other quantities in equation (4) are de\u00aened as r Z \u00b4 e \u02c6 12 Zer 0 e Z0 e \u00a1 r00 e \u00b4 \u20266\u2020 era \u02c6 2\u2026re \u00a1 r0 eZe\u2020, erb \u02c6 2r0 eZe \u20267\u2020 re \u02c6 1 h \u2026h 0 r dz \u20268\u2020 r0 e \u02c6 1 h2 \u2026h 0 r \u2026z 0 1 Z\u00a4 dz0 dz \u20269\u2020 r00 e \u02c6 1 h3 \u2026h 0 r \u2026z 0 z0 Z\u00a4 dz0 dz \u202610\u2020 Ze \u02c6 h\u201e h 0 \u20261=Z\u00a4\u2020 dz , Z0 e \u02c6 h2\u201e h 0 \u2026z=Z\u00a4\u2020 dz \u202611\u2020 The boundary conditions of equation (4) are p\u2026xin, t\u2020 \u02c6 p\u2026xout, t\u2020 \u02c6 0, p50 \u2026xin < x < xout\u2020 \u202612\u2020 In equations (9) to (11), Z\u00a4 is the equivalent viscosity of the non-Newtonian lubricant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002838_isie.2006.295907-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002838_isie.2006.295907-Figure3-1.png",
        "caption": "Fig. 3. Stator pole arc and rotor pole arc of the SRM 6/4",
        "texts": [],
        "surrounding_texts": [
            "When a current is following through stator winding the phase voltage is governed by [4]: U =Ri ij + doj dt (7) 0 <S<01 01 = -_ rA 01 <0<02 Nr 2 02 =- 02 <0<03 Nr 2 03= 2 02 - 01 03 --ST Where Rj is the phase coil resistance and u represents the input dc voltage. According to (4) and assumption concerning magnetic linearity and mutual inductances, (7) can be rewrite as follow: (5) di, dL ''Ri '(0) dt + ij dt (8) Which can be also becomes: The phase excitation currents are synchronized with the rising inductance region for motoring torque and with the decreasing inductance region for generating torque. The optimum performance of an SRM depends on the appropriate positioning of the phase currents relative to the rotor angular position. This is can de deduced from (6). The motor controller selects the turn-on and turn-off angles in such away that having appropriate output as the torque or speed. dij dL u=Rii +Lj (0) d +1jwds ''' dt 'dO (9) Where corepresents the angular velocity in radian per second. The last term in (9) is the back EMF of the SRM. At high speeds, the back EMF opposes the rise and the fall current in the phase winding, this is because the proportionality between back EMF and speed."
        ]
    },
    {
        "image_filename": "designv11_28_0003717_08ias.2008.78-Figure12-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003717_08ias.2008.78-Figure12-1.png",
        "caption": "Fig. 12. PM material is filled between the poles. Figs. 12 and 13 show where the PM material is placed to block the flux diffusion between poles.",
        "texts": [
            " The core loss can be reduced by a lower flux density in the main air gap between the armature and the rotor. A rotor end-view of the prototype machine is shown in Fig. 10, and the opposite end-view is shown in Fig. 11. B. Injected PM Injected PM material is used to fill the gaps between the rotor outer ring and inner ring of the prototype machine. A high residual flux density and a strong coercive force of the PM may improve the field-enhancement performance of the HSUB machine. Fig. 14 shows the test setup of an HSUB prototype motor that has the rotor shown in Fig. 12. A torque gauge is attached between the HSUB machine shaft and the dynamometer shaft. Additionally, an optional rotor position encoder is mounted at the non-driving end of the HSUB machine shaft for running the machine as a brushless dc motor. Fig. 15 shows a significant advantage of the HSUB motor. Based on the results of the locked-rotor-torque test, there is a torque increase of more than 50% with the PM of the rotor magnetized compared with the torque before it was magnetized. The PM material used in the prototype is Magnequench\u00ae MQP-S spherical powder with Br = 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001172_s0928-4931(02)00063-2-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001172_s0928-4931(02)00063-2-Figure1-1.png",
        "caption": "Fig. 1. The experiment set-up.",
        "texts": [
            " If the complex impedance Zi of the sublayers i can be determined by analysis of the measured impedance in terms of an electrical equivalent circuit, the thickness of the sublayers (e.g., the thiacalix[4]arene or the silicon dioxide monolayer) can be determined according to equation: di \u00bc e0eiA Ci \u00f02\u00de e0 is the vaccum dielectric constant (8.85 10 14 F/cm2), ei is the dielectric constant of the layer i and A is the area of the surface. The impedance analysis was performed with the Voltalab 40 impedance analyzer (Fig. 1). We plot the impedance modulus | Z(x)| versus frequency x, which is sufficient for the discussion of impedance data. For analyzing the measured data, the second polar coordinate of the complex impedance u(x) is of course considered as well. To fit the measured spectra with the impedance spectra out of ideal elements, we replaced the ideal elements with the constant phase elements (CPE): ZCPE \u00bc Kx a \u00f03\u00de The frequency exponent is a = 1 and K = 1/C for an ideal capacitance, and a = 0 and K =R for an ideal resistance, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003577_ieeestd.1977.80497-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003577_ieeestd.1977.80497-Figure6-1.png",
        "caption": "Fig 6 Pulse Magnetization Characteristics with Reset",
        "texts": [],
        "surrounding_texts": [
            "FOR MAGNETIC CORES IEEE Std 393-1977\nFig 3 [l]. A current transformer or noninductive shunt will yield a signal proportional to H which is then displayed as a function of time. This probe must of itself introduce no appreciable tilt during the display time, and its pulse recovery time must be negligible compared to the test pulse repetition rate.\nSuitable element values in Fig 3 are: Q 1 = 2N3253; R 1 = 3300 R ; R2 = 47 s2 ; C 1 = 0.05 /JF.\nR 1 and C1 are used only to filter the negative dc voltage from the pulse generator. The transistor must have a high current rating and a low capacitance. Suitable diodes, D2 and D3, which must have fast switching characteristics, are used across each inductor in order to clip the possibly excessive voltage kickback as each pulse is terminated.\nThe function of the current sink, D1 (which must have excellent fonvard-bias characteristics) and V, , is to maintain the constant voltage, Vi, across the test sample, L , throughout the measurement interval. The voltage, Vi, is equal to the sum of V E and the drop across the diode, D1. The inductor, L1, which should be similar to the test core both in material and turns, serves to prolong the conduction interval of the diode, D1, and thus, to make the droop of Vi be negligible. The use of L1 is to be preferred to a current-limiting resistor because it effectively provides more current from the supply. V,, as the test sample demands it, and thus does prolong the conduction of the cur-\nrent sink with its constant voltage characteristic.\nVE is initially adjusted to the desired value of Vi less the value of the forward voltage drop of D1. Vc is adjusted to minimize the droop of Vi.\nThe circuit of Fig 4 is more convenient for the usual laboratory or production testing [2]. I t is a transistor switch which connects the constant voltage source. V,,, across the test core winding. The tilt associated with this circuit is of the order of 1 percent. Isolation of the generator from the varying input impedance of the transistor is provided by R2. C1 decreases the transistor tum-on time. The resistor R4 reduces the backswing of the magnetizing current to a negligible level and may be replaced by a diode as D 3 in Fig 3. Core winding voltage is determined by Vi = V,, - V,,, the saturation voltage of the transistor being nearly zero. The resistor R3 merely reduces ringing due to the capacitance of the voltage monitoring cable.\nSuitable element values in Fig 4 are: R 1 = 51 a; R2 = 300 C l ; R3 = 47 C L ; R4 = 100 f2 (all resistors are '/z W, noninductive); C1 = 500 pF; C2 = 50 pF, 25 V; Q 1 = 2N2905A.\nThe pulse repetition rate must be slow enough to assure no distortion of the characteristics due to recovery phenomena and also to avoid internal core heating.\n6.2.2.3 Major and Minor Loop Unipolar Characteristics. The unipolar pulse magnetiza-\n15\nAuthorized licensed use limited to: Univ of Calif Santa Barbara. Downloaded on March 26,2016 at 17:22:53 UTC from IEEE Xplore. Restrictions apply.",
            "IEEE Std 393-1977 IEEE STANDARD FOR TEST PROCEDURES\ntion characteristics will differ depending on whether the core remains on a minor hysteresis loop or whether it is driven on a major hysteresis loop (saturation). Figs 5 and 6 show the differences to be expected.\nWhen a minor loop characteristic, curve a, is obtained, the maximum flux density to which the core is driven should be stated with the data.\nWhen a major loop characteristic, curve b,\n16\nAuthorized licensed use limited to: Univ of Calif Santa Barbara. Downloaded on March 26,2016 at 17:22:53 UTC from IEEE Xplore. Restrictions apply.",
            "FOR MAGNETIC CORES IEEE Std 393-1977\nis obtained, the minimum flux density to which the core must be driven to ensure its entering saturation should be stated with the data.\nNOTE : The pulse magnetization characteristic should be observed at 10 min and 100 min after magnetic preconditioning in order to observe any effects due to disaccommodation.\n6.2.2.4 Bipolar Excitation (Reset). Duplicating the circuit of Fig 4 t o excite a reset winding will provide pulse magnetization characteristics will reset as indicated in Figs 5 and 6, curve c. When working on a major loop, the reset circuit need not be as elaborate as long as all of the flux is reset by that pulse.\n6.2.2.5 Test With Bias. In some circuit applications, a dc bias current is present. Curves for this condition may be generated with the circuit of Fig 4 and the addition of a suitable bias winding. The bias supply must have a high impedance so that it does not constitute a load on the core.\nFig 7 shows the nature of these curves for one member of the family.\nIt can be seen that aiding (positive) bias decreases the available flux; whereas, opposing (negative) bias increases the available flux.\n6.2.2.6 Measurement Conditions. Core Configuration. The test sample will be any core having pulse transformer applications. In all cases, the dimensions of the sample will be reported because geometry as well as material determines the pulse magnetization characteristic.\nEnvironment. Because these measurements\nare not time consuming and have an accuracy of graphical order, excessive care in maintaining constant temperature is not necessary. However, the temperature during the tests will be reported and will not vary by more than * 2\" C throughout the measurements.\nTime Interval. If U is set equal to V i in Eq (2), it is seen that, for a particular core at a specified voltage level, the time interval (pulse duration) to be used is limited by the magnetization characteristics of the material. Because the flux density is directly proportional to time, the magnetizing current would have to increase to prohibitive values as the material enters saturation.\nFor uniformity in reporting data, the time interval at each voltage will extend to a point where the incremental permeability has decreased to one-tenth the value of the initial permeability or to a flux density corresponding to a magnetizing force equal, at least, to ten times the coercive force of the material if the latter leads to a longer interval. The maximum value of flux density will be reported in all cases.\nIn certain cases, it may be desirable to expand the time scale toward zero time, measurement accuracy permitting.\nVoltage Increments. The curves will be generated for uniform increments of V i / N A e over a span suitable for the material such as 2 X lo4, 4 X l o4 , 6 X l o 4 , -, 16 X l o 4 , 18 X lo4,\nTurns. The number of turns used in these tests is very important for obtaining accurate characteristics. For cores having an initial permeability of 400 or less, twenty-five (25) turns are recommended. For high permeability cores, five (5) turns are recommended. The measurements should be repeated with two significantly different numbers of turns, one higher and one lower, in order to verify the results. The turns must be uniformly distributed around the test sample.\nTemperature Dependence. The pulse magnetization characteristics will normally be reported as in Fig 2 at temperatures of -25\", 0\", 25\", 50\", and 75\u00b0C. Other temperatures, higher and lower, may be used if the core material has useful properties at these temperatures; however, equal temperature increments should be observed.\n20 x 104.\n17\nAuthorized licensed use limited to: Univ of Calif Santa Barbara. Downloaded on March 26,2016 at 17:22:53 UTC from IEEE Xplore. Restrictions apply."
        ]
    },
    {
        "image_filename": "designv11_28_0000496_ip-d.1989.0042-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000496_ip-d.1989.0042-Figure3-1.png",
        "caption": "Fig. 3 DCIAC convertor",
        "texts": [
            ": \u2018Linearization and inputloutput decoupling for general nonlinear systems\u2019, Syst. Control. Lett. 1984,5, pp. 27-33 41 SU, R.: \u2018On the linear equivalents of nonlinear systems\u2019, Syst. Control Lett., 1982,2, (1) 42 TAKATA, H.: \u2018Transformation of a nonlinear system into an augmented linear system\u2019, IEEE Trans., 1979, AC-24, (5) 43 VIDYASAGAR, M.: \u2018New directions of research in nonlinear system theory\u2019, Proc. IEEE, 1986,74 7 Appendix Here we give the model of a DC/AC convertor. This model was taken from Reference 37. The system is depicted schematically in Fig. 3. In Reference 37, R = R, = 1, which are normalised values. The system equations are The possible inputs are U,, U, and V,, and the outputs are o and V,. The inputs to the system must be chosen to make good physical sense, and so that the resulting system is linear and analytic (for the theory described in this paper to apply). Choose u2 and V, as inputs and let U, = 1. The system eqns. 25 become eqns. 26: Throughout the paper we let x1 = o, x2 = V,, U, = VI and U, = u 2 . IEE PROCEEDINGS, Vol. 136, Pt"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003380_isie.2007.4374779-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003380_isie.2007.4374779-Figure1-1.png",
        "caption": "Fig. 1. Cross-section of the 8/6 SRM",
        "texts": [
            " It exhibits much faster learning, good convergence properties and accuracy for function approximation while using a fewer number of weights and processing units [9]. The SRM is a double salient motor. It only has concentrated winding on the stator pole. There is no winding or magnet on the rotor pole. The motor is driven by the reluctance torque produced by the electromagnetic field excited by the current flow in the stator winding. The cross section of the four-phase 8/6 pole SRM studied in this paper is shown in Fig. 1. The values of some constructive parameters of the SRM are: R=1.5\u2126, Lmin=0.0112H, Lmax=0.126H. The power converter used in this paper is a classical asymmetrical half-bridge power converter as shown in Fig. 2. 12581-4244-0755-9/07/$20.00 '2007 IEEE For the high saturation of magnetic circuit and the double salient structure, the flux linkage of one phase is in function of phase current and rotor position. From the mathematical model of SRM, it can be seen that building up the nonlinear mapping relationship of flux linkage with respect to phase current and rotor position is the base of precise analysis of the characteristics of SRM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003704_ecce.2009.5316465-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003704_ecce.2009.5316465-Figure2-1.png",
        "caption": "Fig. 2. Growler test setup [5] and flux measurement",
        "texts": [
            " Some of the traditional non-electrical off-line tests for detecting rotor bar damage are visual inspection, tap test, and the fluorescent dye penetrant test (detection of hairline cracks) [2, 5, 16]. The low resistance ohmmeter test compares the \u03bc\u03a9 resolution DC resistance measurement across each bar or on two bars on one side of the rotor to check for cracks in rotor bars or end rings [5, 16]. The growler test and rated rotor flux test (high current AC excitation test) are more commonly used off-line tests for rotor testing [2-3, 5, 16-17]. In the growler test, the core is excited as shown in Fig. 2 to induce current in the rotor bars. If a bar is defective, the current flow in the bar and the flux produced by the bar is reduced compared to other bars. The amount of current or flux produced by each bar is indirectly observed with the 120hz vibration of a hacksaw blade placed along the bar or iron filings or magnetic viewer placed on the rotor surface. In the rated rotor flux test, an AC voltage source is applied across each side of the shaft to produce high shaft current and yoke flux. This induces circulating current between the rotor bars and shaft, and the current or flux of each bar is indirectly observed using iron filings/magnetic viewer or a thermal imaging camera",
            " The off-line growler and single phase rotation tests and on-line MCSA were performed in addition to the proposed technique before and after introducing the rotor faults for each number of broken bar (0, 1, 2, 3 broken bars), to verify the fault and for comparison. The growler test has been performed to check if the bars have been broken properly and to observe the sensitivity of offline tests performed with motor disassembly. Although the standard growler test observes the vibration of a hacksaw blade or the pattern of bar current indirectly, the pattern of the flux produced by the current in each rotor bar was measured with a gaussmeter for sensitive observation, as shown in Fig. 2. The flux density measurements at the rotor surface are shown in Fig. 11 for 0~3 broken rotor bars. The presence of the broken bars is clearly observable in this figure, and it can also be seen that the rotor current is redistributed to the bars adjacent to the broken bars. The single phase rotation test has also been performed with phases A-B excited with 60hz, 12.5% rated voltage. The stator current magnitude as a function of rotor position with the rotor rotated between 0o to 180o (mechanical degrees) in 5o intervals, is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002315_1.2192974-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002315_1.2192974-Figure3-1.png",
        "caption": "FIG. 3. A rolling sphere on a rotating table.",
        "texts": [
            " The other possible -admissible sequence corresponds to , + ,Pinst ,Pinst + c+,2Pinst dx , + , but renders the same decisive point. In the case of an inelastic impact, Proposition 5.5 yields that the unique -decisive point is Pinst, . After the impact, the ball continues its motion along the wall under the dynamics specified by the vector field X+ inst, . Consider again a homogeneous sphere of radius r and unit mass. Assume that the sphere rolls without sliding on a horizontal table which is rotating with certain constant angular velocity about a vertical axis through one of its points see Fig. 3 . Let \u2212 and + be two angular velocities. Here we consider the following situation: each time the sphere reaches the hypersurface x=y, an impulsive force is exerted on the table to put it spinning with a different angular velocity. That is, if the angular velocity of the table was \u2212, the force applied on its rotation axis changes it to + and vice versa. We assume that \u2212 +. This can be modeled as thinking of a system which is subject to two different affine constraint distributions. In order for this model to be consistent, we also assume that the surface of the table is rough enough so that the sphere is rolling without slipping at all times"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002768_9780470116883.ch2-Figure2.14-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002768_9780470116883.ch2-Figure2.14-1.png",
        "caption": "Figure 2.14 Differential section of a straight wire above a perfect ground.",
        "texts": [
            "5 Single Line Over a Perfectly Conducting Ground Plane A transmission line structure may consist of a single conductor above a conducting ground plane that serves as the return conductor. The current excited by an incident field on the line consists primarily of the transmission line mode with the antenna mode being negligibly small due to the symmetry of the excitation. The induced currents and voltages along the line can also be analyzed using somewhat modified telegrapher\u2019s equations. Namely, the incident electric and magnetic fields exciting the line that exist near the line but with the line removed, as shown in Figure 2.14, are now composed from incident- and ground-reflecting components, respectively. On the PEC ground the boundary condition for electric field requires Ex \u00bc 0, Ey \u00bc 0, and Ez 6\u00bc 0. Similarly, for magnetic field it follows Hz \u00bc 0, Hx, and Hy 6\u00bc 0. Further to these modifications, the per-unit-length parameters of the line are different from those related to the twoconductor line in free space. The derivation of the corresponding telegrapher\u2019s equations can be carried out using the total voltage formulation as in the case of two wires in free space. The Maxwell eqn (2.259) is integrated over the shaded area shown in Figure 2.14. Instead of decomposing the magnetic field into incident and scattered components, the magnetic field is divided into excitation and scattered components, respectively, that is, ~Hexc \u00bc ~Hinc \u00fe ~Href \u00f02:290\u00de Following the same steps in the derivation as in section 2.17.2.1, the first telegrapher\u2019s equation is obtained, dV\u00f0x\u00de dx \u00bc joL0I\u00f0x\u00de \u00bc V 0S1 \u00f0x\u00de \u00f02:291\u00de where per-unit-length inductance is L0 \u00bc m0 2p ln 2h a \u00f02:292\u00de The voltage source V 0S1 \u00f0x\u00de distributed along the line is expressed in terms of the incident- and the ground-reflecting magnetic fields: V 0S1 \u00f0x\u00de \u00bc jom0 Zh 0 Hexc y \u00f0x; z\u00dedz \u00bc jom0 Zh 0 Hinc y \u00f0x; z\u00de \u00fe Href y \u00f0x; z\u00de h i dz \u00f02:293\u00de The second telegrapher\u2019s equation can be derived by decomposing the electric field into excitation components and line scattered components, that is, ~Eexc \u00bc ~Einc \u00fe~Eref \u00f02:294\u00de Incident, reflected, and scattered electric and magnetic fields are shown in Figure 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001806_1.2199857-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001806_1.2199857-Figure6-1.png",
        "caption": "Fig. 6 Region of the center of rotation",
        "texts": [
            " Thus we can simplify the algorithm 1 in case where the difference between the COF and the ECOF is small enough. Their difference becomes smaller as the radius of rotation becomes larger. In the next algorithm, we do not need to discretize the COR space and do not need to calculate the ECOF position for the given COR position. Transactions of the ASME Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F Algorithm 2\u2014The set of pusher COR using COF. Step1 Obtain the set of v1 subject to [C1] and [C2], and rotate it \u00b190 deg around the COF of object 1 Fig. 6 a . Step2 Obtain the set of vG subject to [C3] and [C4], and rotate it \u00b190 deg around the COF of the system of two objects Fig. 6 b . Step3 Obtain the common set of Steps 1 and 2 Fig. 6 c . Also, we can further simplify the algorithm if we consider only the case where the objects translate. When the objects translate, the COF position can be defined. Algorithm 3\u2014The set of pusher translational velocity. [Step1] Obtain the set of v1 subject to [C1] and [C2] Fig. 7 a . [Step2] Obtain the set of vG subject to [C3] and [C4] Fig. 7 b . [Step3] Obtain the common set of Steps 1 and 2 Fig. 7 c . We note that this algorithm is an extension of the cone of pure forces 2 to multiple objects"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003154_1.2540572-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003154_1.2540572-Figure2-1.png",
        "caption": "Fig. 2 Surface distress regions on a roller",
        "texts": [
            " Paper presented at the STLE/ASME 2006 nternational Joint Tribology Conference TRIB2006 , San Antonio, Texas, October 2\u201325, 2006. ournal of Tribology Copyright \u00a9 20 om: http://tribology.asmedigitalcollection.asme.org/ on 01/27/2016 Terms response of the cam-rocker-roller system. When these induced stresses exceed the allowable fatigue stress level, surfaces experience, with time, surface wear that may appear first as micrometerscale pitting and evolve into full-fledged pitting of the cam and roller. Figure 2 provides examples of two wear modes on an injector cam. The primary mode typically occurs on the cam region corresponding to the portion following the maximum follower lift. This wear mode appears to be due to a combination of impact load and pronounced sliding between the cam and roller, leading to scuffing. The second mode appears as fatigue pits near the maximum lifting load. It is likely that the primary scuffing failure aggravates the secondary fatigue pitting by introducing a worn particle in the cam-roller contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001732_cdc.2003.1272193-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001732_cdc.2003.1272193-Figure1-1.png",
        "caption": "Fig. 1. The cm pendulum system",
        "texts": [],
        "surrounding_texts": [
            "Pmeeedmgs of the 4Znd IEEE Conference on Deeision and Control Maui, Hawaii USA, December 2003 ThP08-5\nGtobal stabilization of the cart-pendulum system using saturation functions\nIsabelle Fantoni, Rogelio Lozano Heudiasyc, UTC\nUMK CNKS 6599, BP'20529 60205 Compiigne, France\nemail:{ifantoni/rlozano}@hds.utc.fr\nAbsfracI- This paper provides a new control methodology for the stabilization of the well-known inverted pendulum. Starting Cmm a pendant position or any initial position, the pendulum is slabilized around its upper equilibrium position without snitching to a stabilizing local controller, while the cad displacement is brought to zero. The control strategy i s based on the use of saturation functions.\nI. INTRODUCTION\nThe inverted pendulum on a can is a standard experiment used for educational purposes in most control laboratories. It is a pole which has a pivot on a cart that can be moved horizontally. The pole moves freely around the cart and the control objective is to bring the pole to the upper unstable equilibrium position by moving the cart on the horizontal plane. Since the angular acceleration of the pole can not be controlled directly, the inverted pendulum is an underactuated mechanical system. The cart and pole system is also known because the standard nonlinear control techniques are ineffective to control it. Indeed the relative degree [9] of the system is not constant (when the output is chosen to be the swinging energy of the pendulum), the system is not input-output linearizable. Jakubczyk and Kespondek [IO] have shown that the inverted pendulum is not feedback linearizable. An additional difficulty comes from the fact that when the pendulum swings past the horizontal, and the controllability distribution does not have a constant rank. Many control strategies for swingup and stabilization of the system have been proposed in the literature [21, [31, [51, [SI, [ I l l , [13], [14], [161, 11 81, [20]. Many differences exist in the control methodologies. For instance, in [2] and [SI, the model does not include the cart displacement. The technique developed by [13] is used to stabilize the inverted pendulum in its upper equilibrium position when the pendulum is initially above the horizontal plane. Moreover, their approach is such that the cart displacement converges to zero. Olfati-Saber in [14], [15] also stabilizes the cart-\npole system to a point equilibrium over the upper half plane. Semi-global stabilization is achieved using fixed point controllers. In [SI, [12], the control algorithm is obtained by considering the total energy of the canpendulum and is derived from Lyapunov functions. This scheme solved the swing-up of the system. In most of the control laws, we need to switch to a local controller for the stabilization part. Indeed, a recent paper [4] also uses a switching controller for the swing-up and upright stabilization of the inverted pendulum on a cart with a restricted track length. Furthermore, a hybrid control strategy has been proposed in [22], of bangbang nature, with local stabilization effected once the pendulum reaches close to the upright.\nIn the proposed paper, we develop a new approach without using a switching controller. Our main contribution is to provide global stabilization of the system using saturated functions. The paper is organized as follows. In Section 11, the model of the inverted pendulum system is given. Section III deals with the stabilization of the system using saturated functions. In Section TV, we present the stability analysis of the proposed control law. The performance of the control law is exposed in simulation examples, in Section V. Finally, Section VI gives some conclusions.\n11. THE CART-PENDULUM SYSTEM\nConsider the cart and pendulum system as shown in Figure (1). We consider the standard assumptions, i.e. massless rod, point masses, no friction, etc.. A i is the mass of the cart, na the mass of the pendulum, concentrated in the bob, .9 the angle that the pendulum makes with the vertical and I the length of the rod. The equations of motion can be obtained either by applying Newton's second law or by the Euler-Lagrange formulation The system can be written as\n47803-7924-1/03/$17.00 02003 IEEE 4393",
            "where\nNote that M(q) is symmetric and\n( 5 )\nTherefore, M ( q ) is positive definite for all Q. The potential energy of the pendulum can be defined as P = mgl(cos6 - 1). Note that P is related to G(q) as follows\ndet(AJ(q)) = (AJ +m)m12 - mZlZcosZ8 = AJmlZ + mZIZsinZB > 0\nThe control objective is to stabilize the system around its unstable equilibrium point, i.e. to bring the pendulum to its upper position and the cart displacement to zero simultaneously.\n111. STABILIZING CONTROL LAW\nThe general non-linear equations are given by (see ( I ) , (2). ( 3 ) and (4))\nx = [m sin O ( / P - g cos 0) + f] (7) AJ + msin20\nl ( A 1 + msin'8) [- . mlsZ sin 8 cos 8\n1 8 =\n+(AJ+m)gsii iO-fcosO] (8)\nLet us define the desired behavior for the position x, through the variable T I :\n1 1 k k E = T 1 ( . T , i ) * - - u ~ * ( i + u l l ( - z + ~ ) ) (9)\nwhere k is a positive constant greater than unity. The definition of linear saturation functions ui j ( . ) is described below.\nDefirrition 3.1: Given positive constants L and A f , with L 5 M, a function U : R -, IR is said to be a linear saturation for (L,A?') if it is a continuous, nondecreasing function satisfying\n(a) u ( s ) = s when Is1 5 L (b) Iu(s)l 5 A?' for all s E R\nA second definition in terms of linear saturation functions is also given and will be used throughout the paper.\nDefinition 3.2: Given positive constants L, A?', N with L 5 min{Af, N}, a function u : R + R is said to be a 2-level linenr saturation for (L? Ab? N ) if it is a continuous, nondecreasing function satisfying\n(a) u(s) = s for all s E [-L? L] (b) -A?' < u(s) < A$ for all s E (-N, N) (c) u(s) = - A f for all s 5 -N (d) u(s) = A f for all s 2 N\nThe idea developed here, is to choose the controller f, such that limt-= ?(t) = TI. by means of the definition of a desired roll angle 8 d . Let us first apply the following feedback law\n1 f = - [(nr+m)gsine-u21(nl+msin2e)] cos8 ,\n-mlB2 sin 8 (10)\n0 = ug (1 0 where u2 is the new controller. The objective is to determine an appropriate uz that makes B follow a desired motion expressed in E d . such that lim,-, x(t) = T I . Then, let us define the desired roll angle\nwhich reduces the dynamics of 8, using (8), to satisfy\nWhen 0 = 8d. from the second equation in ( I ) , we obtain\nWe will prove in the stability analysis that B d . 6 d and e d are bounded and directly influenced by the parameter k. Therefore, we can choose a bound of e d arbitrarily small",
            "such that the system described by (13) is stable. As a consequence, limt,, Z ( t ) = T I . The aim is to achieve e( t ) + &d(t) as t -+ w. The selected functions rl and u2 are based on the saturation functions defined in [7], [I91 and 1211. Therefore, they are defined in terms of linear sarurarion [19, Def. I ] functions. Here, we present the main result of the paper.\nTheorem 3.1: Consider the can-pendulum system ( I ) and let us define\n-u2l(A4 + m sin2 B ) ] - ml@ sin& (14)\nwhere the functions U,,(.) are linear saturations for given (L,,, A L ) such that the following conditions are satisfied\n(a) Af4Z < Af3l (b) 2 n t 4 2 + 211131 < L32 (c) A442 + 2 A f 4 3 + 2Bo, < Lsi (d) 211142 + A431 + A t 4 3 + Be, <\nwhere Be, = arctan as l ig . The function T~ is defined\n1 1 IC k\n(9 TI(z,~) = - - ~ i z ( i + ~ l i ( - x + i ) ) (17)\nwhere k is a positive constant greater than unity and the functions uij (.) are twice differentiable linear saturations for given (Lij. M i j , Nij) such that Mil < \u2019.; Vi = 1: 2. Then, provided k is sufficiently large, global asymptotic stabilization of the closed-loop system dynamics ( I ) towards (z, x, 8,s) = (O,O, 0.0) is achieved.\nIv. STABILITY ANALYSIS\nIn this section, the proof of Theorem 3.1 will be developed.\nProot The proof is divided in two parts. The first part shows that the bounds on &d. 6dr and & are directly influenced by the parameter k. The second part details the closed-loop stability analysis.\nFirsr parr\nLet us begin by noting, from the strict increasing property of arctan(.) and the definition of T~ in (9) that\nled(t)l 6 arctan (F) Be,, Vt 2 0, which brings to the fore the direct influence of k on Bo,. From the definition of &d (161, one can easily verify that\nwith\n1 + u ; ] ( p + f) (Si + 41\n(20) Let us note that twice differentiability of ui, (s) (i = 1 , 2 , j = 1 , 2 ) on R ensures boundedness of uij(s) and U:$(.) on [-Nij,Ni,] (see [ I , Theo. 4.27]), i.e. there exist positive (real) constants Ai j and Bi j (i = 1 , 2 , j = l , Z l such that I u : ~ ( s ) ~ 6 Aij and lu~~(s)l 5 Bij, Vs E [-?Vij, Ncj]. Taking into account the functions uu(s) chosen in the present paper (see Appendix A), we will simplify the calculations and consider that l u i j ( s ) / 6 1 and lu:$(s)l 6 1, Vs E [-Nij>Nij] . On the other hand, U:,(.) = u:$(s) = 0 when Is1 2 Nij. Consequently, for any nonnegative scalar p . /sPu:,(s)I 5 A:\u201d, and Ispu:i(s)I 6 A:\u201c,, Vs E R, V i , j = 1 , 2 . Assuming the existence of a time ti 2 0 such that lb(t)l 6 Bg, Vt L t l and the existence of a time t2 2 t i 2 0 such that I tanB(t)l 5 To, Vt 2 t 2 , for some initial-conditionindependent positive constant To, i.e. t an B is bounded\u2019, we obtain from (7), (14) and (15) that i: is bounded, Vt L t i . Let us call its bound Bi.. Then, recalling that 1 . is less than unity, we obtain\nl+i(t)l 6 1 [2& + Niz + dfi i ]\nV t 2 tz. Using 5 1 , it results from the above that\n[2B$ + iVn + A t i l l = - 1 n Bi, 18d(t)l 5 h ( t ) l 6\n(21) k\nV t 2 t z (see (IS)) , showing the boundedness of 8 d , but also the direct influence of k on its hound. Furthermore,\n\u2019In rhe second pan of the proof. such assumplions will be proved to be satisfied"
        ]
    },
    {
        "image_filename": "designv11_28_0002069_iros.2005.1545605-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002069_iros.2005.1545605-Figure1-1.png",
        "caption": "Fig. 1. Improving the clearance along a path traversed by an articulated robot with six degrees of freedom. Fig. (a) shows the start and (blurred) goal placement of the robot arm. In (b), we zoom in on the initial path. The swept volume of the significant parts of the robot is shown. As can be seen, the clearance along this path is very small. Our new algorithm successfully increases the clearance along the path which is visualized in (c).",
        "texts": [
            " This research was also supported by the IST Programme of the EU as a Shared-cost RTD (FET Open) Project under Contract No IST2001-39250 (MOVIE - Motion Planning in Virtual Environments). for instance, it is used to guide multiple units in a virtual environment. Indeed, enlarging the clearance is important in various applications. It is though far from trivial how to do this. Previous work limited their efforts to rigid, translating bodies. In this paper, we present a new algorithm that improves the clearance along paths for a broader range of robots including planar, free-flying and articulated robots, see Fig. 1. Many motion planning algorithms create a roadmap (or graph) which represents collision-free motions that can be made by the moving object in an environment with obstacles. From this graph a path is obtained by a Dijkstra\u2019s shortest path query. Since these calculations can be performed offline, we refer to this stage as preprocessing. The paths usually are optimized in a post-processing stage. In [5], an augmented version of Dijkstra\u2019s algorithm is used to extract a path based on other criteria than length"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001895_b:tril.0000032440.19767.17-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001895_b:tril.0000032440.19767.17-Figure1-1.png",
        "caption": "Figure 1. A ball in contact with a rough surface. (a) A smooth ball with radius R and a rough half-space. (b) An asperity subjected to thermal and mechanical loading.",
        "texts": [
            " This provides a more realistic analysis of how rough surfaces respond to thermal and mechanical loading. For simplicity, strain hardening is not considered in the current model. Two common engineering materials, 52100 steel and an aluminum alloy 2011 T3, were studied. Results with and without considering the thermal softening effect are compared and discussed. The contact of two elastic bodies subjected to a normal load and a tangential relative velocity may be simplified into the contact between an ideally smooth ball and a rough but nominally flat surface, as illustrated in figure 1(a). The ball radius R is the equivalent radius of the curvature found at the contact of real engineering elements. The roughness of the halfspace surface is the composite roughness obtained from surfaces of the two elements. Figure 1(b) shows the deformation of one asperity of the rough surface, which is decoupled into downward elastic deformation and upward thermal growth. Thermal softening will enhance plastic flow due to reduced yield strength. Some of the basic equations used in Liu and Wang\u2019s thermomechanical asperity-contact model [10] are listed below for completeness. The elastic normal surface displacement caused by the contact pressure, p\u00f0x01; x02\u00de, is given by the Boussinesq formula [4]: up\u00f0x1; x2\u00de\u00bc 1 pE Z 1 1 Z 1 1 p\u00f0x01; x02\u00de dx01 dx02ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0x1 x01\u00de 2\u00fe\u00f0x2 x02\u00de 2 q \u00f01\u00de If mechanical properties of the two contacting bodies are identical, the normal surface displacements caused by the frictional shear are mathematically canceled out"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001334_bf01202688-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001334_bf01202688-Figure2-1.png",
        "caption": "Fig. 2. Essential constituents of the urea analyzer",
        "texts": [
            " Results of urea determinations in a large number of blood serum samples are summarized, and an intercomparison is given between the enzymatic method and a clinical-chemical routine method (diacetyl monoxime method). Measuring system: The essential components of the urea analyzer are shown schematically in Figs. 1 and 2. The reactor column (inner diameter: 3 mm, height of packing material: ~30 mm) consisted of a plexiglass tube packed with a solid carrier material on which the SAMPLE I INJECTION REACTOR COLUMN TO WASTE (VACUUM) ~ PUMP J ELUANT I SOLUTION I WASH ...... SOLUTION ELECTRODE CELL ~] TO WASTE Fig. 2[. Schematic representation of the measuring system enzyme was immobilized. The catalyst was held between a platinum frit (top) and a nylon netting (bottom). A plexiglass block mounted to the upper end of the reactor column contains a sample injection port and a channel for the inlet of the eluant or the washing solution. This solution was delivered at a constant rate from a peristaltic pump. The lower end of the column was screwed into a plexiglass support that incorporated a Teflon three-way valve",
            " was d e t e r m i n e d fo r the f o l l o w i n g e l ec t rochemica l cell inc o r p o r a t i n g e i ther of the t w o i n d i c a t o r e lec t rodes : H g ; Hg2C12; KC1 sa td ] 1 M L i O A c ] s a m p l e s o l u t i o n I I re fe rence e l ec t rode I N H 4 \u00a7 m e m b r a n e I 0 . 0 1 M NH4C1; AgC1; Ag (220 C) I I ion-se lec t ive e l ec t rode In order to increase the e. m. f. stability, the potentials of indicator and reference electrodes were measured relative to a common electrode of low resistance (platinum wire introduced at the bottom of the plexiglass cell, not shown in Fig. 2). The electronic equipment used for the potentiometric measurements corresponds to the specifications in 7,s. Immobilization of the enzyme: The technique introduced by Weetall and Hersh 2 and described in detail by Johansson and Ogren 3 was adopted. Urease together with bovine serum albumin (weight ratio: 2 :1 ) was immobilized onto porous glass beads (CPG/3-amino-propyl-glass, particle size: 37--74/~m, pore diameter: 7.5 nm; Pierce Chemical Co., Rockford, Ill., U. S. A.) by covalent cross-linkage with the bifunctional reagent glutaraldehyde"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002641_tmag.2006.872518-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002641_tmag.2006.872518-Figure2-1.png",
        "caption": "Fig. 2. Simple model: (a) model description, (b) subdivision at y = 0.",
        "texts": [
            " When \u201cMethod 1\u201d is applied to the thin element and become unknown variables as shown in (2). Then, in the element , two possibilities of selecting and as the unknown variable instead of can be considered. In these cases, the following equations are considered, respectively: (5) (6) These methods are called as \u201cMethod A\u201d and \u201cMethod B,\u201d respectively, in this paper. In order to examine the effectiveness of the several leaf elements described in Section , the linear magnetostatic analysis of the simple model shown in Fig. 2(a), is carried out using the method. In the uniform magnetic field, two cores with the width mm are placed at the shifted position in order to make the flux distribution three-dimensional. Fig. 2(b) shows the subdivision at the cross-section a-b-c-d shown in Fig. 2(a). The leaf element is applied to the thin elements in the gap. The gap is subdivided into the irregular elements in order to compare Methods 1 and 2. The effects of the thickness of the element on the convergence characteristics of the ICCG method and the accuracy of the flux density are investigated by changing the gap length shown in Fig. 2. Fig. 3 shows the effects of the thickness of the element on the number of iterations for the ICCG method and the flux density at the point o shown in Fig. 2. When the thickness of the element in the gap becomes thin, of the ordinary method increases rapidly, but that of the leaf element does not change so much, as shown in Fig. 3(a). Moreover, the numerical error of the obtained from the ordinary method can be also removed by the leaf element as shown in Fig. 3(b). In Fig. 3, the difference by the treatments for the leaf element is not appeared. This means that the ill-condition of the matrices can be removed by using any types of leaf elements. The leaf element is applied to the analysis of eddy currents in the surface layer of a laminated core in an actual magnetic bearing system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000605_880571-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000605_880571-Figure1-1.png",
        "caption": "Figure 1. The \"fixed sleeve\" design. Two lock nuts hold the inner sleeve to the outer liner. Strain gauges are mounted on the outer liner.",
        "texts": [
            " FIXED SLEEVE EXPERIMENTAL METHOD The \"fixed sleeve\" method, reported herein, is an at- 0148-7191/138/0229-0571$02.50 Copyright 1988 Society of Automotive Engineers, Inc. 2 880571 tempt to make measurements of piston and ring friction forces which are more precise than those given by the Instantaneous IMEP method, and without the vibration and elaborate engine modifications required of moveable bore methods. The perceptive reader will note that the path taken is somewhat of a middle road between the \"moveable bore\" and Instantaneous IMEP methods. Figure 1 is a drawing showing the design of the fixed sleeve method. It was implemented on the number 1 cylinder of a Cadillac 4.1 litre gasoline engine and has yielded satisfactory results under a variety of motoring and firing conditions. This engine was selected because it appeared to be an ideal test bed for the technique. Some relevant engine parameters are listed in Table 1. In the fixed sleeve method the cylinder head is not modified, except a flush mounted, water cooled, Kistler 7061 pressure transducer was installed",
            " This gave a total of 16 active and 16 dummy gauges. The arrangement provided temperature and bending compensation, and enough sensitivity to resolve better than one pound force. The production cylinder head and gasket seal against the outer liner as in the production engine. A smaller 80 mm piston and specially built cast iron liners were used with an otherwise production engine, except that a carburetor and mechanical distributor were used for experimental convenience. All cylinders were fired for the tests. Referring to Figure 1, other features of the design are: tensioned piano wire (0.5 mm dia) near the maximum side thrust region to pilot the inner sleeve and keep it from contacting the outer liner (This gives no axial restriction.), soft silicon 0-rings for isolating the cooling water and combustion gases, and several holes between inner and outer sleeves to admit cooling water. The top of the inner sleeve was machined slightly to avoid any contact with the head. The two sleeves were held together by a pair of lock nuts at the base of the assembly"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001477_ip-nbt:20040839-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001477_ip-nbt:20040839-Figure3-1.png",
        "caption": "Fig. 3 Manipulator unit",
        "texts": [
            " The precision of the coarse positioning mode equals the minimal rotation of the spheres during one period of the sawtooth driving signal. The minimal step width for the platform in coarse positioning mode is approximately 110nm, as measured in [8]. The second main component of the microrobot is the micromanipulator unit. The robots used in these experiments use a version of a tripod as a manipulation unit. In some cases the micromanipulator has to work with nanometre accuracy, while offering a working distance of several mm. This manipulator, shown in Fig. 3, has been described in detail in [8]. The levels of three small tables are controlled by electromagnetic micromotors. A removable end-effector mounting frame is placed on top of these tables via piezoelectric stacks, which undertake the fine positioning, while the micromotors overtake the coarse positioning over a distance of 8mm. The position of the tables is measured by LVDT sensors, while the overall movement of the robot is determined by image processing. In these experiments, a standard capillary for cell holding was used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002649_1464419jmbd12-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002649_1464419jmbd12-Figure8-1.png",
        "caption": "Fig. 8 Vertical sections through test rig",
        "texts": [
            " The latter condition (3) may be met with taper-roller bearings unlike the angular-contact bearings investigated by Walford [17]. To make the results comparable with those of Walford, it was decided to use taper-roller bearings of the same bore size in as geometrically similar an arrangement as possible. Consequently, Gamet micro-precision machine tool bearings (Type 113060/113100) of 60 mm bore and 100 mm outside diameter were chosen. A vertical section of the final arrangement of the test rig is shown in Fig. 8. The bearings (5) weremounted on the shaft (1) and in the housing (4). To increase the deflection across the bearings, the mass of the shaft was increased by adding weights (3). The weights and inner races of the bearings were clamped against the shoulder on the shaft by the end plates (2). Oil was supplied through the end rings (12) and drained by gravity from the four drains shown in the housing. The annular spigot on the end rings also served to apply the precisely required preloads to the bearings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003007_6.2006-6147-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003007_6.2006-6147-Figure4-1.png",
        "caption": "Figure 4. Rotor system response to lateral cyclic control.",
        "texts": [
            " For example, moving the right pedal forward causes the forward rotor TPP to tilt to the right, whereas the rear rotor TPP will tilt to the left, resulting in a clockwise directional moment about the center of gravity as illustrated in Figure 3. Conversely, a left pedal input causes a counter-clockwise directional moment. Lateral control is achieved by applying equal lateral cyclic pitch to the blades with the cyclic control stick. Moving the cyclic control stick to the left results in both rotors\u2019 TPP tilting to the left as illustrated in Figure 4. Conversely, a right cyclic input tilts both rotors\u2019 TPP to the right. Th h the cyclic control stick using Differential Collective Pitch (DCP); whereby the pitch of the forward and rear rotor blades are all collectively changed equally yet in the opposite direction. Moving the cyclic control stick forward simultaneously causes a decrease in collective pitch on the forward rotor and an increase in collective pitch on the rear rotor, thereby creating a nose-down pitching moment about the helicopter\u2019s center of gravity as illustrated in Figure 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001862_bio.875-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001862_bio.875-Figure1-1.png",
        "caption": "Figure 1. Schematic diagram of the flow injection system for the determination of dihydroxybenzene. a, Fe3+(HCl) solution; b, H2O2 solution; c, Rh6G solution; d, sample(dihydroxybenzene); e, carrier(H2O); P1, P2, P3, peristaltic pumps; V, eight-way valve; F, flow cell; D, detector; W, waste; L1, L2, L3, mixing tube (L1 = 25 cm, L2 = 5 cm, L3 = 3 cm).",
        "texts": [
            " Polyphenols have been used to eliminate free radicals in physiological research (13). However, in this work, it was observed that polyphenols could enhance the weak CL reaction of hydroxyl radical and rhodamine 6G. Hydroxyl radicals were generated on-line by reacting Fe3+ ions with a H2O2 solution. Based on the above phenomenon, a novel CL system for the determination of dihydroxybenzene, including hydroquinone and catechol, was developed and a possible mechanism of the CL reaction proposed. The flow system used in this work is shown in Fig. 1. Three type HL-2 peristaltic pumps (Huxi Equipment Plant, Shanghai, China) were used to deliver all flow streams. PTFE tubing (0.8 mm i.d.) was used to connect all components in the flow system. The CL signal was detected and recorded with a BPCL ultra-weak The applications of dihydroxybenzene isomer are of paramount importance in the food chemistry, pharmaceutical, cosmetic and printing and dying industries, therefore, the determination of polyhydroxy phenols is of great importance. There were many analytical methods available for the determination of polyhydroxy phenols, such as spectrophotometry (1, 2), chromatography (3\u20135) and electrochemiluminescence (6) techniques",
            " Hydroquinone solution (1.0 g/L) was prepared freshly by dissolving hydroquinone (Chongqing, China). A stock solution of iron(III) (0.1 mol/L) was prepared by dissolving 6.76 g FeCl3\u20226H2O in 250 mL 0.01 mol/L HCl solution. The stock solution of rhodamine 6G (0.005 mol/L) was prepared by dissolving 0.240 g Rh6G (Acros Organics) in 100 mL water. Hydrogen peroxide was prepared daily by diluting 30% H2O2 (Chongqing, China) to a corresponding degree. Resorcinol was obtained from Chongqing Huabo Co. Ltd. As shown in Fig. 1, flow lines were inserted into the sample solution, water carrier, iron(III) solution, H2O2 solution and Rh6G solution, respectively. After the pumps were started to wash the whole flow system, the iron(III) was mixed with H2O2 solution and then with Rh6G solution and the CL was measured and recorded as the background signal. An 80 \u00b5L portion of the sample solution was injected into the water carrier stream via an eight-channel injector valve, then the strengthened CL signal was recorded by PMT"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000524_nafips.2000.877478-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000524_nafips.2000.877478-Figure4-1.png",
        "caption": "Fig 4. A nonlinear switching curve and its corresponding control surface",
        "texts": [
            " This is how a Sliding Mode Fuzzy Controller reduces the rule base size. To illustrate how the rule base size is reduced, we use a 2- dimensional system. Under the typical Sliding Mode Fuzzy Controller, with each input fuzzified into three fuzzy subsets as shown in Fig 5, there are 9 partitions of the state space, and 9 rules are needed. However, with the following simplified rule: 1 e+ Aie + ci IF e is 4 , THEN ui = ksat( 4i The rule base size may be less than 9. To approximate the switching curve in Fig 4, e may need more fuzzy subsets. It has been show that five membership functions for e are enough to approximate the switching curve in Fig 4 [24]. The control surface of such a 5 rule FSMC and the corresponding sliding surface is shown in Fig 6. -1.5 error As mentioned before, in a Sliding Mode Controller, the sliding surface is a hyperplane [l]. In the case of 2- dimensional systems, the sliding surface will be just a line without any width. Control action then alternatively changes its sign when the system state switches from one side of the line to the other side of the line as the line has no width. A boundary layer can alleviate the chattering problem",
            " A nonlinear boundary does not add much control performance since it is the width of the boundary layer that influence the controller performance, not the form of the boundary layer [4]. From authors\u2019 point of view, FSMC has little practical value, if not totally useless. Sliding mode control is a kind of time sub-optimal control. The well known solution for time optimal set point control of a system with bounded control action is a bang-bang controller across a nonlinear switching curve. For 2-dimensional systems, the nonlinear switching curve often has the form depicted in Fig 4 instead of a linear switchng line. Fig 4 also shows there can be a switching band around the switching line to alleviate chattering. Fig 4 also illustrates how the control surface may look like with a nonlinear switch function. In a Takagi-Sugeno (TS) type FLC [23], the rule output function typically is a liner function of controller inputs. The mathematical expression of this function is similar to a switching function. This similarity indicates that the information from a sliding mode controller can be used to design a fuzzy logic controller, resulting in a Sliding Mode Fuzzy Controller (SMFC). Wu proposed such an approach in which parameters in the output functions for different rules that covers different partitions of the state space are determined by different sliding mode controllers that also cover the corresponding partitions of the state space [3]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002462_s00466-006-0120-3-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002462_s00466-006-0120-3-Figure8-1.png",
        "caption": "Fig. 8 The damping force in the fiber",
        "texts": [
            " Note that, in general, the spring force will not act along the fiber because the spring stiffnesses in the normal and tangential direction are different. The damping force in the fiber is proportional to the time rate of change of the fiber displacement and is given by d Fd = Cn dn d\u03c4 n\u0302 + Ct dt d\u03c4 t\u0302 (5) where dn d\u03c4 and dt d\u03c4 are the time rates of change of the fiber displacements in the normal and tangential direction, respectively. The damping force opposes relative motion between the elements and hence acts in the direction opposite to the displacement rate vectors. Figure 8 shows the damping force acting on element i at point A. An equal and opposite force acts on element j at point B. Note that the damping force is developed only during the transient part of the simulation and at steady state, the force in the fibers is due to the spring effect. The resultant force on element i at point A, located at a distance x from the midpoint M of the contacting side (see Fig. 9) is d F = d Fs + d Fd (6) The total force acting on the contacting side of element i is then found by integrating the normal and tangential forces in each of the connecting fibers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002635_j.chaos.2006.01.092-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002635_j.chaos.2006.01.092-Figure2-1.png",
        "caption": "Fig. 2. The control Lyapunov function: its maximal value and variational difference.",
        "texts": [
            " (iii) For any x 2 CnXc, D or D falls into between u(1)(x) and u(2)(x). It can be easily verified that u \u00bc Dsgn\u00f0ax\u00de \u00f010\u00de is a D-modulated feedback to make V(x) decreasing for x 2 CnXc, and to make V(x) increasing for x 2 Xc. Note that Xc X and when jaj < 2, X C. The proof then splits into two parts: (iii.1) X is invariant with respect to fc.For any x 2 XnXc, V \u00f0x\u00fe\u00de < V \u00f0x\u00de 6 max x2XnXc V \u00f0x\u00de \u00bc D2. For any x 2 Xc, since V \u00f0x\u00fe\u00de \u00bc a2x2 2Djaxj \u00fe D2; the maximal value of V(x+) on Xc is reached at x = 0 (see Fig. 2), therefore, V \u00f0x\u00fe\u00de 6 max x2Xc V \u00f0x\u00fe\u00de \u00bc D2. So, in both cases, x+ 2 X, showing that fc(X) X.We can also show that X fc(X), as follows. For any y 2 X, choose x \u00bc y sgn\u00f0y\u00deD a . Then, it verifies that j xj 6 jy sgn\u00f0y\u00deDj \u00bc jjyj Dj 6 D; i.e., x 2 X, and fc\u00f0 x\u00de \u00bc y. Hence, fc(X) = X. So, X is invariant with respect to fc. (iii.2) The attracting region of X is C.For any x 2 CnX, denoting x0 = x, x1 = fc(x), and xk = fc(xk 1), for k = 1,2, . . ., there can only be two cases: (1) there is an integer N such at xN 2 X; (2) for any k, xk 62 X"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000521_robot.1994.350999-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000521_robot.1994.350999-Figure1-1.png",
        "caption": "Figure 1: Stance phase of the one legged hopper.",
        "texts": [],
        "surrounding_texts": [
            "The dynamics of Raibert 's planar one legged hopper have been studied quite extensively in the particular case of vertical hopping and no translational velocity. These studies have pointed out the possibility of complicated behaviors (see [l]' [8]). The forward motion of the one legged hopper has also been investigated in recent literature, with the restriction of low velocities (see [.Y]). It appears from these references that the control of the energy of the hopper is a dificult problem due to the necessity of integrating the hopper's dynamical equations during the stance phases. In this paper, we consider the problem of controlling the leg's forward motion under the assumption that the energy of the hopper is constant. We unveil results that do not depend on the spring of the leg and analyse a few simple control schemes.\n1 Simplified Model of the One Legged Hopper\n1.1 Description of the model It is assumed here that the leg itself has no mass and no inertia. The body has a mass M concentrated in one point so that the problem of controlling the attitude can be discarded. There is no dissipation of energy during the stance phases and the mechanical energy during the flight phases is constant. Since we do not try to regulate this mechanical energy, the control of the thrust is not a concern in our study. When the hopper is running, its motion is decomposed into steps, which are the succession of a flight phase, during which the robot is not in contact with the ground, and a stance phase, used by the robot to bounce up. During the stance phase, the motion of the robot is completely passive. The leg has a given length ro when the robot hits the ground. Then the leg's spring compresses and decompresses back to ro. At this moment, the robot clears the ground and starts another flight\n1.2 Some General Properties of Running In this section, we aim at finding a general expression for the variation of the forward velocity through the stance phase. We will show that only the knowledge of two real valued functions is needed to describe these variations locally about any regime such that the forward velocity is constant, also called nominal regime.\nDue to the conservation of the overall energy, the three variables (i, i, 0) that describe the state of the robot at the beginning of a step are not independent:\nThe state of the robot at the beginning of a step is thus completely characterized by the the pair ( 2 , This state of the robot will be denoted as (z', at the time instant when the robot leaves the ground. It is completely determined from the touch-down conditions. We can then consider the operator F:\n131 1050-4729/94 $03.00 0 1994 IEEE",
            "Using the symmetry properties of running that are presented in [5], we see that F is involutive:\nAlso, for each forward velocity h, there exista a unique leg angle e,(;) such that the forward velocity is unchanged after the stance phase. By symmetry, the leg angle at lift off is the opposite of the one at touch down. Hence:\nThe invariant curve ( z , O m ( z ) ) will be denoted as (r). This curve is invariant point by point in the sense that the image of each point of this curve by the function F is the point itself.\nFrom now on, we will assume that the mapping F is differentiable. The nominal leg'angle gm(z) has some immediate properties: it is equal to zero when the robot is only hopping vertically, it is odd (em($) = -Bm(-h) ; 8,(0) = 0), and has the same sign as the forward velocity.\nDifferentiating (3) at a fixed point (i , 8, (i)) yields:\nTherefore, the eigenvalues of the gradient of F at any fixed point are either +1 or -1. If both of them are -1, then F is locally a central symmetry, which contradicts the fact that the curve (I')is invariant point by point. If both eigenvalues are +1, then F is the identity, which is not true either. Therefore the eigenvalues of B F m ( i ) are equal to +1 and -1 respectively. A consequence of these properties is that there exist two real valued functions a(;) and @(i) such that BJ\"(Z) has the following form:\nThen for each angle 0 in the neighborhood of Om(&), a first order Taylor expansion of F yields:\n(7) which in view of (6) provides us with the lift-off\nforward velocity:\nDifferentiating this expression with respect to i and identifying with (6) shows that we necessarily have /3(i) = @,(z). We now define Cm(i.) as:\nFrom (6) and (7), it appears that, in the vincinity of a point (i ,e,(Z)) of (r), F can geometrically be approximated by the symmetry with respect to the direction of the eigenvector v + l ( i ) = (l,Ok(i))T associated with the eigenvalue +1 (this vector is tangent to (r) at ( i ,Om(h) ) ) , along the direction of the eigenvector u-l(i) = associated with the eigenvalue - 1.\nSo far, it has been shown that only the knowledge of two real valued functions cm and Om is needed to describe locally the variation of the forward velocity through the stance phase, and that we have:\n2 = k - w(i)(e -em(*)) (10) with : 2 W(2) = Cm(i) - OL(2) We are now going to analyse the case of zero gravity, and show that, the knowledge of the nominal leg angle em(i) is sufficient to describe locally the variation of forward velocity through the stance phase. All the properties that are induced by the zero gravity stem from the fact that the angular momentumof the robot with respect to its foot is then constant through the stance phase. These properties are still valid, in the first approximation, when gravity is present and when the angle 8 remains small.\n1.3 Special Case: no gravity In this section, we assume that the robot is hopping in zero gravity. This problem can be thought of as a two legged hopper that bounces between two parallel walls [SI. The conservation of angular momentum implies:\n(12) x X I V V arcain - - arcain - = 8 + 8'\nwhere V = d m is the magnitude of the robot's velocity vector during the flight phases. Differentiating this last equation with respect to i and identifying the result with (10) shows that:"
        ]
    },
    {
        "image_filename": "designv11_28_0000199_s0925-4005(00)00626-2-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000199_s0925-4005(00)00626-2-Figure1-1.png",
        "caption": "Fig. 1. Scheme of the biosensor fabrication process: (a) amperometric transducer with the epoxy graphite composite; (b) membrane solution deposition and photopolymerization; (c) development of membrane with ethanol. (1) PVC electrode body; (2) connector; (3) copper disk; (4) epoxy-graphite conductive layer; (5) enzymatic membrane.",
        "texts": [
            " A platinum auxiliary electrode and a double-junction Ag/AgCl reference electrode (Orion 900200) with the external cham- ber \u00aelled with a 0.1 M KCl solution were used to evaluate the sensors. pH was measured with a Crison micro-pH 2002 pH-meter. A combined glass electrode Ingold was used. The conductivity of the membrane with graphite was tested with a multimeter. The working electrode was based on a conductive graphite\u00b1epoxy composite. This device was built in our laboratories following a procedure described elsewhere [21]. The body of the electrode was a PVC tube where a female electrical connector was placed (Fig. 1). A copper disk was attached to this connector using tin solder. The conducting composite was prepared by mixing the epoxy resin components (Araldit M and hardener HR in a ratio 1 : 0.4 by weight, respectively) and the graphite powder in a ratio 1 : 1 by weight. This composite was placed in the hollow end of the tube to form the body of the electrode and cured at 608C for 24 h. After curing, the surface was polished. For membrane fabrication a pre-polymer solution was prepared by mixing the acrylated urethane oligomer IRR 213, the crosslinker TPGDA, and the photoinitiator (Irgacure 651)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002844_kem.306-308.211-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002844_kem.306-308.211-Figure5-1.png",
        "caption": "Fig. 5 Configurations of (a) initial design and (b) optimal design",
        "texts": [
            " 4 shows the comparison between actual simulation and the prediction of kriging model for two usage factors and volume at additional validation points. Fig. 4 indicates that usage factors are relatively more nonlinear than volume. It is also observed that R-squares calculated at validation points are 0.7994, 0.7444, and 0.9975, respectively. Feasible direction method is used to execute classical optimization. Total 96 computer simulations are accomplished during optimization process. It means that classical design optimization requires 24 analyses more than metamodel-based design optimization. Fig. 5 shows initial and optimal configurations, respectively. As shown in Fig. 5, outer radius out R outstandingly decreases while inner width in W increases in optimum configuration. Maximum von Mises stress of optimal design is )MPa(485 that is below yielding stress. Table 1 represents the optimal solutions of connecting rod obtained by both classical optimization and metamodel-based design optimization. Optimal volume obtained by using kriging model is )(102247.1 35 m\u2212\u00d7 and is almost consistent with the solution of typical optimization, )(1024.1 35 m\u2212\u00d7 . Volume reduction of 21"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001667_robot.2004.1307171-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001667_robot.2004.1307171-Figure3-1.png",
        "caption": "Fig. 3 Aeesoible lines. a) Object profile, b) Lee pints and their p r o j d o w e) Rightpina andtheirpmjenions. N o t e t h a t p o i n a p ~ a n d p , ~ ~ ~ ~ t p m j ~ e d becaurc they an under line 1. d) None ofthc left pinu are projected 011 line 2 because they are hated above L or d e r b e 2. e) h l t i n g acessible lines and f ) Modified object. Note thatp, is contained in the righrser wen thwb its",
        "texts": [
            " For both object types, a set of lines can be used to represent the object a line segment is defined as that covered by another line located within a certain distance d- away Gom the object. With this distance, we can ensure that sufficient space is available for the fingers. The definition used here assnmes that once the hand is placed over the object and ready to grasp, the fingers will contract in straight lines t o m fully open directly to the contact points. The following methodology is illustrated in Fig. 3. We have a set of line segments L making up the profile of the object. Every line Li, i = l , ..., n, is defined by a starting point pi, a unit vector ui and a length 1, so that L=[@,,ut,l,) ,_.., @n,u&,)]. In our algorithm, all lines are processed simultaneously, but we will consider line 1 separately for illustration. We first divide the lines in two sets. A left set constitutes lines located on the left of line 1 and a righr set includes lines located on the right. The separating point is located on the opposite line of the profile. In the case of line 1 in Fig. 3a, this falls betweenp6andp7. We then take the points in the leff set projection is on the lel?. In that edse line 1 is not accasible at all. that are located within a distance d- above line 1 and project them as shown in Fig. 3b. The extreme right projection defines the left boundary. Similar procedure is implemented for the right set to d e h e the right boundary (see Fig. 3c). This process is implemented simultaneously for all lines by using simple matrix operations to give the accessible line segments in Fig. 3e (indicated by thick lines). Revolved Objects A non-accessible region for revolute objects is a line segment of the profile that is covered by another line segment located further from the axis of revolution. This definition reflects the fact that revolute objects (considered as planar) can only be grasped with fingers closing towards the axis of revolution. Here we suggest that revolute objects can be treated similarly to planarobjects. This is true if the following rules are respected: 1) all contact points and the axis of revolution must lie in a common plane and, 2) all three contact points must be on three lines belonging to the same group"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001221_aim.2001.936456-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001221_aim.2001.936456-Figure4-1.png",
        "caption": "Figure 4. Grasp on polygonal object",
        "texts": [
            " The problem is described as follows: Given a set of edges of the polygonal objects, determine the optimal locations of contact points on the edges so that the quality measure of the grasp is maximized. The location of each contact point is represented as follows pi = v i + A i U , (13) where ui is the unit vector in the direction of vivi+,. ai = [lpi -vi 11 is the distance from contact point p i to vi , which parameterizes the location of the contact point. Thus, the grasp configuration is represented by a set of real numbers A. = {Al, Az, .- - , A.\"}. Denote the 3-D wrench space by 3'. Let f: and f; be two edge vectors of the friction cone at point pi (see figure 4). Define The set of primitive wrenches are given by w * (G, a) = C ; (AX w ; (a),. . , w; (A)} (1 5 ) In what follows we denote the feasible wrench set and the quality index of the grasp by W (G, A.) and qQ (G, A), respectively. They are dependent on the grasp configuration A. In order to synthesize optimal grasp, it is required to determine the grasp configuration so that the radius of g -sphere contained in W (G, A) is maximized. Here we assume that the convex constraint on the contact forces is employed, the algorithm can be extended to handle other types of constraints such as maximum constraint and hybrid constraint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002641_tmag.2006.872518-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002641_tmag.2006.872518-Figure7-1.png",
        "caption": "Fig. 7. Flux distribution (9000 rpm): (a) without surface layer, (b) with surface layer (D = 0:016 mm).",
        "texts": [
            " 6(b) shows the effect of on number of iterations of the ILUBiCGSTAB method when the leaf element is applied. In the ordinary method, the ILUBiCGSTAB method does not converge when is less than 0.5 mm. The leaf element can get the convergence until mm. The reason why increases with should be investigated in the future. Table I shows the discretization data and the CPU time. When the leaf element is applied, the number of nonzeros in the coefficient matrices becomes slightly larger compared with the ordinary method, but the convergence solutions can be obtained. 2) Flux and Eddy Current Distributions: Fig. 7 shows the flux distributions without and with the surface layer at 9000 rpm. When the surface layer is neglected, most of the fluxes reach to the shaft due to the gap between the steel sheets as shown in Fig. 7(a). On the other hand, when the surface layer is considered, the flux density in the surface layer is high because the gap between the steel sheets is broken in the surface layer. Fig. 8 shows the flux and eddy current distributions in the surface layer at 9000 rpm and mm. This figure shows the flux is biased to the rotational direction by the eddy current. 3) Iron Losses: Fig. 9 shows the iron losses of the rotor. In this section, the iron losses are normalized by the measured one. Fig. 9(a) shows the effect of the thickness of the surface layer on the iron losses at 9 000 rpm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000234_bf02442675-Figure16-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000234_bf02442675-Figure16-1.png",
        "caption": "Fig. 16 Cartoon of a redox mediator modified enzyme. Electron transfer from the active site to the electrode is proposed to occur by a number of shorter steps involving the bound mediators, in this case ferrocene groups",
        "texts": [
            " In nearly all cases there is little evidence of direct electron transfer between the flavin prosthetic group of the enzyme and the polymer although FOULDS and LowE (1988) suggest that this may happen in the ferrocene derivatised polymer. Direct, unmediated, electron transfer between redox proteins and conducting polymers remains a tantalising goal. Finally, an alternative approach which looks very promising is to modify the enzyme by the covalent attachment of redox centres to the protein (HILL, 1984). In this case the suggestion is that the covalently attached redox centres act as 'stepping stones', allowing the electrons to get from the active site out to the electrode by a number of sequential, short steps (Fig. 16). Note that this is very similar to the mechanisms of charge propagation through a redox polymer film, discussed above. Thus when glucose oxidase is modified by attachment of ferrocene carboxylic acid (DEGANI and HELLER, 1987) or ferrocene acetic acid (BARTLETT et al., 1987) direct electrochemical oxidation of the reduced flavoprotein at a clean metal electrode becomes possible. This approach can be extended to other flavoproteins (DEGANI and HELLER, 1988) and may prove to be a general one. B15 6 Conclusions In this paper I have tried to provide an overview of the field of chemically modified electrodes and the way that it impinges upon bioelectrochemistry"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001978_s0022-0728(81)80454-8-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001978_s0022-0728(81)80454-8-Figure1-1.png",
        "caption": "Fig. 1. M u l t i c y c l i c v o l t a m m e t r i c c u r v e s o f 2 \u00d7 10 -3 M Ni ( I I ) in 4 . 8 M N a S C N a t 9 5 \u00b0 C , r e c o r d e d w i t h H M D E . S c a n r a t e 20 V m i n -1. ( ) 1 cyc le , ( . . . . . . ) 2 cyc l e s ; ( . . . . . ) 3 cyc l e s ; ( . . . . . . ) 10 a n d s u b s e q u e n t cycles .",
        "texts": [
            " The temperature of the electrolytic cell sealed with a water jacket was kept constant within +0.1 \u00b0 C. RESULTS Behaviour at potentials less negative than the formal potential of the Ni(II)/ Ni(Hg) couple In our earlier paper [4] we presented results which indicated that there is NiS formation during the electroreduction of the Ni(II)--thiocyanate comolexes. This formation is markedly favoured by higher temperatures. In the following experiments 95\u00b0C was selected. In the multicyclic voltammetric experiments with HMDE, the electroreduction rate increases from cycle to cycle (Fig. 1). The first anodic scan, in addition to the oxidation peak of the nickel amalgam (E~a) formed during the cathodic scan, shows a second peak which results from the oxidation of Hg to HgS according to NiS + Hg -- 2 e -+ HgS + Ni(II) (I) In the second cathodic run, there is a peak corresponding to electroreduction of HgS formed by reaction (I). This cathodic reaction leads to the retransformation of HgS to NiS, according to reaction (I) proceeding now from right to left, as discussed earlier [4]. This new peak occurs at potentials approximately 200 mV less negative than the potentials o f the cathodic reactions observed in the first cathodic scan",
            "ectrolyses performed at more cathodic potentials do not produce NiS on the electrode, while S 2- ions are present in the bulk of the solution. The absence of NiS on the electrode surface may reflect either desorption or electroreduction. Investigation of the process of adsorption--desorption and electroreduction of NiS was carried ou t using pulse polarography with the DME, at 95\u00b0C. The anodic part of the pulse-polarographic curve (Fig. 3) shows two distinct waves which correspond to the oxidation peaks observed in the first anodic cycle of the voltammetric curves (Fig. 1). If the oxidation of the products obtained at different initial potentials is carried out at the potential corresponding to the limiting current of the first oxidation wave (EIa), there is only a limited oxidation of nickel from the amalgam (Fig. 4, curve b). The corresponding electroreduction charge is approximately 10 times larger (curve a in Fig. 4). If oxidation is performed at the less negative potential (E~ I ) an increased charge is recorded (Fig. 4, curve c). This charge is due to the oxidation of the mercury electrode in the presence of NiS produced during the electroreduction step in the potential region --0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001985_0026-0800(78)90031-9-FigureI-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001985_0026-0800(78)90031-9-FigureI-1.png",
        "caption": "FIG. I(a). Tensile specimen geometry.",
        "texts": [
            " The cracks were opened carefully by mechanical means and examined by SEM Analysis. Three of the 146 D. Hoeppner I - E- x i t , d \"~ FIG. 10, WOL Specimen E-8. 3-hour hold detonized water room temperature. Fractography of Flaw Growth-Invited Paper 147 (c) Flat flacture mode in prccrack to test transition region. 300\u00d7. (d) Prccrack region. 300\u00d7. (c) Prccrack--To~,t transition region. 2~,0\u00d7. (1\") Tcsl Fegion. 300\u00d7. fracture surfaces are shown in Figs. 11-15. The fracture surface of Specimen B-A as seen in Fig. II exhibits many of the fracture modes encountered in previous test specimens. Quasicleavage areas are seen in Figs. l l(b) and I I(d) while fatigue striated areas are evident in Figs. 11(c), I l(e), and I l(f) is a view of the probable origin area and is seen in greater detail in Fig. 12. The darker fan-shaped area is the suspected origin because all fracture flow lines originate or propagate from this region. Figs, 12(b) and 12(c) detail the left portion of the region shown in 148 D. Hoeppner Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003488_robot.2007.363548-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003488_robot.2007.363548-Figure3-1.png",
        "caption": "Fig. 3. Six-terminal model of two-four-phase motor",
        "texts": [
            " The total characteristics including the effect of induction will be discussed in the latter part of the paper. The schematic diagram of the two-four-phase electrostatic motor (without induction) is shown in Fig. 2. This chapter analyzes the force characteristics of the motor in Fig. 2 based on the method described in [12]. Since two-four-phase electrostatic motor has six phases in total, it can be represented by a six-terminal capacitance network. The six-terminal capacitance network model of the motor is shown in Fig. 3. In the model, all the six terminals are connected by capacitors. Those capacitances can be mathematically represented using a 6\u00d76 capacitance coefficient matrix. In the matrix, element in i-th row and jth column expresses the relationship between i-th terminal and j-th terminal. Exactly speaking, when 1 V is applied to the j-th terminal whereas the other terminals remain zero volt, the i-th terminal has electric charges which total amount is equal to the element at i-th row and j-th column. As the general nature of the coefficient matrix, off-diagonal elements are always negative, and diagonal elements are positive"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000297_s0736-5845(01)00037-0-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000297_s0736-5845(01)00037-0-Figure1-1.png",
        "caption": "Fig. 1. Camera-fixed reference system.",
        "texts": [
            " Unlike the situation where new parameter estimation is begun \u2018\u2018from scratch\u2019\u2019 following alteration of the cameramanipulator juxtaposition, such capability would carry with it no need for arm motion beyond that which is mechanically required to perform the actual task, and hence a maneuver that requires continuous arm movement even across camera-space transitions can be accommodated. Consider the local, nonlinear relationship between the physical location and the corresponding camera-space response of the centroid of a visual feature attached to a given manipulated object. This relationship is described by the pin-hole camera model as xci \u00bc f Xi Zi ; \u00f01\u00de yci \u00bc f Yi Zi ; \u00f02\u00de where, according to Fig. 1, f represents the focal length of the camera while \u00f0Xi;Yi;Zi\u00de represents the location of the ith visual feature with respect to the XYZ system attached to the camera. The origin of the XYZ system lies at the focal point of the camera while the X - and Y -axis are parallel to the xc- and ycaxis on the image obtained by the camera. The Z-axis points in the direction of the camera\u2019s optical axis. As demonstrated by Gonz!alez-Galv!an et al. [11], when the camera is located far from the physical region where the visual features are located, Eqs",
            " As explained in [12], the six view parameters can be estimated using samples of both camera-space location of visual features and the corresponding physical location of the features obtained with the robot\u2019s kinematic model, using a nonlinear estimation scheme such as the least-square differential correction described by Junkins [13]. Once the six view parameters are estimated, the Euler parameters e0;y; e3 which describe the relative orientation of the camera-fixed coordinate system XYZ (see Fig. 1) to the manipulator-fixed coordinate system xyz can be obtained. This approximation, as explained in [11], is given by ei 1E Ci jjCjj ; jjCjj \u00bc C2 1 \u00fe C2 2 \u00fe C2 3 \u00fe C2 4 1=2 i \u00bc 1;y; 4: \u00f06\u00de The relative nominal orientation between the XYZ coordinate system attached to the camera and the xyz robot-fixed coordinate system is described by the following 3 3 direction cosine matrix (see [14]); R \u00bc e2 0 \u00fee2 1 e2 2 e2 3 2\u00f0e1e2 \u00fee0e3\u00de 2\u00f0e1e3 e0e2\u00de 2\u00f0e1e2 e0e3\u00de e2 0 e2 1 \u00fee2 2 e2 3 2\u00f0e0e1 \u00fee2e3\u00de 2\u00f0e1e3 \u00fee0e2\u00de 2\u00f0e2e3 e0e1\u00de e2 0 e2 1 e2 2 \u00fee2 3 2 64 3 75: \u00f07\u00de When the camera is panned or tilted, the change in orientation of the coordinate system attached to the camera can be quantified depending on the amount of angular rotation and depending on the geometry of the computer-controlled platform used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001901_robot.2004.1308084-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001901_robot.2004.1308084-Figure7-1.png",
        "caption": "Fig. 7 Proposed method far a hybrid robot composed of a planar 3DOF mobile robot and a 6DOF serial robot",
        "texts": [
            "# TDW v;1, YPAI, rC1 \"PLI Then, the dynamic model for the independent joints of the hybrid robot is obtained as The dynamic model of the serial arm with the virtual joints is expressed as Where And The number of multiplications and summations of the open-tree structure method for this hybrid system is represented in Table III. 2) The proposed method The mobile robot and a serial arm are separated into two parts in the proposed method. Then, the virtual joints are attached to the base of the serial arm as shown in Fig. 7. And the dynamic model of the 6DOF serial arm and the virmal joints is calculated and added to the dynamic model \"z, with respect to the independent joints of the mobile robot [I 11. \"5 = \"[I,] \"$ + ,\"q4 - - 9x1 9x9 9x1 1x9 9 ~ 9 x 9 9x1 Where \"[I;] = ~(mjt['C;]'['G;]+[G~]r[~it][G~]), (46) 9x9 i=4 9.3 1x9 911 3x3 Id And \\ , +(([GikIr [r\"]) 0 [Hi ] ) + [G~k]'([G~k]' 0 [P'*])[GF]} 9x3 3 x 3 3x919 9x3 9 r 3 3r3r3 3r9 Eventually, the dynamic model of the hybrid robot is obtained, with respect to the independent joints, as by employing Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003294_00032710701603876-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003294_00032710701603876-Figure1-1.png",
        "caption": "Figure 1. Multicommuted flow injection chemiluminescence system for hydrogen peroxide determination. Vi\u2014three-way solenoid valves, Y\u2014confluence joint point, D\u2014lab-made luminometer, C\u2014carrier (water), S\u2014sample or reference solution, R1 \u20132.5 1023 mol l21 luminol solution in carbonate buffer pH 11.0, R2\u2014 1.0 1022 hexacyanoferrate(III) solution, RC\u2014reaction coil, W\u2014waste vessel. Arrows indicate points of actuation of the peristaltic pump. All solutions were propelled at 3.0 ml min21.",
        "texts": [
            " The diluted solution was processed into flow system and the H2O2 content was determined by interpolation from a calibration graph obtained previously. The lab-made luminometer comprised of photodiode with the coiled polyethylene tubing that work as a reactor and flow-cell at the same time in front. The flow-cell was constructed with polyethylene tubing because it is transparent to electromagnetic radiation emitted by chemiluminescence in the range from 420 to 440 nm (Rocha et al. 2005). The multicommuted flow system is showed in the Fig. 1. It comprised four three 3-way solenoid valves. In the initial status, all valves are switch-off, the carrier stream is propelled through V3 to the manifold while sample and reagent solutions are recycled back to their vessels. In the sampling step, all valves are simultaneously switched on, the carrier solution is recycled and aliquots of sample and reagents merge at the confluence point Y. The sampled volume depends on the switching time of the valves and the corresponding flow-rate. Solutions undergo fast mixing and the sample zone is transported to flow cell to measure the emitted radiation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001806_1.2199857-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001806_1.2199857-Figure4-1.png",
        "caption": "Fig. 4 Physical interpretation of \u2020C1\u2021, \u2020C2\u2021",
        "texts": [
            "org/about-asme/terms-of-use Downloaded F F = rC21 \u2212 rC22 f1 + rF22 f1 + f2 rF22 \u2212 rF12 f1 + f2 8 where rCij =xCi\u2212xOj i , j=1,2 and rFi2=xFi\u2212xO2 i=1,2 . From these equations, the contact forces and the position of the zero moment points can be obtained uniquely as a function of the friction forces. Now, we can find the following observations: C1 Let v1 be the velocity vector of object 1 at xO1. From Eq. 5 , since v1 is antiparallel to f1, the slip may not occur between the objects 1 and 2 if the direction of v1 is included strictly inside of the friction cone between the objects 1 and 2 Fig. 4 a . C2 Let nC1 and nC2 be the moment which object 2 exerts to object 1 at each end of the contact segment. Rewriting Eq. 6 by using nC1 and nC2, we obtain 0 nC2 nC2 \u2212 nC1 1 9 As shown in Fig. 4 b , both nC1 0 and nC2 0 are satisfied if the line of action passes through strictly inside of the contact segment between the objects 1 and 2. C3 Let vG be the velocity vector of objects at the ECOF of the system of two objects xG. From Eq. 7 , since vG is antiparallel to f1+ f2, the slip may not occur between the object 2 and the pusher if the direction of vG is included strictly inside of the friction cone between the object 2 and the pusher Fig. 5 a . 424 / Vol. 128, JUNE 2006 rom: http://dynamicsystems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000603_2001-01-1007-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000603_2001-01-1007-Figure10-1.png",
        "caption": "Fig. 10. Statistical distribution of the random vector representing the k-th order harmonic component of the gas-pressure torque for cylinder \u201ci\u201d.",
        "texts": [
            " Thus, for the half harmonic order (k=1/2), the vectors will have the same phase angle diagram as in Fig. 2, but rotated with the angle k\u03d5 . Because of the random character of the vectors interpreting a harmonic component of the cylinder torque, their magnitude and phase will be randomly distributed. Assuming a normal distribution, the tip of the vector interpreting the harmonic component of order k for cylinder \u201ci\u201d will be situated inside the ellipse of dispersion having as half axes the values ikT\u03c33 and iikT \u03d5\u03c33 (Fig. 10) The projections of this random vector on the coordinate axes will be also random vectors, normally distributed, having the mean values [6], [7]: iiyi iixi kkk kkk TT TT \u03d5 \u03d5 cos sin = = (9) and the standard deviations: ikiiikyik ikiiikxik kkkTT kkkTT T T \u03d5\u03c3\u03d5\u03c3\u03c3 \u03d5\u03c3\u03d5\u03c3\u03c3 \u03d5 \u03d5 222222 222222 sincos cossin += += (10) The two vectors resulting from the projection of the same random vector are correlated random variables having a covariance: [ ]222 2 2sin ikiik ik ii kTyxk TK \u03d5 \u03d5 \u03c3\u03c3 \u2212= (11) If all N cylinders of a multi-cylinder engine are operating uniformly, the mean values and standard deviations will be the same for all cylinder torques: Ni TT kki Tkk ,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002551_robot.1984.1087151-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002551_robot.1984.1087151-Figure1-1.png",
        "caption": "Figure 1; Schema of a Se l f -Tming System",
        "texts": [],
        "surrounding_texts": [
            "whereas , Figure 9 shows the b i a s term i n t h e same d i r e c t i o n .\nThe second task i s s i m i l a r t o t h e f i r s t one e x c e p t t h a t a c o n s t a n t f o r c e i s t o be a p p l i e d i n t h e X d i r e c t i o n . T h i s r e p r e s e n t s a hybrid cont r o l problem. The des i r ed fo rce was increased from zero to 5 n e w t o n s d u r i n g t h e i n i t i a l l e a r n - i ng pe r iod and kep t cons t an t a f t e rwards . F igu re 10 shows t h e r e s u l t of the second circle drawn, whi le F igure 11 i n d i c a t e s t h e f o r c e p r o f i l e i n t h e X d i rec t ion . Typica l pseudo c n t ro l and t y p i c a l c o e f f i c i e n t of t h e f o r c e c o n t r o l a x i s a r e shown in F igure 1 2 and Figure 13, respect i v e l y .\nIn o rder to demonst ra te the robus tness of t h i s c o n t r o l a l g o r i t h m , t h e t h i r d l i n k of the man ipu la to r ( t he boom) was assumed to be f l e x i - ble . For this example a s t a t i c d e f l e c t i o n term was added to the dynamic simulation model of the manipula tor . The t a sk i s s imi l a r t o t he p rev i - ous o n e s e x c e p t t h e c i r c l e i s t o be drawn i n t h e h o r i z o n t a l X-Y p lane w i th t he 2 a x i s p o s i t i o n servoed a t 0 s e tpo in t . F igu re 14 shows t h e a c t u a l c i r c l e drawn. Figure 15 compares the motion in the 2 d i r e c t i o n f o r t h e t a s k c o o r d i - n a t e c o n t r o l l e r and a j o i n t c o o r d i n a t e c o n t r o l l e r [17] which i s unaware of t h e l i n k f l e x i b i l i t y . C l e a r l y t h e t a s k c o o r d i n a t e c o n t r o l can compensate \u20ac o r unknown dynamic cond i t ions ,\nV I . CONCLUSIONS\nA new se l f - tun ing adap t ive f eedback cont r o l l e r h a s b e e n d e v e l o p e d t o d i r e c t l y compens a t e f o r e r r o r s i n e n d - e f f e c t o r p e r f o r m a n c e i n the task based coordinate systern. The method does not requi re a mathematical model for implementation and can be used i n p o s i t i o n , f o r c e O r h y b r i d c o n t r o l s i t u a t i o n s . The method au tomat i - ca l ly compensa tes for manipula tor compl iance , f r i c t i o n and l i n k f l e x i b i l i t y t h r o u g h t h e Onl i n e l a r n i n g mechanism. The proposed method has been shown to have s ign i f i can t advan tages ove r j o in t coord ina te based con t ro l sys t ems .\nV 11. REFERENCES\n1.\n2.\n3 .\nLe in inge r , G . , \"Adaptive Control of Manipul a t o r s Using Self- Tuning Methods,\" Intern a t i o n a l Symposium of Robotic Research, New Hampshire, USA, August 29 - September 2 , 1983.\nLe in inge r , G . , \"Self-Tuning Control of M a n i p u l a t o r s , \" I n t e r n a t i o n a l Symposium on Advanced Software in Robot ics , Leige, Belgium, May 1983.\nDubowsky, S. and DesForges, D. T . , \"The Appl ica t ion of Model- Referenced-AdaptiveCon t ro l t o Rob t i c Man ipu la to r s , \" J . Dynamic Systems, Measurement, Control, 151 0.-\n4. Freund, E., \"Fas t Nonl inear Cont ro l wi th A r b i t r a r y P o l e - P l a c e m e n t f o rI d u s t r i a l Robots and Manipulators,\" x. J-. Robotics Research , 1, 1 (1982).\n5. Go l l a , D. F . , Garg, S. C . , and Hughes, p. c . , \"Linear State-Feedback Control of Manip u l a t o r s , \" e. Machine Theory, 1 6 (1981).\n6 . Luh, J. Y . s . , Walker, M . W . , and Paul, R. p . c., \"Resolved Accelerat ion Control of Mechanical Manipulators,\" I E E E Trans.\nAutomatic Control, 25, 3 (1980).\n7 . Mason, M. T . , \"Compliance and Force Control f o r Computer Control led Manipulators ,\" I E E E Trans. Systems Man and Cybernetics, SMC-11, 6 (1981).\n8 . P a u l , R. P. and Shimano, B . , \"Compliance and Control ,\" Proc. 1976 Jo in t Automat ic Control Conf. , San Francisco, CA, 1976.\n9 . R a i b e r t , M. H. and Craig, J . J., \"Hybrid Pos i t i on /Force Con t ro l of Manipula tors , \" J . k 1 9 8 1 ) . D namic Systems, Measurement, Control, 152\n10. Luh, J. Y. S . , \"An Anatomy o f I n d u s t r i a l Robots and Their Controls,\" I E E E Trans. Auto. Control. February 1983. --\n11. S a r i d i s , G. N . , \" I n t e l l i g e n t R o b o t i c Cont rol ,\" Proc. 1981 Joint Automatic Control Conf . , Cha r lo t t e sv i l l e , VA, June 1981.\n1 2 . Whitney, D. E . , \"Resolved Motion Rate Cont r o l of Manipulators and Human Pro theses , \" I E E E Trans. Man-Machine Systems, MMS-10, (1969).\n13. Whitney, D. E . , \"Force Feedback Control of Manipulator Fine Motions,\" J. Dynamic Systerns, Measurement, Control, (June, 1977). -\n14. Pau l , R. P . , Robot Manipulators: Mathemati C S , Programming, Co trol, The MIT P r e s s , 1981. -\n15. Horn, B. K. P. and R a i b e r t , M . H . , \"Configu ra t ion Space Con t ro l , \" The Indus t r i a l Robot (June, 1981).\n16. Wu, C. H . and Paul, R. P . , \"Resolved Motion Force Control of Robot Manipulator ,\" Trans. Systems 5, Cyberne t i c s , SMC-12, (MayjJune, 1982).\n1 7 . Le in inge r , G . and Wang, S . , \"Pole Placement Self-Tuning Control of Manipula tors , \" P r e s e n t e d a t IFAC Symposium onComputer Aided Design of Mul t ivar iab le Technologica l Systems, September 15-17, 1982, West Lafaye t t e , I n d i a n a , USA.\n55 1",
            "18. Koivo, A . J. and Guo, T . H . , \"Adaptive Linear Cont ro l le r for Robot ic Manipulat o r s , \" I E E E Trans. on Automatic Control, February, 1983. __- -\n19. Wells tead, P . E . , e t a l . , \"A PoleAssignment Self-Tuning Regulator,\" =. I E E , 126, 8 (1979). _.\n20. Wellstead, P. E . , e t a l . , \"Extended SelfTuning Al orithm,\" =. 2. . Cont ro l , 1 9 8 1 .\n2 1 . C la rke , 1). W . , e t a l . , \" S e l f - T u n i n g Cont r o l l e r , \" =. =, Vol. 1 2 2 , No. 9, 1975.\n2 2 . Harris and Bi l l ing , Se l f -Tuning and Adap- -- -~ t i ve Con t ro l , Pe reg r inus Pub l i she r s , 1981 .\n23. Brady, Hollerback, Johnson, Lozano-Perey, Robot Motion: Planning and Control, The MIT P r e s s , 1982. __.- -~\nDisturbance\nDeslgn Rule",
            "I\n-"
        ]
    },
    {
        "image_filename": "designv11_28_0003771_mawe.200900466-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003771_mawe.200900466-Figure5-1.png",
        "caption": "Fig. 5. Distribution of clamping stresses for outer and inner clamping",
        "texts": [
            " Details of this simulation procedure can be found at So\u0308lter et.al. [15]. A further important input parameter is the clamping power at the different machining steps. By taking into account the corresponding clamping forces during outer and inner clamping, respectively, the influence of the elastic stresses due to clamping on the tangential residual stresses in circumferential direction after unclamping can be considered. The distribution of the clamping power for outer and inner clamping is documented in Figure 5. For outer clamping, a three jaw chuck was used. In this case, the clamping stresses concentrate on a small angular range (27 ) at the outer surface. Second clamping was realized by a segment jaw at the inner surface. Clamping stresses are distributed on an obvious larger angular range (113 ), whereas the stresses point to a preferential direction of 60 . After the computation procedure \u201cGeneration of residual stresses\u201d, the computed results were compared with experimental residual stress states"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002044_iros.1992.601931-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002044_iros.1992.601931-Figure1-1.png",
        "caption": "Figure 1: Experimental setup for force control experiments.",
        "texts": [
            " First the plant model of the arm /sensor / environment system is reviewed. Then forcebased explicit force control techniques will be presented and analyzed. Similarly, position-based explicit force control strategies will be presented and analyzed. It will then be shown how the two are the same, indicating which particular schemes will be most successful. Finally, conclusions will be drawn from the analysis and experimental predictions will be made. 2 Arm / Sensor / Environment Model The physical system employed in this study is depicted in Figure 1. The environment is a cardboard box with an aluminum plate resting on it. The box is resting on a table that is considerably more stiff than the box, and is therefore considered ground for these tests. The force sensor is mounted on link six of the CMU DD Arm 11. Attached to the force sensor is a steel probe with a brass weight on its end. The brass weight serves as an end effector substitute and provides a flat stiff surface for applying forces on the environment. Previous analysis has indicated that a fourth order model of the arm / sensor / environment is necessary and sufficient for force control [4, 141"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001067_095441002760179771-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001067_095441002760179771-Figure5-1.png",
        "caption": "Fig. 5 Geometry of the photoelastic specimens",
        "texts": [],
        "surrounding_texts": [
            "Although FE analysis is nowadays well established and extensively used in engineering analysis, its reliability and accuracy in three-dimensional contact problems with friction needs veri\u00aecation. This is particularly important in the analysis of three-dimensional Curvic couplings where contact may occur across 250 or more separate contact surfaces and it is impractical to use a very re\u00aened mesh at the contact surfaces. This paper presents a veri\u00aecation of threedimensional FE results by comparing them to experimental photoelasticity results. The FE analysis is concerned with elastic contact conditions with friction.\nElastoplast ic analysis of curvic joints under a blade release condition has been dealt with elsewhere [11].\nTo obtain contact over the entire length of the coupling halves, one of the halves is machined by the external tool surface and the other by the internal tool surface. This produces a different geometry on either side of the coupling. If the coupling half is machined by the external tool surface then the teeth will have a concave geometry. If the coupling half is machined by the internal tool surface then the teeth will have a convex geometry; this is illustrated in Fig. 4.\nA large number of dimensions are required in order to de\u00aene the geometry of a Curvic coupling. Referring to F ig. 1, the dimensions used at the inside tooth radius for the present investigation were as follows: w, tooth width \u02c6 2.28mm; hc, chamfer height \u02c6 0.28mm; rf , \u00aellet radius \u02c6 0.6 mm; bh, bedding height \u02c6 1.10 mm; lg, angle of inclination of the gable (i.e. the gable angle) \u02c6 4.28; lc, angle of inclination of the chamfer \u02c6 458; y, tooth pressure angle \u02c6 308; a, addendum \u02c6 1.24mm; d, dedendum \u02c6 1.56 mm; t t , tooth thickness \u02c6 3.95mm; fh, \u00afange height \u02c6 1.88 mm; ht , whole depth (total depth) \u02c6 2.80mm; and hg, gable height \u02c6 0.08mm. The overall dimensions of the coupling are de\u00aened by the inside tooth radius \u02c6 30.2 mm, the tooth outside radius \u02c6 38.1 mm, the facewidth \u02c6 7.9 mm, the \u00afange backing thickness \u02c6 40.0mm for both Curvic halves, the diametrical pitch \u02c6 0.31, the inside \u00afange radius \u02c6 15.0 mm and the outside \u00afange radius \u02c6 52.0 mm.\nG01102 # IMechE 2002 Proc Instn Mech Engrs Vol 216 Part G: J Aerospace Engineering at The University of Iowa Libraries on July 1, 2015pig.sagepub.comDownloaded from",
            "The general dimensions of the photoelastic models,\nin mm, are shown in F ig. 5.\nThe photoelastic model (F igs 2 and 3) was manufactured according to the geometry shown in F ig. 5 using a demonstration model Curvic as a template. The two halves of the coupling were manufactured to the same basic dimensions. The shape of the teeth was not the same on both halves, one of the halves having concave teeth and the other convex. This required the two halves of the model to be moulded from their respective coupling halves, even though the dimensions of the two halves were similar.\nThe photoelastic models were made using Araldite CT-1200-1 resin with HT907 hardener in the ratio 2.2:1. The resin and hardener were heated to 130 8C and then mixed. The mixture was poured, at a temperature of 128 8C, into the mould, which had been pre-heated to about 100 8C in an oven. The mix was left to cure in the mould, within the oven, for 5 days, after which the mould was opened and the casting was cured in\ntransformer oil at a temperature of 140 8C. Further detailed descriptions of the casting process used in the photoelastic model manufacture can be found in references [12] to [16].\nThe demonstration model Curvic was chosen for the analyses presented because it was a continuous faced Curvic of small dimensions for which it was relatively easy to produce a photoelastic model. Constructing a photoelastic model of the complexity and size of a typical aero-engine Curvic coupling with a split facewidth would be very dif\u00aecult.\nTwo types of fringes are observed in a polariscope; these are called isoclinics and isochromatics. The isochromatics can be numbered and the fringe number, nf , is related to the magnitude of the difference between the principal stresses, at the point of interest, by the stress optic law, i.e.\ns1 \u00a1 s2 \u02c6 Fmnf\nt \u20261\u2020\nwhere s1 and s2 are the principal stresses \u2026s1 > s2\u2020, Fm is the material fringe value (a constant for a given\nProc Instn Mech Engrs Vol 216 Part G: J Aerospace Engineering G01102 # IMechE 2002 at The University of Iowa Libraries on July 1, 2015pi .sagepub.comDownloaded from",
            "material) and t is the component (or slice) thickness. The material fringe value, Fm, Young\u2019s modulus, E, and Poisson\u2019s ratio, v, for the photoelastic models were obtained from uniaxial specimens machined from blocks of material cast at the same time as the models. The uniaxial specimens were loaded in an oven and taken through the same temperature cycle as the frozen stress photoelastic models.\nThe results for the \u00aegures presented were obtained by using the frozen stress technique and then slicing the three-dimensional model. This enabled the production of two-dimensional thin slices of known thickness, which can be used to measure the difference in principal stresses in the plane of the slice.\nSome optical materials, including the Araldite (CT1200)/hardener (H T907) material used in the present work, exhibit the biphasic property necessary for frozen stress analysis. Fessler [6] presented the requirements for frozen stress work.\nThe model was cast to the dimensions speci\u00aeed in F ig. 5. Some dimensions on the specimens were then machined so that they \u00aetted smoothly into the rig, although the Curvic teeth were not altered by the machining process.\nThe important dimensions for location and load application are the central bore and the sets of holes on PCD 123 mm and PCD 99 mm. These dimensions were accurate to within +0.03mm. The mould and subsequent casting procedures for the two halves of the Curvic joint were manufactured in the same way and hence the dimensional accuracy of the teeth on the\nmodels are expected to be of similar accuracy to the metal components. A blue bed check was carried out in order to check the accuracy of the moulding compared to the demonstration model coupling.\nThe two halves of the coupling were then assembled ready for loading with the convex-shaped toothed coupling half on the top and the concave-shaped toothed half on the bottom. The surfaces of the teeth were cleaned with compressed air before they were placed together. This check proved that the contact surfaces of the photoelastic model were suf\u00aeciently similar to the demonstration model.\nHowever, there were a small number of areas of noncontact in the photoelastic models which were not present in the metal components. It was considered that these small differences in dimensions due to the casting process would have a small overall effect on the results at the contact regions because of the relatively large displacements that occur due to the very low Young\u2019s modulus of Araldite at high temperature.\nFollowing assembly, the components were placed in an oil bath inside a hot air oven. The rig was restrained at the bottom by clamping the base to the oven. A diagram of the arrangements for the loading of the model can be seen in Fig. 6 and photographs of the rig set-up are shown in Figs 7 and 8. The models were then totally immersed in oil in order to eliminate self-weight effects.\nFollowing immersion of the models in the oil bath, the oven was closed, switched on and left to heat up to 135 8C, which is above the glass transition temperature\nG01102 # IMechE 2002 Proc Instn Mech Engrs Vol 216 Part G: J Aerospace Engineering at The University of Iowa Libraries on July 1, 2015pig.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv11_28_0001930_s10665-005-9007-0-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001930_s10665-005-9007-0-Figure1-1.png",
        "caption": "Figure 1. (a) General fixator assembly in neutral configuration (b) Measured parameters of fixator on lateral plane (c) Measured parameters of fixator on AP plane (d) Measured parameters of fixator on axial plane.",
        "texts": [
            " The inverse kinematic problem, in which bar lengths are computed for desired positions, has found interesting applications in different areas; see e.g., [12, 13]. As a fixator, a G-S Platform Mechanism is applied in such a way that the base platform is connected rigidly to the proximal fragment, while the moving platform is located on the distal fragment. The circles circumscribing the base triangle (A1A2A3) and the movable platform triangle (B1B2B3) will be referred to as proximal and distal rings, respectively, both in concept and in the physical arrangement as shown in Figure 1(a). When the proximal and distal ring planes are parallel to each other, this is to be understood as the neutral configuration. It is possible that the orthopaedist may join the fragments at the fracture site with the rings of the fixator in several different ways. In a first case, it is assumed that the bone fragments are fixed to the ring planes, so that the bone axes and plane normals are parallel. It may be thought, in a second case, that the bone axis is connected perpendicular to the ring plane in the proximal part of the fracture site, while the distal fragment is located arbitrarily on the relevant ring of the fixator",
            " Furthermore, it is realistic to assume in all cases that the bone and ring centers are not coincident. In dealing with the different cases, we will perform an inverse kinematic analysis on the G-S Platform model fixator. Input to that analysis will come from radiographic data as well as from clinical examination results. The analysis will provide the leg lengths (L1\u2013L6) of the Stewart Platform Mechanism. As radiographic data, lateral and anteroposterior (AP) views projected along the x- and y-axes are needed, as shown in Figure 1(a). An axial view, when clinically performed, will yield further data for the analysis. The mentioned xyz co-ordinate system is located at the center of the proximal ring, G (Figure 1(a)), so that the xy-plane formed by the A1, A2, A3 spherical joints is coincident with the base of the G-S Platform and the x-axis passes through the center of spherical joint A1. The spherical joints B1, B2, B3 seen in Figure 1(a) belong to the moving platform fixed to the distal fragment. The center of the distal ring G1 will also be the origin of a movable uvw co-ordinate system attached to the moving platform, whereby the uv-plane is defined by the distal ring and the u-axis is defined by G1B1; see Figure 1(a). Based on the above assumptions and notation, a detailed analyses of the three cases will be presented. See Appendix D for a list of symbols. 2.1. First case We consider the situation as shown in Figure 2. Both bone fragments are perpendicular to the respective circles. First, it is necessary to recognize the parameters which characterize the initial and final configurations of the Stewart Platform, one of them being the neutral configuration. The values of these parameters are to be taken from measurements on the lateral, AP, radiographs and on the axial clinical examinations; see Figure 1(b\u2013d). Parameter h designates the distance between the proximal and distal ring planes along the z-direction, when the fixator is at its neutral configuration; see Figure 1(b). Parameters qx, qy signify the distances between the centers G of the proximal ring and G\u2032 of the proximal fragment along the x,y-directions in the proximal ring plane, respectively; see Figure 1(d). Similarly, rx, ry, rz are the corresponding distances, measured along the x,y,z axes, respectively, of the G\u2032\u2032 1 distal bone axis from the distal ring center G1 in the distal ring plane, in the fixed Gxyz-system; see Figure 1(d). Both axial clinical examination, as well as lateral and AP radiographs, are used to get data relevant to qx, qy, rx, ry, rz for subsequent evaluation. The distances ex, ey, ez are the quantities representing relative translations of the fragment bone ends along the x,y,z, axes, respectively, which are necessarily measured from lateral and AP radiographs, as shown in Figure 1(b), (c). The projected lengths bL, cL of the proximal and distal fragments on the lateral plane are shown in Figure 1(b). The angles \u03b2L, \u03b2AP are measured between the vertical z-axis and the projected axis of the distal fragment on the lateral (L) and on the AP planes, respectively, as shown in Figure 1(b), (c). Similar angle definitions apply for the parameters \u03b2 \u2032 L,\u03b2 \u2032 AP , this time for the proximal bone, as shown in Figure 1(b), (c). These angles can be easily determined from the AP and lateral radiographs. The projected relative angular displacement \u03b4Ax of the distal fragment with respect to the proximal fragment in the axial view is seen in Figure 1(d). Determination of \u03b4Ax makes it necessary to refer to clinical examination. Finally, parameter \u03b40 designates the relative rotation of the distal ring with respect to the proximal ring, as shown in Figure 1(d). This angle can be pre-determined from the initial mounting configuration of the fixator as applied to the fracture site. Given the above data and the accompanying assumptions, it will now be possible for us to express the unit vectors eu, ev, ew of the moving co-ordinate system G1uvw attached to the distal ring at G1 according to the following calculations (see Appendix A). tan \u03b2Ax = tan \u03b2AP tan \u03b2L , (1) tan \u03b2wz = tan \u03b2AP sin \u03b2Ax , (2) tan \u03b2wy = \u221a 1+ tan2 \u03b2wz sin2 \u03b2Ax tan \u03b2wz cos\u03b2Ax , (3) tan \u03b2wx = \u221a 1+ tan2 \u03b2wz cos2 \u03b2Ax tan \u03b2wz sin \u03b2Ax ",
            " (28) When the platform is in its first configuration, Figure 2(a), the bar lengths (L1\u2013L6) can be evaluated by taking into account distance formulae between the relevant points specified in the same system: L2i\u22121 =|GAi \u2212GBi | ; L2i = \u2223\u2223GAj \u2212GBi \u2223\u2223 , i =1,2,3; j =\u22122+5\u00b75i \u22121\u00b75i2 (29) For the final configuration of the platform, Figure 2(b), the link lengths L1s ,L2s ,L3s ,L4s ,L5s , L6s are computed in the same way by the formula (29), except that, GA1, GA2, GA3 being same, the vectors GB1, GB2, GB3 are replaced by GB1s , GB2s , GB3s as given below: GB1s = (R1 cos \u03b40 +qx\u2212rx)i + (R1 sin \u03b40 +qy\u2212ry)j+ (b+ c)k (30) GB2s = (\u2212R1 cos(2\u03b41 \u2212 \u03b40)+qx\u2212rx)i + (R1 sin(2\u03b41 \u2212 \u03b40)+qy\u2212ry)j+ (b+ c)k (31) GB3s = (\u2212R1 cos(2\u03b43 + \u03b40)+qx\u2212rx)i + (\u2212R1 sin(2\u03b43 + \u03b40)+qy\u2212ry)j+ (b+ c)k (32) 2.2. Second case The second case may result for several reasons. One of these might be that, after imposing the requirements of the first case and after fracture fixation, radiographs and clinical investigations might point to a residual deformity at the neutral configuration. In that case, all the characteristic data pertaining to the parameters described in the first case, as shown in Figure 1, should be determined again and re-evaluated in such a way that, with proper bar lengths, the bone is finally brought to its anatomically correct position, as shown in Figure 3(b). Here it is to be understood that proximal parts retain their normal positions, while the relative positions of the distal parts have taken on an arbitrary appearance, as shown in Figure 3(a). In addition to the co-ordinate systems Gxyz and G1uvw defined earlier, (cf . Figure 1(a)), one more reference frame G\u2032\u2032 1u \u2032v\u2032w\u2032 with origin at the point of intersection, G\u2032\u2032 1, of distal fragment axis (w\u2032) with the distal ring plane B1B2B3 is needed to formulate the process. Unit vectors of each reference system will be obtained through the transformation matrices both at the initial and final configurations of the fixator assembly, as shown in Figure 3. Since the Guvw system is obtained by rotating the Gxyz reference system through an angle \u03b40 about the z-axis, the transformation matrix [AG1uvw Gxyz ]1 and hence the unit vectors [eu e v ew]1 at the initial configuration \u201c1\u201d, are determined by setting \u03b3 = 0, \u03b7 = 0 and \u03b1 = \u03b40 in (7)",
            " Third case During the attachment phase of the platforms to the fragments at the fracture site, the orthopaedist may fail to comply with the assumptions of the previous two cases or the correction of a residual deformity may be desired. As a result, the fragments may have been attached to the rings on both the proximal and the distal sides of the fracture in an oblique position, bringing the inverse kinematic problem into the subject matter of the third case. In the third case, a new co-ordinate system G\u2032x\u2032y\u2032z\u2032 (c.f. Figure 1(a)) is required at point G\u2032, where the proximal fragment axis meets with the proximal ring plane, in order to describe the oblique position of the proximal bone. The system G\u2032x\u2032y\u2032z\u2032 is obtained by rotating the Gxyz-system about the fixed x, y, z-axes through the angles \u03b3 \u2032, \u03b7\u2032 and \u03b1\u2032 =0, respectively (i.e., first a \u03b3 \u2032-rotation about the x-axis, then a \u03b7\u2032-rotation about the y-axis). Thus, the description of the G\u2032x\u2032y\u2032z\u2032-system with respect to the reference frame Gxyz is to be made as follows: [AGx\u2032y\u2032z\u2032 Gxyz ]=\u2217 [ex\u2032 ey\u2032 ez\u2032 ]=   cos\u03b7\u2032 sin \u03b7\u2032 sin \u03b3 \u2032 sin \u03b7\u2032 cos\u03b3 \u2032 0 cos\u03b3 \u2032 \u2212 sin \u03b3 \u2032 \u2212 sin \u03b7\u2032 cos\u03b7\u2032 sin \u03b3 \u2032 cos\u03b7\u2032 cos\u03b3 \u2032   "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003895_bf01984665-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003895_bf01984665-Figure1-1.png",
        "caption": "Fig. 1. Reciprocating friction machine",
        "texts": [
            " The corresponding sliding speeds are about 5 cm/sec in the hip and almost zero in the knee when the joints are under load. Durat ions of loading are usually under one second. The present communicat ion ana lyses the lubricat ion process which is so efficient t ha t most joints suffer only mild wear in a lifet ime and t h a t produces a coefficient of friction between the sliding surfaces as low as .005 (Charnley, 1960, Dowson, 1967). To s tudy the frictional characterist ics a machine was buil t a round a sledge micro- tome (fig. 1). Specimens were held in a holder a t t ached at one end of a p ivoted arm, and the specimens then loaded on to a flat plate which could be rec iprocated to and f rom at variable speeds and ampli tudes, The pivot in the arm was an air bearing, so t ha t there was a negligible fr ict ion force acting. The end of the arm remote from the specimen was res t ra ined by a double-act ing load t ransducer , the frict ion forces being char ted on a pen recording ins t rument . A summary of the magni tudes of variables is: Reciprocating motion very close to sinusoidal, maximum speed 4 in/see"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003789_j.jsv.2008.03.072-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003789_j.jsv.2008.03.072-Figure4-1.png",
        "caption": "Fig. 4. Displacement configuration (deflected beam).",
        "texts": [
            " The differential equation of longitudinal displacement has previously been derived by Di Taranto [7]. The analysis we present now leads to the equation of transverse displacement. Geometry of a four-layered sandwich beam of width b is shown in Fig. 3. The analysis is developed for a model of symmetric layers composed of two identical elastic layers of thickness h1 with Young\u2019s modulus E and two identical viscoelastic layers of thickness h2 with shear modulus G* \u00bc G (1+ib). The deflected face of the beam is shown in Fig. 4. ARTICLE IN PRESS B.P. Yadav / Journal of Sound and Vibration 317 (2008) 576\u2013590 579 It will be assumed that shear strains in the elastic plates are negligible, and that longitudinal direct stresses in the plastic plates are negligible. Transverse direct strains in both plastic plates and elastic plates are also neglected, so that the transverse displacements w of all points on a cross-section xx are equal. The longitudinal x-wise displacements of the mid-planes of the elastic plates are u1 and u3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002820_archopht.1973.01000040051012-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002820_archopht.1973.01000040051012-Figure2-1.png",
        "caption": "Fig 2. \u2014Cumulative dose-response curve of untrea cat irides to bethanechol chloride (control), which w then treated with the indicated echothiophate concen tions. Vertical arrows indicate the increase in passive t sion after application of the cholinesterase inhibitor.",
        "texts": [
            " echothiophate, all of these changes were reversed by treatment with pra\u00ac lidoxime chloride. An approximately 10% increase in the resting or passive tension of iris strips was noted after incubation with \"7 M echothiophate. This fur\u00ac ther increased to 30% after -6 M echothiopate (Fig 1). The increased passive tension reverted to normal after incubation with pralidoxime chloride, IO-3 M, for 15 minutes. Threshold responses to bethanechol chloride occurred at IO-4 M, with maximal tensions developing at 10~' M, (Fig 2). Incubation with echothio\u00ac phate resulted in increases of passive tension but no shift of the doseresponse curve (Fig 2). Comment This study identified and exam\u00ac ined some of the properties of extra\u00ac cellular or functional ChEs involved in the echothiophate induced altera\u00ac tions in drug responses of intact cat irides. The radiometrie assay tech\u00ac nique used in this study permits monitoring of enzyme kinetics with 14C labeled substrates in the pharma- Downloaded From: http://archopht.jamanetwork.com/ by a University of Iowa User on 05/23/2015 Table 2.\u2014Percentage Inhibition of True and Pseudocholinesterase of Cat Iris and Ciliary Body* Echothiophate DFP % % % % Echothiophate Inhibition Inhibition DFP Inhibition Inhibition Tissue Concentration of AChE of BuChE Concentration of AChE of BuChE Iris 5 \u00bb M 35 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003065_ecc.2007.7068593-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003065_ecc.2007.7068593-Figure1-1.png",
        "caption": "Fig. 1.",
        "texts": [
            " From Lemma 2, all the eigenvalues of \u2212L = [\u2212li j] are located in the union of the following n disks: Di = {z \u2208 C : |z+ lii| \u2264 \u2211 j\u2208n, j =i |li j| di}. And Lemma 1 implies that \u2212L has exactly one zero eigenvalue and all the other nonzero eigenvalues are in the open left half plane. Note that, \u2211 j\u2208n, j =i |li j|+ \u03b1ii \u2211n j=1 \u03b1i j = 1, \u03b1ii > 0, from which we obtain maxi{di} < 1. Since lii = \u2211n k=1,k =i \u03b1ik \u2211n j=1 \u03b1i j < 1, maxi{|lii|}< 1 holds; thereby, all these n disks are contained in the disk D that is centered at z = (\u22121)+0 j, with radius 1 (See Fig.1(a)). Furthermore, all the eigenvalues of \u2212L are inside the disk D except eigenvalue 0 with algebraic multiplicity equalling to one. And in turn, all the eigenvalues of D =\u2212L+ I are located in the disk D\u2217 that is centered at z = 0 + 0 j, with radius 1 (See Fig.1(b)). Furthermore, all the eigenvalues of D are inside the disk D\u2217 except eigenvalue 1 with algebraic multiplicity equalling to one. This means that D has an eigenvalue \u03bb = 1 whose algebraic multiplicity is one, and all the other eigenvalues satisfy |\u03bb | < 1. Proof of Theorem 1 : (Sufficiency) From Lemmas 8 and 4, limm\u2192\u221e Dm = 1\u03bdT follows. Therefore, x[k] = Dkx[0] \u2192 1\u03bdT x[0] = (\u03bdT x[0] \u00b7 \u00b7 \u00b7 \u03bdT x[0])T , k \u2192 \u221e i.e., scheme (8) asymptotically achieves consensus. On the other hand, incorporating the balance condition into Lemma 7, we get 1T D = 1T "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003631_j.jtbi.2008.01.029-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003631_j.jtbi.2008.01.029-Figure1-1.png",
        "caption": "Fig. 1. Schematic transverse section of the axoneme; the axoneme is viewed base to tip. The diagram was drawn from data published by Schoutens (1994). The numbers indicated inside and outside the axonemal cylinder are relative to the pinching of the tubulin and the dynein arms expressed in Angstro\u0308m, respectively (Table 1). Negative and positive values correspond to compression and dilation of these periodic elements, respectively. The calculations were done when the axoneme was bent towards the right side of the diagram: axonemal arc is p and its length equals 10mm. The inset shows the spermatozoon viewed from the top, in the bending plan; the double broad arrow is the cross section. We consider here that all the outer doublet intervals are equivalent in terms of sliding. The A and B tubules are located on the scheme of the first outer doublet. In this scheme, all the outer doublets are equivalent in terms of sliding.",
        "texts": [
            " ARTICLE IN PRESS We postulated that even if the microtubules are uncompressible and inextensible, the equilibrium between compression and dilation of their walls that necessarily occurs during their bending must adjust the length of the two opposite sides of each outer doublet during the propagation of a wave train along the axoneme. Assuming that the bending plane contains the outer doublet #1 and passes through the middle of the 5\u20136 outer doublet pair and that the axoneme does not twist, when the bending angle equals p and the length of the curved segment equals 10 mm, the modifications of the distances between two consecutive b-tubulin monomers (dt) and two successive dynein arms (dd) are those indicated (in A\u030a) in Fig. 1. The spatial frequencies of the b-tubulin monomers Ft and the dynein arms Fd equal the inverse of these intervals: Ft \u00bc 1/(80+dt) A\u030a 1 and Fd \u00bc 1/(240+dd) A\u030a 1 when 80 and 240 A\u030a are the canonical intervals between the b-tubulin monomers and the outer dynein arms, the b-tubulin isoform interacting with the dynein arms (Mizuno et al., 2004); the spatial frequency is the frequency in space with which a recurring feature appears as defined in the imaging field (Inoue\u0301, 1987). In 1976, the relationship between two facing A- and B-tubules when the shear equals 720 A\u030a was schematized (Warner, 1976)",
            " Along a given curved segment, the interval between two consecutive maxima of coincidence of the putative active domain of the b-tubulin monomers and the active stalk head of the dynein arms (D, expressed in the number of dynein arms) is easily calculated with the following conditional formula: D \u00bc INT(1/(1-(R-INT(R))) when Ro3 and D \u00bc INT(1/(R-INT(R))) when R43, where R \u00bc (Id7|ahd/ D|)/(It7|aht/T|), INT is the integer part, I is the basic interval between two homologous periodic structures (tubulin monomers (t) and dynein arms (d)) and h is their projection on the beat plan (Table 1), a the angle of curvature of the segment, and T and D the number of tubulin and dynein arms intervals that exist along the curved axonemal segment (Table 2 and Fig. 3); the limit value of R equals 240 A\u030a/80 A\u030a \u00bc 3. This shows the variation of D as a function of the angle of bending between the 9 outer doublet pairs. Correlatively, the numbers of recruited dynein arms (able to trap the tubulin monomers along the ARTICLE IN PRESS These values are those used to construct Fig. 1. C. Cibert / Journal of Theoretical Biology 253 (2008) 74\u201389 77 nine outer doublet pairs) are associated in groups of different sizes (Table 3, Figs. 3A and B). We calculated the direction of the propagation and the speed of the wave of joint probabilities when the facing tubulin and dynein verniers move in opposite directions during the outer doublet shear, considering the bending described in Fig. 1; the results are presented in Fig. 4. Two opposite halves of the axoneme can be defined in this case: those whose dynein arms are oriented toward the center of the curvature (#6 to #9) and those whose dynein arms are oriented in the opposite direction (#1 to #5). Along the two halves of the axoneme, the waves of joint probabilities move effectively either in the same direction as that of the vernier formed by the dynein arms or in the opposite direction. Along a curved segment, the absolute value of the rate of the displacement depends on the doublet pair as indicated in Table 4, and is E50 to E8000 times that of sliding, depending on the location of the outer doublet pair within the axonemal cylinder and the bending angle",
            " d (C) To mimic the shear between the two facing verniers, j equaled with iA[0, 1, 2, 3, 4, 5, 6] and the abscissas of the positive extrema of e plotted as seven horizontal series of dots included in the lower ; these dots correspond to the locations of the dynein arms along a et, and the orientation of the arrows indicates the direction and the ent speed of the dynein displacement when the apparent position of rnier formed by the b-tubulin monomers is constant. In the upper the seven horizontal series correspond to the coincidences of the arms and the b-tubulin monomers calculated as described . As for the lower panels, the orientation of the arrows indicates parent displacements of the metachronal JPI wave. In (B), f1 \u00bc \u20132.82) A\u030a 1, f2 \u00bc 1/(80+0.48) A\u030a 1; this corresponds to the facing doublets #8 and #9. In (C), f1 \u00bc 1/(240+3.00) A\u030a 1, f2 \u00bc 1/(80\u2013 \u02da 1; this corresponds to the facing outer doublets #3 and #4 (Fig. 1). Lindemann, 2003) depends on the effective link between the two molecular partners (dynein arms and b-tubulin. But, the number and locations of the efficient couples \u2018\u2018dynein arm\u2013b-tubulin\u2019\u2019 along a given outer doublet pair depends on the physical law (i.e. the propagation of the JPI waves) that makes them coincident, before their link. For topological and thermodynamic reasons, Lindemann and Hunt (2003) propose that the release and reattachment of the dynein arms on the facing b-tubulin monomer may be independent from the ATP hydrolysis and consequently from the conformational changes of the dynein head",
            " Number of WSs taken by the dynein arms as a function of the doublet pair an able 1. The dashed lines represent the local bending at each of the abscissas as al [ 3 rd, 3 rd]. The P0 points correspond to the zero crossing of these curves. T cal shear (in A\u030a) and 160 A\u030a, when 160 A\u030a is the theoretical maximum of the WS al [ 3, 3]. The ranks of the outer doublets, whose dynein arms are involved in is a periodic function, whatever the actual value of their ordinate, the extrema ropagates along the axoneme. d the local shear. The dynein arms are defined as described in Fig. 1 represented in Fig. 6B; the values of the angles are expressed on the he number of WSs is expressed as the entire part of the ratio between . \u2018\u20180\u2019\u2019 means that this number is lower than 1 being included in the a local skip, are indicated on the graphs. Assuming that the dashed of this function correspond to the inflexion points of the wave train ARTICLE IN PRESS the largest. Because the rate of displacement of the moving P0 points is greater than that of the wave train (Cibert, 2002), the spatial relations that exist between them and the apices of the propelling wave train are not constant along the axoneme",
            " This spatial heterogeneity is one of the elements that must be involved in the mechanism described by the geometric clutch model, because it links topology and molecular events. These molecular processes make the outer doublets and, consequently, the axoneme a giant allosteric system (Stryer, 1988) which is capable of complexity (Cibert, 2004a, b; Ricard, 2003) and whose regulating properties remain to be explored at the molecular level. Hence the answer to the question addressed in the title of this work is undoubtedly \u2018\u2018yes\u2019\u2019. 4. Calculations The topology of the axoneme that we have considered in this study is that described by Schoutens (1994) (Fig. 1). ARTICLE IN PRESS C. Cibert / Journal of Theoretical Biology 253 (2008) 74\u201389 87 The sliding occurring between two facing surfaces was calculated according to St \u00bc ah, where St is the total shear along a bent segment, h is the interval between the two facing surface and a the angle of the bending (Warner, 1976). The values of h in A\u030a are given in Table 1. The facing surfaces are the two opposite sides of the outer doublets located in the bending plan and the surfaces defined by the end of the dynein arms and the surface of the tubule-B with whose tubulin they must interact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000808_s1000-9361(11)60181-7-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000808_s1000-9361(11)60181-7-Figure4-1.png",
        "caption": "Fig . 4 Real too th measur ement After all the measured data are dealt w ith by Eq. ( 5) , the dev iations of discrete points are determined.",
        "texts": [],
        "surrounding_texts": [
            "For minimization of the effect of the random error, there should be an appropriate measurement strategy to measure an enough number of teeth. But dif ferent measurement st rategies lead to different data processing approaches. T here are tw o strategies ( 1) The locat ion and orientat ion of each mea- sured tooth surface are determined alone. T his w ay avoids the ef fect of on the measured data. ( 2) The first tooth surface determines the lo- cation and orientation of the gear w ith respect to CMM . The locat ion of other tooth surfaces is de- termined by the machine index, so the effect of on the measured data must be considered. 2. 3 Measurement of real tooth surface and description of deviation The real tooth surface is measured by CMM according to the grid, which is a set of points on the theoret ical tooth surface. T he grid scheme is accomplished on a topography plane of the theoret- ical tooth surface, and there is a one-to-one and onto mapping relation betw een them . The probe approaches the tooth surface along the normal direction of the grid. F ig . 4 illust rates it . T is the contact point , P is the probe center, N is the nominal point on the theoret ical surface, nt is the normal at nominal point and a is the probe ra- dius. Because the tooth surface is a continuous smooth surface, the distance betw een T and N is so small that the deviat ion betw een the theoret i- cal surface and the real one along the normal direction can be considered approximately as follow s If deviat ions are described directly w ith the measured data of discrete points, a lot of valuable informat ion about the global characterist ics of devi- at ions cannot be utilized suf ficiently. But it is more ef fect ive to use the difference surface of tw o surfaces to describe deviations, and its characteristic parameters have the physical and geometric meaning to evaluate the real surface [ 4, 5] . T he curvature of the difference surface of engineering surfaces is so small that it can be fitted precisely w ith a poly- nomial of 2 orders. The coordinate system of the dif ference sur- face is Sd{M : x , y , z } , xy plane is the topography plane of the theoret ical tooth surface, z represents the deviation betw een the real surface and the theoret ical one in the normal direction, and M is the orig in of coordinates. The dif ferent measurement strategies have the different fitt ing funct ions. The fitt ing function of the f irst measurement st rategy is z = a1x + a2y + a3x 2 + a4y 2 + a5x y ( 6) T he fitt ing funct ion of the second measure- ment st rategy is z = a0 + a1x + a2y + a3x 2 + a4y 2 + a5xy ( 7) In the follow ing part , the parameters of the difference surface are derived from the measured data. Eqs. ( 6) and ( 7) can be represented as fol- low s z = \u2211 5 i= 0 ai\u2200i( x , y) ( 8) The object ive funct ion of the least square method is represented as S = \u2211 m i= 0 ( i - z i) 2 ( 9) w here m is the number of the lat tice points. Differentiat ing Eq. ( 9) , a set of linear equa- tions are obtained S ak = 0 k = 0, 1, \u22ef, 5 ( 10) Then the follow ing equations can be derived \u2211 5 j = 0 aj\u2211 m i= 1 \u2200j i\u2200ki = \u2211 m i= 1 i\u2200ki ( 11) a0, a1 , a2 , a3, a4 , a5 can be calculated through the above equat ions. 3 Modification Principle of Deviation Deviation correct ion is based on compensat ing feedback. The vector function of the theoret ical surface ! t is considered as rt = M( 0 i ) ( 12) w here the designation 0 i ( i= 1, \u22ef, n) indicates n parameters- the theoret ical machine-tool set ting s. Because of the effects of the factors mentioned above, the real surface w hich is represented as Eq. ( 2) deviates from the theoret ical one. Assume that all the measured deviat ions are repeatable. Desig- nating the theoretical surface as the symmetry center, the symmetry surface of ! a is !\u2032a. It is repre- sented as r ap = r t - nt ( 13) Assume that a new set of machine-sett ings ip generates !\u2032a r ap = M( ip ) ( 14) Because of the deformation caused by the same factors in the manufacturing processing, !\u2032a is transformed into r \u2032 ap = rap + \u2032nt = rt + ( \u2032- ) nt ( 15) Except machine-tool sett ings, the manufac- ture processing does not change. So one can as- sume \u2032- \u2248 0 ( 16) Therefore one can consider that this tooth surface is nearly coincident w ith the theoret ical surface. In practical processing , it is dif ficult to obtain the ip according to Eq. ( 13) . One can ap- proximate it by correct ing i0 to minimize the deviations. 4 Approach of Compensation Designate the theoret ical tooth surface as the basis surface, w hich is generated w ith the ma- chine-tool set t ings i0 . The small variat ion of i0 can generate a new tooth surface. T he dif ference surface funct ion betw een it and the basis surface is A( i) X = [M( i) - M( i0) ] nt ( 17) w here i is the new machine-tool set t ing, X= ( x , y , x 2 , y 2 , xy ) - 1 , A ( i) = ( a1 , a2 , a3 , a4 , a5) , it is a vector of 5 dimensions space, and A( i0 ) = ( 0, 0, 0, 0, 0) . The vector funct ion A( i) forms a super sur- face, and the derivat ive of it at i0 is A \u2032 jX = A j X = lim j \u21920 [M( j0 + j ) - M( j0 ) ] nt j ( 18) T he total dif ferential of it at 0 i is represented as follow s A = \u2211 n i= 1 A \u2032 i i ( 19) If Ad is the difference surface of the real sur- face obtained by measurement, the determination of corrected machine-tool sett ing is in essence to solve the follow ing equation Ad = \u2211 n i= 1 A \u2032 i i ( 20) T he solut ion of Eq. ( 20) probably exists, sev- eral but not only one. For minimizat ion of the in- fluence caused by any nonlinear factor of the practice, one should choose a solution that makes \u2211 n i= 0 i minimizat ion. 5 Application In this Sect ion, a practical spiral bevel gear w as measured by Carl Zeiss. T he specification of the gear is show n in T able 1. The machine-tool set tings are show n in Table 2. Nominal data on \u00b7185\u00b7August 2003 Measurement and Compensation of Deviat ions of Real Tooth Surface of S piral Bevel Gear the theoret ical surface are coordinates and its unit normal of 5\u00d79 latt ice points. Both of driving and coast side of four teeth of the gear are measured. The mean value of them is considered as the measured data. The measured results are represented in Fig . 5. Table 2. The deviat ion of the tooth surface manufactured with the corrected machine set ting is less than 0. 003mm . T he measured results of the basic machine set t ing and the corrected one are represented in Fig. 6. F ig. 6 Dev iations o f the driving side o f tooth 6 Conclusions This method, w hich is based upon CMM , can reduce repeatable deviat ions to a great extent . References [ 1] Litvin F L, Kuan C, Wang J C, et al . M inimization of de- viation of gear real tooth surface determined by coordinate measurements [ J] . Journal of Mechanical Design , ASME, 1993, 115( 4) : 995- 1001. [ 2] \u82b1\u56fd\u6881.\u7cbe\u5bc6\u6d4b\u91cf\u6280\u672f [ M ] . \u5317\u4eac: \u4e2d\u56fd\u8ba1\u91cf\u51fa\u7248\u793e, 1990. 1- 10. Hua G L . Precision Measurement T ech nology[ M ] . Beijing: China Metrology Press, 1990. 1- 10. ( in Chinese) [ 3] Wang X C, Ghosh S K. Advanced theories of hypoid gears [ M ] . Amsterdam: Elsevier Science B V, 1994. 112- 130. [ 4] Stardt feld H J. Handbook of bevel and hypoid gears [ M ] . New York: Rochester Inst itute of Technology, 1993. 190- 200. [ 5] Pfeifer T , Kurokaw a S, Meyer S. Derivat ion of parameters of global form deviations for 3-dimen sional surfaces in actual manufacturing processes [ J ] . Measurement , 2001, 29 ( 3) : 179- 200. Biography: WANG Jun Born in 1969, he is a doctoral candidat e of the Xi' an Jiaotong University . T el: ( 029 ) 2673248, Email: wang junstation@ sohu. com"
        ]
    },
    {
        "image_filename": "designv11_28_0003454_isam.2007.4288471-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003454_isam.2007.4288471-Figure3-1.png",
        "caption": "Fig. 3. Possible cases for a candidate grasp in the optimization procedure: a) Non-feasible candidate grasp, b) Discarded candidate grasp, c) Feasible candidate grasp.",
        "texts": [
            " Due to the selection procedure, all the wrenches \u03c9\u2217 \u2208 \u2126k C are external points to CH(W ), therefore, when replacing one vertex \u03c9i from the actual CH with the candidate wrench \u03c9\u2217, the latter will be a vertex of the new CH . The explicit computation of the new CH is not required, as its facets are constructed from the old ones replacing \u03c9i with \u03c9\u2217. The candidate grasps are checked for the FC property using Lemma 1. For the FC candidate grasps, the expected grasp quality Q\u2217 is computed; if for any candidate grasp Q\u2217 > Qk, then the candidate becomes the new grasp Gk. Fig. 3 illustrates three possible cases related with the candidate grasps; case (a) is a non-feasible grasp because it loses the FC property, case (b) is discarded because the grasp has a smaller quality than the previous one, and case (c) is a good grasp that actually improves the grasp quality, thus it becomes the grasp for the next iteration cycle. After this step, if the quality is improved then go back to Step 2. If there is no improvement in Qk once all the points in \u2126k C have been considered, then a local minimum has already been reached, the algorithm finishes and returns the current grasp G"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003296_0022-2569(71)90011-5-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003296_0022-2569(71)90011-5-Figure2-1.png",
        "caption": "Figure 2.",
        "texts": [
            " = angle between St and S_o; and similarly for other parameters . All angles are measured according tb a right-handedscrew convention. The input and output parameters are 0t and 05 respectively. Other variable parameters are 0.,, z~, 03, 04, and z4. The line coordinates of S~ can be expressed as functions of the mechanism parameters in the following manner. Let two sets of car tes ian coord ina te axes x - v i - . z i , x ~ - y j - . z j be a t tached to Links k. i. respect ive ly , as shown in Fig. 2. The line coord ina tes of S: with reference to .v~ - Ya - zj are (Sj)j = (0. O, l, O, O. 0 ) . (13) T o ob ta in the line coord ina tes of Sj with re fe rence to .r~ - y~ - .~. cons ide r the transfo rmat ion of .r0 - )'j - za to .vi0 - Yu - zu. fol lowed by ano the r t r ans fo rma t ion to .r~ - v, - c.. In the first step. by equa t ions (8) and (9). V l i ! (S~)i~ =i L_ 1 0 0 0 0 0 0 % - s,o 0 0 0 0 ,% c'~o 0 0 0 0 0 0 I 0 0 0 - - ~l i jSi j - - (dijCi j 0 Cij - - S i j 0 (lijCij - - {1i)S o 0 Sij ('ij (S~)~"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001245_icsmc.1994.399849-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001245_icsmc.1994.399849-Figure1-1.png",
        "caption": "Figure 1 . (a) Ellipsoid model, (b) a simple pat.h planning and (c) global minimum solution",
        "texts": [],
        "surrounding_texts": [
            "The work presented in this paper has demonstrated the robustness of simulated annealing for solving the path planning problem of an object in 2D and 3D. In the immediate future, it is the purpose of the authors to include in this work more characteristics of a robot for 3D path planning. The authors are currently involved with these interestring research challenges. Refer en c e s [l] W . Bohm, \u201cEifficient evaluation of splines,\u201d Computzng, vol. 33, pp. 171 -177, 1984. [2] P. Lancaster and K . Salkauskas, Curve and Surface E\u2019rtting. San Diego: Academic Press, 1986. [3] \u2019I Tsumura and N . Fujiwara, \u201cAn experimental systern for automatic guidance of robotted vehicle following the route stored in memory,\u201d in Proc. 11th I n t Sym on industrzal Hobots, pp 187-193, Oct 1\u2018181. [4] K Komoriya and S. Tachi, \u201cA method for autonomous locomotion of mobile robot,s,\u201d J of Robotics Soc. Japan, vol. 2 , pp. 222- 231, 1984 [5] T . Hongo and H . Arakawa, \u201cAn automatic guidance system of a self-controlled vehicle ...,\u201d in Proc. IECON, 1985. [6] Y. Kanayama and S. Yuta, \u201cVehicle path specification by a sequence of straight lines,\u201d Zh\u2019EE J . of Robotics and Automation, vol. 4, pp. 265-275, June 1988. [7] P. Jocobs and J . Canny, \u201cPlanning smooth paths for mobile robots,\u201d IEEE J . of Robotics and Automation, pp. 2-7, Aug. 1989. [8] Y. Kanayarna and B. Hartman, \u201cSmooth local path planning for autonomous vehicles,\u201d Tech. Rep. TRCS88-15, University of California, Santa Barbara, 1986. [9] Y. Kanayama and N. Miyake, \u201cTrajectory generation for mobile robots,\u201d in Proc. 3rd I d . Symp. on Robotics Research, (Gouvieux, France) pp. 333-"
        ]
    },
    {
        "image_filename": "designv11_28_0003577_ieeestd.1977.80497-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003577_ieeestd.1977.80497-Figure1-1.png",
        "caption": "Fig 1 Reference Pulse Shape",
        "texts": [
            " For the testing of magnetic cores with pulsed excitation, it is often desirable to specify the shape or other properties of the pulse with a high degree of precision, as in the tests for computer-type cores of Section 6.2.4. This section defines many of the pulse parameters useful for the testing of transformer, computer, and other cores with pulsed excitation. The shape of the reference pulse, which may be either a current or voltage pulse, is given by the current- or voltagetime relationship shown in Fig 1 in accordance with the following definitions: NOTE: ( A ) designates a general amplitude quantity which may be current ( I ) or voltage (V). (a) pulse amplitude ( A , ). That quantity determined by the intersection of a line passing through the points on the leading edge where the instantaneous value reaches 10 percent and 90 percent of ( A , ) and a straight line which is the best least squares fit to the pulse in the pulse-top region. (Usually this is fitted visually rather than numerically.) For pulses deviating greatly from the ideal trapezoidal pulse shape, a number of successive approximations may be necessary to determine A M "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002244_s1064230706030063-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002244_s1064230706030063-Figure5-1.png",
        "caption": "Fig. 5. The time-optimal feedback control for k = 0.35.",
        "texts": [],
        "surrounding_texts": [
            "Let us analyze singular optimal trajectories that reach the terminal states x1 = \u03c0(2n + 1) and x2 = 0 for a constant control either u = +1 or u = \u20131. Let us present the detailed singular trajectory for x1(T) = \u03c0 (n = 0), x2(T) = 0, and u = \u20131. We set the terminal values of the adjoint variables so that p1(T) < 0 and p2(T) = 0 and prove that p2(t) < 0 for t < T. In this case, Eq. (2.3) holds. Without loss of generality, the adjoint variables can be normalized so that (3.1)p1 T( ) 1, p2 T( )\u2013 0.= = Let us substitute u = \u20131 into system (1.5) and find its first integral To find the constant C1, we substitute the terminal conditions x1 = \u03c0 and x2 = 0 into the found expression for the first integral. As a result, we obtain (3.2) For the trajectory that reaches the terminal state under the control u = \u20131, by Eqs. (1.5), we have x2 > 0 and x1 < \u03c0 for small positive T \u2013 t, i.e., at the end of motion. Let us change variables (3.3) and represent Eq. (3.2) in the form (3.4) x2 2 2 ---- x1 kx1+cos\u2013 C1.= x2 2 2 ---- 1 x1 k \u03c0 x1\u2013( ).+cos+= \u03c0 x1\u2013 y= x2 R y( ) 2 1 ycos\u2013 ky+( )[ ]1/2.= = JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL Vol. 45 No. 3 2006 TIME-OPTIMAL CONTROL 387 Therefore, when t varies from T to \u2013\u221e, the variable y monotonically increases from 0 to \u221e. Hence, y can be taken as an independent variable along the considered trajectory. Let us analyze the behavior of the adjoint variable p2(y) for this trajectory. Note that, by (2.3), the sign of p2 determines the control. Let us rewrite the adjoint equations (2.2) using y as an independent variable and taking into account (1.5) and (3.4) (3.6) Eliminating p1 from these equations, we arrive at the following equation for p2: (3.7) Let us multiply both sides of (3.7) by R and transform it taking into account the relation (3.8) which follows from (3.4). We have d p1 dy -------- p2 ycos R y( ) -----------------, d p2 dy -------- p1 R y( ) -----------.= = d dy ----- R d p2 dy --------\u239d \u23a0 \u239b \u239e p2 ycos R -----------------.= R dR dy ------ y k,+sin= d dy ----- R2d p2 dy --------\u239d \u23a0 \u239b \u239e d dy ----- ysin k+( ) p2[ ].= 388 JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL Vol. 45 No. 3 2006 RESHMIN, CHERNOUS\u2019KO Integrating this equation, we obtain (3.9) where C2 is a constant. At the terminal time instant t = T, by equations (1.8), (3.1), and (3.3), we have In addition, (3.1), (3.5), and (3.6) imply that Substituting these data into (3.9), we find C2 = 0 and (3.9) takes the form (3.10) Note that the general solution to this homogeneous R2d p2 dy -------- ysin k+( ) p2\u2013 C2,= y 0, p2 0.= = R2d p2 dy -------- R p1 0 when y 0.= R2d p2 dy -------- ysin k+( ) p2\u2013 0.= equation can be expressed as follows: (3.11) where C is a constant. This can easily be verified using relation (3.8). Finally, we obtain from (3.6), (3.8), and (3.11) the expression for p1 (3.12) Therefore, to satisfy the terminal conditions (3.1) for p1, we should set C = \u20131/k in (3.11) and (3.12). Thus, it is clear that, along the optimal trajectory corresponding to the control u = \u20131, the adjoint variable p2(t) is negative for all y > 0, and, consequently, for all t < T. As a result, the singular trajectory for u = \u20131 satisfies the necessary optimality conditions. The same situation takes place even for the trajectory for u = +1, which is located symmetrically with respect to the trajectory considered above relative to the point x1 = \u03c0, x2 = 0. The singular trajectories arriving at the points p2 CR y( ),= p1 R d p2 dy -------- CR dR dy ------ C ysin k+( ).= = = JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL Vol. 45 No. 3 2006 TIME-OPTIMAL CONTROL 389 x1 = \u03c0(2n + 1), x2 = 0 can be obtained by shifting singular trajectories tending to the point x1 = \u03c0, x2 = 0 by 2\u03c0n."
        ]
    },
    {
        "image_filename": "designv11_28_0002260_j.mechmachtheory.2004.12.003-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002260_j.mechmachtheory.2004.12.003-Figure2-1.png",
        "caption": "Fig. 2. Planar 3R manipulator.",
        "texts": [
            " Generally, the FTW of a manipulator is much more complicated and will be discussed exhaustively in another paper. For articulated manipulators, the FTW is a ring (for planar manipulators) or hollow rotation volume (for spatial manipulators) if the fault tolerance relative to movable joints is considered only; the FTW is a part of a ring or a hollow rotation volume if the fault tolerance relative to all joints is considered. Next, the calculation procedures of FTW relative to joint 3 will be explained with a planar 3R manipulator shown in Fig. 2 (1) compute L0 max and L0 min (the maximum and minimum arm length of a reduced manipulator) according to h3max and h3min; (2) compute the outer and inner boundaries of maximum workspace and minimum workspace corresponding to L0 max and L0 min; (3) determine the outer and inner boundaries of the intersection between the maximum workspace and minimum workspace. In order to make two coordinating manipulators realize fault tolerance operations, the motion ranges of their end-effectors should lie within their fault tolerant workspaces (FTW) respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002244_s1064230706030063-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002244_s1064230706030063-Figure3-1.png",
        "caption": "Fig. 3. The time-optimal feedback control for k = 0.2.",
        "texts": [],
        "surrounding_texts": [
            "Consider a pendulum that is able to rotate about a horizontal axis O and is controlled by a torque M applied to it. We use the following notation: \u03d5 is the angle between the pendulum and the vertical axis (Fig. 1), m is the pendulum mass, J is its moment of inertia relative to the axis O , l is the distance from the axis O to the center of mass of the pendulum, and g is the gravitational acceleration. The motion equation of the pendulum has the form (1.1) where the dot means the derivative in t . Assume that, on the control torque, the constraint is imposed (1.2) where M 0 is a given constant. J \u03d5\u0307\u0307 mgl \u03d5sin+ M,= M M0,\u2264 \u2014A time-optimal feedback control is synthesized that steers a nonlinear pendulum to the top unstable equilibrium position. The solution is based on the maximum principle and involves an analytical investigation in combination with numerical computations. As a result, for a number of values of the maximum admissible control torque, the switching curves and dispersal curves that delimit the domains in the phase space that correspond to different values of the bang\u2013bang optimal control are constructed. DOI: 10.1134/S1064230706030063 384 JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL Vol. 45 No. 3 2006 RESHMIN, CHERNOUS\u2019KO Let us take the notation (1.3) Here, \u03c9 is the fundamental frequency of small oscillations of the pendulum, and t ' is the dimensionless time. Let us introduce dimensionless variables (1.4) and rewrite Eq. (1.1) in the following form: (1.5) The dots denote derivatives in dimensionless time t ' . In what follows, we omit the prime of t . Constraint (1.2) can be rewritten in the form (1.6) \u03c9 mgl J ---------\u239d \u23a0 \u239b \u239e 1/2 , t ' \u03c9t.= = x1 \u03d5, x2 d\u03d5 dt' ------, u M M0 ------ , k M0 mgl ---------= = = = x\u03071 x2, x\u03072 x1 ku.+sin\u2013= = u t( ) 1.\u2264 JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL Vol. 45 No. 3 2006 TIME-OPTIMAL CONTROL 385 The initial conditions for system (1.5) are arbitrary (1.7) and the terminal coordinates correspond to the top unstable equilibrium position (1.8) where n is an arbitrary integer. The control that satisfies constraints (1.6) for all t \u2208 [0, T ] and steers the system (1.5) from an arbitrary state (1.7) to a terminal state (1.8) in a minimum possible time will be found both in an open-loop form and in a feedback form."
        ]
    },
    {
        "image_filename": "designv11_28_0002027_1.2179460-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002027_1.2179460-Figure3-1.png",
        "caption": "Fig. 3 Planet worm-gear center-distance offset a",
        "texts": [
            " With the coordinate transformation, the above can be rewritten as r2 = x2 i2 + y2 j2 + z2 k2 where x2 = cos v + r2 y2 = cos u sin v z2 = sin u sin v 2 Vector r2 is the vectorial expression of a point P of the generating surface in the planet worm-gear rotatable coordinate frame S2 . There are several latency errors in manufacturing and assembly of a toroidal drive system. In this analysis, three typical latency errors are discussed. They include the worm-gear center-distance offset, the sun-worm lateral misalignment and the worm-gear angular misalignment. The worm-gear center-distance offset a occurs in a manufacturing process and is reflected in the assembly as in Fig. 3. Each planet worm-gear has a center-distance offset. Since this error in each worm-gear is the same, the study focuses on one worm-gear. The worm-gear center-distance offset is critical to the meshing process of a toroidal drive since the tooth profiles of the sun-worm and the stationary internal gear are formed by the enveloping movement of the meshing rollers. MAY 2006, Vol. 128 / 611 7 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F The sun-worm lateral misalignment w exists in assembly and dominates the meshing property and load capacity of a toroidal drive"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003620_978-3-540-89933-4_5-Figure5.5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003620_978-3-540-89933-4_5-Figure5.5-1.png",
        "caption": "Fig. 5.5. Parameters in F2 method",
        "texts": [
            " A force field is defined as a virtual field of repulsive force in the vicinity of a robot when it travels in a working space. The magnitude and orientation of a force field are determined by and vary with the robot\u2019s status. This virtual repulsive force increases with the decrease of the distance to the robot. Parameters in the F2 method are listed in Table 5.2. For any point (x,y) in the 2-D space, assume \u03b8r is the robot\u2019s orientation in global coordinate, \u03b80 is the orientation of this point in global coordinate, thus \u03b8 denotes the relative angle of this point to the robot\u2019s orientation (Fig. 5.5). C is a positive number which assigns the environmental influence to the force field with C > 1. Er is a positive decimal fraction with 0 \u2264 Er < 1. k is a positive multiplier which determines the coverage area of the force field. Dmax is the maximum active distance of a robot\u2019s force field and Dmin is the distance at which this robot has maximum repulsive force. Dmax shows how far this robot can affect others in its vicinity. Dmin provides a safe distance for the robot to prevent other objects from moving into this area"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001914_05698190490439346-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001914_05698190490439346-Figure10-1.png",
        "caption": "Fig. 10\u2014Typical shank distortion.",
        "texts": [
            " It must be noted that the effects of the interference fitted bearing and the pre-loaded bolts are both considered. In a four-stroke engine, the connecting rod shank can be distorted because of the dynamic loading. A typical gas-loading diagram is shown in Fig. 7. The maximum gas load is at \u03b8c = 20\u25e6. The loading diagram on the piston pin is shown in Fig. 8. The inertia force at a reference node in the shank is a good indicator of how the amplitude and direction of the inertia load changes, shown in Fig. 9. The reference node in the rod shank is located at the point that has maximum lateral deflection. Figure 10 presents the typical connecting rod shank distortion. The distortion is based on the coordinate system (X,Y), which is permanently located on the connecting rod, and includes axial compression and tension and lateral deflection. The connecting rod shank distortion for one engine cycle is shown in Fig. 11. Figure 12 gives the connecting rod distortion in one engine cycle (magnification factor: 200). From Fig. 11(a), it may be observed that the shank is compressed 0.04 mm at a crank angle of \u03b8c = 0\u25e6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001209_tmag.1987.1065506-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001209_tmag.1987.1065506-Figure1-1.png",
        "caption": "Fig. 1 . Cross section of sample motor.",
        "texts": [
            " They have already reported the experimental result that output, efficiency and power factor, etc., are greatly improved by making slits of the same number with poles into the rotor of the circumferential-flux type (CF-type) hysteresis motor. Further, the authors applied the comparatively simple and accurate analytical method [4] for the motor. In this study, the authors will apply the same method with the CF-type motor to the radial-flux (RF-type) hysteresis motor and improve the RF-type motor performance largely. Fig. 1 shows cross section of a sample motor. One of the remarkable features of this motor is that the Fe-Cr-Co magnet steel with magnetic anisotropy is used instead of Alnico magnet steel. By this substitution of magnet steel, four advantageous points, as described below, can be obtained: (a) Since the area of the hysteresis loop becomes large by magnetic anisotropy, the hysteresis torque becomes large, too. (b) By both magnetic anisotropy and slits in the rotor ring, a large reaction torque generates, (see Fig. 1). (c) Manuscript received June 17, 1986; revised January 31, 1987. The authors are with the Department of Electrical Engineering, Faculty IEEE Log Number 8715101. of Engineering, Ibaraki University, Hitachi, Japan 316. In general, Br of the Fe-Cr-Co magnet steel with magnetic anisotropy is more than 1.3 T. Therefore, the efficiency of the motor is high [5]. (d) By using the RF-type motor, input current at synchronous speed becomes lower and the starting torque becomes larger than that of CFtY Pee The analysis of the motor, considering both the starting and the synchronous characteristics, is comparatively difficult because the configuration of the rotor is rather complicated than that of CF type",
            " In general, however, it is very difficult to obtain a three-dimensional solution directly. Therefore, the following simple method is used in this paper. First, the magnetic field in the machine is determined by two-dimensional finite-element analysis. Secondly, the end effect factor is obtained newly in this paper. Using the so-' lutiori of magnetic field and the end effect factor, starting characteristics are calculated from the equivalent circuit. Finally, the relation between dimensional ratio f slits and the motor performance is investigated quantitatively. 11. SAMPLE ROTOR Fig. 1 shows a cross section of a sample &pole motor. Considering the flux path per pole in the rotor, the reluctance of a-a' path is the lowest, and that of b-b' path, which contains slits, is the highest. Therefore, the mag- 0018-9464/87/0900-3845$01 .OO @ 1987 IEEE 3846 IEEE TRANSACTIONS ON MAGNETICS. VOL. MAG-23, NO. 5, SEPTEMBER 1987 netic energy in the motor varies wih the flux path in the rotor, so that the large reaction torque can be added to the hysteresis torque. Further, since the rotor ring has magnetic anisotropy in the direction of the arrow (broken lines, see Fig",
            " It is seen that as ( 2 P / S ) / 7 increases, TH decreases slightly, while that T,. increases largely. Fig. 18 shows efficiency curves v . It is seen that as ( 2 P + S ) /7 increases, decreases. Fig. 19 shows curves of PF, and it is seen that PF is relatively high, in general. This is one of remarkable features for the RF-type hysteresis motor. VI. CONCLUSION This study can be summarized as follows: (1) The authors proposed the RF-type hysteresis motor with the new configuration of the rotor and new material of the rotor ring (Fe-Cr-Co magnet steel), as shown. Fig. 1. The performance characteristics of this rotor could be improved largely in comparison to that of the improved RF-type hysteresis motor [5], (2) Since the configuration of the motor is comDara- tively complicated, we used the finite-element analysis. At synchronous pull-out, calculated values are nearly equal to measured values. In this paper, it was revealed that the decrease of hysteresis torque due to space higher harmonics and the increase of reaction torque due to magnetic anisotropy approximately canceled each other, so that the agreement between calculated and measured values is good"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002439_0015-0568(80)90002-0-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002439_0015-0568(80)90002-0-Figure2-1.png",
        "caption": "Fig. 2. Notat ion for Mindlin's solution.",
        "texts": [
            " The fibre is then replaced by a distribution of Mindlin-state* and the slender-body analysis developed in Fluid Mechanics (for example, see Batchelor 3) is used to obtain the leading terms of the pull-out force. This technique has been used successfully by the author 4 to treat the analogous problem of a fibre embedded in an infinite elastic matrix. 2. MINDLIN-STATE First, Mindlin's solution 5 of a concentrated force acting at some distance below the horizontal surface of an elastic solid is recorded here. The semi-infinite solid is considered to be bounded by z > 0, (refer to Fig. 2). A force P is applied at point (0, 0, c) where c is a positive constant. For the purpose of this paper we only consider P of the form P = Pk (l) i.e. the applied concentrated force acts in the z-direction. By superimposing various Galerkin vectors, Mindlin shows that the displacement field due to Pk is given by, in cylindrical co-ordinates, P r )'z - c + (3 - 4 v ) ( z - c) 4(1 - v)(l - 2 v) 6 c z ( z + c) ] u~ - 16nr/(1 - v) ).--R31--1 R 3 R 2 ( R 2 + z + c) + R 5 (2) * Analogous to the terminology used by M"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000570_095440802760075021-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000570_095440802760075021-Figure1-1.png",
        "caption": "Fig. 1 General kinematic scheme of rotation spatial transformation between skewed axes 1\u20131 and 2\u20132",
        "texts": [
            " It is necessary to note that the technological details of the generation of conjugate surfaces S1 and S2 as a backlash between S1 and S2, geometrical and dimensional accuracy of the instrumental surface Sj and initial position and technological motion of Sj are not discussed. This paper deals with a spatial gear pair that transform rotation with constant angular velocities oi \u02c6 jwij \u02c6 constant \u2026i \u02c6 1; 2\u2020 between xed skewed axes, with the centre distance aw \u02c6 constant and the angle d \u02c6 \u2026w1; w2\u2020 \u02c6 constant [3]. Figure 1 shows a kinematic scheme of this gear pair. The transformation of the rotation is performed between the axes 1\u20131 and 2\u20132 with angular velocity ratio equal to i12 \u02c6 j1 j2 \u02c6 o1 o2 \u02c6 1 i21 \u02c6 constant \u20261\u2020 First the notions of geometrical and kinematic conjugation of high kinematic joints applied as meshed tooth surfaces are de ned [3]: 1. Geometrical conjugation. The geometrical elements of the kinematic joint, namely surfaces, lines and points, are considered. A conjugate contact point (a point of tangent contact) is de ned as a common point of two surfaces which have a common tangent plane",
            " A kinematic conjugationof the joint (S1 : S2) de nes the motion transformation from each geometrical element S1 to the geometrical element S2. In the speci c case of skew axes gears with xed axes and constant angular velocity vectors of the gears, the following speci c restrictions concerning tooth surfaces S1 and S2 are imposed: present the contact at one conjugate point P and at given moment as a contact between two in nitesimally small areas of S1 and S2 that lay in a common tangent plane T (see Fig. 1). Then it is evident that these areas slide relatively with the velocity V 12 \u02c6 V 1 \u00a1 V 2 V 12 lies in the plane T. Since the relative velocity vector V r;i \u2026i \u02c6 1; 2\u2020 of the conjugate point also lies in T, then normal components of the absolute velocity vectors are equal to each other, i.e. V n;1 \u02c6 V n;2. This is true for any kinematically conjugated joint \u2026S1 : S2\u2020. Therefore ni \u00a2 V 12 \u02c6 ni \u00a2 \u2026V 1 \u00a1 V 2\u2020 \u02c6 0 \u202619\u2020 Equation (19) is known as a basic equation of meshing [1] and de nes practically a condition for the existence of a common tangent plane T in the conjugate contact point P of the kinematically conjugate joint \u2026S1 : S2\u2020 at a given moment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002110_2005-01-1927-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002110_2005-01-1927-Figure1-1.png",
        "caption": "Figure 1. Hyundai AGCS vehicle",
        "texts": [],
        "surrounding_texts": [
            "(AGCS) System Sangho Lee, Hyun Sung and Unkoo Lee Hyundai Motor Company Copyright \u00a9 2005 SAE International"
        ]
    },
    {
        "image_filename": "designv11_28_0003154_1.2540572-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003154_1.2540572-Figure5-1.png",
        "caption": "Fig. 5 Contact patch and measured surface patch",
        "texts": [
            " Thus, the input force needed in the simulation of contact with roughness is important to establish the corresponding force for the sampled region. This force is obtained through an iterative process in which the simulation software SDAT is used with the assumption of elastic contact between smooth surfaces so as to obtain the same maximum contact pressure. Hence, the force applied to the measured patch yields the same maximum pressure as that obtained from a Hertz contact analysis of the contact patch. As depicted in Fig. 5, the force exerted to the surface patch is obtained, and it yields the same maximum contact pressure for smooth surfaces as that found in Hertz analysis. Figure 6 depicts the iteration process. For a given force, maximum pressure is calculated using the SDAT. In this the geometric and mechanical properties of the cam and roller are included. Each simulation run yields values of maximum contact pressure. It is shown in Fig. 6 that the iteration converges rapidly. For a measured patch, the required force to yield a maximum pressure of 1880 MPa is about 2391"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002015_j.mechmachtheory.2004.03.003-Figure16-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002015_j.mechmachtheory.2004.03.003-Figure16-1.png",
        "caption": "Fig. 16. Roller drive testing rig.",
        "texts": [
            " (52) and analysis results, it is found that as the geometric parameters of the roller drive, R2i , R4, R3i , r2 and r3, approach the relationship R2i \u00fe R4 \u00bc R3i \u00fe \u00f0r2 \u00fe r3\u00de, then there is less speed fluctuation as shown in Fig. 15. The value of abscissa in Fig. 15 is the value of dg \u00bc R2i \u00fe R4 R3i \u00f0r2 \u00fe r3\u00de. Each curve in the plot corresponds to change the value of one of the parameters from the set value in the equal condition while the other parameters are kept fixed. A roller drive, whose dimensions are as shown in Table 1, was built for the test. As shown in Fig. 16(a), a rig was constructed to test the roller drive consisting of a power source, an external load and associated instruments. A detailed arrangement of the test rig is illustrated in the schematic diagram as shown in Fig. 16(b). An AC motor having two magnetic poles (FUKUTA, 7.5 kW) with an inverter (ADLEE AP2G3-75) is used as the power source. The external load of the roller drive is provided by a powder brake (MITSUBISHI ZKB-20XN, 200 Nm). The instruments of the test rig include two torque transducers (KYOWA TP-2KMCB, 20 Nm and TP-20KMCB, 200 Nm) and two optical encoders (NIDEC NEMICON CORP. OEK-50-2, 50 P/R and OEK2-05-2, 500P/R) for measuring the input and output torques and angular displacements of the roller drive, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003186_i160039a011-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003186_i160039a011-Figure1-1.png",
        "caption": "Figure 1 . The rotating dialysis cell, disassembled",
        "texts": [
            " (1968), in their analysis of the stirred batch dialyzer, discuss the magnitude of errors resulting from this assumption and also point out the possible dependence of CY on Par, D, q , and w for that apparatus. We have not tested the constancy of CY with Pv, but assume an insignificant change in CY for hemodialysis membranes of similar permeabilities. The validity of our Wilson plots was tested by intercomparison of PM values determined by entirely different methods. Once c was established, then a plot of In (Pbl) us. a n appropriate function of D , p , and q for several solutes was used to find b and CY. Experimental Procedure The Rotating Cell. T h e disassembled cell is shown in Figure 1. Each compartment was machined from 2.4-cm thick X 12.7-cm diameter Lucite disks to form cavities 0.55 cm deep and 9.3 cm in diameter. Two filling holes were drilled into each compartment and provided with threaded nylon plugs fitted with O-rings. Large O-rings (10.0-cm diameter) fit into grooves machined in the face of each disk in order to seal the membranes clamped between the two halves. The maximum available volume in each compartment is 60.0 em3, and the membrane area exposed to solution is 73"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003986_imtc.2008.4547183-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003986_imtc.2008.4547183-Figure2-1.png",
        "caption": "Fig 2: Simple triangulation method for distance measurement [4].",
        "texts": [
            " The laser source has a high beam quality that is able to focus the laser on small spot over a considerable distance [4,5]. For computing the range via triangulation, a simple concept of perspective is implemented. The whole system is represented by an Image Plane, Focal Point and Optical Axis [4]. The laser pointer is placed under the camera at a certain angle, so that it is able to illuminate the obstacles with its laser point. The height between the camera and laser pointer is immaterial as the calculations below only deal with the path of the laser beam [5]. From Figure 2 below, the obstacle is at point P with coordinates of x and y. The projection of point P on the image plane is at point i. To arrive at the distance equation, points P1 and P2 need to be used in the calibration of the system. The points that can be measured physically are xi, x2, il and i2 [4]. Using similar triangles, the origin of the coordinate system, which represents the robot, is denoted as point 0; the focal point. The equations for the slope and the y-axis intercept of the laser path are formed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002525_1.2429700-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002525_1.2429700-Figure1-1.png",
        "caption": "Figure 1 c shows the bolted joint model, in which the fastener ension is Fb and the corresponding clamping force in the joint Fc. t initial assembly of the joint, both Fb and Fc are equal to some nitial value Fi. Subsequently, the bolted joint is subjected to an xternal force Fe that is cyclic and fully reversed as shown in igs. 1 a \u20131 c . During the first half cycle, the external force Fe ncreases the fastener tension and simultaneously reduces the lamp force. The opposite is true during the second half cycle; the ompressive action of Fe on the joint reduces the bolt tension nd increases the clamp load. As long as the external force Fe has nonzero value, the fastener tension and the clamping force will ot be equal. When the external force Fe is completely removed, he new equilibrium point between the fastener tension and the oint clamping force occurs at a lower value which is below their",
        "texts": [],
        "surrounding_texts": [
            "I w d j m n y o q m t t\nj s i o t l f p p w o n t\nc\no N E C\nJ\nDownloaded Fr\nSayed A. Nassar e-mail: nassar@oakland.edu\nPayam H. Matin\nFastening and Joining Research Institute, Department of Mechanical Engineering,\nOakland University, Rochester, MI 48309\nCumulative Clamp Load Loss Due to a Fully Reversed Cyclic Service Load Acting on an Initially Yielded Bolted Joint System The amount of clamp load loss due to a fully reversed cyclic service load is determined for a bolted assembly in which the fastener and the joint were both tightened initially beyond their respective proportional limits. The cyclic reversed load acts in a direction parallel to the bolt axis. During the first half of each cycle, the cyclic load acts as tensile separating force that increases the fastener tension further into the nonlinear range; it simultaneously reduces the joint clamping force. Thus, after the first one half of the cycle, the clamp load is reduced from its initial value due to the plastic elongation of the fastener. During the second half cycle, the cyclic load compresses the joint further into the plastic range; simultaneously, it reduces the fastener tension. Due to the permanent set in the compressed joint, the clamp load is decreased further at the end of the second half cycle of the service load. The cumulative clamp load loss due to the permanent set in both the fastener and the joint is analytically determined using a nonlinear model. Variables investigated in this study include the joint-to-fastener stiffness ratio, the ratio of the initial fastener tension to its elastic limit, and the ratio of the external force to its maximum tensile value that would trigger joint separation. DOI: 10.1115/1.2429700\nKeywords: threaded fasteners, clamp load loss, yield tightening, flanged connections\nntroduction Yield tightening strategies are often used in critical applications here a repeatable and consistent high level of the clamp load is esired, in order to enhance fatigue performance and/or prevent oint leakage 1\u20134 . Examples of such critical applications include\nany automotive power-train joints as well as many flanged conections in power plants in particular nuclear power plants . The ield control process of threaded fastener tightening eliminates the bjectionable level of high scatter in the clamp load that freuently results from torque-related control methods. The scatter is ainly due to the sensitivity of the fastener torque-tension relation o normal variations in friction between threads and between the urning head/nut and the joint surface 4 .\nSubsequent to its initial assembly, a bolted joint may be subected to an external service load during its normal operation. A eparating tensile service load reduces the joint clamp load and ncreases bolt tension, while a compressive service load does the pposite; it would increase the clamp load and reduce the fastener ension 5 . Nassar and Shoberg 6 investigated the permanent oss of clamp load after the removal of a tensile separating force rom a joint in which the fastener preload slightly exceeded its roportional limit. In their model, the joint behavior remained erfectly elastic. Hence the validity of the model used in Ref. 6 as confined to a scenario in which the fastener tension produced nly a small plastic deformation in the fastener. The model could ot accurately predict the clamping force loss for joints in which he fastener stress was much higher than its elastic limit.\nIn a more recent study, Nassar and Matin 7 investigated the lamp load loss in bolted joints, in which the fastener preload was\nContributed by the Reliability, Stress Analysis, and Failure Prevention Committee f ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received ovember 11, 2005; final manuscript received April 8, 2006. Review conducted by rol Sancaktar. Paper presented at the ASME 2005 Design Engineering Technical onferences and Computers and Information in Engineering Conference DETC2005 , Long Beach, CA, USA, September 24\u201328, 2005.\nournal of Mechanical Design Copyright \u00a9 20\nom: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ash\nwell beyond its proportional limit, while the joint remained in the elastic range. However, they did not consider the effect of strain hardening on the clamp load loss, because their model was close to a perfectly elastic, perfectly plastic, behavior for the fastener material, with no significant strain hardening.\nIn a follow up study, Nassar and Matin 8 provided some experimental insight into the effect of the fastener material strain hardening on the clamp load loss using an iterative numerical scheme. In a subsequent study 9 , however, Nassar and Matin developed closed form formulas for the clamp load loss due to a cyclic separating service load, but they did not consider the effect of cyclic compressive service loads. A fully reversed cyclic service load would alternate between a separating action during one half cycle that is followed by a compressive action on the joint during the next half cycle. It should be noted that the compressive loading on bolted joints is practically possible in rotary machines that are bolted to their base or floor foundation; even a small unbalance weight m0 on the rotor, disk or blades that rotate at a high speed may cause a significant harmonic fully reversed service load with an amplitude Fe =m0e 2 as shown in Figs. 1 a and 1 b . This service load will change both the fastener tension and joint clamp load 9 .\nIn this study, both the fastener and the joint have been initially tightened beyond their respective elastic limits; this resembles applications in which the joint materials are weaker than the bolt material, such as steel bolts in aluminum joints. During operation, the bolted joint system is subjected to a fully reversed cyclic load as shown in Figs. 1 a \u20131 c . A nonlinear strain hardening model is implemented in order to determine the clamp load loss due to the cumulative effect of a permanent set in the fastener and the joint after the service load have been completely removed. Various rates of strain hardening are used for modeling the behavior of the fastener and joint materials. The effect of three variables on the amount of clamp load loss is investigated; namely, the joint-tofastener stiffness ratio, the fastener preload, and the amplitude of the external service load.\nAPRIL 2007, Vol. 129 / 42107 by ASME\nx?url=/data/journals/jmdedb/27846/ on 02/16/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use",
            "t\nA\ni\ne\nF\ni\nc\nc\na\na\nn\nt\nj\ni\n4\nDownloaded Fr\nnitial level Fi; explained in the next few sections. The objective\n22 / Vol. 129, APRIL 2007\nom: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ash\nof this study is to determine the new equilibrium position and to calculate the corresponding clamp load loss in an initially yielded bolted joint system.\nLinear Behavior of the Fastener and Joint Have the fastener and the joint been kept in their respective linear elastic range, the corresponding joint diagram will have been represented by Fig. 2. The preload Fi elongates the fastener by the amount of b, and the corresponding clamping force simultaneously compresses the joint by the amount of c. In general, b and c are not equal, unless the stiffness of the fastener and that of the joint Kb and Kc, respectively , are equal. For this elastic model, the cyclic force Fe will increase the fastener tension linearly to point D during the first quarter of the cycle and will simultaneously decrease the clamp load until it reaches point O, which is vertically below point D. By the end of the next quarter cycle, the fastener tension goes back from point D to point C along its original elastic line DA, while the clamping force increases to point C along its own elastic line A C, and there will be no clamp load loss. In the elastic range, the effect of the cyclic force Fe on the fastener tension Fb and the joint clamping force Fc is given by 5 as follows\n1a Fb = Fi + Kb\nKb + Kc Fe\nFc = Fi \u2212 Kc\nKb + Kc Fe\nduring the separating half cycle of Fe\n1b\n2a Fb = Fi \u2212 Kb\nKb + Kc Fe\nFc = Fi + Kc\nKb + Kc Fe\nduring the compressive half cycle of Fe\n2b\nwhere Kb and Kc are the stiffnesses of the fastener and the joint, respectively. Line segments CD and CO represent the linear behavior of the system during the second half cycle, where Fe compresses the joint.\nEquations 1a , 1b , 2a , and 2b show that the difference between the bolt tension and the clamping force is always equal to the tensile separating force Fe as follows\nFb \u2212 Fc = Fe 3\nDuring the separating half cycle of Fe, joint separation will begin to occur if point O reaches the x axis in Fig. 2 1\u20135 . Hence, in order to avoid joint separation, the separating force must remain less than Fe max, which is obtained by setting the clamping force equal to zero in Eq. 1b , which yields\nFe max = Kb + Kc\nKc Fi 4\nIf a purely separating action of the external force Fe is harmonic, as is the case of head bolts in an internal combustion engine, both the increase in the fastener tension and the corresponding reduction in the clamping force, given by Eqs. 1a and 1b , will be harmonic as well.\nNonlinear Behavior During the Separating Half Cycle Figure 3 shows the joint diagram; at initial tightening both the joint and the fastener were yielded. Line segment AB C and ABC show the load\u2013deflection curves for the yielded joint and fastener, respectively. In the nonlinear joint diagram ACA , point C represents the initial tightening condition at which the fastener tension and the joint clamp load are both equal to some initial value Fi. Point C is represented by its coordinates Xi and Fi as follows\nTransactions of the ASME\nx?url=/data/journals/jmdedb/27846/ on 02/16/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use",
            "w s\nc f l d s\nw s t\nt f p i v p n a t p\nf d\nw s\nin t\nJ\nDownloaded Fr\nC xi\nFi\n5\nhere xi=initial fastener elongation; and Fi=initial fastener tenion preload .\nAs the force Fe tries to separate the joint during the first half ycle, the fastener tension is increased by F, while the clamping orce is decreased by FClamp. The fastener tension increases noninearly along curve CD to point D, while the clamp load Fc ecreases linearly along its new elastic line CO. Point D is repreented by its coordinates as follows\nD xi + x\nFi + F 6\nhere x=increase in the fastener elongation due to the external eparating force Fe; and F=increase in the fastener tension due o the external separating force Fe.\nBecause the fastener is well into the plastic region at D Fig. 3 , he reduction of the external separating force Fe will cause the astener tension to decrease along a new elastic line DH, which is arallel to the original elastic line AB. Simultaneously, the clampng force will increase along its new elastic line OC. When the alue of Fe goes to zero, the system achieves a new equilibrium at oint H, which is lower than the initial equilibrium point C. At the ew equilibrium point H, the residual value of the fastener tension nd joint clamping force are reduced from their initial value of Fi o a lower value FH. The difference between Fi and FH is the artial clamp load loss Fc during the separating half cycle of Fe\nFc = Fi \u2212 FH 7\nSolving for the vertical coordinate of point H and subtracting it rom that of point C provides the partial clamp load loss Fc uring the separating half cycle as follows\nFc = Kb + Kc x \u2212 Fe\n1 + Kb\nKc\n8\nhere Kb=fastener stiffness in the elastic range; and Kc=joint\ntiffness in the elastic range.\nournal of Mechanical Design\nom: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ash\nThe quantity x in Eq. 8 is yet to be solved for. Referring to line ABCD in Fig. 4, the force\u2013elongation relationship for the fastener may be written as\nF = f x 9\nwhere F=clamp force; x=fastener elongation; and f x is a known function for the fastener; the slope of f x represents the fastener stiffness 2 . It must be noted that f x is determined experimentally. The strain hardening rate of the fastener material, the effective cross-sectional area of the fastener, and the fastener grip length joint thickness , as well as the material stress\u2013strain relationship, are all represented by f x . In the elastic range, the function f x is linear and the fastener stiffness is equal to Kb. Past point B, the function f x becomes nonlinear with a continuously varying slope representing the fastener stiffness in the plastic range. As outlined in Ref. 9 , the function f x may be approximated by\nf x KA0\nLn xn 10\nwhere K=fastener strain hardening coefficient K value ; n =fastener strain hardening exponent n value ; A0=fastener tensile area; and L=fastener effective grip length.\nThe tensile area A0 is tabulated in Refs. 1,2 for various fastener sizes with fine and coarse threads; a procedure for determining the fastener effective grip length L is provided as well.\nThe initial fastener elongation xi prior to the application of the separating force was estimated 9 using the function f x given by Eq. 10 in terms of the initial fastener tension Fi as follows\nxi L Fi A0K 1/n\n11\nSubsequently, when the external separating force Fe is applied to the joint, the fastener elongation is increased by x and the cor-\nhe elastic range\u2013joint diagram\nresponding fastener tension is represented by\nAPRIL 2007, Vol. 129 / 423\nx?url=/data/journals/jmdedb/27846/ on 02/16/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use"
        ]
    },
    {
        "image_filename": "designv11_28_0000738_mfi.2001.1013506-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000738_mfi.2001.1013506-Figure5-1.png",
        "caption": "Fig. 5. Peg-in-hole task with error",
        "texts": [
            " This mot,ion primitive assures the \u201cface-twface contact\u201d . The determination whether the t,arget state is achieved or not is based on logical OR of two different sensing condition: a threshold test of the change of external force exerted on the object along tlre vertical axis, or a threshold test of the translation distance of the object along vertical ayis. B. Execution of Peg-in-hole and Detection of Slzp We made peg-in-hole experiments using a cylinder wit.h 40mm of diameter, 12Smm of height, and lO0g of weight. Fig.5 shows a sequence of state transitions together with initial grasping position of fingertips. \u201cVertical Move-twtouch\u201c successfully achieved its goal state. \u201cHorizontal Move-btouch\u201dtried to achieve a new additional contact while keeping the formerly achieved contact of the bottom of the cylinder with the upper fringe of the hole. However, it continued to move the peg even after the new contact has been achieved because the threshold value was too large to detect the change of the external moment exerted on the peg by the new contact. Since the grasping forces were set to be small, the fingertips slipped and the peg began rotating around the contact point with the edge of the hole. Then a vision-based error detection procedure detects the error based on the measurement of the leaning angle of the peg and the primitive stopped(2E in Fig.5). Finally \u201cRotatetwinsert\u201d succeeded the peg insertion although the fingertips slip had been caused by larger resisting force of collision and friction. In this experiment, we have observed the fingertip slip which occurred in 2E and 3E in Fig.5. Figs.6 and 7,,,show the results of the slip detection on the finger 3 (fin3 :in Fig.5). The vertical dashed lines in the Figs.6 and 7 divide execut,ion of different primitives. Values of parameters /3, 7, k, T a r e 0.45, 0.45, 3, and 0.013 rcspectively. The y-axis of the slip detection frame is selected to he parallel with lines. As shown in the upper two charts in the figure, the measured slip velocity has large noise. The reason is that the slip velocity is computed using the pose of the grasped object which contains larger noise mainly caused by the vision syst,ern. Sliv distance a l o n ~ each axis is obtained bv internal of the axis of the cylinder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000877_bf00384690-Figure3.1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000877_bf00384690-Figure3.1-1.png",
        "caption": "Fig. 3.1. A membrane model of the tube. The internal pressure is q and the axial load is P. The radial displacement is u, and the axial one is w.",
        "texts": [
            " Apparently, the stresses o 5 at the inner and outer circles are inversely proportional to the two radii. It is obvious that the variation of a, will grow with increasing flexure, so the arguments put forward in this section hold only for moderate curvature. Summarizing we can say that for the purpose of this paper it makes sense to apply the simple formulae at = qa/h and o- a = qa/2h. Anyhow, using these expressions we join the existing standard calculations of the strength of flexible hoses. We consider a composite thin walled cylindrical shell, consisting of rubber and elastic wires (Fig. 3.1). The latter are considered as a two-dimensional continuum in common with the rubber sheet. The calculations are referred to a cylindrical coordinate system r, 0, z, as depicted in Fig. 3.1. The equation of the undeformed cylinder is r = r0. Its length is not relevant to our analysis. There are two families of wires. Ribbons of these are interlaced along helicoidal lines, the two families being symmetric. The uniform angle between the tangents to the wires and a cross-section is called ~0 (Fig. 3.2). We shall call q~ the pitch angle, and we note that the so-called helix angle is the complementary angle of ~o. It is assumed that the cylinder deforms axisymmetrically after exerting an axial load P and an internal pressure q to it"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002036_iccis.2004.1460382-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002036_iccis.2004.1460382-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of a flexible transmission system",
        "texts": [
            "i,'glgki to Lyapunov function, we have 1 \" 2 i:l Substituting (35) into (36), we get L i=l Now by choosing the adaptivc law as We have Assuming (39) Simply choosing yi < 1 / 2 , then the Lyapunov stability is verified. Using the adaptive law in (329, by Substituting (34) in it, we gct In order to prevent highly increasing in updating parametcr values, which leads to system instability, adaptive law limited to IV. SIMULATIONS To illustrate the above design technique, a flexible transmission system is considered. This system consists of three horizontal pulleys connected by two elastic belts. The schematic diagram of the system is shown in Fig. 1. The objective is to control the position of the third pulley which may be loaded with small disks. This can be done by measuring its position and applying the required forces using a dc motor to the first pulley. There are three plant models depending on the load configuration; no-load, half-load (1.8Kg) and full-load (3.6Kg). Each model contains two ,flexible modes (with damping factors of less than 0.05). The dynamics of the system can be described as [9] - 1 2 3 4 5 2 0 1 - \"0 1 3 4 5 time(s) ~ ,/I-- -I 1 1 /------ 1 3 4 5 time(s) 1 0-' 0 1 - 2 3 4 , 5 0 1 2 time(s) 4 5 x = [8, 0, 4 d3] and r, J , f and k represent the radius of the pulley, inertial momentum, friction factor and stiffness of the belts between pulleys, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000877_bf00384690-Figure4.1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000877_bf00384690-Figure4.1-1.png",
        "caption": "Fig. 4.1. A membrane model of the tube. The cylindrical coordinates in the undeformed configuration are R0, 0, Z, and in the deformed configuration r0, 0, z. The pitch angles in these configurations are \u2022 and q~, respectively.",
        "texts": [
            " Since we shall pursue non-linear effects in a later paper, we now present an analysis applying to a pseudo-linear rubber material and in which the kinematical constraint figures exactly. Ultimately we will linearize all our equations to make a comparison with the results of the preceding section feasible. We refer the undeformed and the deformed cylinder to one and the same cylindrical coordinate system, the coordinates in the undeformed (or Lagrangian) state being R, O, Z, and those in the deformed (or Eulerian) state being r, 0, z (Fig. 4.1). The equation of the undeformed cylinder is R = R0, and that of the deformed one is r = r 0. Further we assume 0 = O and z = 2Z, (4.1) with 0 < 2 < oe. Obviously the deformation is described by two positive numbers, viz. r 0 and 2. We denote the pitch angle of one family of wires in the undeformed state by the angle q~, and the corresponding quantity after deformation by q~. A simple analysis yields the following condition expressing the inextensibility of the wires r~\u00b0 cos 2~ + 22sin 2q) = 1, (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003251_156855307780429820-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003251_156855307780429820-Figure5-1.png",
        "caption": "Figure 5. Computation of (erq)1. Event 1 refers to the cases where at least one hpt lies inside A(q) \u2229 Vu(s). If event 1 were to occur, q would be in collision with a sensed obstacle (sensed hpt).",
        "texts": [
            " The expected C-space entropy reduction is simply a sum of these marginal terms. 3.1. erq(s) computation Recall that the environment is composed of free space and point obstacles, called pt . With occlusion constraints, the sensor only detects the very first point obstacle, called a hit point and denoted by hpt , along each sensing ray. Note the subtle but important difference between a hpt and a pt . For a robot configuration q, the possible outcomes for a sensing action s can be grouped into event 1 and event 2. Event 1 (Fig. 5) corresponds to cases where the sensor would sense at least one hpt inside A(q) \u2229 Vu(s), the unknown region occupied by the robot (if it were at configuration q) that lies inside the sensor FOV, if the sensor were to be placed at sensor configuration s, i.e., \u2203hpt \u2208 A(q) \u2229 Vu(s). Event 2 (Fig. 6) corresponds to a set of outcomes in which there does not exist any hpt inside A(q) \u2229 Vu(s). We accordingly decompose the entropy reduction computation into two parts: erq(s) = (erq)1 + (erq)2 = E{ event1H } + E{ event2H }"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001373_cira.1999.810044-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001373_cira.1999.810044-Figure2-1.png",
        "caption": "Figure 2: (a) The parameters used to reach a target configuration (z* , y*), without a specified target orientation. (b) The adjustment of 0 to 0\u2019 to reach a target configuration of the form (z* , y* , q 5 * ) .",
        "texts": [
            " Also, the target configuration can be given as a function of time to allow for the controller to reason about intercepting the trajectory of a moving target. 3.1 Differential Drive Control for Position and Direction We begin with some basic control rules. The rules are a set of reactive equations for deriving the left and right wheel velocities, VI and U,., in order to reach a target position, (X*, Y*): A = e - 4 (1) ( t , r ) = (cos2 A sgn(cos A), sin2 A . sgn(sin A)) VI = v( t - r ) v, = v ( t +P), where 0 is the direction to the target point (z*,y*), 4 is the robot\u2019s orientation, and v is the desired speed (see Fig. 2(a))\u2019. A few aspects of these equations deserve explanation. The use of sin2 and cos2 restricts the values (t f r ) to the interval [0,13, which bounds the magnitude of the computed wheel velocities by V. These equations also do not necessarily drive the robot forward, possibly driving the robot backwards towards the target. We extend these equations for target configurations of the form (z*, y*, d*), where the goal is for the robot to reach the specified target point (z*, y*) while facing the direction 4\u2019. This is achieved with the following adjustment: (3) \u2019 e/ = e + m i n cr,tan-l ( where 0\u2019 is the new target directkn, cr is the difference between our angle to the target point and d*, d is the distance to the target point, and c is a clearance parameter (see Fig. 2(b).) This will keep the robot a distance c from the target point while it is circling to line up with the target direction, d*. This new target direction, e\u2019, is now substituted into equation 1 to derive wheel velocities. An example trajectory using these equations is shown in Figure 3 (a). In addition to our motion controller computing the desired wheel velocities, it also return? an estimate of the time to reach the target configuration, T(z* , y* ,d*) . This estimate is a crucial component in our robot\u2019s strategy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000516_tpcg.2003.1206940-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000516_tpcg.2003.1206940-Figure4-1.png",
        "caption": "Figure 4: An aeroplane making a level turn",
        "texts": [
            " Proceedings of the Theory and Practice of Computer Graphics (TPCG\u201903) 0-7695-1942-3/03 $17.00 \u00a9 2003 IEEE In this version of the simulation boids are constrained to move at a constant speed in a horizontal plane. The boids motion is based upon a simple model of an aeroplane performing a level turn [9]. For an aeroplane flying in a straight line, at a constant altitude, with a constant speed, to make a level turn it must use its ailerons to force the aeroplane to bank at an angle \u03c6, as shown in Figure 4. In its original state the lift force, L, created by the wings is equal, but opposite, to the force of the weight of the aircraft, W. Since the wings are no longer horizontal, L is no longer acting in the opposite direction to W and is inclined at the angle \u03c6. For the turn to be level the vertical component of L must be equal to the weight. This leaves the horizontal component of L, F, which causes the angular acceleration that forces the aeroplane to turn. The planes load factor, n, is defined as: W L n = (3) It is normally quoted in terms of \u201cg\u2019s\u201d and is a measure of the planes angular acceleration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000678_irds.2002.1041739-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000678_irds.2002.1041739-Figure10-1.png",
        "caption": "Fig. 10 Example of Search-Type Motion",
        "texts": [
            " The search-type motion primitive searches the center of the hole which is represented by a small black small circle in this figure. Breadth-fmt search [lo] from the start point (the white small circle) is used here. In this paper, we deal with a round peg. Since the bottom face of the peg is a circle, 2D search is done here. If the peg is not a round peg (i.e. the bottom face of the peg is not a circle), rotation with respect to the z-axis should be taken into consideration and 3D search should be done. 4. Example Figure 10 shows an example of search-type motion. The motion demonstrated by a human operator in the teaching stage is shown in Figure 11. Figure ll(5)-(6) is the identified search-type motion. This part of the motion is replaced with the search-type motion primitive that will be explained next. The Pseudo-contact-point method [ 111 is used in order to measure the position of the contact points. Four times sensing of the position of contact points gives us the information of the contact points (Figure 12a-d)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002559_tmag.2005.846213-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002559_tmag.2005.846213-Figure2-1.png",
        "caption": "Fig. 2. Position of off-centered rotor (1/1 region).",
        "texts": [
            "846213 where is the total volume of elements related the node , is the Maxwell stress tensor, and is the interpolation function of elements related the node . The electromagnetic force is given as follows: (3) where is all the nodes contained in an object to calculate the force. Fig. 1 shows the analyzed model of an IPM motor with a cantilevered rotor, which is used for compressors of air-conditioners. The analyzed region is the whole region in order to carry out the dynamic calculation taking into account the off-center of rotor. Fig. 2 shows the position of the rotor with off-center. The parameter is the distance from the original position to the off- 0018-9464/$20.00 \u00a9 2005 IEEE center position. Fig. 3 shows the 3-D finite-element mesh, which rotor is off-centered. Fig. 3(b) shows the meshes near the air gap with off-center. Table I shows the analyzed conditions. We analyzed with and without the off-center. Fig. 4 shows the calculated waveforms of torque and electromagnetic force acting on the rotor when the parameter of is 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000371_elan.1140020807-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000371_elan.1140020807-Figure1-1.png",
        "caption": "FIGURE 1. Schematic diagrams of the flow-injection manifolds used with a flowthrough reactor (A-D) and with a membrane biosensor (E). P, Peristaltic pump; S, sample injection point; D, flow-through amperometric detector; DL, dialyzer; GOD, enzyme flow-through reactor with immobilized glucose oxidase; W, waste.",
        "texts": [
            " The following membranes were used in this investigation: a Teflon-based strong cationic membrane (k ipore K-1010, k i Research Co., Hauppauge, New York), a nylon NY 13 membrane (Schleicher and Schuell, Dassel, West Germany), and a polyester membrane (Nucleopore, Pleasanton, California). Several control serum preparations were used: Seronorm and Pathonorm I1 (Nycomed, AS Oslo, Norway), SeraChem (Fisher Scientific, Orangeburg, New York), and Serum 1 (Medical Care Foundation, Warsaw, I\u2019oland). Flow - Injection Manifolds Scliematics o f the flow-injection systems used in this study are shown in Figure 1 . A configuration without a dialyzer was used with the flow-through enzynic reactor (A, H ) and with the membrane biosensor (E). The diaIyzer used in contigurations C and D with various niembranes allowed dialysis through a used membrane area o f 2.8 cmL, The measuring system was assemb~ecl from ITFE tubing (0.7 nini i.d.). In each manifold contiguration, a sample solution was injected into the carrier stream of distilled water, which was merged with :i stream o f 0.1 M phosphate buffer (pH 6.50) containing 0",
            " Flow Systems with the CPG-GOD Reactor without a Dialyzer In the optimization of the flow-injection-measuring system for clinical glucose determination with an enzyme flow-through reactor, attention should be paid to linear range o f the amperometric detector and t o the interferences caused by the electroactive constituents of physiological samples. For the platinum disk electrode covered with the polyester Nucleopore membrane, even for a very small injection volume (6 pL), the linear response was observed only up to 10 mM glucose (Figure 4A) using the simplest configuration o f the flow-injection system (Figure 1A). In a flow system in which part of the carrier solution with the injected sample was pumped to waste (which is a convenient method of on-line dilution) (Figure lB), the linear response range was extended to 50 mM (Figure 4H). This allows the utilization of such mea- 61 0 Matuszewski and Trojanowicz suremetits for natural serum samples with high patholog- Among the particular potential interfering species, the effect o f ascorbic acid, urea, uric acid, and citrate o n glucose determination was examined i n various flow-injection system configuration",
            "6 mM glucose was analyzed amperometria l ly for a glucose content and was correlated with the Kone Dynamic discrete clinical analyzer. All 17 analyzed natural human serum samples were simultaneously tested for urea, uric acid, atid total protein content. The determined glucose content ranged from 2.6 t o 17.6 mM, urea from 3.5 t o 21.8 mM, uric acid from 0.22 t o 0.56 niM, and total protein from 47 t o 84 g/L The correlation plot for glucose determination is shown in Figure 10, and an example o f the flow-injection recording is shown in Figure 1 1. The obtained correlation coefficient ( 0 . 9 4 ) ;IS well as tlie parameters o f the linear correlation plot (y = 0.93% + 0.443) show a much better correlation o f the flow-injection results with the Kone Dynamic analyzer than with Ikckman Glucose kialyzer. Our attempt t o correlae the observed deviations o f the results o f glucose determination with the three previously mentioned parameters WJS not successful. W e also found that replacing the phosphate huffer solutions used i n our system with those iised earlier by Petersson 1121 had no influence o n the results o f glucose cletermination in n~tur;ll serum samples"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003740_1.2975154-Figure13-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003740_1.2975154-Figure13-1.png",
        "caption": "FIG. 13. a Helicoidal magnet and cylindrical coaxial regions for evaluating field distribution; b integration domain sizing and positioning for B evaluation; c cylindrical coordinates k, xBi, and rcj of the points Pi,j,k , where B has been computed; d cylindrical coordinates x, , and rcj of the generic point P where B is interpolated.",
        "texts": [
            " Consequently, the integrals in Eqs. A26 \u2013 A37 have been computed by Gauss\u2013Kronrod quadrature19 and trapezoidal rule20 formulas. Global and local adaptative strategy integrations21 have also been used. No meaningful differences in results with respect to the quadrature technique utilization have been obtained. The values of Bx, By, and Bz were computed in the points of ten cylindrical surfaces coaxial to the magnet axis and in the points of the same axis. All these surfaces had the same length. Figure 13 a shows these ten surfaces and the points where B has been computed by Eqs. A26 \u2013 A37 and 101 \u2013 103 . Then, from these B values, by a bidimensional interpolating function, it has been possible to estimate B in any point of each cylindrical surface. Obviously, better the interpolation is the higher the number of points necessary to compute B is. In particular, it is convenient to increase the number of points in the regions where there are high B gradients. For the sake of simplicity, in our case study, a uniform distribution of points on each cylindrical surface has been utilized. Figure 13 b illustrates the generic cylinder where B has been computed. We observe that the cylinder has been positioned so as to come out of the same quantity x from the tips of the helicoidal magnet whose total length is denoted by lm Fig. 13 b . All the ten cylinders have the same length lt and are far d from the origin O of the reference system. In Fig. 13 c the identification of the generic point Pi,j,k where B has been computed is shown. This point belongs to the cylindrical surface j characterized by a radius rcj and it is defined by the three cylindrical coordinates k, xBi, and rcj. In the case study j =1,2 , . . . ,10, i=1,2 , . . . ,31, and k=1,2 , . . . ,15. Therefore B has been computed in 10 31 15=4650 points. More- over, we have fixed x=20 mm and d =30 mm. Then, in Eqs. A26 \u2013 A37 d=20+30=50 mm see Fig. 13 b . Table I sums up the geometrical data as well as the positioning with respect to the reference system O X ,Y ,Z of the helicoidal magnet. Table II reports the values of corresponding to n=5 coils , the free space permeability 0, and the magnitude M of the magnetization M used to evaluate the integrals. Table III shows the geometrical data relative to the domain integration. In particular, this table reports the values of the cylindrical coordinates k, xBi, and rcj by which the Cartesian coordinates px , py , and pz of the 4650 points Pi,j,k see Fig. 13 c have been evaluated. The numeric values of px , py , and pz so obtained have been directly substituted in Eqs. A26 \u2013 A37 . The B computation along the axis of the magnet has been performed in 50 equidistant points in correspondence to the length lt relative to the cylindrical integration domains see Fig. 13 b . Also in this case, it has been possible to evaluate B by interpolation in any point of the magnet axis of length lt. The numerical computation of the integrals in Eqs. A26 \u2013 A37 with the data reported in Tables I\u2013III has been performed by using FORTRAN programs and the scientific software MATHEMATICA.22 In practice, both softwares have produced the same results. Nevertheless, to compute the field with a reasonable precision, very short integration steps have been necessary in certain points and time computation has been correspondently increased",
            " B computation in 50 points equally distant among themselves on the axis of the magnet does not imply any difficulty. In this case, time computation is equal to a few seconds or much less, using MATHEMATICA or FORTRAN, respectively. The components Bx, By, and Bz of B have been computed by an interpolation in two dimensions on the whole surfaces of each coaxial cylinder characterized by the radius rcj j=1,2 , . . . ,10 . The generic point P of these surfaces has been identified by the three cylindrical coordinates x, , and rcj. Figure 13 d shows these coordinates relative to the reference frame O X ,Y ,Z . Then, fixing the cylinder with radius rcj, once that B has been calculated in the 465 points, changing with continuity x and , a very fast B evaluation in any point of this cylinder is possible. By this method, the three-dimensional surfaces illustrated in Figs. 14 and 15 have been obtained. These surfaces show Bx, By, and Bz versus x and in correspondence to each of the ten coaxial cylinders with radius rcj. With reference to the position in the O X ,Y ,Z of these cylinders whose length lt=492 mm, x changes from \u22120.0300 to \u22120.5220 m see Fig. 13 b and Tables I and III . The angle varies from 0 to 2 rad. These graphics show complex B changes and a certain periodical variation in B components, above all versus x. In addition to this, we see a very high increase in B on the cylindrical surfaces with the radii rc8=64.5 mm and rc9=95.5 mm. In fact, rc8 and rc9 are the values closest to the inner and outer radii ri=65 mm and re=95 mm of the magnet, respectively. Although these graphics are quantitative, to gain some more knowledge about field space configuration B flux lines should be drawn",
            " Using an opaque coloration for the cylinder with unitary radius, the positive values of Bny are represented by the dark regions of the surface that are external to the same cylinder. Vice versa, the negative values of Bny are defined by light regions that are internal to the cylinder. Figure 16 b clearly indicates the meaning of the cylindrical graphics reported in Fig. 16 a : a transversal section with respect to the axis of the opaque cylinder at x=\u22120.1968 m from the origin O of the reference system O X ,Y ,Z is illustrated see also Fig. 13 d . In this way we see the polar diagram of Bny versus . In Figs. 17 and 18, some graphics obtained by the above mentioned procedure and relative to the cylindrical surfaces with radius rc7 ,rc8 ,rc9, and rc10 are reported. These figures also indicate the normalized components Bnx and Bnz, all multiplied by the usual reduction scale factor equal to 25. Figures 19 and 20 show the polar diagrams similar to that one illustrated in Fig. 16 b . These diagrams have been drawn performing four sections at x=\u22120"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002741_cca.2006.286027-Figure16-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002741_cca.2006.286027-Figure16-1.png",
        "caption": "Fig. 16. Schematics of (a) installation tilt error and (b) the effects of tilt installation error around the y axis, y .",
        "texts": [
            " We assume that the difference arises from differences in the intensity of the light reflected from each moving object. Although the measurable distance ranges differ between object surfaces, all measurable distance ranges are much wider than the range we previously reported for the affixed-grating method (i.e., 0.05 mm) [25]. An estimation of the effect of installation error on the operation of a \u03bc-LDV is a very important practice. We calculated the theoretical beat frequencies for tilt installation error around the x-, y-, and z-axes, as shown in Fig. 16(a). For a tilt installation error around the y-axis (Fig. 16(b)), the Doppler-shifted frequencies fL and fR in (1) and (1) are replaced, respectively, by: f L = \u2212 V \u03bb cos(\u03b8 + y) (4) and f R = V \u03bb cos(\u03b8 \u2212 y). (5) Then, the beat frequency for tilt installation error, fd y is: fd y = 2 V \u03bb cos\u03b8 \u00b7 cos y . (6) The error around the z and x axes can be calculated in a similar way: fd z = 2 V \u03bb cos\u03b8 \u00b7 cos z (7) and fd x = 2 V \u03bb cos\u03b8, (8) where fd z and fd x are the beat frequencies for tilt installation errors around the z and x axes, respectively. In order to ensure that the \u03bc-LDV operates in accordance with the theoretical equations (6\u20138), we performed an experiment for tilt installation error using the same set-up used previously"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003662_1.3072447-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003662_1.3072447-Figure3-1.png",
        "caption": "FIG. 3. Coil and phase MMF vectors. FIG. 4. Schematic of FSPM motor drive under current hysteresis control.",
        "texts": [
            " Hence, an equivalent 12-slot/20-pole surface-mounted PM SPM motor is introduced to equalize the 12-slot/10-pole FSPM motor, as shown in Fig. 2. Theoretically, the PM flux-linkage wave form of the SPM motor employing concentrated windings with a fractional number of slots per pole can be sinusoidal, as shown in Fig. 2 b , i.e., the winding layouts can also be A1B1C1A2B2C2A3B3C3A4B4C4 Fig. 2 a . However, the MMF vectors due to magnets of two motors with concentrated windings are different, as shown in Fig. 3, and it can be seen that by appropriate connections, the resultant three-phase PM flux flux linkage of the FSPM motor can be similar to that of the SPM counterpart, which indicates that from the viewpoint of electromagnetic performance, the a Author to whom correspondence should be addressed. FAX: 86-25- 83791696. Electronic mail: huawei1978@seu.edu.cn. TABLE I. Key specifications of FSPM motor. Items FSPM motor Phase number m 3 Stator outer diameter, Dso mm 128 Stator inner diameter, Dsi mm 70"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002594_robot.2005.1570431-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002594_robot.2005.1570431-Figure1-1.png",
        "caption": "Fig. 1 Car-like robot model",
        "texts": [
            " For this reason, it is beneficial to split the path into shorter segments, optimize these segments separately and finally optimize the entire path, which is the concatenation of the optimized segments. Such a scheme has been implemented and the path is subdivided recursively, until a minimum predefined length is reached. VI. CASE STUDY phas RRT+GD) approach neric gorithm to pe trajectory optimization for a large class of systems. In this paper we consider the motion of a non-holonomic car-like robot in the plane among static obstacles (Fig. 1). rear wheel axle mid t [ ]Tx y=P . The unit vector v has en by \u03b8, its origin at P and lies along the direction of motion. The robot\u2019s orientation is giv the angle between the positive x-axis and v. The front-wheel turning angle is \u03c6 and the linear velocity is v. The robot state is T[ \u03b8]x y=x and the control vector is T[ ]v\u03c6=u . A simple ki crete model for the car\u2019s mo sed in this case study: 1x x v nematic dis tion is u y y v v L 1 1 cos sin tan / k k k k k k k k k k k k \u03b8 \u03b8 \u03b8 \u03b8 \u03c6 + + = + \u2206\u03a4 = + \u2206\u03a4 (20) een the front and rear-wheel tion Criterion as chosen to be the total t k k k k k D v T = = = \u2206 =\u2211 \u2211 u Qu (21) here "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000520_20.952650-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000520_20.952650-Figure6-1.png",
        "caption": "Fig. 6. Geometry and dimensions of the pot core.",
        "texts": [
            " The block diagram of the implemented closed loop system is shown in Fig. 5. The output of the inverter ( ) is compared with a reference and the error , obtained by this comparison, is applied to the sliding mode control technique (8) with the purpose of achieving . In presence of large disturbance, the sum of and the reference is clamped. The fixed frequency characteristic is given by a PWM regulator [2]. B. The Non-Linear Electromagnetic Device The saturated inductor is built using a ferrite pot core (Fig. 6) and its corresponding finite element mesh is presented in Fig. 7. Simulations are performed using the curve of the ferromagnetic material. The magnetic vector potential is related to flux density through rot , permeability is also function of . So, system equation (7) becomes a nonlinear equation system, and the Newton\u2013Raphson method [1] is employed to solve it. An induction map is shown in Fig. 8 where it can be seen the high magnetic induction value in central leg of the ferrite pot core which characterize the saturation effect that introduces harmonics in the current waveform, as can be seen in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001235_robot.2001.933066-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001235_robot.2001.933066-Figure1-1.png",
        "caption": "Figure 1: Robot 2 performs a PMO",
        "texts": [
            " Siich a Coordinated Plan (CP,) consists of a sequence of actions and execut ion events to be signaled to other robots as well as execution events that are planned to be signaled by the other robots. Such execution events correspond to temporal constraints bet ween,actions involved in the different coordinated plans. At any moment, the temporal constraints between all the actions included in the union of all the coordinated plans constitute a directed acyclic graph [3] which is a snapshot of the current situation and its already planned evolution (Fig. 1). When Ri receives its j- th goal G i , it elaborates a plan IP: which achieves i t ; then it performs a P M O (fig. 2 state 2) under mutual exclusion (fig. 2 state 1): it collects the cc,ordinated plans CPk of the robots which may interfere with IP:, and builds their union GP = U k Cpk. Then do the insertion of I @ in GP. If it succeeds, it adds temporal order constraints to actions in IP? and transforms it into a coordinated plan CPi. The out-coming CPi is feasible in the current context, and does not introduce any cycle in the resulting GP"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002603_3-540-29461-9_77-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002603_3-540-29461-9_77-Figure1-1.png",
        "caption": "Fig. 1. (a) Walking robot Max; 2D robot based on the principle of passive dynamic walking. (b) 5-link simulation model of Max with arced feet",
        "texts": [
            " The concept shows that a walker with two legs can perform stable walking when it is placed on a shallow slope, without the need for actuation or control. A cyclic motion is obtained by utilizing the natural dynamics of the system, being the passive pendulum motion of the swing leg and the inverted pendulum motion of the stance leg. In recent years the concept of passive dynamic walking has been used as a starting point for designing actuated dynamic walkers that are able to walk on a flat surface, one of which is the robot \u2018Max\u2019 [10] (shown in Fig. 1a.) that was developed at the Delft Biorobotics Laboratory. Max is equipped with arced feet, similar to most of the current passive dynamic walkers in the world [1, 2, 7], as well as to the actuated dynamic walkers based on this concept [9, 10]. This foot design is widely used because of its simplicity and the fact that it limits the vertical excursions of the walkers\u2019 center of gravity and thus is beneficial to both the efficiency and the robustness of the walkers [12]. In this paper, we replace the arced feet by flat feet that are connected to the lower legs of the robot through an ankle joint",
            " The main assumptions that were made for the simulations are the following: \u2013 All body links are assumed infinitely stiff. \u2013 Joints are free of damping and friction. \u2013 Heel, knee and toe impacts are fully inelastic. \u2013 Contact between foot and floor is without slip. \u2013 Heel and toe are released from ground when the contact force becomes tensile. \u2013 Floor is rigid and perfectly flat. \u2013 No rolling damping is present between foot and floor. The basis of the simulations is a two-dimensional 5-link model of the existing prototype robot Max, as depicted in Fig. 1b. The model consists of an upper body, two upper legs and two lower legs. There are three joints present in the model; the hip joint and two knee joints. In the hip joint a kinematic constraint is present that keeps the upper body at the intermediate angle of the two upper legs [10]. In the knee joint a constraint is present which fixes the lower leg to the upper leg when they are aligned. This models a latch mechanism that is present in the prototype. The actual prototype is actuated in the hip joint by McKibben air muscles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002527_1.1828454-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002527_1.1828454-Figure2-1.png",
        "caption": "Fig. 2 Schematic of the groove structure",
        "texts": [
            " The pores at the inner surface, both end faces, and the corners of the porous sleeve can be obstructed in the manufacturing process, such that the permeability at those surfaces may be lower than that inside of the sleeve. The local surface porosity obstruction can control lubricant flow at its region, and various combinations of the local obstructions might be effective to develop a wide range of hydrodynamic design options. The flanged rotating shaft surface is smooth, and herringbone grooves are formed on the stationary members only. Figure 2 is a schematic of the groove structure of the bearing system. The HGJBs are partially grooved with a central circumferential land along the bearing width, while the s of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F HGTBs are fully grooved, the inward and outward pumping grooves meet midway along the radial direction. Figure 3 describes herringbone groove configurations. 2.1 Assumptions. For modeling the bearing system, we accept the following assumptions: 1. The lubricant is an incompressible isothermal Newtonian fluid with a constant density",
            " The desire to suppress cavitation occurrence makes it a design requirement that no subambient ~negative! pressure generation is allowed, and there is no trapped air bubble in Chamber 5. 2.2 Governing Equations. The cylindrical sleeve volume is divided into a three-dimensional mesh in circular cylindrical coordinates (r ,u ,z) for the purpose of numerical analysis. An equal spacing of gridwork is given in the j or u direction ~Du!, and the grid spacing is set to be equal within each sub-region ~Fig. 2! in the r and z directions (Dr ,Dz). In this paper, the mesh is 35345 3149 for the r, u, and z directions. In order to accommodate the bearing films and the chamber regions facing the sleeve, the grid points are extended toward 6r and 6z directions by one more grid spacing, respectively, thus creating ~383453152! nodal points. Then according to the NGT, the mass flow rates in the direction of j and z in HGJB lubricant film are expressed, using Sommerfeld scaling for an incompressible film, as DM\u0304 j52DZH F1 ]P ]X 1F3 ]P ]Z 1F4 sin2 bgJ 1F5DZ (1) DM\u0304 z52DXH F3 ]P ]X 1F2 ]P ]Z 2F4 sin bg cos bgJ (2) JANUARY 2005, Vol",
            " 127, JANUARY 2005 rom: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Term DM\u0304 r52RDuH F3 1 R ]P ]X 1F2 ]P ]R 2RF4 sin bg cos bgJ (6) DM\u0304 u52DRH F1 1 R ]P ]u 1F3 ]P ]R 1RF4 sin2 bgJ 1RF5DR (7) where Eqs. ~3! and ~4! are applicable again, and Hg5Hr1 d\u0304g (8) Note that Eq. ~8! is nondimensionalized not by the overall axial gap ca but the radial clearance cr . It is required that the groove angle bg in the above equations be replaced with p2bg in the sub-regions @Z3,Z4# , @Z7,Z8# , @R2,R3# , and @R6,R7# in Fig. 2, where the fluid is pumped inwardly. Making use of Darcy\u2019s law, the basic equations for the porous sleeve inside pressure q are written in the form of dimensionless mass flow rates in the direction of r, u, and z, respectively, DM\u0304 r52J3 ]Q ]R R Du DZ DM\u0304 u52J3 ]Q R]u DR DZ (9) DM\u0304 z52J3 ]Q ]Z R Du DR where dimensionless permeability parameter J is defined with the porous material permeability k as J5 A3 12kr0 cr (10) A pore obstruction model is proposed for the sleeve circumferential surfaces as shown in Fig",
            "org/ on 01/28/2016 Term the inner and outer radii create a net inward pumping effect. It may be noted that the absolute value of a nodal pressure in the porous material does not exceed that of the bearing gaps and chambers because it is calculated merely as a weighted average of the surrounding nodal pressure values. Chamber 3 is therefore most susceptible to becoming negative. Besides, if the bearing is produced to have the radial clearance of the HGJBs tapered to decrease linearly over the axial region with the largest clearance at Z9 and the smallest at Z0 in Fig. 2, a negative pressure is more likely to occur since the extra inward pumping action of the upper HGJB diminishes. Under this downwardly tapered-off clearance condition, while the eccentricity ratio \u00ab0 is zero, the dimensionless pressure values in Chamber 3 are plotted in Fig. 6 as a function of permeability parameter J with another plot in the upwardly tapered-off case. The radial-clearance inclination is set at 1/10,000, and the clearance is kept to be equal to the nominal value cr at the center of the lower HGJB for both tapered-off conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003809_speedham.2008.4581077-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003809_speedham.2008.4581077-Figure2-1.png",
        "caption": "Fig. 2. Space vector when the rotor position is 7.5 [deg.] (60 [ele. deg.]).",
        "texts": [
            " ( )0 1 2 a uL L L= + (6) ( )1 1 2 a uL L L= \u2212 (7) where La and Lu show the phase inductance at the aligned position and the phase inductance when the rotor and stator poles are unaligned. The stator windings are displaced by 120 ele. deg. in space in the 3-phase SRM. Therefore, the space vector of the phase inductance L is described by the following equation using (4). 4 2 03 3 1 3 2 ele j j j u v wL e L e L e L e \u03c0 \u03c0 \u03b8= + + =L (8) From this equation, the angle of space vector L equals the rotor position. Fig. 2 shows the space vector of the phase inductance when the rotor position is 7.5 deg. According to this figure, the \u03b1-axis inductance L\u03b1 and the \u03b2-axis inductance L\u03b2 in Fig. 2 are calculated by the next equations. ( )1 2v w uL L L L\u03b1 = \u2212 + (9) ( )3 2 w uL L L\u03b2 = \u2212 (10) From Fig. 2, the angle of the space vector L can be calculated by ( ) ( ) w u 1 1 v w u 3 2tan tan 1 2 ele L LL L L L L \u03b2 \u03b1 \u03b8 \u2212 \u2212   \u2212    = =     \u2212 +    . (11) Accordingly, the rotor position can be estimated by calculating the angle of space vector L using (11). At standstill, the phase inductances of all phases are computed by (3). The DC bus voltage 140 V is applied to all phases over a short time 100 \u00b5sec. And the detected current is used to obtain the phase inductance. Fig. 3 shows the phase current waveforms when the bus voltage is applied to all phases at standstill"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003759_jst.84-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003759_jst.84-Figure2-1.png",
        "caption": "Figure 2. Six degrees of freedom along and about the three orthogonal principal axes of the ski jumper with origin at the CG (positive senses are in the directions shown).",
        "texts": [
            " The principle for static pitch stability is that dM/dao0 at equilibrium (negative curve slope) [5]. However, the angle between the ski jumper\u2019s zero-lift line and the oncoming flow (aw) must be positive at equilibrium in order to produce useful lift. Static stability refers only to the direction of the system\u2019s initial response to a disturbance, while dynamic stability involves gradual damping of a disturbance over time [3,6]. Stability in pitch is known as longitudinal stability about the lateral (y) axis (Figure 2), stability in roll is termed lateral stability about the longitudinal (x) axis, and stability in yaw is called directional stability about the normal (z) axis [2]. Lateral motion depends on cross-coupling of roll and yaw [7]; however, longitudinal stability can be assessed independently. We might expect to find different postural configurations of the ski jumper that vary in terms of aerodynamic efficiency [8,9] and longitudinal stability [10]. Airfoil theory and principles of aircraft stability [e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002392_j.physa.2005.01.004-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002392_j.physa.2005.01.004-Figure2-1.png",
        "caption": "Fig. 2. Synchronized accelerometers system (SAS).",
        "texts": [
            " In this study, we used shoe insoles that were made by observing movements during actual walking. Thus they are called dynamic shoe insoles by Iritani method (Fig. 1). The state of foot alignment, the toes, and the arch of the sole during walking are taken into consideration. The relationship between the feet and the body as a whole is considered in weight-bearing positions and movement sequence patterns, therefore this decides the position and shape of the various pads on the back of the insoles. The synchronized accelerometer system (SAS) (Fig. 2) consists of two ADXL (Analog Devices) accelerometers, each having dual axes, that are easy to connect to a small wristwatch-type computer (WPC). The WPC, which controls the synchronization of the two accelerometers, contains a ceramic resonator called \u2018\u2018CERALOCK\u2019\u2019. Rechargeable lithium batteries supply electrical power to the two sensors. When a switch is turned on, accelerations of the lower- back and one knee are recorded in two dimensions by the WPC. The WPC was attached to the wrist of the subjects (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000652_0470867906-Figure8.18-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000652_0470867906-Figure8.18-1.png",
        "caption": "Figure 8.18 Finite element of a rectangular plate with four nodes and four degrees of freedom per node",
        "texts": [
            " The following representation deals with rectangular plate elements, which are treated in detail in Gasch and Knothe et al. [113]. The description of modelling is dealt with more briefly here in comparison with the previous demonstrator because \u2014 like the beams introduced in Chapter 6 \u2014 small deflections result in constant mass and stiffness matrices for the rectangular plate elements used. Furthermore, the customisation of the element matrices according to geometric and material parameters is very simple in this case. Each element has four nodes, which lie at the corners of the plate element, see Figure 8.18. Each node again has four degrees of freedom (uz, rx, ry, rxy), where uz represents the displacement perpendicular to the plane of the plate, rx and ry the cross-sectional tiltings in the x and y direction, and rxy the torsion: rx = \u2212\u2202uz \u2202x , ry = \u2212\u2202uz \u2202y , rxy = \u2212 \u22022uz \u2202x\u2202y (8.20) The interpolation functions for the rectangular plate element can be obtained in an elegant manner by the multiplication of pairs of interpolation functions of a beam, see for example equation (6.35). One interpolation function covers the x-direction, the other the y-direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000678_irds.2002.1041739-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000678_irds.2002.1041739-Figure9-1.png",
        "caption": "Fig. 9 Search-Type Motion Primitive",
        "texts": [
            " After the degrees of freedom in which maintaining DOF changes to constraining DOF are automatically identified in the teaching stage, the corresponding search motion is performed in the degrees in the execution stage. Our system generates a reusable program in which the \u201cnondeterministic\u201d part of the demonstrated motion is automatically replaced with the motion which is achieved by a search-type motion primitive. Note that this \u201cnondeterministic\u201d part of the demonstrated motion is recorded as a sequence of contact states in one trial and this sequence itself is not used for generating a reusable program that achieves the same task as the demonstrated task. Figure 9 illustrates the search-type motion primitive. The left band side of this figure illustrates insertion of the manipulated object and the right hand side illustrates the top view of face contact between the bottom face of the manipulated object, BOTTOM-FACE, and the bole, HOLE. Assume that the face contact between BOTTOMFACE and the face that includes HOLE are made, and that the center of gravity of BOTTOM-FACE is positioned at that lime on the point which is represented by the white small circle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002559_tmag.2005.846213-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002559_tmag.2005.846213-Figure1-1.png",
        "caption": "Fig. 1. Analyzed model (1/1 region).",
        "texts": [
            " The fundamental equation of the magnetic field can be written using the magnetic vector potential as follows [4]: (1) where is the reluctivity, is the current density, is the reluctivity of the vacuum, and is the magnetization of permanent magnet. Nodal force method is to calculate a local magnetic force in the 3-D finite-element method. The force acting on each node can be calculated as follows [5]: (2) Digital Object Identifier 10.1109/TMAG.2005.846213 where is the total volume of elements related the node , is the Maxwell stress tensor, and is the interpolation function of elements related the node . The electromagnetic force is given as follows: (3) where is all the nodes contained in an object to calculate the force. Fig. 1 shows the analyzed model of an IPM motor with a cantilevered rotor, which is used for compressors of air-conditioners. The analyzed region is the whole region in order to carry out the dynamic calculation taking into account the off-center of rotor. Fig. 2 shows the position of the rotor with off-center. The parameter is the distance from the original position to the off- 0018-9464/$20.00 \u00a9 2005 IEEE center position. Fig. 3 shows the 3-D finite-element mesh, which rotor is off-centered. Fig. 3(b) shows the meshes near the air gap with off-center"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002852_iros.2006.281799-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002852_iros.2006.281799-Figure2-1.png",
        "caption": "Fig. 2 Forming process of workspace ofjoint 3",
        "texts": [
            "5 0 90 where di is the distance between xi_1 and xi along zi; ai is the distance between zi-1 and zi along xi; ai is the angle between zi-1 and zi around xi; and the length of end-effector is 0.3m. The workspace of the reduced manipulator with the locked joint 3 can be achieved by rotating the end-effector three times about joints 4,2 and 1 in sequence. The first rotation about joint 4 results in a circle; the second rotation of the circle about joint 2 results in a finger ringlike cured surface; the last rotation about joint 1 yields a solid of rotation, which is the workspace of joint 3. Fig. 2 shows a graph of this process. For a fixed motion range of joint 3, the intersection of its maximum workspace and minimum workspace, the FTW of joint 3 shown in Fig. 3(a), can be determined. Following this procedure, we can determine the FTW of joint 2 and 1 respectively, as Fig. 3(b) and 3(c) show. Thus, if the fault tolerance with respect to any one joint of the manipulator is considered, the final FTW shown in Fig. 4 can be obtained by calculating the intersection of all joints' FTW. Lon (b) Second rotation (c) Third rotation For a given end-effector's motion, a redundant manipulator has an infinite of joint motions that will result in different reduced manipulability and FTW"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000652_0470867906-Figure6.3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000652_0470867906-Figure6.3-1.png",
        "caption": "Figure 6.3 Modelling of a wheel suspension by a two-mass oscillator",
        "texts": [
            " In this case the movements of the axles are almost independent of each other, which means that we can restrict ourselves to the consideration of one axle. If we further assume that the road conditions are the same for the left and right-hand wheel, then for reasons of symmetry it is completely adequate to consider only one wheel including half an axle and a quarter of the car body. Using the assumptions described yields a two-mass oscillator, which describes the vertical dynamics very well, see Figure 6.3. The mass ma describes the wheel and the associated part of the axle and mb describes a quarter of the body. Both masses are of course subject to gravity, but also to the forces that are exerted by the adjacent springs and dampers. Shock absorbers and body springs themselves are characterised by the parameters b and ks respectively. The tyres can also be considered as springs, but with a spring constant kw that lies around an order of magnitude above that of the body spring. The damping effect of the tyres can be disregarded here"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000485_robot.2002.1014296-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000485_robot.2002.1014296-Figure6-1.png",
        "caption": "Figure 6: Inscribed hyperspheres of 2D polyhedron",
        "texts": [],
        "surrounding_texts": [
            "U,, will be divided into 2 convex polyhedrons(shown in Fig.3) as the following:\nV~,=(ZI(Z%+b)hi,>O, (lTA+b)hi,lO, 051<L}, (25) V:,={ZI(Z?4+b)hiq~0, (l?4+b)hlr 20, O<l<L}. (26)\nThus, the GFPR can be represented by Vqr = V:r U Vir, (27)\nand Vi, or V:, can be represented such as D D\nl = x l v d P d , P d Z 0 , x P d = I r (28) d=l d= 1\nwhere, lvd, d = 1,2, -. 1 , D are the vertexes, p d is the barycentric coordinates. The GFPRs are located in the union set of the all of the Vir and Vi,. Generally the union set is a polyhedron but not a convex. 3.3 GFPR Formed by m Hyperplanes\nNow, we give a method for obtaining GFPR formed by m hyperplanes. According to eq.(13), for the set of k formed by m span vectors, the set of 1 can be represented by\nWI= l)x(ZTA+b)hij~j=O, aj20, j = l , 2 , . * * ,m . (29)\nFrom m span vectors of I C , m hyperplanes of Pj , j = 1,2, . . ., m are obtained.\nProposition 2: For the set of k formed by m span vectors, the set W [ can be expressed by the union set U1 of all of the set U,, { m j = 1 1 m\nU I = U uqr = 9 (u&U U&), (30) p,r=l,q#r q,r=l,q#v\nwhere U,, is formed by 2 arbitrary hyperplanes P , and P,, q, r = 1,2 , . . . , m, q # r (which has been proved in the literature [SI).\nMoreover, by considering the length bounds of object edges, from proposition 2 and eq.(27), the GFPR can be expressed as\n(31)\n4 Determining Stable GFPR In the previous section, the GFPR has been obtained as an union set of convex polyhedrons, but is not a convex polyhedron. In general, the stabler grasp can be achieved at these h g e r configuration points where the distances between the points and each hyperplane\nof GFPR polyhedron are farther. If we can iind the biggest inscribed hypersphere of the GFPR polyhedron, the grasp near to the center of the hypersphere will be stabler, when a few errors of the contact points on the actual object exist. In addition, if the volume of a convex polyhedron of GFPR containing the hypersphere is larger, the stable finger position region is larger.\nFrom what has been said above, for the obtained GFPR polyhedron, the Stable GFPR is defined as the convex polyhedron that contains the biggest inscribed hypersphere of the GFPR, and has larger volume. 4.1 Convex Polyhedron of Containing\nIn fact, for a GFPR formed by a boundary hyperplanes, the convex polyhedrons in the GFPR are encircled by the plural boundary hyperplanes from 2 to m and object edge length bounds. In this paper, we give a proposition for considering what convex polyhedron the biggest inscribed hypersphere may lie in. For the finger position set formed by m boundary hyperplanes, the convex set U:, is enclosed by the 2 arbitrary boundary hyperplanes P z and P; , and the U:, is enclosed by Pp and P:. The convex sets, that are enclosed by plural boundary hyperplanes including P: and P; , belong to U:,. The convex sets, that are enclosed by plural boundary hyperplanes including P i and P:, belong to U:,. At first, we consider the convex sets formed by 3 boundary hyperplanes. A hyperplane P , is chosen from m hyperplanes arbitrarily. Because P a does not pardel to P , or P,, the 2 convex sets that are enclosed by P:, P; and Pa(q # r # s) are represented as\nu:f = (p,+np; nP$) c (P:nP;) = U:,, uif = (p,+np; np;) c (P,+np;) = U:,.\nBiggest Hypersphere of GFPR\nproposition 3:\nproof\n(32) (33)\nSimilarly, the 2 convex sets that are enclosed by P i , P,' and P,(q # T # 8 ) are represented as\nU:: = (P;nPf nPt) c (P;nPf) = U:,, U:? = (P;nP: nP;) c (PpnPf) = U&\n(34) (35)\nFrom eqs. 32 - 35), we have U::CU!,, )&cU:,, tJ::CU:,, U:?CU&. (36)\nThus, the convex sets enclosed by P;, P; and P, (q # r # s) belong to the convex set U,, enclosed by P;, P ; . The convex sets enclosed by P; , P$ and P . (q # T # s) belong to the convex set U$ enclosed by Pi, P:.",
            "By the same way, we can also draw the conclusion that the convex sets enclosed by dural hvmmlanes including P i , P; (or P; , P:J defong to the convex sets U!, (or U!-). v , .\nFrom $;position 3, taking the object edge length limits 0 5 1 5 L into account, for the GFPR formed by m hyperplanes, the convex sets that are encircled by more than 2 hyperplanes including P,, P,, and object edge length bounds, belong to the convex polyhedrons ~ & o r V $ . ( q , r = 1 , 2 , . . . , m, q + r ) .\nTherefore, the biggest inscribed hypersphere of the convex polyhedron, that is enclosed by more than 2 hyperplanes including P,, P , and edge length bounds, belongs to the convex polyhedron V& or Vir. It can be seen that the biggest inscribed hypersphere of the GFPR lies in the convex polyhedrons Vt, or V& (q, T = 1, 2 , - . * , m , 42'). 4.2 Distances from One Point to Hyper-\nplanes of Convex Polyhedron The radius of an inscribed hypersphere i s the distance from the hypersphere center to the tangent hyperplane of the convex polyhedron. To find the biggest inscribed hypersphere of a convex polyhedron, we consider the distances from one point to the hyperplanes.\nAs shown in Fig.5, each convex polyhedron Vi, or V:, of GFPR is formed by the boundary hyperplanes\n(ZTA+b)hy=O, j = q , r , q#r, 9 , ~ = 1 , 2 , . . * , m , (37)\nand the edge bound hyperplanes l i = 0, li = Li, i = 1 ,2 , . - . , n. (38)\n(a j , I!) = bj , j = 1,2, ., J, (39) We can rewrite these hyperplanes as - 1\nwhere, J is the number of the hyperplanes forming the convex polyhedron. a; is the normal vector (inward the convex polyhedron shown in Fig.5) of the hyperplane P j . aj and 6; for eq.(37) can be obtained as\n(40) a; = Ahlj, 3 = -bhl j , if (ITA + b)hlj 2 0,\na; = -Ahij, 83 = bhlj , if (ITA+ b)hlj 5 0, (41)\nfor eq.(38), aj and b; can be obtained as a;=@ O...O]T~Rnxt &j=O, i f Z i = O , (42)\n3 -\naj=p . . .p -2 o . . . o l T ~ W X 1 , &=-L;, i f ~ i = ~ i ( 4 3 )\nAs shown in Fig& 1; is the intersection of the hy-\nj\nperplane Pi and the normd line lC1; of P;. distance from the point 1, to Pi . We have\nis the\n(44)\n(45)\n(46)\n1, - 1' - tc.a:. 3 - 3 3\nSince the point 1; is on Pj , from eq.(39) we have (at, J 1:) J =5- j'\nt! I J = (a- , lc) - 3, 3 = 1,2, - a , J. Eqs.(44) and (45) give the distance t: as\n4.3 Biggest Inscribed Hypersphere of Convex Polyhedron\nLet us consider the biggest inscribed hypersphere for each convex polyhedron Vi, or V& (q, r = 1 ,2 , . ... m, q # r ) . Then, we will determine the biggest inscribed hypersphere of GFPR.\nAs shown in Fig.G(a), for a 2D polyhedron, the center of an inscribed hypersphere is determined by 2 bisectors of 2 interior angles formed by 3 hyperplanes. In the same way, for an nD polyhedron, the center of an inscribed hypersphere is determined by n bisectors of n interior angles formed by (n + 1) hyperplanes.\nNow, we consider the method for determining the inscribed hyperspheres of an nD convex polyhedron formed by J ( J 2 (n + 1)) hyperplanes. At first, (n + 1) hyperplanes are chosen arbitrarily from J hyperplanes. The inscribed hypersphere for these (n+ 1) hyperplanes can be solved. Since the distances from the center of the inscribed hypersphere to the tangent hyperplanes are radiuses and meet\n...... t; = t; = tin+1] = ~ c . (47)\n(al, z,) - 81 = (az, le) - 82, (48)\n(al, - Sr = (a3, lc) - 83 , (49)\n=\nFrom eq.(46), we rewrite the above equation as\n.............................. (a19 l c ) - 61 = (a(n+i), lc) - b(n+l)* (50)\nThe inscribed hypersphere satisfying eqs.(48) N (50 is one hypersphere inscribed the (n + 1) hyperplanes dosen from J hyperplanes of the nD convex polyhedron. But it may not be an inscribed hypersphere of the convex polyhedron (reference Fig.G(c)).\nThen, according to eq.( 46), the coefficient of the distance t!. from 1, to hyperplanes forming convex polyhedron and radius rc can be obtained. If 3\nr c < t ; , ;= 1 ,2 , . . . , J (51)",
            "is met, the hypersphere is one of inscribed hyperspheres of the convex polyhedron (see Fig.G(b)).\nFor a convex polyhedron Vir or V$ formed by J hyperplanes, the number of inscribed hyperspheres for hyperplane combinations is JC(,+l). If the number of the hyperspheres satisfying eqs.(48)-(51) is N, the radius of the biggest inscribed hypersphere is given as\n(52) where, T I , ~ 2 , , rN represent the radiuses of the inscribed hyperspheres for hyperplane combinations.\nNrthermore, for the GFPR polyhedron, the biggest inscribed hyperspheres for Viv and V&.(q, r = 1, 2, ... ,m, q # r ) can be obtained. If the radiuses of these hyperspheres are given as rcmaxl, T c m a z , ***,rCmar&, the radius of the biggest inscribed hypersphere for GFPR is\n(53) The convex polyhedron containing the above hypersphere will be selected. If plural convex polyhedrons containing the biggest hypersphere with the same radius exist, it is need to compare their volumes further. 4.4 Volume of Convex Polyhedron\nThe volumes of convex polyhedrons can be obtained by the method expressed in [9].\nTo solve the volume for an nD convex polyhedron, at first, we must subdivide the nD convex polyhedron into simplexes, each of which can be given by its vertexes. For example, an nD simplex is given by the its vertexes as lull lu2, . , Then, its volume V, is\n= max (r1, rz, - * . , r ~ } ,\nrcma = max {TcmwIr r c m m 2 , ***,rcmaxfi}-\nkzi - IC = kza - Iijij If a nD convex polyhedron is subdivided into S sim-\nplexes, the volume of the polyhedron can be given as S - v = pa. (55)\nS=l\n5 Numerical Example We give a numerical example using the proposed ap-\nFor the object shown in Fig.7, the vertex positions proach to determine the Stable GFPR with 3 fingers. of the object with respect to CO are:\np7, 7.000 c o z = ~ . ~ ~ o ] , 2.000 y-q, 2.000 ro4=~.000~ 7.0 *\nThe direction vectors of the edges are:\nt l=[ - l :OOo] \u2019 tz=[O:OOO]\u2019 *=[ 0.704\u2019 t4=[ 0.00d *\nThe lengths of the edges are:\n0 000 1 000 -0.707 -1.000\nLi = 5.000, Lz = 11.000, Ls = 7.071, L4 = 6.000.\nThe coefficient of friction between the object and fin-\nrO.OOO 0.000 0.566 0.000 0.000 0.000 0.000 0.566 0.707 0.000 0.424 0.707 0.000 0.707 0.000 0.000 (56) 0.707 0.000 0.000 0.000 0.000 0.707 0.707 0.4241\n-\n-\ngers is set as 0.5, so that we have 0.894 0.894 -0.447 0.447\ne11=[0.447] \u2019 e1P\u2019[-0.447] \u2019 0.894] ezz=[0.894]1\nVertex 1\nVertex 3 Vertex 2\nFigure 8: Boundary hyperplanes and edge bounds of 3\nfinger grasp\n.............................."
        ]
    },
    {
        "image_filename": "designv11_28_0000034_robot.1992.220260-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000034_robot.1992.220260-Figure8-1.png",
        "caption": "Figure 8: (1.) Left type-4 curve, (r.) Left type-5 curve",
        "texts": [
            " If R is given, the other parameters and the resulting curve can be computed with well known methods. Two type-1 curves form one type-2 curve (figure 7). It is well suited to depart from small corridors, because p , = p2 . If RI and Rz are known, the two curves can be computed. Our type-3 curve is the dual one to the type-2 curve ( p , = p2) and is well suited to drive into small corridors. The type-4 curve is the result of shifting p , along the extension of the vector p 2 - p l and pe along the extension of vectorp2 - p 3 (figure 8 ) . The type-5 curve is used to change from forward drive to backward drive or vice visa (figure 8). For each different vehicle IC and each curve type j, a list of different radii Rk,j,i exists. Planning a curve for a special vehicle IC0 at corner SI E S, all curve types j (1 5 j 5 4) with their corresponding radii Rko,j,i are tested, whether the area swept by the driven rectangular-modeled vehicle lies within the channel (in-attribute). The first curve-radius combination fulfilling this constraint is taken as curve at the corner si. If no possible combination exists, the algorithm is stopped and the corresponding blocking subpath BS is returned to the right-orientation level"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002768_9780470116883.ch2-Figure2.12-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002768_9780470116883.ch2-Figure2.12-1.png",
        "caption": "Figure 2.12 Differential section of a two-wire transmission line.",
        "texts": [
            " If this is not the case the line acts as a loop antenna and TL models are not appropriate. Therefore, by using these models it is possible to compute only the transmission components of the current, and if the antenna mode current along the line is of interest the full field analysis is required. This section deals with the derivation of Telegrapher\u2019s equations for the two-wire transmission line for the analysis of the behavior of currents and voltages induced along the lines [4]. Differential cross-section of a two-wire transmission line is shown in Figure 2.12. A vertically polarized field is considered but the derivation is also valid for the case of horizontally polarized fields. The incident field illuminating the conductors induces a current and charge on the wires. The charge also causes the voltage between the conductors. Two identical wires are assumed to be perfectly conducting with radius a and insulated in free space. The separation of the conductors d is large compared with radius a\u00f0d a\u00de and is small compared with incident field wavelength \u00f0d l\u00de"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003847_ecce.2009.5316034-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003847_ecce.2009.5316034-Figure3-1.png",
        "caption": "Fig. 3. Power management system",
        "texts": [
            " A charge pump such as t can draw current that is much lower than the can supply and can charge the capacitor to However, a charge pump can not provide s can not boost the voltage of its input Therefore, a boost converter is needed to voltage of the charge pump to 3.3V and s voltage for the load. A charge pump can also draw energy from and accumulate the energy in the capacitor. B the charge pump can also release the accum burst power to the boost converter at certa therefore allow the boost converter to prov current to the load. The devised power management system Fig. 3. The power management system con pump (Seiko S-882Z), a 2.2F super capac converter (built with ST L6920DB chip). T draws low current from the MFC and ch capacitor. Once the super capacitor voltage r charge pump connects the super capacit converter. The boost converter then receives of the MFC and e load require a C and the load. st the voltage of ad. The power energy from the r to the load at gh current to the ould be able to and without any st converter to tage level of the ith using only a FC"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002641_tmag.2006.872518-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002641_tmag.2006.872518-Figure1-1.png",
        "caption": "Fig. 1. Thin elements: (a) single layer, (b) multiple layers.",
        "texts": [
            " Moreover, the leaf element is applied to the analysis of eddy currents in the surface layer of a laminated core in an actual magnetic bearing system, and the effect of the surface layer on the iron losses is investigated. In this section, the several treatments for the leaf element in the edge finite element method are described, and the effectiveness is examined. 1) Definition of Unknown Variables: Two kinds of definitions of unknown variables of the leaf edge element in the edge finite element method are explained by using the mesh shown Digital Object Identifier 10.1109/TMAG.2006.872518 in Fig. 1(a). In the ordinary edge finite element method, the unknown variable on the edge is defined as follows: (1) where and are the magnetic vector potential and the unit tangent vector parallel to the direction of the edge , respectively. When the ordinary method is applied to the thin element shown in Fig. 1(a), the matrices become ill-conditioned. This is because the matrix components related to become large and the condition number of the matrix increases. In the leaf element, the difference between the variables and is chosen as the unknown variable instead of [1]. Then, the following equation is considered: (2) where superscript * means the unknown variable. Equation (2) is introduced into the linear equations of the finite element method [1]. This method is called as \u201cMethod 1\u201d in this paper. On the other hand, the possibility of selecting the difference between the tangential components and of the 0018-9464/$20.00 \u00a9 2006 IEEE potentials as the unknown variable can be also considered. The relationship is expressed as follows: (3) In this case, the following equation modified by (1) is introduced into the linear equations: (4) where is the length of the edge . This method is called as \u201cMethod 2\u201d in this paper. 2) Treatment for Multiple Thin Layers: Two kinds of treatments for applying the leaf element to multiple thin layers are explained by using the mesh shown Fig. 1(b). When \u201cMethod 1\u201d is applied to the thin element and become unknown variables as shown in (2). Then, in the element , two possibilities of selecting and as the unknown variable instead of can be considered. In these cases, the following equations are considered, respectively: (5) (6) These methods are called as \u201cMethod A\u201d and \u201cMethod B,\u201d respectively, in this paper. In order to examine the effectiveness of the several leaf elements described in Section , the linear magnetostatic analysis of the simple model shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003069_978-3-540-88513-9_7-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003069_978-3-540-88513-9_7-Figure1-1.png",
        "caption": "Fig. 1. Two-link mobile manipulator with flexible links",
        "texts": [
            " In this formulation, for a specified payload value, 4m differential equations is given in order to determine the 4m state and costate variables. Control equations with this set of differential equations and the boundary conditions construct a standard form of TPBVP, which is solvable with available commands in different software such as MATLAB, C++ or FORTRAN. A two-link planar flexible manipulator is mounted on a differentially driven mobile base at point F on the main axis of the base as shown in Fig.1. A concentrated payload of mass mp is connected to the second link. All required parameters of the robot manipulator are given in Table 1. 1.25m) to the final point with coordinate ( ex = 2.076m, ey = 2.362m) during the overall time ft = 2 s such that optimal trajectory between these two points at a speci- fied time is desired. It should be noted that final load position is not feasible without the base motion. Simultaneously, the mobile base is initially at point ( 0x = 1m, 0y = 1m, 0\u03b8 (1)=0) and moves to final position ( fx = 2m, fy = 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000855_jra.1986.1087062-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000855_jra.1986.1087062-Figure1-1.png",
        "caption": "Fig. 1 . Moving coordinate frames.",
        "texts": [
            " The vectorial equations are equivalent to those obtained by Luh, Walker, and Paul [5] and Lee [6]. The computational requirements are virtually the same as for the equations of Lee. VELOCITIES AND ACCELERATIONS RELATIVE TO MOVING COORDINATE FRAMES Let the position of point P relative to the base frame be denoted by p and the position of the same point relative to the ith moving frame be denoted by pi. The position of the origin Oi of the moving frame relative to the base frame is denoted by rj as shown in Fig. 1. The position vectors are related by p = r i + p i . (1) The velocity of the point P is given by Up=fi+bj 0 =u j+pj / ;+wixpi where p i denotes the rate of change of the vector pi relative to (2) Manuscript received October 10, 1986; revised May 22, 1986. The authors are with the Department of Electrical Engineering, University IEEE Log Number 8610324. of Houston-University Park, Houston, TX 77004, USA. the base frame, i i / i denotes the rate of change of the vector p i relative to the ith moving frame, and ai is the angular velocity of the moving frame relative to the base frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002193_0471758078.ch2-Figure2.28-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002193_0471758078.ch2-Figure2.28-1.png",
        "caption": "FIGURE 2.28. Comparison of high-scan-rate ultramicroelectrode cyclic voltammetry (~), redoc catalysis ( ), and laser flash photolysis ( ) for the determination of the rate constant of deprotonation of methylacridan cation radical by bases of increasing pKa. Adapted from",
        "texts": [
            "20 The laser flash experiments consist in generating the cation radical by direct irradiation of methylacridan in the presence of a oxidative quencher such as CCl4, which undergoes a reduction cleavage where electron transfer and chloride ion expulsion are concerted (see Section 2.3.4). The resulting cation radical is then deprotonated in a series of buffered media of increasing basicity so as to obtain a Bro\u0308nsted plot relating the rate constant to the pKa value of the opposing base. The results, displayed in Figure 2.28, show a good agreement between the three methods within their range of applicability, noting that nanosecond laser flash photolysis and redox catalysis have similar capabilities, with a slight advantage to the former method. One limitation of the redox catalysis method derives from the fact that when the follow-up is so fast as to thwart back electron transfer, the forward electron transfer becomes the rate-determining step, therefore preventing the derivation of kinetic information on the follow-up reaction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003007_6.2006-6147-Figure13-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003007_6.2006-6147-Figure13-1.png",
        "caption": "Figure 13. Helicopter body-axis coordinate system.",
        "texts": [
            " Once the accelerations were corrected to the center-of-gravity location from the sensor location, the accelerations demonstrated good kinematic consistency as seen in Figure 11. The velocities are also kinematically consistent as shown in Figure 12. IV. Quasi-Steady Model Formulation The helicopter is modeled as a rigid body, assuming symmetry about the X-Z plane, with the incorporation of equivalent time delays to represent unmodeled rotor dynamics. The linear and angular accelerations are referenced to the helicopter body-axis coordinate system as shown in Figure 13. American Institute of Aeronautics and Astronautics 10 The frequency responses for the longitudinal/heave dynamics are identified from the kinematically consistent frequency sweep data using CIFER as described in Sec. II. The body-axis velocity-derivative signals and are useful for state-space model identification and were reconstructed using the kinematic relationships shown in Eq. \u00ae u& w& (3) and Eq. (4). 00 rvqwgau x +\u2212\u2212= \u03b8& (3) 00 qupvaw z +\u2212=& (4) These reconstructed velocity derivatives were used in the identification rather than the velocity signals generated from the Embedded GPS/INS, which exhibited poor coherence"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000102_robot.1993.292243-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000102_robot.1993.292243-Figure8-1.png",
        "caption": "Figure 8 Path OPQRSXYZZ shows the motion of the disk rolling on the s-y plane for the singularity avoidance scheme with a repeatable motion in the z coordinate.",
        "texts": [
            " Since O S = 22.5 degrees # n x / 2 for n = 0,1 ,2 , . . ., we are free to converge either x or y initially. We choose to converge x first. In b.( 12), we substitute xf = -0.4 meters, Xd = 0.1522 meters, and a f = 22.5 degrees. Choosing b = 60 d e grees or 1.047 radians, we obtain a = 3.628 radians or 207.87 degrees. For these values of CL and b, the closed path is given by PQRSP in Fig.7. After moving along this path, the y variable drifts from yd = 0.7654 meters to y& = 1.485 meters, as shown in Fig.8, whereas the x coordinate converges to its desired value. Now the task is to generate a closed path in the 8-a plane that will cause a repeatable motion in x but will converge y to yf = 1.0 meter. Using Eq.(17) we arrive a t b = 135 degrees or 2.356 radians and a = -1.05 radians or -60.15 degrees. For these particular values of a and b, the closed trajectory is given by P X Y Z P in Fig.7. Due to the negative value of a, the direction of this closed path is opposite to our usual convention. The entire motion of the system can be obtained by eliminating the redundant path segment SPS"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000537_s1350-4533(02)00183-2-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000537_s1350-4533(02)00183-2-Figure4-1.png",
        "caption": "Fig. 4. Overview of the dataset frames. On the left, medical imaging of the bone segments and aluminium balls within the CT frame. On the right, joint kinematic data collection described in the GONIO frame. The aluminium balls and GONIO origin are located within the JIG frame. The aluminium balls mounted on the bone segments allowed bone data registration.",
        "texts": [
            " The successive Si matrices described the full motion of the joint of interest and were directly used for motion simulation once data registration was performed as: Bi SGONIO i R B (2) where B is the mobile bone segment before transformation, R is the registration transformation (determined later), SGONIO i is the spatial transformation obtained from goniometry, and Bi is the mobile bone segment after transformation step i. The above motion transformation occurred independently from the axis representation. Any algorithm used to obtain a particular data representation will process the SGONIO i matrices whatever the convention (e.g., helical axis or anatomical axes) adopted by the system developers. In summary, SGONIO i matrices are common to any kind of kinematics data convention. At this stage all the data have been collected (Fig. 4). Prior to motion simulation, data registration must take place to orientate the 3D models obtained from medical imaging (CT frame) in the same frame as the kinematics data (GONIO frame). Both CT and GONIO data were transformed to the JIG frame. Registration matrices were found by applying SVD procedures [15] on the coordinates of the aluminium balls linked to the bone segments in both CT and JIG frames. Once determined these matr- ices were applied to each vertex of the 3D bone models Bj. Registration RCT\u2192JIG j of the proximal joint segment j is first performed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003678_1.36696-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003678_1.36696-Figure1-1.png",
        "caption": "Fig. 1 Helicopter system on a stand as modeled in [45\u201347].",
        "texts": [
            " Theorem 10 (discrete-time synergetic optimal integral tracking): If the following conditions are satisfied, then the system (75) driven by the control strategy (77) asymptotically tracks a constant reference signal rk: 1) The matrix S in Eq. (76) is constructed so that det S2Bu \u2260 0. 2) The system (75) restricted to themanifold f ~xk: 0g is asymp- totically stable. 3) The pair A11;A12 is controllable. Weconsider the problem of tracking control design for a nonlinear helicopter model using the proposed discrete-time synergetic control law. We employ the continuous-time nonlinear helicopter model developed by Pallet et al. [45\u201347]. In Fig. 1, we present the configuration of this helicopter control model. A. Nonlinear Dynamics The vertical dynamics of the helicopter systemmounted on a stand are governed by the following set of differential equations: h !2 a1 a2 c a3 a4 c p a5 _h a6 _h2 a7 (89) _! a8! a10!2 sin c a9!2 a11 u1 (90) D ow nl oa de d by U N IV E R SI T Y O F G L A SG O W o n Se pt em be r 9, 2 01 3 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .3 66 96 _ c a13 c a14!2 sin c a15 _ c a12 u2 (91) where h denotes the helicopter altitude in meters,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003740_1.2975154-Figure12-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003740_1.2975154-Figure12-1.png",
        "caption": "FIG. 12. a Parameters and surfaces S1, S2, S3, S4, S5, and S6 of a left handed helicoidal sector; b infinitesimal plane surfaces dS3 and dS4 of the helicoidal magnet.",
        "texts": [
            " In the previous sections it has been shown that in cylindrical helicoidal magnets with helicoidal magnetization, the volume charge density M is equal to zero in each point of the magnet. In this section surface charge density M expressions for the same kinds of magnets are given. The surfaces to consider are six, and for each one we have to find the corresponding M expression. These surfaces are those that surround the left handed helicoidal sector with rectangular section illustrated in Fig. 2 a . In Fig. 12 a these surfaces have been denoted by S1, S2, S3, S4, S5, and S6. The surface S1, S2, S5, and S6 are coaxial and helicoidal. S3 and S4 are rectangular. Let us obtain the M1 expression for the surface S1. The inner and outer radii of S1 are ri and re, respectively. For each radius ri r re we can define the cylindrical helix illustrated in Fig. 2 b . Consequently S1 can be thought of as a set constituted by an infinite number of curves all adjoining and coaxial. As soon as a point P of is fixed see Fig. 12 a , we can apply one more time all the considerations illustrated in Sec. III for computing the components nx, ny, and nz of the unit vector n in P. However, in the present case of M evaluation we observe that n must always be going out from the surface where M is computed. If we consider again the magnetization M oriented along n and its magnitude M = M =constant, from Eq. 8 we obtain the surface charge density M1 in each point of S1, M1 = M . 85 In the same manner we compute M2 on the surface S2, M2 = \u2212 M ",
            " In fact, in these regions the B gradient is very high, therefore we must consider a high number of points to obtain a good interpolation of the field. This work was supported by Elcon Elettronica S.r.l., Area Science Park, Padriciano, Trieste, Italy, Research contract approved from Department of Mechanical Engineering Council Grant No. 21-05-2005. M With reference to Eqs. 97 \u2013 100 let us achieve the expression of dSi i=1,2 , . . . ,4 . In Fig. 23 an infinitesimal surface dS1 is illustrated. dS1 is a helicoidal neighborhood of the point P belonging to the curve see Fig. 12 a . Neglecting the high-order infinitesimals, the length dl is dl = dl cos , A1 where is the helix angle of . Neglecting again the highorder infinitesimals, we obtain dS1 = drdl , A2 and because dl =rd , substituting Eq. A1 in Eq. A2 , dS1 is given by dS1 = rd dr cos . A3 Furthermore, with cos = 1 1 + tg2 A4 and tg = p 2 r , A5 where p is the step of the cylindrical helix , it follows that cos = 1 1 + p2 4 2r2 . A6 Using Eq. A6 , Eq. A3 becomes dS1 = r2 + p2 4 2drd . A7 We observe that the step p of is also equal to the step of the whole helicoidal surface S1. Then p does not depend on r. Moreover, observing Fig. 12 a we note that the surface S2 has the same shape and dimension of S1. It follows that dS2 = dS1. A8 From Fig. 12 a one infers that dS3 is given by dS3 = bdr , A9 where b is the axial width of the helicoidal magnet. Similarly we have dS4 = bdr . A10 Now let us find the components Bxi, Byi, and Bzi of the magnetic flux Bi P for i=1,2 , . . . ,4. In general, with reference to Figs. 1 b and 12 a , these components may be written as Bix px ,py ,pz = 0 4 Si Mi pix,piy,piz px \u2212 pix px \u2212 pix 2 + py \u2212 piy 2 + pz \u2212 piz 2 3/2dSi, A11 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation",
            " Analogously, for i=2 it results to p2x = \u2212 d \u2212 b \u2212 p 2 , A17 p2y = \u2212 r cos \u2212 , A18 p2z = r sin \u2212 . A19 In Eq. A17 b has a positive sign and represents the axial distance between the two helicoidal surfaces S1 and S2. Finally, the coordinates p3x, p3y, p3z and p4x, p4y, p4z, identifying the position of the surfaces dS3 and dS4, respectively, are p3x = \u2212 d \u2212 b 2 , A20 p3y = \u2212 r cos , A21 p3z = r sin , A22 p4x = \u2212 d \u2212 b 2 \u2212 p 2 , A23 p4y = \u2212 r cos \u2212 , A24 p4z = r sin \u2212 . A25 In Eqs. A20 \u2013 A25 is a positive quantity and defines the angular extension of the helicoidal sector see Fig. 12 b . Successively, substituting Eqs. 85 , 86 , 89 , 91 , A7 \u2013 A10 , and A14 \u2013 A25 in Eqs. A11 \u2013 A13 for i =1,2 , . . . ,4 the components Bxi, Byi, and Bzi of Bi P can be expressed as B1x = 0M 4 ri re 0 px + d + p 2 r2 + p2 4 2 px + d + p 2 2 + py + r cos \u2212 2 + pz \u2212 r sin \u2212 2 3/2 drd , A26 B1y = 0M 4 ri re 0 py + r cos \u2212 r2 + p2 4 2 px + d + p 2 2 + py + r cos \u2212 2 + pz \u2212 r sin \u2212 2 3/2 drd , A27 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003307_1377999.1378055-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003307_1377999.1378055-Figure2-1.png",
        "caption": "Figure 2. Key mapping with Steering wheel with pedals and Joystick",
        "texts": [
            " Wiimote consists of 12 buttons, a 3D acceleration sensor, a Bluetooth communication module, a vibration motor for force feedback, a speaker, two sources of IR light, and 4 blue LEDs. The key mapping that used the Wiimote\u2019s cross-type button interface, the key #1 was used for moving forward the robot, and the key #2 for moving backward, the key # 3 for rotating the robot towards left (counterclockwise), and the key #4 for rotating the robot towards right (clockwise). The key #5 serves to make a command to end the program and log the elapsed time (Figure 2-(a)). All the buttons can be used repeatedly for key checking. The keying of the buttons was ignored by the program if it was made within 500 milliseconds from the previous keying. Acceleration Sensors. The second key mapping that uses the Wiimote does not involve any of the buttons on the Wiimote, but it instead uses only the 3D acceleration sensor (Figure 1-(b)). It detects the tilting of the Wiimote device to activate the corresponding movement to control the robot. The key on the back of the device was also used to terminate the test program as above",
            " The key mapping used in the Wiimote\u2019s 3D acceleration sensor\u2019s X-axis and Y-axis movement is as follows: X-axis corresponds to tilt of acceleration sensor, and Y-axis is the same with pan of acceleration sensor. Tilting down of acceleration sensor (direction number 1) moves the robot forward, and tilting up (direction number 2) backed the robot. Panning left (direction number 4) rotated the robot towards left, and panning right (direction number 3) rotated the robot towards right. The key number 5 completed the task. The acceleration sensor\u2019s X-axis and Y-axis\u2019s output range was fixed -30 to +30 digital values (Figure 2-(b)). Steering wheel with race pedals. We used Logitech\u2019s MONO Racing Force Feedback Wheel, an 11-inch wheel with six programmable buttons, acceleration and brake pedals, two shifting option buttons, and the force feedback function (Figure 2-(a)) for the steering wheel type interface. This is the only interface that uses foot pedals for certain functions in our study. The key mapping used for the steering wheel with pedals is as follows: the pedal #1 was mapped for moving the robot in the forward direction, while the pedal #2 moved the robot backward. Turning the wheel counterclockwise controlled the robot for turning towards left, while turning the wheel clockwise rotated the robot towards the right (Figure 3-(a)). Button #5 signaled the end of task. Joystick. The last interface is a joystick with conveniently placed action buttons. We used Logitech\u2019s Extreme 3D Pro that supports an eight-way rubberized hat, a twist handle, and a rapid-fire trigger function (Figure 2-(b)). The key mapping for the joystick was pretty straightforward. The robot moved forward when the subject pushed the joystick forward. The robot moved backward when the subject pulled the joystick the other way. Moving the joystick to left rotated the robot towards left, and moving the joystick to right rotated the robot towards right. Button #5 also signals the end of task (Figure 3-(b)). 9th Intl. Conf. on Human Computer Interaction with Mobile Devices and Services (MobileHCI\u201907) 463 The system configuration for measuring user performance with 4 types of input interfaces is shown in Figure 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003296_0022-2569(71)90011-5-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003296_0022-2569(71)90011-5-Figure1-1.png",
        "caption": "Figure 1. The RCRCR five-link spatial mechanism.",
        "texts": [
            " Dual Angles and Line Coordinates The scalar product of two unit line vectors is equal to the cosine of the dual angle between the lines.* Therefore , for two unit line vectors L and M, [(L~,L._, .La)+e(L4, L:, ,L6)]\" [ ( M , . M . , . M a ) + e ( M 4 , M~ M~)] = cos 0 - e z s i n 0, (10) where 0 is the angle, and z is the common perpendicular distance between the lines. Hence . in terms of line coordinates. LtS'l~ + L,,M.. + LaMa = cos O, L~M4 + L._,M~ + LaMs + L4M~ + L~M.2 + L~5la = -- z sin 0. (1t) (12) Line Coordinates of Axes of Mechanism Pairs The R C R C R five-link spatial mechanism is schematically shown in Fig. 1. Link 5 is fixed. Links 1 and 4 are the input and output links respectively. S,, Se, Sa, $4. Sa are the axes of the five mechanism pairs whose line coordinates are St = ( S , ~ . Sj._,. S j a . Sj4, Sa.~. Si~),j = 1 to 5. * S e e B r a n d [ l ] , pp. 6 8 - 7 0 . with reference to an arbitrary Cartesian frame. The parameters of the mechanism are: zl = common perpendicular distance between a~ and at.o, measured from as~ to at..,, and positive in the direction of St; 0t = angle between a~ and at.,; at",
            " (18) where i c~ si 0 0 - - SiCij CiCij Sij 0 Z;i = SiSi j - - c i s i j c i j 0 - - ZiSi ZiCi 0 C i [ ( a i j s i s i j - - Z ic i c i j ) ( - - a i f l . ' i s i j - - ZiSiCo) ( loc 0 - - SiCij [_ (ausicu + Zicisu) (-- aucicu+ zisiso) -- ausij 0 0 0 0 0 0 si 0 CiCo Si t S iS i j - - CiSi j Cij Note that Tu is the inverse of Tji. i.e.. TuTji = I, the identity matrix. (19) I n p u t - O u t p u t D i s p l a c e m e n t E q u a t i o n The input-output displacement equation of the mechanism is obtained in the following manner: Referring to Fig. 1, with reference to the Cartesian frame xt - y t - - Zt attached to the fixed link, the line coordinates of So are expressed as functions of 01. and those of $4 as functions of 0s. Next, with reference to the Cartesian frame xa-y: t -z:~ attached to Link 2. the line coordinates of S.., and $4 are expressed as functions of 0a. Since the scalar product of two line vectors is an invariant with respect to the transformation of coordinate axes, the scalar product of S., and $4 with reference to Xl - Y t - - q is equated to that of S, and $4 with reference to x3-ya--z:~"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002080_tfuzz.2004.834819-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002080_tfuzz.2004.834819-Figure3-1.png",
        "caption": "Fig. 3. Experimental setup. (a) Photograph. (b) Block diagram.",
        "texts": [
            " Indeed, the proposed control partially rejects the approximation errors. If the rejection of the output disturbance is not considered, the system performance is poor. The proposed fuzzy switching control reinforces the system performance without sacrificing of the performance of the control input [cf. Fig.2(b) and (e)]. In addition, a suitable selection of the weighting function [e.g., ] for the fuzzy switching control attenuates the high frequency response [13]. Consider a two-joint robot on the horizontal plane (see Fig. 3). The first and second links are individually driven by a permanent magnet (PM) AC motor. The length and mass of the first and second links are 0.25 m, 1.0 kg and 0.36 m, 0.5 kg, respectively. The specifications of the two PMAC motors are described as follows: 1) First motor: a) motor model: P50B05020DXS2B of Sanyo Denki Co.; 200 W, rated rotating speed 50 rps, rated torque 0.637 Nm, rated armature current 1.6 A, torque constant 0.436 Nm/A, electric time constant 2.9 ms, mechanical time constant 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000160_156855389x00073-Figure16-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000160_156855389x00073-Figure16-1.png",
        "caption": "Figure 16. Example of a manipulator and its working environment (2).",
        "texts": [
            " This was the number of cells for the free space and did not include obstacle cells expanded during the free space enumeration. The execution time was about 10 min. In this example, the difference between the number of expanded wavefronts from the initial configuration and that from the final configuration was not very high because the obstacles were scattered and there was no effect of process (2) in Fig. 3. Without process (1) in Fig. 3, 4052 cells of the free space were expanded and the execution time was about 42 min. The problem shown in Fig. 16 was to transfer a block on the table into the box on the left-hand side of the screen and to return it to the initial position. In this example, the manipulator carried a relatively large work-piece compared with its hand, and consequently the situation of the configuration space on the way to the box and that on the way back differed greatly. Figure 17 shows the sequence of the planned motion until the block was inserted into the box. In this example, 7536 cells were expanded from the initial configuration and 278 cells from the final one without process (2) in Figure 14"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002010_0094-114x(79)90028-4-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002010_0094-114x(79)90028-4-Figure2-1.png",
        "caption": "Figure 2. Free body diagrams for chain rollers 2 and 3.",
        "texts": [
            " The final results include an analytical technique which can be applied to determine the distribution of sprocket tooth load and a distribution of chain link tension. As an example, tooth load and link tension distributions for a 31 tooth, double pitch sprocket with 180 \u00b0 chain wrap are given. The analysis presented is for a chain and a double pitch sprocket of thetype shown in Fig. 1 although the analysis is easily modified for use with single pitch sprockets and chains. The load in the chain is a maximum in the tight side and zero in the slack side. Figure 2 shows a free body diagram of enlarged chain rollers numbered 2 and 3. From Fig. 2 it can be deduced that PicosO=Si-~-Sicos7 2<-i<_m (1) where P~ is the force that the ith sprocket tooth exerts on the ith roller; S~ is the force that the ith link exerts on the ith roller; Si-l is the force that the (i -: 1)th link exerts on the ith roller; 0 is the pressure angle; y(=a) is the articulation angle; m is the number of sprocket teeth in contact. tDepartment of Mechanical Engineering, University of Houston, Houston, TX 77004, U.S.A. 135 136 ), / / / / / I zt i pitch fixed sprocket"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000980_jjap.28.l1480-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000980_jjap.28.l1480-Figure2-1.png",
        "caption": "Figure 2. The proposed dual-stage amplification mechanism.",
        "texts": [
            " Lg and Kamp are functions of the flexure hinge position and the length of the lever arm. For high resolution and large measurement range, an amplification mechanism must be designed with maximum W1. To maximize W1, an accurate static analysis should be performed. The conventional microbalance generally uses a singlestage amplification structure, but there is a limit to the increase in amplification ratio because of a geometrical problem. We propose a dual-stage amplifier to enhance the lever gain and the mechanical sensitivity as shown in figure 2. Two levers and three flexure hinges are used and the lever gain is given as Lg = R2 R1 R4 R3 . (3) Lagrange\u2019s method is used to analyse a system in which a rigid beam is connected by a flexure hinge. Since the beam is much thicker than the flexure hinge, it can be assumed to be rigid. The displacement of 6-axes can be obtained by Lagrange\u2019s method [9]. From figure 2, the mass matrix and the stiffness matrix of the amplification mechanism can be obtained and the motion equation is expressed as[ M1 0 0 M2 ] ( q\u03081 q\u03082 ) + [ K11 K12 K21 K22 ] ( q1 q2 ) = ( f 1 f 2 ) (4) wheref 1 andf 2 represent the input force and output force with six components, respectively, and the element of the stiffness matrix in equation (4) is given as K11 = T 1T 1 R1k1 hR 1T T 1 1 + T 1T 2 R2k2 hR 2T T 1 2 K12 = KT 21 = \u2212T 1T 2 R2k2 hR 2T T 2 2 K22 = T 2T 2 R2k2 hR 2T T 2 2 + T 2T 3 R3k3 hR 3T T 2 3 (5) where a constant matrix T i p contains the information on the local coordinates of p, Rk is the rotation matrix and kkh is the stiffness matrix of the kth flexure hinge connected to the rigid body",
            " (6) When f 1 = 1 N and f 2 = 0 N, q2 becomes the compliance of the displacement amplification mechanism (Camp = K\u22121 amp). When a band spring is used, the compliance of the flexure hinge is given by ch =   x Fx 0 0 0 0 0 0 y Fy 0 0 0 y Mz 0 0 z Fz 0 z My 0 0 0 0 \u03b1 Mx 0 0 0 0 \u03b2 Fz 0 \u03b2 My 0 0 \u03b3 Fy 0 0 0 \u03b3 Mz   =   L EA 0 0 0 0 0 0 L3 3EIz 0 0 0 L2 2EIz 0 0 L3 3EIy 0 L2 2EIy 0 0 0 0 L k1Ghb3 0 0 0 0 L2 2EIy 0 L EIy 0 0 L2 2EIz 0 0 0 L EIz   (7) where L is the length of the flexure hinge, E is the elastic modulus, I is the moment of inertia andG is the shear modulus. From figure 2, the length of the lever arm (Ri) and the position of the lever (ai) can be chosen as variables. R1 is not independent of W1. As R2 and R4 increase and R3 decreases, W1 increases. These results show that a larger lever gain induces a larger W1. Furthermore, the distances between the flexure hinges are important. This tendency is shown in figure 3. When the distance between the first and second flexure hinges (a2 \u2212a1) is the same as the length of the flexure hinge (L) and when the distance between the second and the third flexure hinges (a3 + a4) is zero, the maximum W1 can be obtained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000581_amc.1996.509331-Figure12-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000581_amc.1996.509331-Figure12-1.png",
        "caption": "Fig. 12: Experimental robot",
        "texts": [
            " three kind of test trajectory references are selected. The first trajectory ( W 1 line) is a straight line as shown in Fig. 4. The initial position in the joint space is (30\". 30\", 30\") that means end-effector position (0.76,0.50)(m), and the final position is selected as (0.1Ol0.90)(m). The second (# 2 line) is also a straight line but it includes the return path back to initial point, as shown in The trajectory references generated by the proposed method are tested on a three-link manipulator as shown in Fig. 12. Each joint of the manipulator is driven by a DC servo motor with a 1/100 reduction gear. The characteristics of each motor and each arm are shown in table I. The manipulator is controlled by the CP(Continuous Path) control strategy, based on a combination of disturbance observer and sliding mode control [91. One DSP(NEC - pP077230) accomplishes all computation from reference data acquisition to voltage control of each motor. The sampling time for CP and servo control is 200psec. The measurement of the consumed energy from the robot system is realized by measuring the terminal voltage and the current that flow from the DC power source to the robot system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001626_0094-114x(81)90040-9-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001626_0094-114x(81)90040-9-Figure6-1.png",
        "caption": "Figure 6.",
        "texts": [
            " By varying the proper two parameters of the reach maximization procedure, this location will serve as the starting point for the surface generation. The first parameter is the previously fixed 0~. From its arbitrary angle, it is now varied a full 360 degrees. This will produce a circle of absolute maximum reach about the S, axis. The second parameter is the choice of a base point other than the intersection of S~ and a~2. An alternate base point suggests a manipulator that geometrically differs only in $1, al2, al2 and $22. This member is drawn in dashed lines in Fig. 6. The original manipulator is made to coincide with the other members of the new arm. The maximization procedure is then applied to this alternate arm, giving a different hand location. Simply, this configuration gives the longest attainable reach of the original arm with respect to the $2 axis and the new base point in this direction. With the varying of the first parameter, this hand location will generate its own circle about the S~ axis. Thus, the entire surface will be made up of circles of various radii about this axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000844_kem.245-246.351-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000844_kem.245-246.351-Figure4-1.png",
        "caption": "Fig. 4 Grinding operation scheme.",
        "texts": [
            " This covers crack nucleation, that was originated by the thermal process, to crack propagation of the small fatigue cracks, that may be attributed to some different causes, such as the influence of oil pressure inside the cracks, influence of crack face friction on the jagging phase, and mechanical fatigue. Crack nucleation. It was discussed and concluded in [5] that nucleation of cracks on crankshaft journals could not be attributed to any other source apart from the grinding process. A brief explanation of how thermal fatigue could originate such cracks is provided below. The grinding process is basically explained in fig. 4. The journal rotates with a low rotation speed, \u03c9j, and the grinding wheel rotates with a high rotation speed, \u03c9w,. Some features can occur during the grinding process that may cause some small cracks, as those observed in this work. These features are: Excessive depth of cut; If during the first revolutions there is an excessive depth of cut the material may \u2018burn\u2019. There are cases where the surface of the material even changes in color, becoming blue [6]. It\u2019s common that, when the grinding process is finished, the journals seem normal because on the last revolutions, the operator works with a normal depth of cut, and the blue color (burnt surface) disappears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000570_095440802760075021-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000570_095440802760075021-Figure8-1.png",
        "caption": "Fig. 8 Archimedean Helicon gear pair: 1, Helicon pinion; 2, Helicon gear; number of threads of the pinion z1 \u02c6 1; number of teeth of the gear z2 \u02c6 56; centre distance (offset) aw \u02c6 105 mm",
        "texts": [
            " The output information is written in Table 1 containing the geometric, constructional and technological parameters that are necessary to make a design drawing needed for producing the hob and the gear pair. A global scheme of the CAD system is shown in Fig. 7. Considering the technologicalpoint of view, software for the initial synthesis of a Helicon gear is also developed. Most of all, the calculation takes into account the capabilities of the hobbing machines available in Bulgaria and used for Helicon gear cutting. The software is written in Turbo C and runs under MS-DOS for the PC. The input is introduced in the dialogue regime. Figure 8 shows an Archimedian Helicon gear pair, which is designed by using the described computer program. A gear box with this gear pair has withstood a durability test. A basis of the modelling of skew axes gears of Spiroid and Helicon types, by using the mesh region, is the design of the kinematic model of action surfaces. The optimization process consists in determining the optimal borders of the mesh region. Proc Instn Mech Engrs Vol 216 Part E: J Process Mechanical Engineering E0101 # IMechE 2002 at MICHIGAN STATE UNIV LIBRARIES on June 14, 2015pie"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003236_proc-1038-o05-09-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003236_proc-1038-o05-09-Figure5-1.png",
        "caption": "Figure 5: Comparison of the state of each system prior to nucleation and growth. All system parameters are held constant except for the crucible design. Temperature contours are plotted with a spacing of 2 K on the left of each image, and streamfunction contours are spaced at 7 cm2/s on the right.",
        "texts": [
            " In this system, the new support clearly increases the axial flow of heat out of the ampoule tip and produces much lower temperatures and increased axial temperature gradients. (Note that a steeper axial temperature profile appears flatter in the plots shown here, with temperature on the abscissa and position on the ordinate.) This is a generally desirable outcome which will be discussed further in the conclusions section. A more significant effect in the crystal growth system is achieved by changing the ampoule design (as indicated by the right pane of Figure 3). Figure 5 depicts both systems, with temperature contours shown on the left-side and streamfunction contours for flow within the melt shown on the right. The velocity of the melt is everywhere tangent to the streamfunction contours (also known as streamlines), and the volumetric flow is proportional to the differences between the streamfunction values. For equally spaced streamfunction contours, as are shown here, the flow is stronger where the streamlines are more closely spaced. All other features of the system are unchanged for these two computations, and we consider the design of the new support system indicated by the left pane of Figure 3",
            " However, in the tip region and through most of the bulk of the melt, the flow is relatively weak. This flow is strong enough for convective effects to flatten the temperature contours in the radial direction. Near the top of the melt, temperature-dependent surface tension drives relatively intense, Marangoni flows; however, this flow cell is placed far enough away from the cone region to be unimportant for the initial stages of growth. The situation is markedly changed for the system with the PBN ampoule, shown on the right of Figure 5. First, there is a significant increase in the thermal gradient though the cone region of the ampoule, while much of the remaining melt is nearly isothermal. The difference in the centerline temperatures is shown in Figure 6 for the two cases. (Again, a flatter curve on this plot corresponds to a steeper axial gradient.) Observing the temperature contours, one also sees the influence of the strong melt flow, which causes a boundary layer to form near the ampoule walls and deflects the isothermal temperature contours there"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001838_1.1809403-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001838_1.1809403-Figure1-1.png",
        "caption": "Fig. 1. Plot of the Lambert W function.",
        "texts": [
            " Since the Lambert W function, which may arise in a wide scope of practical problems in mathematics and mathematical physics, received little attention in Russia, it is expedient to illustrate how to use it in practice. This is the subject of the present paper, in which specific examples will be given of mathematical problems in theoretical plasma physics that can be solved completely and in explicit form only with the help of the Lambert function. The function is defined by (1) The fact that the Lambert W function is inverse to the function F = xexpx makes it possible to easily plot it (see Fig. 1) and to determine its simplest properties. The Lambert W function is neither even nor odd. It is defined on the interval [\u20131/e, \u221e), takes on values from \u2013\u221e to \u221e, and is two-valued for negative x. Point A with the coordinates (\u20131/e, \u20131) separates two branches of the function\u2014the upper branch W0(x) and the lower branch W\u20131(x). Both branches have a common vertical tangent at point A. The upper branch W0(x), which is often called the main branch, passes through the coordinate origin and behaves everywhere in a regular manner",
            " The critical value \u03c3 = \u03c3# is a root of the equation (37) 1 2 -- d\u03d5 dx ------    2 V \u03d5( )+ E= V \u03d5( ) \u03d5exp \u03c3 v 0 2 2\u03d5\u2013+( ),\u2013= dV \u03d5( ) d\u03d5 --------------- \u03d5exp\u2013 \u03c3 v 0 2 2\u03d5\u2013 ----------------------+ 0.= = \u03c32 v 0 2 \u2013( )exp max 2\u03b3 2\u03b3( )exp\u2013( )< 1 e -- 0.37,\u2248= v 0 2 v 0 2 \u03d51 2, 1 2 -- v 0 2 W 1\u2013 0, \u03c32 v 0 2 \u2013( )exp\u2013( )+[ ],= W 1\u2013 \u03c3# 2 \u2013( ) W0 \u03c3# 2 \u2013( ).= PLASMA PHYSICS REPORTS Vol. 30 No. 10 2004 This root is easy to determine: it corresponds to the conjugation point A of the real branches of the Lambert W function in Fig. 1, \u03c3# = e\u20131/2 \u2248 0.60653. To find the locus of the conjugation points, note that each of them corresponds to the conjugation point of the real branches of the Lambert W function (point \u00c4 in Fig. 1). Consequently, we must insert \u03c32 = exp( \u2013 1) into each of solutions (36). As a result, we obtain (38) In Fig. 3, the locus \u03d5S is shown by the heavy curve. To conclude, it is pertinent to recall the arguments given in [6]: \u201c\u2026 a newly introduced mathematical function should satisfy certain requirements \u2026. Thus, the function should possess the following features. The first is its applicability to various fields of mathematics, i.e., to different mathematical problems \u2026. The second is its convenience in performing numerical computations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001274_robot.1986.1087415-Figure4-1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001274_robot.1986.1087415-Figure4-1-1.png",
        "caption": "Fig. 4-1 Circle Fig. 4-2 Rectangle",
        "texts": [
            "'s . Now the following proposition is giben; [Proposition] The system is reconstructable if and only if N dim el R{Bi)= 0 The proof is omitted here because it is as similar as the one given in section 3 of [81. If the system is reconstructable then dx is obtained by N N dx= (El Bi')-liclBiLAidvi. (4-3) If not s o , only the elements of dx contained in subspace N N R { & B ~ ~ I or R 3 0 / i = l ~ ~ ~ i ~ are recovered by N N dx= (zl Bi*)'Z1BiLAidvi. (4-4) [Example 4-11 of r and fingers shown in Fig. 4-1. a) If d a i is available, then we have Let's consider a circle with a radius B ~ = ( 0. 0. l/rlt , i=1,2. .. , N therefore N 1=1 R{BiI= R{( 0. 0, llt1. Hence we can reconstruct dxo and dye, but cannot recover ds . b) If d a i is not gvailable, then B .= -L*S (pi) 1 j L*r;Ii) , where L=R+r. Therefore we have R{BiI= R{ Nov assume that N=2. If p1=0 [degl and ~~'180 [degl, then N 1 = 1 ? R{BiI= R{ f i 0 0 I . I: :I This shows that we cannot recover not only ds but also dy . On the other hand, if plgO [des] andopZ= 90 [degl, then we can reconstruct dyagain without tactile sensors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000919_1.1415057-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000919_1.1415057-Figure2-1.png",
        "caption": "FIG. 2. Parameters of describing equilibrium configuration of the contact induced by the liquid bridging.",
        "texts": [
            " The aim of the present study is to obtain an exact mathematical solution for this coupled microscale contact problem. Let us consider a two-dimensional plane strain problem in which a rigid cylinder is in contact with the surface of an elastic half space without external load. A small liquid drop is introduced between the surfaces of the cylinder and the half space. The liquid wets with the two solid surfaces and forms the liquid bridging between the solid surfaces. Attractive force between the two solid surfaces induced by the liquid-bridging force produces a finite contact radius c, as shown in Fig. 2. Equilibrium is eventually established between the contact pressure and the liquid-bridging force. The equilibrium configuration of a solid/liquid/vapor system, including the meniscus and the triple-point line at the junction of the liquid, the solid, and the vapor, is described by the so-called Laplace\u2013Young equation, Dp5kgLV , on the meniscus, ~1! rticle is copyrighted as indicated in the article. Reuse of AIP content is sub 71.86.144.106 On: Fri, 1 gSV5gLS1gLV cos u , on the triple-point line. ~2! In Eq. ~1!, Dp is the difference in hydrostatic pressure across the meniscus interface and k is the local mean curvature of the meniscus. In Eq. ~2!, u stands for the equilibrium contact angle at a triple-point line, and gSV , gLS , and gLV denote the surface tensions between the liquid, vapor, and solid, respectively. In Fig. 2, u1 and u2 denote the equilibrium contact angles at the two triple-point lines. One is on the cylinder surface and another on the half-space surface. They are system constants. Other parameters shown in Fig. 2 are geometric parameters. R0 is the radius of the cylinder, c is the filling angle that characterizes the volume of the small liquid drop, and l is the size of the liquid-bridging area on the plane. Since the characteristic length considered in the present analysis is so small, the effect of gravity can be negligible and the mean curvature is assumed to be nearly uniform. In other words, the meniscus profile can be modeled by an arc of the circle, as shown in Fig. 2. Following Orr\u2019s scheme,8 we obtain the mean curvature of the meniscus as k5 cos~u11c!1cos u2 R0~12cos c!2h , ~3! where h denotes the height of the part of the rigid cylinder in contact with the half space in the equilibrium state, as shown in Fig. 2. Substituting Eq. ~1! into Eq. ~3!, we obtain Dp5gLVFcos~u11c!1cos u2 R0~12cos c!2h G . ~4! With Eq. ~3!, the dependence of the liquid-bridging area on filling angle c and contact angle u1 as well as u2 is given by l5R0 sin c1R1@sin~u11c!2sin u2# ~5! with R15 R0~12cos c!2h cos~u11c!1cos u2 . ~6! As another important issue in the present contact problem, the liquid-bridging force is formulated based on the above-given relations. The total force exerted through the liquid bridge between the cylinder and the half space consists of two parts, namely, a surface tension force that resides in the meniscus, and a capillary pressure force due to the hydrostatic pressure difference across the liquid/vapor interface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003391_coase.2008.4626479-Figure12-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003391_coase.2008.4626479-Figure12-1.png",
        "caption": "Figure 12 Deviation plots for NAS Test piece (a) Shrinkage model (b) Machine manufacturer suggested scaling factors",
        "texts": [
            " Since this paper studies the scan length variation along scan direction only, it is beyond the scope of the present work to present models for Y direction. The cylindricity of the circular section also shows greater improvements for flexible scaling part. The cylindricity for flexible scaling part is 0.046 mm whereas the cylindricity of the rigid scaling part is 0.07mm. (a) Further to visualize the improvement in accuracy, deviation plots are constructed using point cloud data from ATOS white light scanner for NAS Test parts. The deviation plots along +X +Y +Z viewing direction are shown in Figure 12. It is observed that maximum deviation of shrinkage model part is within \u00b1 0.15 mm while the rigid scaling part has errors more than \u00b1 0.25 mm. Thus it is observed that the new compensation approach proposed in this paper not only reduces the dimensional error, it also reduces the form error. In the present work, an attempt has been made to study the improvement in accuracy by including the nonuniform shrinkage into the shrinkage compensation factors. These shrinkage factors earlier remained rigid with respect to the size of the part and have been made flexible by the use of experimental empirical relationships that correlates to the dimensions of the part"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000865_s0389-4304(03)00084-5-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000865_s0389-4304(03)00084-5-Figure3-1.png",
        "caption": "Fig. 3. Motor drive circuit.",
        "texts": [
            " The control strategy is shown schematically in Fig. 2. The 4WD controller calculates the target torque needed at the rear wheels, based on the accelerator position and the wheel speed(s) and provides the generator field current, the motor field current and the clutch current on the basis of the target torque, the engine speed, motor speed and other information. Moreover, by changing the direction of the motor field current, it also facilitates 4WD control in both forward and reverse orientations. The motor drive circuit is shown in Fig. 3. The drive torque, T, produced by the motor is determined by the armature current and the field current of the motor, and is given by the following equation: T \u00bc KaF\u00f0If \u00deIa; \u00f01\u00de where T: drive torque produced by the motor, F: magnetic flux, Ia: motor armature current, If : motor field current, Ka: constant determined by the motor specifications. Eqs. (2) and (3) below hold true on the basis of the electrical circuit: Eg \u00bc Ia\u00f0r \u00fe R\u00de \u00fe Em; \u00f02\u00de Em \u00bc KaF\u00f0If \u00deo; \u00f03\u00de where Eg: generator output terminal voltage, r: harness resistance, R: motor resistance, Em: back-electromotive force produced by the motor, o: angular velocity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003904_j.apm.2007.12.011-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003904_j.apm.2007.12.011-Figure2-1.png",
        "caption": "Fig. 2. excitat the kn joints contro delay strengt cycle.",
        "texts": [
            ", an afferent delay Da and an efferent delay De [9] moreover, the following relationship was assumed, D \u00bc Da \u00bc De; \u00f02\u00de because neurophysiological experiments show that the time delay of the efferent pathway De almost equals that of the afferent pathway Da in a sensorimotor loop [23,24]. The body consists of an interconnected chain of 5 rigid links in the sagittal plane, as shown in Fig. 7. The reaction forces from the ground are modeled as a two-dimensional spring and damper. The motion of the body can be represented by differential equations of a (6 1) vector of mass point positions of 1 link and inertial angles of 4 links. The equations are derived by means of the Newton\u2013Euler method (Appendix A). The CPG, composed of 12 neurons (Fig. 2) that are described by a BVP model [19], is represented by the following differential equations: si _ui\u00f0t\u00de \u00bc ui\u00f0t\u00de vi\u00f0t\u00de ui\u00f0t\u00de3=3\u00fe P12 ij\u00bc1 wijyi \u00fe u0 \u00fe awF i\u00f0x\u00f0t D\u00de\u00de; s0i _vi\u00f0t\u00de \u00bc ui\u00f0t\u00de \u00fe a bvi\u00f0t\u00de; yi \u00bc f \u00f0ui\u00f0t\u00de\u00de; f \u00f0u\u00de \u00bc max\u00f00; u\u00de; \u00f0i \u00bc 1; 12\u00de; 8>>< >>: \u00f03\u00de where ui is the potential of the ith neuron; vi is responsible for the accommodation and refractoriness of the ith neuron; wij is the connecting weight from the ith neuron to the jth neuron; si and s0i are the time constants of the potential and the accommodation and refractory effects, respectively; yi is the output of the ith neuron; u0 Central pattern generator (CPG) and feedback pathway"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002942_00423110600871319-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002942_00423110600871319-Figure1-1.png",
        "caption": "Figure 1. Schematic of the measurement setup.",
        "texts": [
            " In parallel, weather data have been collected, which included temperature near the ground, temperature at 3 m from the ground, atmospheric pressure, presence of moisture and rainfall. Later on, also the wheel diameters have been measured. The vehicle identification numbers have been recorded manually. These numbers allowed the comparison of data from the same vehicle at different transits. Considering the constant orientation of the train and of the single vehicle, the behaviour of each single wheel-set could be studied. Figure 1 shows schematically the measurement setup. To avoid confusion between curve squealing and brake squealing, only departing trains have been considered. The microphones and the accelerometers delivered a continuous (analogue) signal, which was converted to digital information and stored in a computer hard disk. Therefore, the data were filtered with a low-pass filter at 22.4 kHz and afterwards sampled with a frequency of 60 kHz. The meteorological data have been stored separately in a data logger"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001983_b:inam.0000041399.99257.b3-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001983_b:inam.0000041399.99257.b3-Figure1-1.png",
        "caption": "Fig. 1",
        "texts": [
            " Keywords: seismic isolation, rolling friction, sliding friction, frictional bond The behavior of some mechanical systems cannot be studied without considering frictional bonds that may break and then recover. Dynamic models of such systems are described by equations of variable structure, which represent varying modes of motion and require establishing conditions for the existence of these modes. In the present paper, we address one of such problems that may apply to, for example, seismic isolation systems of buildings [3, 11]. Figure 1 depicts supporting and supported solids (1 and 2). They interact via rigid inertialess spheres 3 of radius r rolling within the spherical recess of radius R (R > r) in body 2 and over the flat surface of body 1. Body 1 is either fixed or executes polyharmonic back and forth motion along the Ox-axis, specified as an analytical function of time. Body 2, bearing upon several identically located spheres 3, translates in the plane zOx. We will neglect static indeterminacy due to the presence of more than three supports 3 and assume that all the loads acting on the spherical supports 3 are applied to one of them",
            " The situation may be different in other systems, including seismic isolation mechanisms, where dissipation during sliding and rolling of the contacting bodies is intentionally increased to absorb the energy of a seismic load. The dissipative resistances due to rolling friction and sliding friction, which manifests itself upon breaking of frictional bonds, influence the modes of motion and damping of vibrations and, thus, should be taken into account in dynamic analysis. The structure of the dynamic model (Fig. 1) depends [1, 5] on whether the sphere rolls, or slides, or has no motion relative to bodies 1 and 2. To derive the equations of motion for various modes (structures) and to establish existence conditions for these modes, it is first necessary to analyze the static equilibrium equations for the inertialess sphere 3 subjected to the normal forces N1 and N 2 , the forces of friction F1 and F2 , and the moments of forces of rolling friction M13 and M 23 . 702 1063-7095/04/4006-0702 \u00a92004 Plenum Publishing Corporation S",
            " Let us introduce angles of rolling friction \u03b1 i : \u03b1 \u00b5 i i r = arctan , i = 1 2, , (2) where r is the radius of the sphere. In view of (1) and (2), the equilibrium equations for the sphere as a two-dimensional system are as follows: N F F2 1 2 0sin cos\u03b2 \u03b2+ + = , N N F1 2 2 0\u2212 + =cos sin\u03b2 \u03b2 , \u2212 \u2212 + \u2212 =N k N k F F1 1 3 2 2 3 1 2 0tan tan\u03b1 \u03b1 , (3) \u03b2 is the angle between the vertical diameter of the spherical recess in body 2 and the radius O O2 3 ; \u03b2 is positive in the counterclockwise direction. To analyze the dynamic processes in the system (Fig. 1), Eqs. (3) should be supplemented with the differential equations of motion of solid 2 and the constraint equations. For the results thus obtained to reflect the real motion of the system, the general solution must satisfy the following unstrict inequalities: | |N F N f k ii i i i i *\u2265 \u2264 \u2212 \u2264 \u2264 =0 1 1 1 23, , , , , (4) where f1 and f2 are constant [4, 12] coefficients of sliding friction between sphere 3 and bodies 1 and 2. The structure of the dynamic system (Fig. 1) changes as soon as one of the inequalities in (4) becomes an equality or, vice versa, an equality turns into an inequality. After that, it is necessary to apply appropriately modified equations of motion and constraints. The equilibrium equations (3) of the inertialess spheres 3 do not change. The structures of the dynamic system (Fig. 1) may be grouped by analyzing the equilibrium conditions of the inertialess sphere 3 according to Eqs. (3). These equations contain five unknowns: N N F F1 2 1 2, , , , and \u03b2; i.e., by specifying the direction \u03c9 3 , we can express any three of them (for example, N 2 , F1, and F2 ) in terms of the remaining two (N1 and \u03b2). Thus, Y A B= \u22121 , (5) where [ ]Y N F F T= 2 1 2 , A = \u2212 \u2212 \u2212           sin cos cos sin tan \u03b2 \u03b2 \u03b2 \u03b2 \u03b1 \u03c9 1 0 1 12 3sign , B N= \u2212           1 1 3 0 1 tan \u03b1 \u03c9sign , (6) and T denotes the operation of transposition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001681_robot.2004.1307975-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001681_robot.2004.1307975-Figure5-1.png",
        "caption": "Fig. 5. Compliance Center Setting",
        "texts": [],
        "surrounding_texts": [
            "I I . EXPERIMENTAL ENVIRONMENT In this section. the difference between nroblems in urevious\n..... works and the focused problem is presented. The target task is shown in Fig.1. A peg is inserted into a tandem shallow\nassembly tasks in processes making an automatic transmission. In this paper we focus the task to insert a peg into a tandem\na 12.0\";;. 2 0 1\nhole through a floating part which has a hole. This is one of i....\nshallow hole ignoring assembly of the floating part. A. Influence of Shallowness of Hole\nFig. 2. Tolerance of Insertion Hole\nFirstly, we describe the influence of the shallowness of a hole. The tolerances of a hole and peg are shown in Fig.2. Consider a condition of contact between the hole and the peg depicted in Fig.3, where F, is insertion force on a tip of peg, Fz is force which press the peg against the inside of a hole,\nthe length of the inserted peg. Whitney[l] explicated the relation the possibility of insertion and the contact force using the Jamming Diagram. the\nM is moment of rotation, r is the radius of the peg and 1 is Fx Fx\n(a) Shallow Insenion (b) Deep Insertion\nJamming Diagram is shown in Fig.4, where Fig. 3. Insertion Depth\n1 A = - -^.. A' P\nand , 1.1 is friction coefficient between the inside of hole and the peg. Two contact states are defined to express the force condition between the hole and the peg. One is the one-point contact, another is twcFpoint contact. When a state is onepoint contact, the combinations of F,,F,, and ill are located on the inside of parallelogram. On the other hand, when a state is twopoint contact, the combinations lie on the upside line and the downside ones. The combinations on the outside of parallelogram cause the jamming of the peg, because the insertion force become less than the friction force.\nThe insertion length of the peg have an influence on the acute angles of Jamming Diagram. Because the vertex of an acute angle moves vertically in proposition to A, the capacity of parallelogram increases depending on the insertion length of the peg. In the case the insertion is shallow (Fig.3(a)), the Jamming Diagram became small parallelogram on vertical direction as shown in FigA(a). n l / rFz should be held down in order to keep availability of insertion. On the other hand, the deeper the peg is inserted as shown in Fig.3(b), the bigger the Jamming Diagram gets above and below as shown in Fig.4@). Compared with condition of Fig.3(a), an upper limit on M / r F z which provides the insertion availability grows larger. At our focused task, even if a peg is inserted deeply, the Jamming Diagram still keeps thin shape because the hole is shallow. Therefore, the condition for insertion possibility on focused task is more strict than when a hole and peg are same depth.\nIn addition, compliance center must be fixed when the RCC device is used. As for general Peg-In-Hole problems, the compliance center is set on the tip of a peg as shown in Fig.S(a). On the other hand, in the case of a through-hole the compliance center should be set behind the through-hole as shown in Fig.S(b). The fact shows that link length from\nmanipulator to compliance center always should be renewed when the manipulator system proceeds with the insertion operation. Therefore, manipulator system will not achieve the insertion operation with the RCC devices.\nB. Influence of Length of Peg\nNext, we describe the influence of the length of a peg. The length of the peg which we deal with for an experiment is 270 mm. As indicated above, the necessity to change the link length of the compliance center requires to use not the RCC devices but the force sensors for the achievement of the task. We express the force i moment on the compliance center as follows (See Fig6).\nFyr = Fw, Fzr = F,,, (2)\nai,, = ai,, + F,,L, - F,,L,,\nwhere, Fy,,Fz, and ,Ifzr are force i moment on compliance center, Fy,,F,, and M,, are force I moment on force sensor, and Ly,L, are the deflection from force sensor to compliance",
            "center. In the process to calculate MZ,, F,, is multiplied by L,. Because the output of force sensor implies the noises and the noises are also multiplied by L,, the accuracy of Mz, is not ensured. If the gain of force feedback control for M,, is increased the vibration of the manipulator will occur. On the contrary, if the gain is decreated the force to correct the orientation of the peg will not occur. At all, a adjustment of the gain becomes difficult under the condition using a long\nC. Influence of Endem Hole\nFinally, we describe the influence of a tandem hole. The positional precision is required when the tip of a peg is inserted into the second hole as shown in Fig7. When the peg is restricted by the first hole the tip of the peg P, and the gripping point Pg are located with the central focus on the middle of the first hole Po, having radii L1 and LZ respectively. Under this condition, the deflection of P, from a central axis (a horizontal broken line) is Ll/Lz times larger than the deflection of Pg.\n111. CONTROL SYSTEM\nThe experiment i s performed with manipulator PA10 made by Mitsubishi Heavy Industries. A proportional and derivative (PD) control algorithm is used to control the manipulator\npeg.\nsystem, and the input values are desired position of a gripping point on Cartesian coordinate system (Fig.8). Where, X d is desired position on Cartesian coordinate system, qd is desired joint angle of manipulator, q is current joint angle, q is joint angular velocity, and K,,, K , are feedback gains. There is a force sensor on the wrist of the manipulator. It is not used for feedback control of manipulator, but only used to observe for the evaluation of a experiment.\n1v. PROPOSED ALGORITHM\nIn this section, The algorithm that. a manipulator finds correct posture of a peg inserted into a tandem shallow hole is detailed. We call this algorithm insertion using search trajectory generation. The algorithm is shown in Fig.9. A basic idea is that firstly a manipulator recognizes the availability of insertion operation and secondly if insertion operation is available the manipulator continues the task keeping a trajectory, otherwise the manipulator searches the correct p o s t u ~ of the Peg.\nA . Fme Wrist A peg could get four degrees of freedom of posture due to the clearance, when a manipulator inserts the peg into a shallow hole(Fig.10). Where, X h , & are positions of the peg , and W X h , W Z h are posture of the peg around the hole. Combinations of four parameters make search area so large that a manipulator will not find a correct posture. Thus we make a free wrist device to reduce number of position and posture which the manipulator must correct(Fig.11). The free wrist is attached between the tip of manipulator and a",
            "gripper, and has structuTe that float part is put to the inside of the base part with balls. With the described structuh, the free wrist has stiffness for Dosition. and zero-stiffness for Dostwe\nD. Insertion Using Search Trajectory Generation We show the generation method of trajectory as follows when the manipulator recognized that an insertion operation has been unavailable.\nYd Yc- dy, (4) dy7.f = Yd -Yref, ( 5 )\n2 0 = a,dy,,f + xrefr (6) zo = azdyref + zrefr (7) Xd = Xo+dx, (8) Zd = 20 + dz, (9)\ndx = U T , cos&, (13) dz = U ri s in&, (14)\nwhere, Xd,yd,Zd are desired position of gripping point, y, y,, z, are current position of gripping point, dy,,f is distance from base position to desired position on y axis, x,,f, yTef, zref are the base position to generate desired position. dx.du.dz are distance from current Dosition to desired . I \", position, ax,az are inclinations of insertion direction, r o is an initial radius at search action, dr is the radius increase when the trajectory makes one revolution, N is the number\naround wX,, wY, and wZ,. By virtue of the free wrist, the number of position and posture to correct can be reduced from two directions of position and two orientations of posture to two directions and zero orientation.\nE. Condition of Experiment\nof search circle division, i is the continuation number counted while the insertion operation is unavailable(See Fig.P.), 00 is initial angle of search, L,,, is the length of inserted peg, and Lt is the full length of peg.\nIn this paper, a manipulator starts the insertion operation with condition that the tip of a peg was already inserted into the shallow hole. Firstly, the manipulator inserts the peg into negative direction on y axis with force F. Secondly the manipulator changes the trajectory of gripping point according as insertion operation is available or not.\nC. Recognition of Task Condition\nThe period of the recognition of insertion availability and changing the mathod of trajectory generation T, is enough large than manipulator control period Tc. Because to take the effect of change a trajectory and to recognize the insertion availability need the enough time. In this paper, task condition is evaluated as follows\nCondition A = Ivy1 > Ivydl U a~vy > 0, (3)\nwhere, V, is insertion velocity, Vyd is required insertion velocity and ay is insertion acceleration. If condition is A the manipulator continues the operation with keeping the trajectory, otherwise the manipulator behave to find the condition in which an insertion operation is available.\ndy is set to make the insertion force F suitable. The trajectory of gripping point on the xz plane is shown in Fig.13. In this paper, we adopt Xd,Yd,Zd at the last time when the insertion is available as xr..f, yTef, zref. We consider that inclinations of insertion direction make the jamming phenomenon. To avoid jamming, the manipulator should estimate the inclinations and revise the insertion direction. The revision method is that a,dy,,j, a,dy,,f are added to desired position of gripping point respectively. The inclinations a and a, are calculated with linear regression using the position of gripping point at the time when insertion operation is available. We illustrated the desired position of the gripping point, the base position to generate desired position, and the current position in Fig.14.\nFig.15 shows the cone where gripping point can be placed, where pa is radius ofcircle where gripping point can be placed when the task begins, and ppc is radius of circle when peg is inserted. The ideal condition of peg and hole is one-point contact, because friction force of one-point contact is less than one of tw&point contact. However the positioning accuracy of manipulator is required to realize the one-point contact, because the deeper peg is inserted the smaller pc becomes. Therefore, the method to realize one-point condition and to"
        ]
    },
    {
        "image_filename": "designv11_28_0003789_j.jsv.2008.03.072-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003789_j.jsv.2008.03.072-Figure10-1.png",
        "caption": "Fig. 10. Rubber impedance and beam impedance combined.",
        "texts": [
            " Response of primary system With the solution for the beam thus obtained, the primary system with its spring and damper can now be considered as attached to the center of the beam (see Figs. 1 and 2). In Fig. 1 the beam can be replaced by its dynamic stiffness as shown in Figs. 9 and 10. The dynamic stiffness of the beam at the junction point, which may be defined as the ratio of force to displacement is given by Z \u00bc F 0=W \u00f00\u00de \u00bc 1 ,X6 j\u00bc1 Bj (41) The equivalent dynamic stiffness of the system (see Fig. 10) is given by Zeq \u00bc 1 , X6 j\u00bc1 Bj \u00fe 1 K\u00f01\u00fe id\u00de ( ) (42) The equation of motion for the system as shown in Fig. 10 is m \u20acy1 \u00fe Zeqy1 \u00bc F exp\u00f0ift\u00de (43) Since the motion is harmonic, y1 may be assumed to be of the form y1 \u00bc Y 1 exp\u00f0ift\u00de (44) ARTICLE IN PRESS B.P. Yadav / Journal of Sound and Vibration 317 (2008) 576\u2013590 587 Substituting Eq. (44) in Eq. (42) gives Y 1=F \u00bc 1=\u00f0 mf 2 \u00fe Zeq\u00de (45) Combining Eqs. (42) and (45) then yields Y 1=F \u00bc X6 j\u00bc1 Bj \u00fe 1 K\u00f01\u00fe id\u00de ( ), mf 2 X6 j\u00bc1 Bj mf 2 K\u00f01\u00fe id\u00de \u00fe 1 ( ) (46) which is the response of the primary system to an exciting force of unit amplitude. 4.3. Transmissibility With reference to Fig. 10 the exciting force at the junction of the beam and the primary system can be expressed in the form F 0=F \u00bc Zeq=\u00f0 mf 2 \u00fe Zeq\u00de (47) From Eq. (37) for the shear force at any section of the beam, the right-hand support force F1 can be obtained by substituting Eq. (32) into it and putting x \u00bc l/2. This gives F1 F0 \u00bc Dt\u00f0d1 d2\u00de g\u00f02d1 d2\u00de X6 j\u00bc1 s5j \u00fe g \u00f0Y 1 \u00fe Y 2\u00de\u00f0d1 d2\u00de \u00fe \u00f02d1 d2\u00de \u00f0d1 d2\u00de s3j \u00fe \u00f0mf 2=Dt\u00desj Bj exp\u00f0sj l=2\u00de (48) The transmissibility, which may be defined as the ratio of the total dynamic force transmitted at the end support to the impressed force [15], is given by T \u00bc 2F1=F (49) Combining Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000299_an9881300755-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000299_an9881300755-Figure7-1.png",
        "caption": "Fig. 7. Calibration graphs for procarbazine hvdrochloride obtained with carrier B and with various HC104 concentrations: (A) 2.0 X 10-4; (B) 2.6 x 10-4; and (C) 3.4 x lo-4u. Statistical detection limits: (A) 7.0 x 10-4; (B) 8.9 x and (C) 1.5 x lo-3u",
        "texts": [
            "501og C + 58.63 0.9997 0.7 0.1-0.7 * Calculated analyte concentration corresponding to a At,, equal to three times the standard deviation of the most dilute standard of the calibration graph. 20 40 ae $ 5 .- m, a0 !- 100 ~~~~ ~ Time - F 5. FIA pseudotitration curves of the0 hylline. Concentrations: 8 1.0 x 10-3; (B) 2.5 x 10-3; (C) 5.0 x 8 - 3 ; (D) 1.0 x 10-2; and [E) 2.0 X 10-ZM. Titrant, malachite green, 1.2 x 10-SM, HC1O4, 2.0 x l o - 4 ~ ; times measured, 10.19-39.18 s concentrations of the titrant. Fig. 7 shows calibration graphs for the determination of procarbazine hydrochloride obtained with three different HC104 concentrations. As can be seen, all the lines have the same slope, kl [equal to the constant parameters V,lQlnlO of equation (l)], and a varying intercept, kZ, which decreases with increasing titrant concentration. From equations (1) and (2), the observed molar ratio, n, of each titration reaction at the selected triggering level can be calculated from the experimental data shown in Table 1 according to the equation n = V,/(VmC~10k2\u2019ki) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001626_0094-114x(81)90040-9-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001626_0094-114x(81)90040-9-Figure2-1.png",
        "caption": "Figure 2.",
        "texts": [
            " These parameters have been developed into loop equations[3, 4] which express the combined effect of displacement and orientation as one proceeds from the base to the hand. These equations are not derived here, but a brief listing is given in the Appendix. s3 tApplications Manager, Interactive Computer Graphics Center, Rensselaer Polytechnic Institute, Troy, NY 12181, U.S.A. 255 We select the intersection of offset SH and link al2 as the reference point for measuring the maximum reach. This is the last point which remains fixed no matter what values angles 0t, 02 or 03 take, and therefore the base point. We locate the robot hand at the end of offset $33 (Fig. 2). If in practice the hand is located at the end of a link, an additional offset of zero length is inserted between them. The actuator for each joint could be located anywhere along an offset, but for convenience will be considered at the far end of each offset. The maximum reach will be independent of 01 since whatever the configuration, the reach defines a circle centered around and in a plane normal to axis $1. Therefore, 01 can be set to an arbitrary position (Fig. 3). The angle 03 is located near the hand and does not affect the reach"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003717_08ias.2008.78-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003717_08ias.2008.78-Figure10-1.png",
        "caption": "Fig. 10. Rotor end-view with poles of an HSUB machine before injection of PM material.",
        "texts": [
            " During field enhancement, the PM material in the rotor prevents diffusion of flux between the rotor magnetic poles, thereby guiding more flux to the main air gap to interact with the armature flux. During field weakening, a great portion of the main air gap flux is diverted from the air gap by controlling the dc current in the dc-excitation stator. The core loss can be reduced by a lower flux density in the main air gap between the armature and the rotor. A rotor end-view of the prototype machine is shown in Fig. 10, and the opposite end-view is shown in Fig. 11. B. Injected PM Injected PM material is used to fill the gaps between the rotor outer ring and inner ring of the prototype machine. A high residual flux density and a strong coercive force of the PM may improve the field-enhancement performance of the HSUB machine. Fig. 14 shows the test setup of an HSUB prototype motor that has the rotor shown in Fig. 12. A torque gauge is attached between the HSUB machine shaft and the dynamometer shaft. Additionally, an optional rotor position encoder is mounted at the non-driving end of the HSUB machine shaft for running the machine as a brushless dc motor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000848_s0039-9140(03)00304-7-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000848_s0039-9140(03)00304-7-Figure1-1.png",
        "caption": "Fig. 1. Electrochemical response of p-1-NAP modified electrodes at different pH, (A) pH 1, (B) pH 13, v /0.025 V s 1. Fig. 2. Current /time response curves for the single potential step method, overpotential ( / / / / / /) h / /0.140 V, (*/) h / / 0.180 V. Inset: shows details of Zone II.",
        "texts": [
            " The glassy carbon electrodes (pretreated as described in Section 2) were immersed in a 6 / 10 4 M 1-NAP solution with 0.1 M HClO4 as supporting electrolyte. Then, the working electrode potential was continuously scanned at 0.025 V s 1 between 0 and 0.800 V during five cycles. The thickness of the polymeric film thus obtained could be estimated to be 300 A\u030a [35]. The polymeric films obtained were mechanically stable and their electrochemical response was analyzed by cyclic voltammetric experiments in aqueous 0.1 M HClO4 solutions at a potential range from / 0.100 to 0.600 V (Fig. 1A). The redox behavior of the film is strongly dependent on the pH of the electrolyte solution [36]. The electrochemical activity of the film is lost when it is cycled at pH 13 (Fig. 1B). However, the film is not degraded and the electrode response is recovered upon its immersion in a pH 1 solution. This behavior is the same of other polymer film electrodes like poly-aniline [38]. The traces shown in Fig. 1A and B are those obtained after the electrode reached a steady current /potential response. The glassy carbon electrodes modified with the p-1-NAP polymeric film were then immersed in 0.03 M CuSO4 solution of pH 1 during 20 min prior to the potential step experiments. This procedure allowed for the saturation of the poly- meric matrix with Cu2 ions [34,35]. Then, the working electrode potential was stepped from / 0.100 V (i.e. the rest potential value) to a given cathodic overpotential (h ), which was held constant during 10 s while the current was registered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002365_iros.2005.1544973-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002365_iros.2005.1544973-Figure1-1.png",
        "caption": "Fig. 1. Configuration of a typical under-actuated underwater vehicle and its motion in strong sea flow.",
        "texts": [
            " Index Terms \u2013 Markov decision process, Q learning, motion digitizing method, artificial neural network, nonholonomic underwater robot. I. INTRODUCTION Motion planning and control of under-actuated robots are very important issues in robotics research. The development of a practical motion planning and control algorithm becomes especially difficult when the target under-actuated robot has complex and unknown dynamics and is operated in an environment where disturbances are unknown. An underactuated autonomous underwater vehicle cruising in the sea is a typical example of robot with such properties. As shown in Fig. 1, a typical under-actuated underwater vehicle has a main thruster for forward movement and a rudder for turning movement. The vehicle cannot go straight in the lateral direction, so that the basic kinematical characteristics of the vehicle are very similar to those of four-wheel mobile robots. The motion of a four-wheel mobile robot is dominated by non-holonomic constraints and therefore the robot cannot be stabilized at a point by smooth state feedback [2]. For this reason, motion planning of a four-wheel mobile robot often takes the kinematical characteristics of its motion into consideration and the results have been impressive (for example, Laumond et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002107_1.1611500-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002107_1.1611500-Figure7-1.png",
        "caption": "Fig. 7 Finite element model of the HDB spindle motor for the analysis of thermal deformation",
        "texts": [
            " The HDB spindle motor is composed of several components with different thermal expansion coefficients. Table 5 shows the thermal expansion coefficients of each component of the HDB spindle motor. Elevated temperature deforms the HDB spindle motor, and it changes the clearance of the journal and thrust bearings. Once the temperature distribution is determined from the analysis of heat conduction, the HDB spindle motor is divided into several isothermal areas. ANSYS is also used to determine the deformed shape of the HDB spindle motor due to elevated temperature. Figure 7 shows the finite element model of the stationary and the rotating part of the HDB spindle motor. They are modeled by three dimensional eight-node brick elements, and the numbers of total elements are 12,768 and 8,016 for the stationary and the rotating part of the HDB spindle motor, respectively. The clearances of the journal and thrust bearing of the thermally-deformed HDB spindle motor are determined by subtracting the outer radius of the shaft Table 4 Measured temperatures around the periphery of the HDB spindle motor Surrounding temperature @\u00b0C# 28"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003419_vss.2008.4570721-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003419_vss.2008.4570721-Figure1-1.png",
        "caption": "Fig. 1. throttle valve",
        "texts": [
            ". INTRODUCTION Throttle valves are used to adjust the amount of air entering gasoline engines. Due to a mechanical connection of the valve and the accelerator pedal by a bowden cable, the angle of the throttle-blade solely depends on the accelerator position in conventional throttle valves. In electronic throttle valves as shown in Fig. 1 the throttle-blade is driven by a dc-motor so that the opening angle \u03d5 and the accelerator position are decoupled. By evaluating the accelerator position as well as a number of sensor signals the engine-control-unit (ECU) computes a suitable reference opening angle r. The goal of the throttle valve controller is to make the angle \u03d5 track the reference signal r. This \u201delectronic throttle system\u201d makes it possible to realize modern driver-assistance systems, e.g. the electronic stability program (ESP)",
            " While preserving the structural simplicity and the performance of standard sliding mode controllers no antichattering techniques have to be applied in this case. The paper is organized as follows: In Section II the mathematical plant model, which serves as a basis for the controller design is presented. In Section III the two control strategies are outlined. Section IV presents simulation results, whereas Section V is dedicated to the realtime application of the control laws. Section VI concludes the work. The major components of the throttle valve depicted in Fig. 1 are the dc-motor with reduction gear-drive and the throttle-blade with a spring-mechanism. In case of a failure the throttle-blade is positioned into an emergency position, which is characterized by the limp-home angle \u03d50. The opening angle \u03d5 is measured by means of a position sensor, which consists of two potentiometers for reasons of redundancy. The sufficiently smooth reference signal is denoted by r. The differential equation which describes the rotation \u03d5 of the throttle-blade as a function of the motor voltage u is assumed to be of second order"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000550_robot.2000.844843-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000550_robot.2000.844843-Figure5-1.png",
        "caption": "Fig. 5: The schematic diagram of impact performance index based on velocity direction",
        "texts": [
            " 4.1 Impact performance index based on velocity direction The basic idea is the change of linear momentum which is equivalent to the magnitude of impulsive force: where P is a linear momentum. Therefore, if we reduce the momentum to the velocity direction using null motion of redundant manipulators, the impulsive effects are also reduced. Now, let's replace the direction vector n of Eq.(21) by the task velocity direction of manipulators as if we know the wall is lying in velocity direction like Fig. 5. Then, we define Eq. (23) as the impact performance index based on velocity direction: AP = A(mp), (22) m\"(q) = uT(JM-'JT)u, (@d - @ = 0) (23) where v = is the task velocity direction of manipulators. We will use above U instead of U = &, assuming good velocity servo performance. This simple strategy will reduce the first impact even for uncertain environment. After the first impact, however, the geometry information of environment can be obtained from a forcetorque sensor. So, we can use the same impact performance index with others from the second impact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003978_6.2009-6139-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003978_6.2009-6139-Figure3-1.png",
        "caption": "Figure 3: Turn Types. For waypoint following, an aircraft can maneuver in a variety of ways to intersect a waypoint.",
        "texts": [
            " Aircraft in real-world as well as simulated environments may not be able to exactly intersect the waypoint location, so a tolerance is usually employed to determine sufficient closeness. Also, a mission may require that an aircraft handle waypoints and route-following under a set of constraints. It may be necessary to maintain close proximity to the ideal route path, perhaps there is a particular heading requirement when passing the waypoint or it may be important to stay clear of an obstacle, requiring the aircraft to turn prior to reaching the waypoint. Figure 3 shows the four waypoint-following techniques that are described in this paper. Each of the techniques are described as follows,  Turn-Past. A turn-past maneuver simply flies the aircraft toward the waypoint. Two conditions are required for initiating a turn to the next waypoint: a tolerance distance for the waypoint, and an aspect angle requirement. The aircraft turns toward the next assigned waypoint when it calculates an aspect angle of greater than 90 degrees (the waypoint is behind the aircraft) and the aircraft is within the declared tolerance distance for that waypoint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000652_0470867906-Figure6.2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000652_0470867906-Figure6.2-1.png",
        "caption": "Figure 6.2 Description of the position of two particles joined by a mass-free rod",
        "texts": [
            " This is possible if all constraints are holonomous, i.e. they relate exclusively to the possible geometric positions of the bodies or can at least be put into such a form. Regardless of the selection of coordinates, the number of degrees of freedom of the system in principle remains constant. It corresponds with the number of independent coordinates minus the number of independent constraint equations. A small example, see Greenwood [125], should clarify the relationship between cartesian and generalised coordinates, see Figure 6.2. 6.2 MULTIBODY MECHANICS 103 Two mass points in the plane are rigidly joined together by a mass-free rod. Their position is determined by two pairs of cartesian coordinates (x1, y1) and (x2, y2). The condition induced by the rod can be described by the following equation (x2 \u2212 x1) 2 + (y2 \u2212 y1) 2 \u2212 k2 = 0 (6.6) We therefore have four cartesian coordinates and a bond equation, thus a total of three degrees of freedom. In principle, however, the configuration of the two particles can be described by the following generalised coordinates: q1 = x coordinate of the mid-point of the rod q2 = y coordinate of the mid-point of the rod q3 = angle \u03c6 of the rod",
            " In electronics the unknowns are normally in the form of node voltages, which is because of the nodal analysis that is prevalent in circuit simulation. In the systemoriented modelling of mechanics, on the other hand, it is of decisive importance to specify a suitable set of generalised coordinates. For holonomous systems, which can be described using generalised coordinates, the \u2014 sometimes very complex \u2014 constraint equations are dispensed with. As was shown by the relatively simple example from Figure 6.2, it is not a question of selecting from a fund of existing coordinates, but one of an independent engineering task. The methods described supply sets of ordinary differential equations in symbolic form. These can easily be formulated in analogue hardware description languages. This is true under the prerequisite that the size of the equation set remains within limits. In Section 7.2.3 the obtaining and formatting of the equations of motion for an automotive wheel suspension system using the Lagrange approach is illustrated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003694_jst.104-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003694_jst.104-Figure1-1.png",
        "caption": "Figure 1. Design of the instrumented bowling ball (Pro/ENGINEER, different views); 1: connectors; 2: 6D-transducers; 3: thumb tube; 4: finger tubes; 5: base plate; and 6: screws (connecting bottom and top half of the ball).",
        "texts": [
            " The basic idea behind the design was to measure the thumb and finger forces, applied to the ball, or more specifically, to the finger and thumb holes. Thus, it was essential to replace these holes by tubes, which are connected to transducers, hidden inside the ball. The transducers, in turn, are connected to the ball itself. A small gap between the shell of the ball and the tubes ensures that all forces applied to the tubes flow through the transducers. The width of the gap must be maintained even under large forces. Furthermore, the grip span needs to be adjustable to accommodate for different bowlers. The instrumented ball (Figure 1) was designed in Pro/ ENGINEER Wildfire 3.0 (Parametric Technology Corporation, Needham MA, USA). Some parts were CNC (computer numerical control) machined after converting their Pro/E files to Pro/MANUFACTURING (Parametric Technology Corporation, NeedhamMA, USA). A commercially available bowling ball (Columbia 300 Blue Dot, Columbia 300 Inc., Hopkinsville KY, USA) was sawn in half, the core was removed, and an aluminium base plate was inserted between the two halves (Figure 2). The three transducers, one for each finger, were mounted on the base plate through aluminium connectors, the position of which was adjustable along several slots machined into the base plate (Figure 2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000570_095440802760075021-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000570_095440802760075021-Figure2-1.png",
        "caption": "Fig. 2 Kinematic scheme of spatial gear pair with linear or pitch contact between toothed surfaces S1 and S2 synthesized using a pitch contact point P",
        "texts": [
            " The characteristics that are the elements of this subset are the eld of relative sliding velocity vectors in the process of rotational spatial transformation [6], the eld of normal vectors used to conjugate surfaces S1 and S2, which perform a transformation law at singular points [1], etc. Research into the spatial gearing treated here states that gear synthesis can be realized by applying two mathematical models [7\u201310] which will be discussed below. This model is based on the assumption that necessary quality characteristics could be satis ed at only one contact point which belongs to both active anks S1 and S2 (see Fig. 2). It is evident that this model can be applied to gear synthesis observing both Olivier\u2019s principles, i.e. to the synthesis of gear sets having either linear or point contact. According to this model, a common contact point P of the kinematically conjugate anks S1 and S2 is a common point of two circles whose centres Ci \u2026i \u02c6 1; 2\u2020 lie on the axes 1\u20131 and 2\u20132. Note that spatial transformation of rotations is E0101 # IMechE 2002 Proc Instn Mech Engrs Vol 216 Part E: J Process Mechanical Engineering at MICHIGAN STATE UNIV LIBRARIES on June 14, 2015pie"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000319_1.1519275-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000319_1.1519275-Figure3-1.png",
        "caption": "Fig. 3 Nomenclature for bending deflection",
        "texts": [
            " To model the crack, the tooth under mesh is divided into many segments. The bending stiffness of the tooth is calculated from the deflection of a tooth computed from a summation expression as shown in Eq. ~3! @20# below: yB5 L cos2 fL8 E ( i51 n d iF l i 22l id i1d i 2/3 I\u0304 i 1 2.4~11m!1tg2fL8 A\u0304 i G (3) Transactions of the ASME 13 Terms of Use: http://asme.org/terms Downloaded F where yB is the bending deflection of the tooth pair under mesh. i is the segment index. All the nomenclature used in Eq. ~3! is displayed in Fig. 3. In Eq. ~3! the terms 1/I\u0304 i and 1/A\u0304 i are given by: 1/I\u0304 i5~1/I i11/I i11!/2 (4) 1/A\u0304 i5~1/Ai11/Ai11!/2 (5) Where I is the moment of inertia and A is the area of the tooth cross section. Both of these two parameters are related to the thickness of the tooth. From Fig. 2~b!, it is apparent that the thickness of the tooth has a significant effect on the crack area. When substituting the thickness of the tooth with a crack into Eq. ~3!, the crack will affect the deflection and bending stiffness of the tooth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002960_jsen.2006.877992-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002960_jsen.2006.877992-Figure9-1.png",
        "caption": "Fig. 9. Photograph of the SU-8-based structure microchannels. (Color version available online at http://ieeexplore.ieee.org.)",
        "texts": [
            " The filter fabrication starts with the deposition of an 80-nm TiO2 layer (layer 1 in Table I) after completion of the standard CMOS process, including the metalization and the etching of the two oxide layers on top of the photodiode. Then, the eight subsequent layers of SiO2 and TiO2 are deposited with the thicknesses described in Table I. A scanning electron microscopy (SEM) photograph of the cross section of the optical channel is shown in Fig. 8. A commercially available passband optical filter on top of the MCM-based microsystem is used to block the nonvisible part of the spectrum. Fig. 9 shows a photograph of the microchannels fabricated using SU-8 techniques. The SU-8-based fabrication is a lowcost process, biocompatible, UV lithography semiconductor compatible, and does not require expensive masks. Moreover, SU-8-based processing enables the fabrication of deep microchannels with very low sidewall roughness and is suitable for optical absorption measurement [8]. A negative mask of the microchannels\u2019 die layout is fabricated from a regular transparency foil (like the one used in printed circuit boards)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003694_jst.104-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003694_jst.104-Figure3-1.png",
        "caption": "Figure 3. Coordinate systems; sensor: top row; ball: bottom row.",
        "texts": [
            " During the assembling of the ball, additional weight blocks were added to restore the original weight of the ball and to accommodate for heavy ball strokers and crankers, and light ball spinners. It is important to notice that the transducers are connected to interface power supply boxes by cables. These cables did not compromise the experiments, as, once the ball is released, the fingers no longer applied forces to the ball and thus the ball was not required to roll or skid after release and could be stopped by foam cushions. The orientation of the sensor coordinate systems is shown in Figure 3. The coordinate system of the ball is: x-axis www.sportstechjournal.com & 2009 John Wiley and Sons Asia Pte Ltd Sports Technol. 2009, 2, No. 3\u20134, 97\u201311098 Research Article F. K. Fuss pointing from ring and middle finger towards the thumb, y-axis from the centre of the ball to a point between the openings of the finger and thumb holes, and z-axis from ring to middle finger. When holding the ball with supinated right hand, thumb in opposition to the fingers, and hanging arm, the ball coordinate system is: x-axis forward, y-axis upward, and z-axis to the right",
            " The latter filter, however, shortens the moment spikes and alters the initial and final segments of the data set. The forces (Fx, Fy, Fz) and moments (Mx, My, Mz) of the thumb, middle and ring finger were processed as follows: The resultant finger force Fd is calculated from Fd \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fx2d \u00fe Fy2d \u00fe Fz2d q \u00f01\u00de where the subscript d denotes either the thumb, the middle or the ring finger. After rotating the sensor coordinate system about the x-axis by 1291, i.e. the inclination angle of the tubes (Figure 3), Fy0Th \u00bc FyTh cos \u00f029 \u00de \u00fe FzTh sin \u00f029 \u00de \u00f02\u00de Fz0Th \u00bc FyTh sin \u00f029 \u00de \u00fe FzTh cos \u00f029 \u00de \u00f03\u00de Fy0MiRi \u00bc \u00f0FyMi \u00fe FyRi\u00de cos \u00f029 \u00de \u00fe \u00f0FzMi \u00fe FzRi\u00de sin \u00f029 \u00de \u00f04\u00de Fz 0 MiRi \u00bc \u00f0FyMi \u00fe FyRi\u00de sin \u00f029 \u00de \u00fe \u00f0FzMi \u00fe FzRi\u00de cos \u00f029 \u00de \u00f05\u00de Sports Technol. 2009, 2, No. 3\u20134, 97\u2013110 & 2009 John Wiley and Sons Asia Pte Ltd www.sportstechjournal.com 99 Instrumented bowling ball where the subscripts Th, Mi, and Ri denote thumb, middle and ring finger respectively. The ball forces (Figure 4) are Fxball \u00bc Fy0Th Fy0MiRi \u00f06\u00de Fyball \u00bc Fz0Th \u00fe Fz0MiRi \u00f07\u00de Fzball \u00bc FxTh FxMi FxRi \u00f08\u00de Fball \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fx2ball \u00fe Fy2ball \u00fe Fz2ball q \u00f09\u00de Fxball is the reaction force of the inertial force FI and the gravitational force FG times sin y (5FG sin y), where y is the angle of the ball coordinate system during the swing relative to the ground (Figure 4; 01 if Fxball is pointing forward, 901 www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003836_j.jala.2007.12.005-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003836_j.jala.2007.12.005-Figure1-1.png",
        "caption": "Figure 1. Outline of BioRobot platform.",
        "texts": [
            " Clinical tests consist of elementary operations of robots such as transportation, manipulation such as pick and place or mixing, and sensing (including inspection), in general. However, just assembly of the commercial products can satisfy the functional requirements, but does not provide the best solution in terms of performance, cost, and needed space. The major issue in the design of robotic automation has been the effective integration of individual functions into the system. The robot system dedicated to the clinical test is demanding, even though the commercial products are used partly. Figure 1 shows the BioRobot platform under development for near-patient testing in small- or medium-sized hospitals or laboratories. For miniaturization and modularization, most of the equipments were newly designed without adopting the off-the-shelf products except for the syringe pump, etc. It provided sufficient functions prerequisite in clinical at UCjla.sagepub.comDownloaded from diagnosis such as analytical methods of about 70 clinical tests. The BioRobot platform is composed to a 4-DOF robot arm, end effector, reagent chamber module, elevator module to supply microplates, sample tray module, insert and eject modules, incubator module, and photometry scanner, and so on"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001063_imece2002-33568-Figure17-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001063_imece2002-33568-Figure17-1.png",
        "caption": "Figure 17. Surface Profile Change from Increase in Percent Overlap",
        "texts": [
            " As shown in Figure 16, the powder flow initially is unfocused as it passes through the powder delivery nozzle, but the nozzle guides the powder concentrically towards its center, and essentially \"focuses\" the beam of powder. The smallest diameter focus of the powder \"beam\" is dependent upon the design of nozzle. If the laser beam diameter is getting small in diameter, e.g., 100\u00b5m, much of the supplied powder may never reach the cladding melt pool. Thus, there is unacceptably low powder utilization, which must be improved upon. Beam width overlap has strong influence in top surface roughness. The reason for this decrease in surface roughness is depicted in Figure 17. As the cladding pass overlap increases, the valley between passes is raised due to the overlap therefore oaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/31/2016 Ter reducing the surface roughness. In order to obtain the best surface quality, the percent pass overlap should be increased as much as possible. However, in order to decrease the wall surface roughness, the cladding layers should be made as thin as possible.17 Either or both of these changes should not have a significant impact on material strength"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002179_s11432-006-0397-z-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002179_s11432-006-0397-z-Figure4-1.png",
        "caption": "Fig. 4. Scheme of the reactions involved in the determination of the HIgG.",
        "texts": [
            " After modification of Au electrode and immobilization of anti-HIgG, the HIgG presented in the sample was captured by anti-HIgG, remaining connected to the solid phase; the anti-HIgG-HRP reacted with the immunocaptured HIgG. The addition of substrates solution to this immuno-reaction system initiated the redox reaction catalyzed by HRP. The current intensity produced in the redox reaction mentioned above was proportional to the amount of HIgG in the sample. A scheme of the reactions involved in the determination of the HIgG is presented in Fig. 4. The enzymatic reaction of HRP occurs in three steps[22], as shown in the reactions (1)\u2015(3). The enzyme catalyzes the reduction of H2O2 oxidizing the heme group (1): (1) 3+ 2 2 2HRP(Fe )+H O compound I+H O\u2192 The oxidized enzyme (compound I) is reduced to compound II (2) that is further reduced to the active form (3): 3+HRP(Fe ) compound \u0399+AH compound II+A\u2192 (2) (3) 3+ 2compound \u0399\u0399+AH HRP(Fe ) A+H O\u2192 + Reducing agents (AH) like iodide are able to donate electrons to both compounds I and II. Consequently, the reduction of iodine on the electrode surface can be used to follow the peroxidase-catalyzed reaction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000034_robot.1992.220260-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000034_robot.1992.220260-Figure7-1.png",
        "caption": "Figure 7: (1.) Left type-2 curve, (r.) Left type-3 curve",
        "texts": [
            " Our type-1 curve (standard curve) bases on a method introduced by Nelson (refer to [4], figure 6): the sequence S = (so,. . . . s,,) of line segments and fit- 0 r, 4: polar coordinates, IC: curvature Figure 6 shows our left type-1 curve fitted into the corner p2 defined by the subsequence (pl,pz,p~) of S. The start and the end of the curve are indicated by p , and pe. The center of the polar coordinate system is marked by c. If R is given, the other parameters and the resulting curve can be computed with well known methods. Two type-1 curves form one type-2 curve (figure 7). It is well suited to depart from small corridors, because p , = p2 . If RI and Rz are known, the two curves can be computed. Our type-3 curve is the dual one to the type-2 curve ( p , = p2) and is well suited to drive into small corridors. The type-4 curve is the result of shifting p , along the extension of the vector p 2 - p l and pe along the extension of vectorp2 - p 3 (figure 8 ) . The type-5 curve is used to change from forward drive to backward drive or vice visa (figure 8). For each different vehicle IC and each curve type j, a list of different radii Rk,j,i exists"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002325_j.triboint.2006.09.003-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002325_j.triboint.2006.09.003-Figure5-1.png",
        "caption": "Fig. 5. Total contact deformation in the vertical direction dz of a wire race ball bearing with a preload acting on it.",
        "texts": [
            " 4, the equations of equilibrium below can be formed to calculate the force of the individual contact point: Z\u00f0F 1 F2\u00desin a F a \u00fe Gi\u00f0 \u00de \u00bc 0, (8) \u00f0F 1 \u00fe F2\u00decos a cos\u00f0c\u00de\u00bd \u00fe cos\u00f02c\u00de\u00fe; ;\u00fecos\u00f0\u00f0Z 1\u00dec\u00de \u00fe cos\u00f0Zc\u00de 0, \u00f09a\u00de \u00f0F 1 \u00fe F2\u00decos a sin\u00f0c\u00de\u00bd \u00fe sin\u00f02c\u00de\u00fe; ; \u00fe sin\u00f0\u00f0Z 1\u00dec\u00de \u00fe sin\u00f0Zc\u00de 0, \u00f09b\u00de where c is the rolling element location distribution angle: c \u00bc 2p Z . (10) When the bearing is subjected to no external loads, the only resultant force is that produced by its own mass. Since the outer framework is fixed, the inner one at contact point no. 1 will experience that resultant force due to its mass, while at contact point no. 2 no force will be realized, namely F 2 \u00bc 0. Therefore F1 sin a F a \u00fe Gi Z \u00bc 0, (11) F3 \u00fe F 4 F1 \u00bc 0, (12) \u00f0F3 F 4 F1\u00decos a\u00fe Gb \u00bc 0. (13) Total contact deformation of the bearing in the vertical direction (see Fig. 5) can be defined as: dz \u00bc cos\u00f0a\u00de\u00f0d1 \u00fe d2 \u00fe d3 \u00fe d4\u00de. (14) Because the normal contact force at contact point no. 2 is equal to F 2 \u00bc 0, the resulting contact deformation is equal to d2 \u00bc 0. In this case, the minimum magnitude of d2 occurs, it is defined as dzmin. Even though shear failure is not expected to occur in practical engineering situations, the critical condition for shear failure of contact can be achieved by increasing an external preloading force. In this situation, the mathematical description is as follows: F4 \u00bc F2, (15) F1 \u00bc F3, (16) sin\u00f0a\u00de\u00f0F 1 F2\u00de F a \u00fe Gi Z \u00bc 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001768_iecon.2003.1280576-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001768_iecon.2003.1280576-Figure1-1.png",
        "caption": "Fig. 1 . Coordinates of SynRMs.",
        "texts": [
            " Sensorless control from standstill state t o high-speed raiiges can be realized by the combination of these methods. The construction of t,his paper is shown as follows. First, we discuss mathematical models of SynRMs, and indicate the EEMF model. Second, the positioii estimation methods based on the EEMF model and the system identification method are proposed. Finally, we describe the results of experiments on the proposed sensorless control system. 11. Mat,hematical models of synchronous relnctance mnt.nrs Coordinates used in this paper are defined as Fig.1 shows. The a-p' coordinate is defined as the fixed coordinate. The d-q coordinate is defined as the rotating coordinate. The 7-6 coordinate is defined as the estimated rotating coordinate. The largest value in rotor inductances is defined as L,,,, and the smallest value in rotor indiictance is defined as L,in. In this paper, the d-axis direction of motor models is selected in the same direction as L,;,, we shall return to this point later. The circuit equation on rotating coordinates is written as eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002244_s1064230706030063-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002244_s1064230706030063-Figure6-1.png",
        "caption": "Fig. 6. The time-optimal feedback control for k = 0.5.",
        "texts": [],
        "surrounding_texts": [
            "Let us analyze singular optimal trajectories that reach the terminal states x1 = \u03c0(2n + 1) and x2 = 0 for a constant control either u = +1 or u = \u20131. Let us present the detailed singular trajectory for x1(T) = \u03c0 (n = 0), x2(T) = 0, and u = \u20131. We set the terminal values of the adjoint variables so that p1(T) < 0 and p2(T) = 0 and prove that p2(t) < 0 for t < T. In this case, Eq. (2.3) holds. Without loss of generality, the adjoint variables can be normalized so that (3.1)p1 T( ) 1, p2 T( )\u2013 0.= = Let us substitute u = \u20131 into system (1.5) and find its first integral To find the constant C1, we substitute the terminal conditions x1 = \u03c0 and x2 = 0 into the found expression for the first integral. As a result, we obtain (3.2) For the trajectory that reaches the terminal state under the control u = \u20131, by Eqs. (1.5), we have x2 > 0 and x1 < \u03c0 for small positive T \u2013 t, i.e., at the end of motion. Let us change variables (3.3) and represent Eq. (3.2) in the form (3.4) x2 2 2 ---- x1 kx1+cos\u2013 C1.= x2 2 2 ---- 1 x1 k \u03c0 x1\u2013( ).+cos+= \u03c0 x1\u2013 y= x2 R y( ) 2 1 ycos\u2013 ky+( )[ ]1/2.= = JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL Vol. 45 No. 3 2006 TIME-OPTIMAL CONTROL 387 Therefore, when t varies from T to \u2013\u221e, the variable y monotonically increases from 0 to \u221e. Hence, y can be taken as an independent variable along the considered trajectory. Let us analyze the behavior of the adjoint variable p2(y) for this trajectory. Note that, by (2.3), the sign of p2 determines the control. Let us rewrite the adjoint equations (2.2) using y as an independent variable and taking into account (1.5) and (3.4) (3.6) Eliminating p1 from these equations, we arrive at the following equation for p2: (3.7) Let us multiply both sides of (3.7) by R and transform it taking into account the relation (3.8) which follows from (3.4). We have d p1 dy -------- p2 ycos R y( ) -----------------, d p2 dy -------- p1 R y( ) -----------.= = d dy ----- R d p2 dy --------\u239d \u23a0 \u239b \u239e p2 ycos R -----------------.= R dR dy ------ y k,+sin= d dy ----- R2d p2 dy --------\u239d \u23a0 \u239b \u239e d dy ----- ysin k+( ) p2[ ].= 388 JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL Vol. 45 No. 3 2006 RESHMIN, CHERNOUS\u2019KO Integrating this equation, we obtain (3.9) where C2 is a constant. At the terminal time instant t = T, by equations (1.8), (3.1), and (3.3), we have In addition, (3.1), (3.5), and (3.6) imply that Substituting these data into (3.9), we find C2 = 0 and (3.9) takes the form (3.10) Note that the general solution to this homogeneous R2d p2 dy -------- ysin k+( ) p2\u2013 C2,= y 0, p2 0.= = R2d p2 dy -------- R p1 0 when y 0.= R2d p2 dy -------- ysin k+( ) p2\u2013 0.= equation can be expressed as follows: (3.11) where C is a constant. This can easily be verified using relation (3.8). Finally, we obtain from (3.6), (3.8), and (3.11) the expression for p1 (3.12) Therefore, to satisfy the terminal conditions (3.1) for p1, we should set C = \u20131/k in (3.11) and (3.12). Thus, it is clear that, along the optimal trajectory corresponding to the control u = \u20131, the adjoint variable p2(t) is negative for all y > 0, and, consequently, for all t < T. As a result, the singular trajectory for u = \u20131 satisfies the necessary optimality conditions. The same situation takes place even for the trajectory for u = +1, which is located symmetrically with respect to the trajectory considered above relative to the point x1 = \u03c0, x2 = 0. The singular trajectories arriving at the points p2 CR y( ),= p1 R d p2 dy -------- CR dR dy ------ C ysin k+( ).= = = JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL Vol. 45 No. 3 2006 TIME-OPTIMAL CONTROL 389 x1 = \u03c0(2n + 1), x2 = 0 can be obtained by shifting singular trajectories tending to the point x1 = \u03c0, x2 = 0 by 2\u03c0n."
        ]
    },
    {
        "image_filename": "designv11_28_0003740_1.2975154-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003740_1.2975154-Figure1-1.png",
        "caption": "FIG. 1. Magnetic flux density in point P generated by a volume and b surface magnetic charges.",
        "texts": [
            " In general, inside the magnet, M depends on the point P where it is evaluated. Let us denote by P the vector that identifies P with respect to an orthogonal Cartesian coordinate system. The starting point of P is fixed in the origin O X ,Y ,Z of the coordinate system and, consequently, is M=M P . Now we define a vector P whose starting point is coinciding with O X ,Y ,Z . Let us indicate by P the magnetic flux density in the final point P of P . P is external or internal with respect to the magnet. With reference to this situation Fig. 1 it can be demonstrated1,2,8 that P is defined by the sum of two terms, BV P and BS P , that is, B P = BV P + BS P , 4 where BV P = 0 4 V M P P \u2212 P P \u2212 P 3 dV , 5 BS P = 0 4 S M P P \u2212 P P \u2212 P 3 dS . 6 P \u2212P is the magnitude of the vector P \u2212P and S is the surface that bounds the volume V of the magnet. In Eqs. 5 and 6 P identifies points inside the volume V Fig. 1 a and points of the surface S Fig. 1 b , respectively. Furthermore, in the present case, we define the volume and surface charge density, denoted by M and M, respectively, as M P \u2212 \u00b7 M P , 7 M P M P \u00b7 n . 8 n is the unit vector of the oriented straight normal line to the surface S in the point P. n is oriented so as to always come out from the volume V of the magnet Fig. 1 b . Then, from Eqs. 7 and 8 , we can write the explicit expressions of M P and M P by the M components Mx, My, and Mz, M P = \u2212 Mx P x + My P y + Mz P z , 9 M P = Mx P nx P + My P ny P + Mz P nz P . 10 III. VOLUME CHARGE MAGNETIC DENSITY M FOR HELICOIDAL MAGNETS WITH CONSTANT MAGNETIZATION MAGNITUDE Let us consider a left handed helicoidal sector with rectangular section. Figure 2 a schematically illustrates the solid shape that has been obtained by two helicoids that have a straight line perpendicular and passing through the relative common axis a\u2212a"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003538_iecon.2008.4758160-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003538_iecon.2008.4758160-Figure7-1.png",
        "caption": "Fig. 7 \u2013 Active circuit during the excitation period using the alternative converter .",
        "texts": [
            " Driving the SRG with a half-bridge converter topology the excitation period of each phase begins when the controlled switches are conducting, the inductance is increasing, the diodes are not conducting and the phase winding generates a positive counter EMF. The generating period begins when the controlled switches are not conducting, the inductance is decreasing, the diode is conducting and the phase winding generates a negative counter EMF. In this case the voltage over the load is that of equation (2). Using the reduced switches count converter topology the remarkable change is that the voltage over the load is E plus the output voltage of the rectifier bridge. Fig. 7 show the active circuit during the excitation period of the alternative reduced switches count converter topology. Fig. 8 shows the active circuit during the generating period for the same topology. It can be observed in Fig. 8 that de applied voltage is in series with de back electromotive force. The SRG mathematical model is evaluated for both converters using a computing program whose inputs are the phase voltages and the mechanical torque. The outputs are the currents at the phases, the angular speed and the rotor position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002425_j.sna.2006.01.016-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002425_j.sna.2006.01.016-Figure2-1.png",
        "caption": "Fig. 2. 3D model of the sensing element.",
        "texts": [
            " The flat sheet of the sensing element is very sensitive to load changes from the rigid centre. The load changes can cause elastic strains in the flat sheet. These elastic strains will then be transferred to the strain gages pasted on the surface of the flat sheet. Three Wheatstone F l r he light from the flash is then recorded by the cameras as the ynchronizing signal. . The shot-put sensor .1. Principle of sensor The shot-put sensor is a strain gauge sensor that can simulaneously measure forces along three orthogonal directions. A D model of the sensing element is shown in Fig. 2. This type f structure is made of high-quality alloy structural steel. The implified analysis model of this sensing element is a flat sheet ith a rigid centre under a concentrated load, as shown in Fig. 3. n this scenario, some key mechanics parameters of the sensing lement have to be calculated, such as the maximum deflection nd the maximum stress. These parameters play a crucial role n the optimum structural design of the sensing element [7]. The maximum deflection and the maximum stress of the flat heet under a concentrated load all emerge at the edge of the ig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000460_robot.1992.219917-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000460_robot.1992.219917-Figure2-1.png",
        "caption": "Figure 2: An articulated finger represented as a generalized impedance.",
        "texts": [
            " The earlier work, that forms the foundation for the resent concept, involved the static grasp analyses by Nguyen [I!, Cutkosky and Kao 21, Hanafusa [6], and Salisbury 71, among others. They developed synthesis methods for grasp stikness only. The present work considers the synthesis of gras s for decoupled dynamic behavior, described via the concept of t i e grasp admittance center 131. 2 Grasp Impedance Matrices 2.1 The Approach As stated earlier, the impedance property of a grasped object is derived from the impedance properties of the graspin fingers. Figure 2 shows a finger tip represented as a generalizedi spring mass damper system. Let Kd, Bd, Md E R N x N be the desired apparent stiffness, damping and inertia matrices of the grasped object, specified numerically. To achieve an admittance center, they must be diagonal and their dia onal elements be positive and are chosen to achieve a desired cfynamic behavior on each object degree of freedom 131. As did Salisbury [7], projecting these matrices onto the finger tips using congruence transformation involving the grasp Jacobian does not always assure positive finger ti impedances To overcome this problem, we use the grasp coniguration mal trix to project the finger tip impedances on to the object frame in symbolic form as was done by Nguyen 11"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003765_09544070jauto969-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003765_09544070jauto969-Figure1-1.png",
        "caption": "Fig. 1 Camshaft pulley torque transducer",
        "texts": [
            " The engine is operated under dry sump conditions, keeping the crankcase windage losses negligible. The total and component friction are measured simultaneously and synchronized with the engine crank angle. The Ricardo Hydra gasoline engine is a four-valve engine having two direct-acting overhead camshafts acting on flat-faced hydraulic lash-adjusted bucket followers driven by a toothed timing belt. The engine valve train friction torque measurement is carried out by using specially designed camshaft drive pulleys incorporating torque sensors fitted to both inlet and exhaust camshafts (see Fig. 1). The torque transducer is a two-part construction with instrumented central hub and toothed pulley gear. The transducers are designed to be insensitive to belt loading through the careful arrangement of strain gauges in the bridge. The calibration of the torque transducers indicated an error less than 0.03Nm for cyclic average drive torque, which is negligible. The engine drivetrain layout with the torque transducers in situ is shown in Fig. 2. The details of the torque transducer, calibration, and signal conditioning can be found in Mufti and Priest [2]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002244_s1064230706030063-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002244_s1064230706030063-Figure10-1.png",
        "caption": "Fig. 10. The transition to a unique (smooth) dispersal curve when k increases, k = 0.60, 0.65, 0.70, 0.75, 0.77, and 0.79.",
        "texts": [
            " The figures show that, when k increases, the number of switching curves and dispersal curves decreases gradually. After passing the threshold value k \u2248 0.80, only singular trajectories (investigated in Section 3) 392 JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL Vol. 45 No. 3 2006 RESHMIN, CHERNOUS\u2019KO and only the smooth dispersal curve passing between them remain. The specified mechanism of transformation of the phase portrait corresponding to the optimal feedback control is depicted on a larger scale in Fig. 10 (singular trajectories are not shown). Let us describe the properties of these phase portraits. Note that, in Fig. 10, the switching curves do not touch the abscissa axis, and the dispersal curve passing through the point (0, 0) has three clearly distinguishable smooth legs. This is explained by the fact that its JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL Vol. 45 No. 3 2006 TIME-OPTIMAL CONTROL 393 middle leg separates the optimal trajectories that belong to two different families, and any of the extreme legs separates optimal trajectories of the same family. A similar pattern takes place in a domain close to the origin and in other ranges of k when the number of switching curves and dispersal curves changes (for example, see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001901_robot.2004.1308084-FigureI-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001901_robot.2004.1308084-FigureI-1.png",
        "caption": "Fig. I Coocepbl figure for a hybrid robot constructed by comb-g two modules",
        "texts": [],
        "surrounding_texts": [
            "An Efficient Dynamic Modeling Methodology for General Type of Hybrid Robotic Systems\nGoo Bong Chung, Byung-Ju Yi, Dong Jin Lim School of Electrical Engineering and Computer Science\nHanyang Universiv Ansan. Gyeongg\u2019 426-791. KOREA\nbj@hanyang.ac.h\nAbstrad- In thIs paper, we deal with the kinematic and dynamic modeling of hybrid robotic systems that are constructed by combination of parallel and serial modules or series of parallel modules. Up to now, open-tree structure has been generally employed for dynamic modeling of hybrid robotic systems. However, it requires not only expensive computation as the complexity of the system increases. hut also must perform dynamic modeling for the whole manipulator again even if the partial portion of the robot structure k changed Therefore, we propose 811 efficient dynamic modeling methodology for byhrid robotic systems. In the proposed method, initiaUy tbe local dynamics of each of modules are obtained with respect to its independent joint coordinates and then the dynamics of the hybrid robot is calculated ntilidng tbe concept of virtual joints that are attached to the base of each module of interest, The virtual joints are assigned to have the appropriate number of DOFs in the operational space to represent the motion of all the proximal modules from the module of Merest to the ground. For general multiple module-based hybrid robots, a recursive dynamic formulation of the proposed method is derived and the usefulness of the method is veriRed by comparing the computational eftieiency of both the proposed method and the existing method. Index Terms - Hybrid Robot, Dynamic Modeling, Kinematics\nI. INTRODUCTION In general, three main methodologies, categorized as the Recursive Newton-Euler formulation [l], the Lagrange-Euler method [Z-31, and Lagrange\u2019s form of the Generalized Principle of d\u2018AlmLmt(open-tree structure method) have been extensively investigated for the dynamic modeling of robots. All these efforts have contributed to the progress in dynamic modeling for robots.\nA hybrid robot denotes a robot system that is constructed by combination of serial and parallel modules or a series of parallel modules. Wittenberg [4] was the first one who suggested a modeling methodology for general type of linkage systems including robotic systems. The Lagrange\u2019s form of the generalized principle of d\u2019Alembert was employed to integrate the dynamic models of open-tree structures into a dynamic model in terms of minimum coordinates. Using the same principle, Freeman and Tesar [5 ] , Sklar [6], Cho [7], Kang, et al [PI, and Park, et al [9] presented dynamic modeling methodologies appropriate to robotic systems. Using this principle, a closed form dynamic model for general class of\nWheekuk Kim Department of Control and Instrumenfation Engineering\nKorea Universiy Jochiwon, Chungnam 339-700, KOREA\nwbeekuk@korea.ac.h\nhybrid robotic systems can be derived. However, the previous dynamic modelmg methodologies have shortcoming in hybrid robotic systems. because it must perform dynamic modeling for tbe whole manipulator again even if the partial structure of the robot is changed a little and that it requires expensive computation as the complexity of the system increases. For example, even though the dynamics of the two independent systems, as shown in Fig. 1, are known, the whole dynamics must he reconstructed when the two modules are combined as one system.\nIn this paper, therefore, we propose an efficient dynamic modeling methodology for hybrid robotic systems that are constructed by adding one robot module to another successively or hy adding one module to an existing robot mechanism. The advantage of our proposed algorithm is that it is not necessary to calculate the whole dynamics again and that the computational efficiency is enhanced remarkably.\nThe proposed method is explained as follows. First, the dynamic model for the proximal module of a hybrid robot is obtained with respect to the independent joint coordinates. Then, we represent the operational output of a lower module as equivalent virtual joints and attach them at the base of the upper module. Next, the dynamic model of the upper module including the virtual joints is obtained. Eventually, the effective dynamic model of the lower model is represented as the sum of virtual joints\u2019 dynamics and its own dynamic model. Here, the physical meaning of the dynamic forces at the virtual join$ is equivalent to the reaction forces exerted on the platform of the lower module by the dynamic motion of the upper module.\n. This work is parfially supported by the Korea Health 21 R&D Project, Minishy of Health and Welfare, Republic ofKorea, under Grant 02-PJ3-PG6-EVW 0003.\n0-7803-8232-3/04/$17.00 82004 IEEE 1795",
            "Note that the virtual joints are the same as the output\n, E of the lower module and the output velocity \u20184 of the hybrid robot is the velocity ,& of the upper module. By rearranging Fq. (I), (2), and (3), we can obtain the velocity equation of the hybrid robot as\nII. In this section, a hybrid robot structured by combination of a parallel 3 DOF 6-bar linkage and a serial type 3 DOF robot is employed as an illustrative example to explain the concept of the proposed dynamic formulation. Fig. 2 depicts the proposed model. In the proposeij method, it is assumed that the whole kinematic and dynamic-models of both the lower and upper modules are already given.\nTo obtain the dynamic model of this hybrid robot, we need to derive the kinematic model ofthe robot first.\nA. Firsf-Order Kinematics The mobility of the given system is 6. Gus, the number of minimum joints required to position the system is 6, which are selected by any three joints of the 6-har~linkage and the three joints of the serial robot. Then, the output velocity ,e of the lower module can be represented in t e p of the independent jo&t.variables. ,fa by .open-chain kinematics as follows [S-8,\nA H Y k D ROBOT CONSTRUCTED BY TWO MODULES\n~\n.\n. . 101\n. ,4= ,[G,\u2019l,&. (1)\nwhere ,[G:-]E R\u201d\u2019 , ,A ;R3, and ?&E Ri .\nincluding the virtual joints is given as Similarly, the velocity \u2019 ,LE R\u2019 of the upper module\nwhere\n(3)\n,in ER\u2019 and ER\u2019 denotes the velocity vector of the independent joints of upper module and that of the virtual joints, respectively and ,[G:]E R3\u201d\u201d6 .\nwhere\nand \u2018do - E R6 given by\ndenotes the independent inputs of this hybrid system, and [O],,, and I,,, are a 3 x 3 null matrix and a 3 x 3 identity matrix, respectively.\nB. Dynamics The dynamic model of the lower module, shown in Fig. 2, can also be obtained by the open-lree structure model formed by cutting the ienter of the platform.\nThe dynamic model with respect to the three independent joints of the lower module is obtained by applying the principle of virtual work between the Lagrangian coordinates and the minimum independent joints as [X, IO]\n,L = ,rCI,ijO+ ,j: , [ C l , A . (7)\nNow, the dynamic model of the upper module including the virtual joints will be described. The dynamic equation can he described as\nwhere ,L ER^ denotes the dynamic load of the upper module itself. ;r, ER\u2019 denotes the dynamic load at the virtual joints to support the dynamics of the upper module. These forces are exerted on the platform of the lower module. Therefore, the dynamic load at the virtual joints is distributed to the independent joints of the lower module.\nFinally, the whole dynamic model w@ respect to the independent joints of the hybrid robot can be represented as"
        ]
    },
    {
        "image_filename": "designv11_28_0000515_robot.2001.933195-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000515_robot.2001.933195-Figure4-1.png",
        "caption": "Figure 4: Model of a Microrover",
        "texts": [
            " The information about the traversability is added to each grid on EEM. By using EEM, path planning can be conducted in such a way as if the rover were a point while the size of the rover is automatically taken into account. 371 2 3 Traversability 3.2 Judgment of Traversable Area 3.1 Rover Geometry The performance of a rover inoviiig in an unstiuctured environment depends upon the geometry, such as, susperision, size, the number of wheels etc. \u2018I\u2019o consider the size of a. planetary rover, a model is introduced as shown in Fig.4. Rover geometry is expressed by three parameters : roll angle, pitch angle, and height. r, l h e maximum roll angle umnZ is equivalent to the capability to go over obstacles. The pitch angle ,Bvaaz iiieaiis the ma.ximurn negotiable angle over which a rover ca.n move. The height hmin means the inininium distance between the body of a rover a.nd the ground to avoid hitting the ground. Though this model shows the case of a five-wheel rover, it is easy to adapt such a inodeling to any other rover with different geometry"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003432_icarcv.2008.4795739-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003432_icarcv.2008.4795739-Figure2-1.png",
        "caption": "Figure 2. Quad-rotor flight vehicle components.",
        "texts": [
            " Two networks are used to communicate i) position and attitude data and ii) command and control data. The system was laid out in a modular fashion such that the various types of vehicles could be added or removed for rapid evaluation and development. The flying vehicles were modified DraganFlyer remotelycontrolled quad-rotor helicopters. While commercially available, the onboard electronics were modified to allow communication with the command and control computers and to enable additional functionality. Figure 2 shows an image of the primary vehicle components. Communication was done via either serial radio or Bluetooth. Furthermore, the helicopters were augmented with Robostix on board logic as well as a gyro sensor to provide additional sensing and control capabilities. The basic control architecture is shown in Figure 3. Two approximate models were used for simulation purposes and the design of the implemented collision avoidance controller; one was designed for both the x- and yaxes. The following state equations are for quad-rotor helicopters controlled with position command in both the x and y direction as well as roll and pitch command"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000880_ijcat.2002.000288-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000880_ijcat.2002.000288-Figure8-1.png",
        "caption": "Figure 8 Angle of misalignment.",
        "texts": [
            " Up to now, the misalignment moments calculated have been based on a \u00aexed angle of misalignment, i.e. the angle of misalignment is assumed unchanged throughout the spline coupling and is equal to the angle of misalignment between the shafts connected to the coupling. However, under the misalignment moments generated at the splines, the coupling will undergo elastic deformation as a simply supported beam subjected to externally applied moments. The deformation would effectively reduce the slopes (or angles of misalignment) at the two end splines, see Figure 8. Figure 8(a) shows misalignment in a very stiff coupling where the angle of misalignment remains constant at go. Figure 8(b) shows a relatively \u00afexible coupling where deformation of the misaligned coupling reduces the \u00aenal angles of misalignment at the two splines to g. Thus, the \u00aenal angle of misalignment will be less than that between the connected shafts depending upon both the tooth and shaft \u00afexibilities. Therefore, one can say that the distribution of the forces and moments throughout the coupling will be dependent upon the stiffness of the spline teeth and the shaft. In this study, the equivalent stiffness of both the spline teeth and shaft was determined by considering the teeth and shaft as two springs connected in series",
            " The angle of misalignment, due to assembly and cumulative manufacturing errors, between the driving and driven shafts that are connected by the coupling is 0.1468; or 0.00255 rad. The coupling stiffness was \u00aerst calculated considering the teeth de\u00afection only as a \u00aerst approximation. The results yielded a stiffness of 1:05 10 9 N=m and only ten teeth, out of a total of 38 teeth of the entire spline, were to share the transmitted load; the rest of the teeth were unloaded. These results are presented in Figure 10(a). If the stiffness of the coupling shaft as well as the teeth stiffness are considered as pointed out earlier in Figure 8, then the net stiffness will be reduced to 0:26 10 9 N=m. This will allow more teeth to come into contact with the mating ones and the transmitted loads are as shown in Figure 10(b); where 18 teeth are transmitting loads out of the total 38 teeth. If the \u00afexibility of the neighbouring components to the spline shaft are considered as well, then the net stiffness is expected to become even less allowing more teeth to share the load transmission. An experimental substantiation scheme or a numerical one (like Finite Element Analysis) is obviously required to reach a balance between the system \u00afexibility (or stiffness) and the exact number of teeth that transmit the load"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001160_tasc.2003.812898-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001160_tasc.2003.812898-Figure3-1.png",
        "caption": "Fig. 3. Connection of power supply of the bending magnets with SMES.",
        "texts": [
            " In this case, power rating of the ac/dc converter for magnet power supply can be reduced, resulting with the reduced cost of the total system. The system shown in Fig. 2(c) is the proposed system and studied hereinafter. The power supply of the bending magnets is divided into six separated power units, because the electric power rate for the bending magnet is too large to construct a power supply as one unit. By this method, the power rating for one power unit is reduced to the possible level about 5 kV and 10 MW. Fig. 3 shows connection scheme between the power units and the bending magnets. As seen in the figure, the 96 bending magnets are divided into three groups and both upper and lower coil of the magnet are connected separately by series in each group, and connected with the power units in turn so as to make one excitation loop. The configuration of one power unit, which is 1/6 of the bending magnet power supply, is shown in Fig. 4. Each of the power unit is composed of a current source ac/dc converter and SMES"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003095_j.jelechem.2007.02.012-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003095_j.jelechem.2007.02.012-Figure1-1.png",
        "caption": "Fig. 1. (a) Drawing showing a cross section of the assembled cryostat and the cell. (1) External stainless steel cell body. (2) Inner stainless steel cell, it is vacuum-tight between the external cell body and the inner cell. (3) Inner CaF2 window. (4) External CaF2 window. (5) Working electrode. (6) Silver wire quasi-reference electrode. (7) Counter electrode: Pt wire. (8) Teflon tubing. (9) Thermocouple of the thermostat for measuring the temperature. (10) Teflon gasket. (11) Tightening brass cap of the inner CaF2 window. (12) Claviform-thermal-conductor. (13) Cryostat bath. (14) Dewar flask (3 L in volume). (15) Cold end of the claviform-thermal-conductor. (16) Brass piston. (17) Lift staff connected with the brass piston. (18) Active carbon. (19) Resistance coil for heating which monitored by the thermostat. (20) Outer jack of the thermostat. (21) Liquid N2 intake. (22) Connection to a diffusion pump used for evacuation. (23) External stainless steel tube connection to the cryostat and the cell. (24) Bellows. (25) Silicon rubber stopper. (26) Inlet quartz capillary for injecting sample and N2 (or Ar) gas. (27) Outlet quartz capillary for releasing N2 (or Ar) gas. (b) Magnifying cross section drawing of the cell. Left: side cross section; right: front cross section. (c) Electrodes geometry of the cell.",
        "texts": [
            " For rapid-scan time-resolved spectroscopic measurements, 30 interferograms were added to each spectrum, the sampling interval is 1.17 s, and the spectral resolution is 16 cm 1. The resulting spectrum is defined as the potential difference spectrum: DR=R \u00bc \u00bdR\u00f0ES\u00de R\u00f0ER\u00de =R\u00f0ER\u00de where R(ER) and R(ES) are single beam spectra collected, respectively, at the reference potential ER and at a sample potential ES. After a potential step, the single-beam was collected while the current back to zero or steady near zero. The schematic view of the complete experiment is shown in Fig. 1, which consists of two main components: the cryostat and the spectroelectrochemical cell. The temperature of the spectroelectrochemical cell is controlled by the cryostat via a claviform-thermal-conductor. While the brass piston was lift with the lift staff, the liquid N2 in 3 L Dewar flask will be apart from the claviform-thermal-conductor, then the temperature in the cell will rise, and vice versa. Besides, there is a heating resistance coil, which monitored by the same thermostat with the measuring thermocouple, twisting around the top of the claviform-thermal-conductor, working as a temperature adjustment too"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001067_095441002760179771-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001067_095441002760179771-Figure3-1.png",
        "caption": "Fig. 3 Single specimen viewed from the top",
        "texts": [],
        "surrounding_texts": [
            "To obtain contact over the entire length of the coupling halves, one of the halves is machined by the external tool surface and the other by the internal tool surface. This produces a different geometry on either side of the coupling. If the coupling half is machined by the external tool surface then the teeth will have a concave geometry. If the coupling half is machined by the internal tool surface then the teeth will have a convex geometry; this is illustrated in Fig. 4. A large number of dimensions are required in order to de\u00aene the geometry of a Curvic coupling. Referring to F ig. 1, the dimensions used at the inside tooth radius for the present investigation were as follows: w, tooth width \u02c6 2.28mm; hc, chamfer height \u02c6 0.28mm; rf , \u00aellet radius \u02c6 0.6 mm; bh, bedding height \u02c6 1.10 mm; lg, angle of inclination of the gable (i.e. the gable angle) \u02c6 4.28; lc, angle of inclination of the chamfer \u02c6 458; y, tooth pressure angle \u02c6 308; a, addendum \u02c6 1.24mm; d, dedendum \u02c6 1.56 mm; t t , tooth thickness \u02c6 3.95mm; fh, \u00afange height \u02c6 1.88 mm; ht , whole depth (total depth) \u02c6 2.80mm; and hg, gable height \u02c6 0.08mm. The overall dimensions of the coupling are de\u00aened by the inside tooth radius \u02c6 30.2 mm, the tooth outside radius \u02c6 38.1 mm, the facewidth \u02c6 7.9 mm, the \u00afange backing thickness \u02c6 40.0mm for both Curvic halves, the diametrical pitch \u02c6 0.31, the inside \u00afange radius \u02c6 15.0 mm and the outside \u00afange radius \u02c6 52.0 mm. G01102 # IMechE 2002 Proc Instn Mech Engrs Vol 216 Part G: J Aerospace Engineering at The University of Iowa Libraries on July 1, 2015pig.sagepub.comDownloaded from The general dimensions of the photoelastic models, in mm, are shown in F ig. 5."
        ]
    },
    {
        "image_filename": "designv11_28_0001469_1350650042128085-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001469_1350650042128085-Figure1-1.png",
        "caption": "Fig. 1 Schematic of 228mm o.d. thrust bearing test rig",
        "texts": [
            " The purpose of the present paper is therefore to clarify this ambiguity and to provide detailed information necessary to quantify the effect of oil viscosity grade on bearing main operating parameters: temperature, power loss and oil film thickness. Two test rigs were used in the experimental programme. A test rig with a 228mm o.d. bearing was employed in the low-speed range, while high-speed runs were carried out in the 267mm o.d. bearing test rig. The test rig with the 228mm bearing is fully discussed in reference [5]. A brief description only is given here. A general arrangement of the test rig is shown in Fig. 1. Two identical test bearings (1, 2) are mounted in the guiding holders (3), which can slide in the housing (4) positioned on steel wheels (5, 6) with rolling element bearings. Such an arrangement allows direct measurement of the bearing power loss since the housing is free for rotation by the action of bearing frictional torque. The rotation is prevented by a load cell (7), which gives the value of torque. The test bearings are loaded back to back against separate collars. The required load is applied by means of four hydraulic cylinders (8, 9) located between the bearing holders"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003481_icelmach.2008.4800054-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003481_icelmach.2008.4800054-Figure3-1.png",
        "caption": "Fig. 3. Circuit model of our proposed test method.",
        "texts": [
            " The results are from measurements taken using our proposed method and a conventional method. Furthermore, there are the results from an FEM analysis. The specifications of the test PMSM are shown in Table II. Figure 2(a) and Fig. 2(b) show models of the circuit used with a conventional AC injection method [2]. The rotor is locked and AC is supplied to the PMSM. The value of AC current is varied, and Ld and Lq are calculated from the AC voltage and AC current with the following equation: ( ) AC ACAC if iRv iL \u03c02 222 \u2212 = (6) Figure 3(a) and Fig. 3(b) shows models of the circuit used with our proposed method, which uses DC and AC superposition. The rotor is locked and DC and AC superposition is supplied to the PMSM. The value of the AC component is held at about 0.5[Arms], frequency is held at 50[Hz], and the value of the DC component is varied. Then, Ld and Lq are calculated as described in Section II. Figure 4 shows the results of measuring \u03c8d\u2019. \u03c8d\u2019 means the gradient of the d-axis magnetic flux. \u03c8d\u2019 was different depending on whether the supplied id is positive or negative"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000102_robot.1993.292243-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000102_robot.1993.292243-Figure1-1.png",
        "caption": "Figure 1. A disk rolling on a flat surface is described by four configuration variables: z, y, 0 , and a. The disk has however two degrees of freedom due to the presence of two nonholonomic constraints.",
        "texts": [
            " As a result of the nonintegrable nature of these differential constraints, it is not possible to obtain functions of the form that will enable us to eliminate some of the dependent variables. Naturally, nonholonomic systems require more coordinates for their description than there are degrees of freedom in the system. An interesting feature of nonholonomic mechanical systems is their ability to access a configuration space of higher dimension than the number of it\u2019s degrees of freedom. A simple example is that of a disk rolling without slipping on a flat surface. The configuration space of the disk rolling on the z-c-y plane, shown in Fig.1, is described by the four coordinates (z, y, 0 , a) , but the system has only two degrees of freedom because of the following two nonholonomic constraints clrc - 1- sin a dB = 0 dy - 1\u2019 cosudB = 0 (3) In spite of having only two degrees of freedom, it is quite intuitive that the rolling disk can arrive at any configuration (z, y, 0 , a ) from any other through proper path planning. Such a property is common to nonholonomic mechanical systems and can be attributed to the nonintegrable nature of their differential constraints. 802 US. Government Work Not Protected by US. Copyright For the rolling disk, our intuition can be strengthened if we consider the following example. Suppose, it is desired that the disk in Fig.1 change its coordinates from (x, y, 8, a) to (xd, yd, 8, a) . Then a feasible trajectory would be the path segments A 0 and OC. The disk would roll forward from A to 0, and then roll backward from 0 to C. The individual path segments A 0 and OC should have equal lengths such that 9 comes back to its initial value at the end of the path. Furthermore, the straight lines AB and CD should be tangent to the path segments A 0 and OC respectively, a t the points A and C. This will ensure that the net change of the variable a will also be zero over the complete path"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000418_095440603767764426-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000418_095440603767764426-Figure3-1.png",
        "caption": "Fig. 3 Reciprocal screw surface",
        "texts": [
            " Then, from equations (22) and (23), and with the help of algebra and line geometry, an algebraic scalar equation can be obtained representing a screw surface on which the reciprocal screw of the chosen pitch progresses. The equation is given as \u00a1 9s4 \u2021 3s2 \u2021 4 6asck \u00b3 \u00b4 xy \u2021 zw \u00a1 d \u2021 2as2 k \u00b3 \u00b4 w2 \u02c6 0 \u202624\u2020 Given a \u02c6 5:0 and d \u02c6 2:0, the direction cosine \u2026l, m, n\u2020 the resultant moments \u2026p\u00a4, q\u00a4, r\u00a4\u2020 and the pitch of reciprocal screw are obtained and plotted with respect to the change of y1 in F ig. 2. The geometric description of the reciprocal screw axes in all its possible positions is shown in Fig. 3, in which the length of the line segment represents the magnitude of the associated pitch. The algebraic surface takes the shape of an \u20188\u2019 with the yz plane as the plane of symmetry. The reciprocal screw with a zero-pitch forms a pure force constraint. Based on equation (23), four special con gurations with the zero-pitch reciprocal screw at y1\u02c6 08, 908, 1808 and 2708 can be given during the movement of one revolution of the input angle. At the special con gurations of y1\u02c6 08 or 1808, the screw Proc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003215_s11249-008-9399-x-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003215_s11249-008-9399-x-Figure1-1.png",
        "caption": "Fig. 1 Schematic illustration of the apparatus",
        "texts": [
            " For situations of spin with rolling and sliding, which usually occur in engineering practices, very limited experimental data are available. In the present paper, a simple method was employed to superimpose spinning motion to a sliding EHL contact, and film profiles under different spin were studied by interferometry. It is intended that this experimental study will provide some basic data for a better understanding of the spin effect on EHL contacts. A custom-made optical EHL test rig was employed in the experiments. Figure 1 gives the schematic of the test rig. The steel ball ` is loaded against the glass plate at an offset r with respect to the rotation axis O 0 O 00 , which can be accurately adjusted by the X\u2013Y table \u00b4. In the experiments, the glass plate is driven by the synchronous pulley \u02c6 and rotates around O 0 O 0 0 at an angular speed x. The steel ball ` is stationary. It can be easily apprehended that on the glass plate the movement of any point A can be decomposed into two components: translation at a velocity u1 in the y direction and rotation around the Hertzian contact center O at an angular speed x (See Appendix)",
            " At high speeds, the film thickness difference of the two side lobes is large. (4) In the present experiments, increasing loads can induce more effective spin effect within the EHL contact, the difference between the two side lobe film thicknesses gets large, and the horseshoe film shape is more distorted. The spin raised by load decreases the overall film thickness. Acknowledgments The authors would like to express their thanks for the financial support from the Ministry of Education of China (NCET07-0474). Appendix In Fig. 1b, the equation of line O0A is y \u00bc x tan a \u00f03\u00de The equation of line OA can be written as y \u00bc tan b\u00f0x r\u00de \u00f04\u00de Then the length of O0B can be readily obtained O0Bj j \u00bc r tan b tan a\u00fe tan b \u00bc cos a sin b sin\u00f0a\u00fe b\u00de r \u00f05\u00de and r1 and r2 are expressed by r1 \u00bc O0Bj j cos a \u00bc sin b sin\u00f0a\u00fe b\u00de r \u00f06\u00de r2 \u00bc r1 sin a sin b \u00bc sin a sin\u00f0a\u00fe b\u00de r \u00f07\u00de Velocity u is u \u00bc r1 x \u00bc sin b sin\u00f0a\u00fe b\u00de r x \u00f08\u00de Considering the projections of u1 and u on line AO are equal, u1 cos p 2 b \u00bc u cos a\u00fe b p 2 \u00f09\u00de Then we have u1 \u00bc u sin\u00f0a\u00fe b\u00de sin b \u00bc r x \u00f010\u00de u2 and u have the same project on the x axis, u2 cos p 2 b \u00bc u cos p 2 a \u00f011\u00de Then u2 can be obtained as u2 \u00bc u sin a sin b \u00bc sin a sin\u00f0a\u00fe b\u00de r x \u00bc r2 x \u00f012\u00de 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001202_0959651011540897-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001202_0959651011540897-Figure8-1.png",
        "caption": "Fig. 8 Operating curves for actuator 2",
        "texts": [
            "7), a gear ratio of 50 : 1 forrants of the eVort\u2013 ow plane an idealized admissible domain delimited by e=\u00d4e max, f =\u00d4f max and hyper- both actuators and the numerical parameters of the mechanical structure shown in Table 1.bolae corresponding to ef =\u00d4Pmax. The operating curve should remain in this admissible domain for the actuator The torque \u00f4 and the speed \u00f6 required from each actuator were computed from the inverse bond graphto be suitable for the task as the appropriateness conditions can be expressed as model of the manipulator and the prescribed output and the results of simulation for diVerent values of T are|e A(t) |\u00a2e max (4) shown in Fig. 7 and Fig. 8. For actuator 1, an example of an admissible operating domain corresponding to| fA(t) |\u00a2 fmax (5) a maximum torque \u00f4 max =1 N m, a maximum speed|PA(t ) |=|eA(t) fA(t) |\u00a2Pmax (6) \u00f6 max =300 rad/s and a power Pmax =100 W is represented. These results show that an actuator with theFigure 2 summarizes the graphical representation for the validation of an actuator where the relative position above characteristics is appropriate for task execution times up to T =0.3 s where the actuator is already closeof the operating curve and the admissible domain gives some indications on whether the actuator is appropri- to speed saturation",
            "064 I06899 \u00a9 IMechE 2001Proc Instn Mech Engrs Vol 215 Part I at NORTH CAROLINA STATE UNIV on May 11, 2015pii.sagepub.comDownloaded from of the operating curve indicates that a suitable actuator at a point x0 if (a) Lgj Lk f h i (x)=0\u2020 for all 1\u00a2i\u00a2m, 1\u00a2 j\u00a2m, k\u00a2r i \u00d51, and x in the neighbourhood of x0for this operational speed should be able to develop a speed of more than 400 rad/s, a torque of at least 1 N m and (b) the m6m matrix \u00e1(x) de ned as follows is nonsingular at x0:and a greater power (more than 200 W ). For the second link of the manipulator, operating curves are also presented in Fig. 8 for diVerent task execution times T. This shows that, for the same value \u00e1(x)= CL g1 Lr1\u00d51 f h1(x) \u00b7 \u00b7 \u00b7 L gm Lr1\u00d51 f h1(x) Lg1 Lr2\u00d51 f h2(x) \u00b7 \u00b7 \u00b7 Lgm Lr2\u00d51 f h2(x) ] ] ] Lg1 Lrm \u00d51 f h m (x) \u00b7 \u00b7 \u00b7 Lgm Lrm \u00d51 f h m (x)D (8) of T, the requirements from actuator 2 are greater in terms of speed but lower in terms of torque than for actuator 1. Figure 9 represents the operating curves of both actuators for T =0.3 s and the admissible domains For each output y i , the number r i is the rst diVerential indicate that, for actuator 1, a motor with characteristics order of y i at which at least one input appears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000458_robot.1994.351033-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000458_robot.1994.351033-Figure5-1.png",
        "caption": "Fig. 5 Hierarchy of approximations b) convex envelopes for the manipulator movements.",
        "texts": [
            " distance calculation capability. This is achieved by calculating the minimal distance vector between the two manipulators, the parts, and environment with a 100 Hz frequency. The method is based on the algorithm by Gilbert and Johnson [I71 and is accelerated by a primitive approximation and a dynamic object hierarchy [18]. Manipulators and obstacles are modelled by convex polytope. In dependence of any specific robot configuration the basic primitive approximations are being encompassed in a tree structure (Fig. 5a) and for every knot a bounding box approximation is being calculated off line. By precalculating this information it is possible to achieve extremely fast end calculations for the minimal distance vector during the operation. The technique of using both manipulators simultaneously but independently is based on the objective to make overlapping workspace areas accessible only to that manipulator which primarily requires the intersecting area. For this reason the convex envelopes (2D), which include the required space during manipulator movements, are being calculated at the execution planning level (Fig. 5b). In case of a likelihood of a path interference it becomes necessary to redirect the normal path of the manipulator which is required only to cross the intersection area, to a path closer to the manipulator base [19]. In a case where both manipulators require the same area it becomes necessary to move them sequentially. Since during the execution planning the intersection area is considered a resource, it is possible for the manipulator scheduling system to consider the above situations during the planning of the assembly sequence and if it is all possible to work around this problem"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002312_j.ijsolstr.2005.03.064-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002312_j.ijsolstr.2005.03.064-Figure4-1.png",
        "caption": "Fig. 4. Deformation of a thin film from Bj (the reference configuration) to B (the deformed configuration) with one-dimensional domain in the horizontal direction given by x 2 (0,L), with unit vectors e\u03021 and e\u03022.",
        "texts": [
            " The second step of the procedure is to write a general form of the strain energy density. This general form will be based on the chosen kinematics and choice of directed continuum theory. Based on the results from Eqs. (3.11)\u2013(3.14), it is apparent that there will be four independent displacement functions, u(x), v(x), /(x), and b(x), which are defined over the domain x 2 (0,L). Since there are four displacement functions for a one-dimensional domain, a micromorphic continuum theory, which is a particular case of directed continuum theories, will be used. Fig. 4 illustrates the columnar thin film model as described using a micromorphic continuum theory. The classical placement of points, described earlier as the placement of B into E, is denoted by v in the reference configuration and by x in the deformed configuration. The displacements u(x) and v(x) will be associated with the evolution of the body in the classical sense, where the displacement vector u(x) is defined in terms of the scalar displacement functions u(x) and v(x) 1 In indepe obviou rotatio consid u\u00f0x\u00de \u00bc u\u00f0x\u00dee\u03021 \u00fe v\u00f0x\u00dee\u03022",
            " \u00f03:15\u00de The resulting displacement gradient H is defined in the standard way H \u00bc ru\u00f0x\u00de \u00bc u0\u00f0x\u00de 0 v0\u00f0x\u00de 0 ; \u00f03:16\u00de where the primes denote differentiation with respect to x and $ is the gradient operator. The right column contains zeros since u and v are only functions of x. Eq. (3.16) is shown as a 2 \u00b7 2 matrix only because this form is more typical in continuum mechanics derivations. For the model presented thus far, there is no physical meaning to derivatives with respect to any other position, i.e., other than x, since the domain of the present problem is one-dimensional. Since H is not constant, the deformation associated with H in Eq. (3.16) is not homogeneous. The director in Fig. 4 is denoted by v\u0302 in the reference configuration (where it is a unit vector) and by x\u0302 in the deformed configuration. The deformation of v\u0302, whose components are taken to be the displacements / (x) and b(x), is associated with the evolution of the microstructure.1 In the microstructure, the deformation of v\u0302 is taken to be homogeneous, although it is not homogeneous as a function of x. Therefore, it is possible to make use of the displacement gradient associated with the evolution of the microstructure, H\u0302, to relate x\u0302 to v\u0302, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000019_28.90359-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000019_28.90359-Figure4-1.png",
        "caption": "Fig. 4. Locus of the flux linkage vector with drift.",
        "texts": [
            " With the drift, the calculated angle is that of the vector ?, DRIFT OR OFFSET COMPENSATION Drift is a common problem encountered in the implementation of integration. A particular source is the thermal drift of analog integrators. A transient offset also arises from the dc components that occur following a transient change. Such drift or offset can greatly influence the accuracy of both the position and the speed calculation. Ideally, in the steady state, the locus of the flux linkage space vector is a circle symmetrical about the origin, Fig. 4 shows that locus of a drifted flux linkage vector XL. The center of the circular locus has drifted by the amount DR + I + DI R + D R ' ( 18) O i L = tan-' ~ The error in angle ABx, = OiL - O x L is plotted in Fig. 5 for two values of drift expressed in per unit of the steady-state flux linkage magnitude. It is seen that the error can be as high as 33\" for a 0.4 per-unit drift. This flux angle error would cause a phase modulation in the current control at fundamental frequency, which in turn would cause an undesired fundamental frequency fluctuation in the electromagnetic torque produced by the PM motor. 1008 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS. VOL. 27, NO. 5 . SEPTEMBERJOCTOBER 1991 The speed calculation obtained by differentiation of the will also be impaired by drift. From Fig. 4, the angle calculated speed is !!& = d [tan-' (-)I. I + DI (19) dt d t In the steady state where R + jI = i LeJwt (20) the ratio of calculated speed to the actual speed becomes deiL 1 dt u l + D R c o s u t + D I s i n u t 1 + 2(DR cos wt + DIsin u t ) + DR2 + D12 - -- (21) Two curves of this speed ratio over a fundamental cycle are shown in Fig. 6. At a drift of 0.4 per unit, the error is seen to be as high as 130%. In a speed control loop, this error would cause a fundamental frequency modulation of the command current amplitude and thus cause a similar modulation in the motor torque. To overcome these drift problems, a compensation program has been devised. It is based on the observation that the locus of the flux vector is a circle in the steady state and departs only slightly from a circle during a transient since most of the flux linkage arises from the motor magnets. Thus, the drift can be determined by measuring the four extreme points P , Q, T , and S on the flux linkage plane of Fig. 4. The maximum and minimum real and imaginary components are determined each cycle to give DR + jDI = ';R(max) + 'LR(min) + j( X;,(max) XLl(min) 2 The calculated angle then becomes The effectiveness of the drift compensation program is demonstrated in Fig. 7 and 8. In each case, the speed command of the experimental system was suddenly reduced 2.0 1 UR =U[ = 0.4 per umr A DR = DI = 02 pm unit eu.( = 909 180. 270\u00b0 360\" Ratio of calculated to actual speed with drift 0, from an inverter frequency of 40 to 10 Hz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002764_11866565_70-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002764_11866565_70-Figure1-1.png",
        "caption": "Fig. 1. Conceptual figures of two equivalent double actuator mechanisms (a) two actuators connected in series, and (b) two actuators connected in parallel using a gear train",
        "texts": [
            " Control of contact force can be achieved through the use of an equilibrium point, as well as the controlled joint stiffness: simply moving the equilibrium point to a point within a contact object will cause the limb to exert a force on that object. One way to implement the control scheme would be placing the positioning actuator and the stiffness modulator in series on one joint axis. In this study we employed an electrical motor with a higher gear ratio as the positioning actuator, and an electrical motor with a lower gear ratio as the stiffness modulator. Fig. 1 (a) illustrates the two actuators placed on one joint axis. With the mechanism, we can control the equilibrium point and joint stiffness at the same time: one actuator commands the equilibrium point (positioning actuator), the other joint stiffness (stiffness modulator). The positioning actuator provides the equilibrium point (angle), and the stiffness modulator controls the restoring torque around the point. The positioning actuator is fixed to the base link, and the moving link is fixed to the output axis of the stiffness modulator. Fig. 1 (b) shows an equivalent mechanism to the one in Fig. 1 (a). Two actuators are connected in parallel by using a gear train: one gear is fixed to the output axis of the positioning actuator, the other to the frame of the stiffness modulator. Fig. 2 illustrates the double-actuator mechanism we have developed based on the idea of Fig. 1 (b). For the positioning actuator and stiffness modulator of the manipulator, BLDC motors were used, where the stiffness modulator had a lower gear ratio for back-drivability when attempting compliant motion control using the proposed control scheme. Fig. 2. Double-actuator mechanism with two parallel actuators When the manipulator equipped with the double-actuator mechanism is in contact with an object, the contact force can be controlled either by moving the equilibrium point further into the contacting object or by modulating the stiffness at the endpoint of the manipulator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003554_978-3-540-30301-5_4-Figure3.6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003554_978-3-540-30301-5_4-Figure3.6-1.png",
        "caption": "Fig. 3.6 The Salisbury hand as the end-effector of a PUMA robot (the drive system is not shown)",
        "texts": [],
        "surrounding_texts": [
            "Manipulator shape and size is determined by requirements on its workspace shape and layout, the precision of its movement, its acceleration and speed, and its construction. Cartesian manipulators (with or without revolute wrist axes) have the simplest transform and control equation solutions. Their prismatic (straight-line motion), perpendicular axes make motion planning and computation easy and relatively straightforward. Because their major motion axes do not couple dynamically (to a first order), their control equations are also simplified. Manipulators with all revolute joints are generally harder to control, but they feature a more compact and efficient structure for a given working volume. It is generally easier to design and build a good revolute joint than a long motion prismatic joint. The workspaces of revolute joint manipulators can easily overlap for coordinated multirobot installations, in contrast to gantry-style robots. Final selection of the robot configuration should capitalize on specific kinematic, structural or performance requirements. For example, a requirement for a very precise vertical straight-line motion may dictate the choice of a simple prismatic vertical axis rather than two or three revolute joints requiring coordinated control. Six degrees of freedom (DOFs) are the minimum required to place the end-effector or tool of a robotic manipulator at any arbitrary location (position and orientation) within its accessible workspace. Most simple or preplanned tasks can be performed with fewer than six DOFs. This is because they can be carefully set up to eliminate certain axis motions, or because the tool or task does not require full specification of location. An example of this is vertical assembly using a powered screwdriver, where all operations can be achieved with three degrees of freedom. Some applications require the use of manipulators with more than six DOFs, in particular when mobility or obstacle avoidance are necessary. For example, a pipe-crawling maintenance robot requires control of the robot\u2019s shape as well as precise positioning of its end-effector. Generally, adding degrees of freedom increases cycle time and reduces load capacity and accuracy for a given manipulator configuration and drive system."
        ]
    },
    {
        "image_filename": "designv11_28_0000817_s0007-8506(07)60577-0-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000817_s0007-8506(07)60577-0-Figure7-1.png",
        "caption": "Figure 7: The final die set",
        "texts": [
            " shortly before the holding terrperature period in the oven cyde begins. The measured surface roughness was Ra= 5.8 v. The denslty and general appearance of the parts were adequate. Measured intermediate weights and specific weights parameters for the green and infiltrated parts are listed in Table 4. The calculated and in ef fed added infiltrated bronze (-72%) and allowances are also given. In the next Figure 6 an example of the obtained surface definition is reported through an eledronic m m s m p e image. while the final die set ready for use is shown in Figure 7. The accuracy of the parts was measured at several significant check points; both diameter values in the xy plane and z heights were checked. As far as the diameters are regarded, an average error value of 0.34rrm Hith a standard deviation of 0 . 1 7 m was observed. On the other hand the height values showed an average error of 0 . 0 3 m Mth a standard deviation of 0 . 1 5 m . A better shrinkage fadors tuning m l d possibly have delivered m e accurate parts. Overall, the tolerances are good enough for the application here addressed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002067_tac.2005.851434-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002067_tac.2005.851434-Figure1-1.png",
        "caption": "Fig. 1. Circular motion of an X-Y gantry system.",
        "texts": [
            " Finally, it is not difficult to see that the dynamic equations of the end-effector of a robotic manipulator which moves along a piecewise real-analytic path in the workspace take the form in (33) and (34) and furthermore satisfy the hypothesis of Corollary 3 [20]. We next present some simulation results using a two-DOF robotic manipulator, in order to demonstrate the practical use of our method developed so far to solve the time-optimal control problem (P). Specifically, we consider the time-optimal path planning of an X-Y gantry system along the circular path C of radius , which is illustrated in Fig. 1. The dynamic equations of the X-Y gantry system are given by (60) where denotes the position E of the end-effector in the Euclidean coordinate system, while, for each , and denote, respectively, the mass and the generated input force of the -axis actuator. Here, the input forces and are subject to (61) where the positive constants and stand for the physical limitation in the generated forces of the -axis and -axis actuators. We denote by the set of all absolutely continuous circular trajectories of the end-effector that traverse in the counterclockwise direction along the circular path C and satisfy the constraints in (60) and (61) a"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001726_978-1-4684-3776-8_1-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001726_978-1-4684-3776-8_1-Figure6-1.png",
        "caption": "Fig. 6. Enzyme electrode configurations: (A) Glass membrane electrode type. (8) Gas-sensing electrode type. (e) Air gap type. Reprinted with permis sion from reference 161.",
        "texts": [
            " The substrate to be determined diffuses into the enzyme layer where the enzymatic reaction occurs producing a product or consuming a reactant which is sensed by the ion-selective electrode. A 32 Robert K. Kobos steady state potential is reached after some time due to the attainment of equal rates of product formation and diffusion out of the enzyme layer. The kinetic method based on the rate of potential change can also be used. Since only small amounts of substrate are consumed in the process, the method is essentially nondestructive. Several enzyme electrode configurations are shown in Fig. 6. The first report of an enzyme-coupled electrode was given by Clark and Lyons in 1962.(40) Two possible electrodes for glucose were proposed. The first involved the use of the enzyme glucose oxidase, held on a pH electrode by means of a cuprophane membrane. The decrease in pH due to the production of gluconic acid via reaction (13) was proportional to the glucose concentration. The second approach involved the polarographic deter mination of glucose using glucose oxidase held between a hydrophobic membrane (e",
            "3) a Analytically useful range. subsequent discussion a survey of reported enzyme electrodes will be undertaken starting with the urea electrode. The many improvements and refinements made in this particular electrode illustrate the developments made in enzyme electrode technology from its conception to the current state of the art. 4.1. Urea Electrodes The first urea electrode(153.154) consisted of physically entrapped urease [reaction (5)] in a polyacrylamide gel held over the surface of a monovalent cation electrode (Fig. 6). The electrode responded to changes in urea concentration in the range 5 x 10-5 to 1 X 10-1 M with a response time of about 35 sec. There was little loss of activity over a 14-day period. By adding a thin cellophane film over the polyacrylamide gel, the lifetime of the electrode could be extended to three weeksY54.155) The cellophane 36 Robert K. Kobos membrane is permeable to the small substrate molecules but prevents the much larger enzyme molecules from leaching out of the gel layer. Tran-Minh et al",
            " Apparently, the reason for the good response of these enzyme electrodes is due to the concentrating effect of the very small volume of the enzyme layer. Guilbault and Tarp(161) described an enzyme electrode for urea based on the ammonia air gap electrode. (29) Commercially available immobilized urease was placed at the bottom of a micro chamber and covered with a piece of nylon net. The sample solution was placed in the microchamber which was then sealed by the insertion of the air gap electrode (Fig. 6). The solution was stirred by means of a Teflon-coated magnetic stirring bar. This configuration is not an enzyme electrode in the true sense, since the enzyme is not immobilized at the electrode surface and total conversion of the sample results. This method would more properly be classified as a stationary solution method using immobilized enzymes (Section 3.3.1). The response slope of the electrode was 0.95 pH units/decade in the range 5 x 10-5 to 1 X 10-1 M at pH 8.5. Response times were 2 min at a concentration of 1 x 10-2 M and 3-4 min at lower concentrations",
            ", which have been shown to adversely affect the conventional ammonia gas membrane, have no effect on the air gap sensor. However, the electrode assembly must be taken apart and reassembled and the electrolyte solution renewed between measurements. A urea electrode suitable for whole blood measurements was reported by Papastathopoulos and Rechnitz. (162) The sensor was based on an ammonia gas-sensing electrode. The enzyme urease was held on the surface of the gas-permeable membrane by means of a dialysis membrane (Fig. 6). The use of the dialysis membrane also prevents proteins from coming in contact with and clogging the gas-permeable membrane. This method of physically entrapping the enzyme is simple and convenient to use when enzyme stability is not a problem. The response of the urea electrode was linear in the concentration range 5 x 10-4 to 7 X 10-2 M with a slope of 90.7 m V / decade. The slope remained constant for a period of 20 days. The response time was about 5 min in the linear concentration range, slightly longer than that reported by Anfalt et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003953_s00170-009-2272-8-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003953_s00170-009-2272-8-Figure2-1.png",
        "caption": "Fig. 2 CCC insert CAD model. a Core, b cavity",
        "texts": [
            " The infiltrated inserts and one of the cubic parts were treated following the process listed in Table 2, and then, two groups of tensile test samples (Fig. 1) made from the cubic parts before and after thermal treatment were processed. There were five tensile test samples in each group, and the final test results were the mean value of five samples in each group. SEM samples made of the cubic parts before and after thermal treatment were also produced to analyze the variation of alloys microstructures. 3.1 Forming of SLS green insert Figure 2 is the three-dimensional model of CCC insert in this work, and the darker pipes are the cooling channels. State \u03c30.2/MPa \u03c3b/MPa Young's modulus (GPa) Elongation (%) Polymer powders are heated by laser beam in the composite powders, and they turn into viscous liquid to adhere other hard powders around them together. It is possible for the powders which do not belong to scanning cross-sections to be softened owing to the heat accumulation and transmission within the powders during sintering process",
            " All these factors will cause the collision force (f) to decrease to a limit, and the powders will be still instead of moving to the entrance of the channel with the advancing of interface. So, there exists a maximum length (Llim) for a certain powder aspirator. It is impossible for the powders in a channel whose length is over Llim to be driven out clearly. In this work, subsidiary channels are produced to divide the cooling channels into several sections, and the length of one section is below Llim (Fig. 2), which solves the above problem. Finally, the entrances of subsidiary channels are blocked with plugs sintered with the same mixed composite powders after the removing process is finished. 3.2 Post-treatment of SLS green insert Green inserts are heated at 1,000\u00b0C/2 h in the same furnace for presintering after they are debinded as in literature [6]. Then, there comes the infiltration process. Two graphite boxes are processed firstly corresponding to the two inserts before infiltration, and they each have a cover with coneshaped holes in them"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003339_bf00929287-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003339_bf00929287-Figure1-1.png",
        "caption": "Fig. 1.",
        "texts": [
            " (7), K is a positive scalar constant and W is a q \u00d7 q positivedefinite weighting matrix. One reduces the magnitude of ~b~[x(tl) ], i = I,..., q, by increasing the magnitude of K. Thus, K should be made as large as numerical stability allows in order to ensure approximate satisfaction of Eq. (5). 9 The choice of W allows one to penalize certain components of ~[x(tl)], more than others, for being nonzero. The relationships between Optimization Problem I and Optimization Problem II are depicted schematically in Fig. 1. Trajectory I is the nominal path and is determined by solving Optimization Problem I with initial state 20 . Trajectory II is the optimal path for initial state x0, and is determined by soMng Optimization Problem I. Trajectory III is determined by soMng Optimization Problem II with initial state \u00b040 and is an approximate solution of Optimization Problem I with initial state x 0 . 7 Another approach is suggested by Dyer and McReynolds in Ref. 12. s The vr\u00a2[ \"] term in the performance index (7) is necessary to ensure that the first-order necessary conditions of optimality for Optimization Problem I and Optimization Problem II are identical"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003007_6.2006-6147-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003007_6.2006-6147-Figure5-1.png",
        "caption": "Figure 5. Rotor system response to longitudinal cyclic control.",
        "texts": [
            " Conversely, a right cyclic input tilts both rotors\u2019 TPP to the right. Th h the cyclic control stick using Differential Collective Pitch (DCP); whereby the pitch of the forward and rear rotor blades are all collectively changed equally yet in the opposite direction. Moving the cyclic control stick forward simultaneously causes a decrease in collective pitch on the forward rotor and an increase in collective pitch on the rear rotor, thereby creating a nose-down pitching moment about the helicopter\u2019s center of gravity as illustrated in Figure 5. Conversely, an aft cyclic input creates a nose-up pitching moment. In addition t binations of directional pedal and lateral cyclic inputs generate unique motions of the helicopter, permitting the helicopter to directionally rotate about either the forward or rear rotor. This control flexibility makes the Chinook very maneuverable in tight quarters. tification approach us Frequency-Response Method, as illustrated in the flowchart in Figure 6 and implemented in the CIFER\u00ae package. Each of the elements of the flowchart will be briefly described in this section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002462_s00466-006-0120-3-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002462_s00466-006-0120-3-Figure5-1.png",
        "caption": "Fig. 5 Visco-elastic model for the connecting fibers",
        "texts": [
            " Thus, initially coincident points Pi (on element i) and Pj (on element j) are displaced with respect to each other under relative motion of the elements. The joint between the contacting elements is assumed to be formed by infinite such fibers along its length. The fibers are modeled as visco-elastic members having certain stiffness and damping coefficients. In addition, for generality, the stiffness of these fibers is assumed to be different in the normal (n) and tangential (t) directions, where the two directions are as shown in Fig. 5. Note that the n direction is perpendicular to the contacting side of the element under consideration and points outwards. The normal and tangential stiffnesses of the fibers are denoted as Kn and Kt respectively. The corresponding damping ratios are denoted as \u03ben and \u03bet respectively. Note that the normal and tangential damping coefficients are related to the stiffnesses by Cn = \u03ben2 \u221a Knm (1) Ct = \u03bet2 \u221a Ktm (2) where m is the average mass per unit length of the discrete elements. Consider a fiber AB which is stretched by dn in the n direction and dt in the t direction at a given time step (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000738_mfi.2001.1013506-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000738_mfi.2001.1013506-Figure1-1.png",
        "caption": "Fig. 1. Relationship among coordinate systems",
        "texts": [
            " To suppress errors, we supplementarily uses information from G-axis force/torque sensor mounted on the fingertip link. When slip start,s at. the COIItact point., the ratio of t.he tangential force with respect to t,be normal force is equal to the maxiniuin static frict,ion coefficient. The direction of the slip coincides with the direction of the tangential force. We use the slip valiie only when t.hese conditions are satisfied. B. Kinematics of Rolling Contact and Slip Velocity Consider each finger in contact with an object as shown in Fig.1. Let Cb be an inertial base frame. Fix a frame CO a t the center of mass of the object, and a frame CJ. at a central position of each hemispherical fingcrt,ip. Let cb., co, and cf . denote each contact point in the frame Cb, C, and CJ, respectively. Let the positions of the origins of CO and Cf. in the frame Cb be denoted by I, and I/,, and the rotation matrices giving the orientation of CO and CJ, be denoted by R, and RI, , respectively. The contact point cb, is described in two ways: one using z0, R,,, and co, and the other using IJ,, Rr,, and c f , , Since these are identical, we obtain a following equation: I"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000980_jjap.28.l1480-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000980_jjap.28.l1480-Figure7-1.png",
        "caption": "Figure 7. The combination of the parallel spring and the amplification mechanism.",
        "texts": [
            " Although the two mechanisms are linked with the flexible link, flexure hinge , the characteristic of each mechanism is preserved, as shown in the previous section. The flexible link transmits the displacement, or force, via the parallel spring to the amplification mechanism. If the flexible link is a wire as an ultimate case, the moment acting on the parallel spring will not be transmitted to the amplification mechanism. Only vertical displacements and vertical forces can be transmitted. On the other hand, if the flexible link is rigid, the moment will be transmitted. In figure 7, if a clockwise moment is applied to the parallel spring, the fifth rigid body will be drawn down. When a vertical displacement by a clockwise moment is transmitted to the amplification mechanism, the seventh rigid body rotates clockwise. However, if the clockwise moment is transmitted to the sixth rigid body, the seventh rigid body rotates counterclockwise. This means that the rotation of the seventh rigid body caused by a moment can be made zero through the design of the flexible link. For a detailed examination, Lagrange\u2019s method can be used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001657_tmag.2004.824772-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001657_tmag.2004.824772-Figure6-1.png",
        "caption": "Fig. 6. Boundary-element model of the motor.",
        "texts": [
            " Although the low order resonance responses do appear to be excited, they are excited only in an extremely inefficient manner by the excitation (except for modes and in this example, as explained previously). However, the introduction of the cradles cause the excitation admittances of the low order resonances to be greatly increased. So much so, that these modes now begin to dominate the response at their resonance frequencies. To evaluate the potential for increase to radiated noise in this example, we use a boundary-element model of the structure as shown in Fig. 6. Each colored grouping of elements in this figure represents a single boundary element. (Note that the cradles are not a part of the boundary-element model, since we desire to focus only on the changes in the stator noise.) This same model is used for radiated sound predictions for the cases with and without the cradle, but with different element velocities as reflected in the two sets of vibration results. The boundary-element analysis software used is detailed in [9]. The radiated sound levels for both cases are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003740_1.2975154-Figure11-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003740_1.2975154-Figure11-1.png",
        "caption": "FIG. 11. a Plane distribution of M associated with the corresponding real one relative to the helicoidal cylindrical magnet; b prismatic equivalent permanent magnet.",
        "texts": [
            " During the operation of development just described we can also think that the plane tangent to in a point P belonging to the same curve can be spread out flat on the plane where we perform the development of the cylinder of radius r. M, applied in P, also belongs to this plane. Then, after this spreading out flat, M will belong to the plane where the development has been carried out. Applying the previous procedure to the magnetization M for all the infinite points P that define , we obtain a uniform plane distribution of M. In Fig. 11 a the result of the previous geometrical operation is illustrated and the rectified cylindrical helix is denoted by the symbol ret. Since the helices of the cylinder are an infinite number on their own plane of development, M will be applied to all the infinite number of points that defines the rectangle, with magnitude and orientation always constant. Consequently, the divergence of this surface distribution of M is always null, that is, M is equal to zero in any point of the rectangle illustrated in Fig. 11 a . By the previous procedure, the distribution of M is strictly associated with the corresponding real one relative to the helicoidal cylindrical magnet. Now, if we apply the development sequence to all the infinite coaxial cylinders whose radius and height are ri r re and h, respectively, it is possible to stack up all the infinite development planes of the same cylinders, together with the relative M distributions that have all the corresponding bidimensional divergence equal to zero. Then, methodically stacking up the planes, we can build up the prismatic solid illustrated in Fig. 11 b . For example, this solid can be thought as symmetric with respect to the plane belonging to the axes X and Y of the coordinate system considered at the beginning see Fig. 2 b . In Fig. 11 b we have fixed a symmetric position of the prismatic solid in relation to the coordinate system. Then, on each rectangle with sides equal to 2 r and h the following equation is valid: Mx P x + Mz P z = 0. 80 Now, since on each rectangle it is always My P = 0, 81 it is obvious that the variation in the component My P of M along the axis Y is null in the whole prismatic solid, My P y = 0. 82 Then, Eqs. 80 and 82 give Mx P x + My P y + Mz P z = 0, 83 that is, from Eq. 9 , we obtain M P = 0. 84 In relation to the case that has been described in Sec"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002560_tim.2006.876396-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002560_tim.2006.876396-Figure4-1.png",
        "caption": "Fig. 4. Photograph of the fully assembled fluidic chip.",
        "texts": [
            " The substrate was a silicon wafer with a silicon-nitride-layer coating. A platinum/titanium thin film (100 nm/20 nm) was deposited by e-beam evaporation and patterned by lift-off technique to define the electrodes. The PDMS cover layer was attached to the substrate by simply pressing against the substrate to seal the interface between the PDMS and the silicon nitride layer. The large patterns of the channel and the actuator electrodes allowed manual alignment of the cover layer with the substrate. A photograph of fully assembled microsensor is shown in Fig. 4. Each time of operation, the proposed microsensor measures the output responses under three different microenvironments: air saturated, O2 saturated (in an O2 bubble), and O2-depleted (in a H2-bubble). Various glucose control solutions (0, 50, 100, 200, 300 mg/dl) and lactate control solutions (0, 18, 36, 54, 72, 90 mg/dl) are used to check the functionality of the sensor. They were prepared by dissolving each substrate into a phosphate buffer solution. The microsensor operation consists of the following steps"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003391_coase.2008.4626479-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003391_coase.2008.4626479-Figure8-1.png",
        "caption": "Fig. 8 (a) Hexagonal part for comparison of absolute deviation (b) Target dimensions for hexagonal part",
        "texts": [
            " Improvement in accuracy is studied by following two different compensation methods: -- First using a constant shrinkage scaling factor (prescribed by RP machine manufacturer) in one part -- Second using the shrinkage model and new shrinkage compensation system in another part. A. Case study I In the first experiment, dimensional accuracy improvement due to new compensation approach is studied. The test part contained four hexagons on top of one another. The test parts and its target dimensions used for comparison are shown in Figure 8. Two versions of the same hexagonal part are fabricated. In order to test the effectiveness of the compensation method, a model for scan length from Ragunath and Pandey [10] is used. In one part, machine manufacturer suggested shrinkage compensation factors [19] are used (constant shrinkage factors) and in second part, a linear shrinkage model is used. For both parts, all other process parameters are kept constant and are listed in Table I. Figure 9 shows the absolute deviations measured for both the parts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002443_s0007-8506(07)60041-9-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002443_s0007-8506(07)60041-9-Figure1-1.png",
        "caption": "Figure 1: Scheme of the experimental device.",
        "texts": [
            " The working principle is that both conductive and dielectric objects are attracted towards regions with a higher electric field in the same way as a dielectric plate is attracted inside the two charged plates of a capacitor. The basic idea is to build a traveling capacitor able to attract and transport the components. The concept is to use a stepping electric field in order first to attract, orient and locate the microparts, after to move them along linear or angular trajectories. The feeder consists of a series of V-shaped parallel electrodes mounted over a conducting and vibrating platform 2 (Figure 1). By charging the electrodes one after the other according a proper sequence it is possible to obtain a stepping electrostatic field towards which the parts are attracted. The experimental apparatus (Figure 1) used to test the performances of the microfeeder consists of a high voltage supply ( I ) , a vibrating platform (2), a series of V-shaped parallel electrodes (4), a PLC based electronic switching and synchronisation system (5). Vibration has been used to reduce friction and adhesion forces and to allow the microparts to move freely on the working area. The vibration frequency and amplitude depend on component mass, contact surface, tribological and environmental conditions. Therefore a piezoelectric element, with a suspended mass, supplied by a digital function generator (3) has been used to generate the vibration and an interferometer to measure the amplitude. The basic electrical configuration of three V-shaped parallel electrodes (Figure 1) is repeated several times. The electrodes have a pitch p and the voltage level repeats at distance 3p in \"three phase\" structures and at distance 4p in \"four phases\" ones. In the Figure 1 a \"three phase\" structure is shown: the electrodes are connected to the HVS and their voltage supply sequence, controlled by the PLC, is given in Table 1.a or 1.b. The travelling field moves from one electrode to the next one with a period of T seconds and speed PIT. When the component arrives under one electrode, attracted by the high electrostatic field, it aligns its axis along the electrode projection on the working plane in order to minimize the system energy, then the voltage is switched to the next electrode and the electrostatic field is shifted of one pitch"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003335_haptics.2008.4479978-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003335_haptics.2008.4479978-Figure1-1.png",
        "caption": "Figure 1: (a) The master; (b) the flexible-link slave.",
        "texts": [
            ", < 3 mm in pediatric surgery), the effect of flexibility becomes more crippling because control laws based on the assumption of a rigid robot are no longer effective or accurate. Previously, we have analyzed the effects of joint elasticity in the slave robot on the transparency of master-slave teleoperation [1]. In this paper, we address transparency and stability limitations resulting from link flexibility (tool flexibility) in a slave robot and examine what added benefits can tip sensors deliver. An ideal 1-DOF teleoperation system, in which the master is rigid but the slave has a flexible tool that couples the actuator to the end-effector is shown in Figure 1, where Im, Ism, \u03c4m and \u03c4s are the master and the slave (excluding the flexible link) inertias and controller outputs, respectively. Also, \u2212 fh and \u2212 fe denote the forces exerted by the operator\u2019s hand on the master and by the environment on the slave, respectively. The hand-master position and the slave-environment position are denoted by \u03b8h and \u03b8e respectively, while \u03b8s is used to show the slave\u2019s joint position, which is different from \u03b8e due to the link flexibility. With a rigid link of length L and defining \u03c9h = \u03b8\u0307h and \u03c4h = L fh, the dynamics of the master are Im\u03c9\u0307h = \u03c4m + \u03c4h (1) The exact dynamics of a flexible link are described by partial differential equations and have infinite dimensions. In the constrained assumed modes method, the deflection of the flexible link in Figure 1b is modeled as \u2206y(x, t) = \u221e \u2211 i=1 Fi(x)qi(t), 0\u2264 x\u2264 L (2) where qi(t) are the assumed flexible modes and Fi(x) are the corresponding time-independent modes shape functions. Considering the first mode q1(t), which is capable of capturing the dominant frequency, Zhu et al. [2] presented a method for lumping the distributed mass of the flexible link to a point mass located at its tip followed by modeling the flexibility of the link by a weightless linear bending spring. Denoting the equivalent tip lumped mass by Mse and the equivalent bending spring stiffness by Ks, the resulting lumped dynamic model of the flexible link in Figure 1b is Mse p\u0308e =\u2212Ks\u2206y\u2212 fe, Ism\u03b8\u0308s = \u03c4s +LKs\u2206y (3) where pe = L\u03b8s + \u2206y is the arc approximation of the link tip position. Noting that \u03b8e = pe/L and defining \u2206\u03b8 = \u03b8s\u2212\u03b8e = \u2212\u2206y/L, Ise = MseL2, ks = KsL2 and \u03c4e = L fe, the lumped model of the flexible-link slave in Figure 1b is rewritten as Ise\u03c9\u0307e = ks\u2206\u03b8 \u2212 \u03c4e (4) Ism\u03c9\u0307s = \u03c4s\u2212 ks\u2206\u03b8 (5) where \u03c9e = \u03b8\u0307e and \u03c9s = \u03b8\u0307s. With \u03c4s as the input, the system (4)-(5) has two poles at \u00b1 j\u03c9R = \u00b1 j \u221a ks(1/Ism +1/Ise) (resonance). For the controller output \u03c4s, if \u03c9s is the output, the system will have two zeros at \u00b1 j\u03c90 = \u00b1 j \u221a ks/Ise (anti-resonance). If \u03c9e is taken as the output, however, the system will show no anti-resonance. Interestingly, the Figure 2: An elastic-joint slave robot. lumped dynamics (4)-(5) of the flexible link are identical to the dynamics of the flexible joint shown in Figure 2 consisting of a motor with inertia Ism and an end-effector with inertia Ise that are coupled via a shaft with a finite stiffness ks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001202_0959651011540897-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001202_0959651011540897-Figure5-1.png",
        "caption": "Fig. 5 Manipulation task",
        "texts": [
            "1 Problem statement Provided that they can be solved, the inverse model equations equations (1) to (3) determine the require-In the design of control systems, one of the factors in uencing the overall performance of the system is the physi- ments from the actuator in terms of the power variables I06899 \u00a9 IMechE 2001Proc Instn Mech Engrs Vol 215 Part I at NORTH CAROLINA STATE UNIV on May 11, 2015pii.sagepub.comDownloaded from where the actuator is oversized or undersized, the characteristics parameters to change for an appropriate sizing also appear graphically. Consider the problem of sizing the actuators of a twoarm robot (Figs 3 and 4) for a manipulation task consisting in moving the end eVector from point P0 to point P1 along a straight line (Fig. 5) with a polynomial speed pro le (Fig. 6). In the bond graph model of the manipulator, the velocity of the end eVector is represented by its two components v x and v y along the x and y axes (see Fig. 4 and the Appendix for the modelling of a rod ). Fig. 2 Validation of actuators in the eVort\u2013 ow plane These are the ow variables of the bonds connected to SS : F x and SS : F y . Analysis of the forward bond graph model shows that each path in the set of minimal-lengtheA(t) and fA(t ) using the load inverse bond graph model and the prescribed output speci cations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000880_ijcat.2002.000288-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000880_ijcat.2002.000288-Figure6-1.png",
        "caption": "Figure 6 Load Distribution along tooth face.",
        "texts": [
            " These friction forces mFn are also acting in opposite directions due to the opposing direction of motion. Thus, a friction moment is also generated in the friction plane, Figure 5, at an angle of (90 f) degrees to the plane of misalignment. The tilting moment is calculated by: Mt X nmax n 1 2Fn cos f n\u00ff 1 ygdn 9 Where dn is the tilting moment arm which can be related to the tooth face width b and the effective contact width Fe. If the load distribution on the tooth is assumed linear as shown in Figure 6 then the tilting moment arm dn is obtained from: dn b\u00ff 2 be 3 10 Similarly, the friction moment is given by: Mf X nmax n 1 2mFn cosf n\u00ff 1 ygD 11 where m is the coef\u00aecient of friction in the splines. Since the two moments, Mt and Mf , are not at 908 to each other, it is more convenient to resolve them into components in two perpendicular planes, planes 1 and 2 as shown in Figure 5. The former coincides with the original plane of misalignment and the latter is at right angle to it. Thus, the moment in the plane of misalignment (plane 1) is: M1 Mt Mf sinf X nmax n 1 2Fn cosf n\u00ff 1 ygdn ( ) X nmax n 1 2mFnD sin f n\u00ff 1 y sin f\u00ff n\u00ff 1 y ( ) 12 and the moment in the plane normal to the plane of misalignment (plane 2) is: M2 Mf cosf X nmax n 1 mFnD cos f n\u00ff 1 y cos f\u00ff n\u00ff 1 y 13 The resultant misalignment moment Mr in the coupling is the vector sum of M1 and M2, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003977_s12213-008-0010-1-Figure13-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003977_s12213-008-0010-1-Figure13-1.png",
        "caption": "Fig. 13 Experimental setup for measuring the displacement",
        "texts": [
            " This simple one-axis microrobot moves like an inchworm with less than 100 nm resolution. We can make two-axial orthogonal microrobots if we connect the microrobot to another microrobot orthogonally as Fig. 12. In this figure, the bottom robot moves itself to the X direction and the upper robot moves its steel base to the Y direction. We can easily set up these orthogonal microrobots in a narrow working space such as a table of an inverted microscope because the size of this robot is very small, i.e. 58 mm in length, 58 mm in width and 37 mm in height. 3.2 Experimental results Figure 13 shows the experimental setup for measuring the displacements. We measure the robot's motion by capacitance sensors whose resolution is 30 nm. However, the output noise is about 60 nm so the measuring resolution is 60 nm in experiments. Figure 14 is the experimental results of the relationship between the displacement and the number of steps at various frequencies. The robot moves up to 300 Hz and the step width is about 1.6 to 3.3 \u03bcm when 100 V is applied to the piezoelectric actuator. Step width less than 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003110_13506501jet341-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003110_13506501jet341-Figure3-1.png",
        "caption": "Fig. 3 Block-on-ring tribometer and contact at cam nose [13]",
        "texts": [
            " To cut down the number of experiments, fractional factorial design (lk\u2212p, where k is the number of factors, l the number of levels, and p the number of generators) was used, instead of complete factorial experiments; 1/9th fraction factorial design yielded a 27-run matrix, where k = 5 represents the factors of interest, l = 3 represents three levels of each factor, and \u2018p = 2\u2019 is the generators in the experiment [12]. Here, all variables of interest were tested at the three levels in combination to obtain the selected optimized design. The purpose of an experiment is to assess the effect of one or more variables on the response of interest to the study. A brief discussion of the experiments performed by Green [13] on an LFW1TM block-on-ring tribometer (Fig. 3) is given in this section. The blockon-ring tribometer was used to evaluate the friction properties of the lubricants by simulating a lubricated sliding motion between two specimens, comparable with severe conditions at the cam and follower contact around the cam nose. Here, the block represents the follower, whereas the ring represents the cam. A line contact is obtained between the block and ring surfaces by anticlockwise rotation of the ring under pure sliding against a loaded block. A nozzle is used to supply lubricant to the contact region from a heated bath"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000008_navfht.29637.0009-Figure9.10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000008_navfht.29637.0009-Figure9.10-1.png",
        "caption": "Fig. 9.10. A train travelling in underground tunnel",
        "texts": [
            " for sleepers placed on the bottom of a tunnel, bulk acoustic waves usually make a major contribution to the ground vibration field near the surface (especially if the tunnel is deep enough), in contrast to the case of above-ground trains, where Rayleigh surface acoustic waves prevail. The approximate analytical approach described here considers the problem in the low-frequency approximation, i.e. the characteristic wavelengths of the bulk acoustic waves generated in the ground are assumed to be much larger than the diameter of the tunnel (Fig. 9.10). For simplicity, we consider only the case of homogeneous ground. In this low-frequency approximation, the formal expression for the vertical component of the particle velocity of ground vibrations generated on the ground surface by a train travelling underground may be written as follows [9.26]: (9.30) Here Gzz(r, \u03c9) is the component of the elastic Green\u2019s tensor (Green\u2019s function) satisfying the boundary conditions on the ground surface and describing the vertical component of the particle vibration velocity due to a vertical point force located on the bottom of the tunnel, r = [(x \u2013 x\u00a2)2 + (y \u2013 y\u00a2)2 + (z \u2013 z\u00a2)2]1/2 is the distance from the ( , , ) ( , , ) ( , )d d dz zzv x y P x y G r x y z\u03c9 \u03c9 \u03c9 \u2022 \u2022 \u2022 -\u2022 -\u2022 -\u2022 = \u00a2 \u00a2 \u00a2 \u00a2 \u00a2\u00da \u00da \u00da 283 Thomas Telford: Krylov 13 March 2001 12:24:57 Downloaded by [ University of New South Wales] on [02/10/16]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000500_acc.2002.1024608-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000500_acc.2002.1024608-Figure3-1.png",
        "caption": "Figure 3: Geometric dependencies for front axle position estimation",
        "texts": [
            "2 Position Estimation based on front wheel signals There are two major advantages in using also front wheel signals instead of the rear wheel signals only. First, the front wheel signals provide additional wheel revolution information independent from the rear wheels. Second, because of the considered vehicle being rear wheel driven, the front wheels have only minimal wheel slip. But, the position calculation at the front wheel is more difficult than the rear wheel based one, due to the complexity of the front axle suspension in passenger cars. Figure 3 shows the geometric dependencies necessary to understand the following equations. The assumption of equal lateral forces a t the front wheels holds for equal tires, normal forces and ground conditions. Thus, the vehicle moves along the same trajectory as if it had an Ackermann-steering, i.e. without lateral tire forces. The effective steering angles ( d $ L , F R ) for both front wheels can then be combined to the steering angle of the third virtual wheel in the middle. First, the changes in the front track width bF and the wheel base L during steering action will be neglected",
            " The driven path length of the virtual wheel is then calculated based on the angle of the partial arc a and the path lengths of the real front wheels by cal- culating the mean value with L R2 = ZqqJ RI = /Rz + (g)' + R 2 . bf .cos(S;, ) (10) RB = ,/R; + (2)' - R~ . b f . COS(^>^). Substituting that into eq. 9 yields + l F L ( k i - 1 ) ,/4L2+b; ~ i n ~ ( 6 ; ~ ) + 2 L b f s i n ( 2 6 ~ ~ ) ' F M ( k + ') = (11) ) I F R ( ~ + ~ ) , / 4L2+b: sin2(6;,)-2Lbf sin(26gA,) ( With this result the angle a of the partial arc is calculated by A secondary-method of calculating a uses the effective track width b f (compare also fig. 3) and thus yields a relatively simple equation for LY (14) L F L ( ~ + 1) - ~ F R ( I C + 1) b f a = which is similar to the result in the previous section. With (15) a p = e ( k ) - - - figM 2 and (3 s = 2 . R 2 . sin The change in the position of the front center point P F s A 4 can be computed by Ax = s . cos@) as well as Ay = s . sin(p) and AOpSh4 = -a. Substituting these values in the basic dead-reckoning equation (2) yields the new position at time step ( k + 1). Finally, the obtained position has to be transformed to the midpoint of the rear axle, which is the center point of the car coordinate system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001241_robot.2002.1013564-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001241_robot.2002.1013564-Figure2-1.png",
        "caption": "Fig. 2. Graphical representation of the distance among the centre of the ellipsoids and its intersections with the tangent to the trajectory of the foot",
        "texts": [
            " MEASURES FOR PERFORMANCE EVALUATION In mathematical terms, we provide four global measures of the overall performance of the mechanism in an average sense. A. Locomobility Measure The motivation for the development of the locomobility index is to apply the concepts of arm manipulability to multilegged walking [18]. This performance measure can be expressed through the Jacobian matrix. In our case, the global index is obtained by averaging the distance among the center of the ellipsoids and its intersections with the tangent to the desired trajectories of the foot (EF), at the centre of the ellipsoid (Fig. 2), over a complete cycle T [13]: In this perspective, the most suitable trajectory is the one that maximises LF. (EF) B. Mean Absolute Power The key measure in this analysis is the mean absolute power per travelling distance. It is computed assuming that power regeneration is not available by actuators doing negative work, that is, by taking the absolute value of the power. At a given joint j (each leg has m = 2 joints) and leg i (since we are adopting an hexapod it yields n = 6 legs), the mechanical power is the product of the motor torque and angular velocity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001161_s0009-2509(00)00353-5-Figure13-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001161_s0009-2509(00)00353-5-Figure13-1.png",
        "caption": "Fig. 13. Di!usion/reaction cell.",
        "texts": [
            " Although this ion is not directly involved in the reaction, an increase of concentration inside the pellet can be observed. This e!ect is called `di!usion barriera (Taylor & Krishna, 1993). Fig. 12 shows the nitrate concentration pro\"le as a function of catalyst loading. One realizes a concentration plateau which is caused by a very low hydrogen ion concentration close to the pellet center. 6. Measurements in a reaction/di4usion cell The concentration pro\"les inside a catalytic membrane were measured in a reaction/di!usion cell (Fig. 13). The details of the experiments will be published elsewhere. In Figs. 14 and 15 some experimental results are presented and compared to calculations obtained from the model described in the previous sections. Fig. 15 shows that from a certain catalyst loading, the pH-value levels out as the nitrate reduction reaction is slowed down due to the high OH concentration. This is corroborated in Fig. 14 where the nitrate concentration drops only slowly and the model shows a #at curve from a certain catalyst loading on"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003955_tsmcc.2009.2030668-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003955_tsmcc.2009.2030668-Figure2-1.png",
        "caption": "Fig. 2. Three-link sagittal biped with nine muscles. ga: gastronemius, s: soleus, ta: tibialis anterior, sq and sh: short heads of the quadriceps and hamstrings, q and h: long heads of the quadriceps and hamstrings as two-joint muscles, p: paraspinal, and ab: abdominal. The gastrocnemius, soleus, and tibialis anterior muscles connect to a massless foot, as shown in Fig. 1.",
        "texts": [
            " The model also has a massless link representing the feet, used to estimate horizontal excursions of the center of pressure, as discussed in Appendix F. Reasonable foot length should be approximately 20 cm [26]. The final equations of motion for the model are in the space \u03b8(t) = [\u03b81(t), \u03b82(t), \u03b83(t)]T and are derived in Appendix B. Explicit dependence of \u03b8 and other variables on time will not be written unless necessary. Thus, equations of motion for the biped can be written as J(\u03b8)\u03b8\u0308 + C(\u03b8, \u03b8\u0307)\u03b8\u0307 + G(\u03b8) = \u03c4. (1) The biped is equipped with a minimal set of nine muscles, as shown in Fig. 2. Note that the soleus, tibialis anterior, and gastrocnemius muscles connect to the feet. The level of muscle activation is represented in a vector of proportional gains \u03b1 and derivative gains \u03b2. Here \u03b1 = [500, 300, 300, 300, 300] N \u00b7 m \u03b2 = 0.25\u03b1 N \u00b7 m \u00b7 s. (2) We refer to this set of numbers as the nominal activity level. This activity level represents the amount of input provided to the muscles by proprioception, learned by experience. \u03b11 and \u03b21 correspond to the soleus\u2013tibialis anterior, \u03b12 and \u03b22 to the short heads of the quadriceps\u2013hamstrings, \u03b13 and \u03b23 to the abdominal\u2013paraspinal pair, \u03b14 and \u03b24 to the long heads quadriceps\u2013hamstrings, and \u03b15 and \u03b25 to the gastrocnemius, which is assumed to have an antagonist muscle group",
            " This idea could be expanded to stabilize a 3-D model under a variety of disturbances. PHYSICAL PARAMETERS Physical parameters used in simulations of the biped are as in Table I. For each link, four parameters are specified. Parameter I refers to the moment of inertia about the CoG of the link, m refers its mass, l refers to its length, and k refers to the distance of its center of mass measured from the lower joint. The gravity constant g is 9.81 m/s2 . DERIVATION OF MODEL EQUATIONS OF MOTION In this appendix, we derive the equations of motion (1) for the model shown in Fig. 2. We begin by writing the equations of motion in the space Z = [x1 , y1 , \u03b81 , x2 , y2 , \u03b82 , x3 , y3 , \u03b83 ]T . Since the model is constrained to move in the sagittal or x\u2013 y plane, there are three equations of motion for each link\u2014 two translational and one rotational. Fig. 12 shows a free body diagram for the model. The terms xi and yi are the coordinates of the center of mass of link i; ki is the distance from the bottom of link i to its center of mass; li is the total length of link i; \u03b8i is the angle of link i measured clockwise from the vertical, with \u03b8i \u2208 (\u2212\u03c0, \u03c0); \u03c4i is the torque on link i; Fij and Gij are the horizontal and vertical forces of connection between links i and j; and Fg and Gg are the vertical and horizontal ground reaction forces acting on link 1 through the feet",
            " After performing this multiplication, equation (9) becomes J(\u03b8)\u03b8\u0308 + C(\u03b8, \u03b8\u0307)\u03b8\u0307 + G(\u03b8) = \u03c4 (10) where J(\u03b8) and C(\u03b8, \u03b8\u0307) are the 3 \u00d7 3 matrices as shown at the bottom of the page, and G(\u03b8) is the 3 \u00d7 1 matrix G(\u03b8) = g   [m1k1 + (m2 + m3)l1 ] sin(\u03b81) (m2k2 + m3 l2) sin(\u03b82) m3k3 sin(\u03b83)   . The term \u03c4 is unchanged. The form of this term is given in Section III and derived in Appendix C. MUSCLE MODEL In this appendix, we describe the muscle model used to actuate the system and derive the form of the system input expressed in (3). There are four muscle pairs and the gastrocnemius, as shown in Fig. 2. We assume that the gastrocnemius is also part of an agonist\u2013antagonist pair, perhaps consisting of a combination of several muscles. Thus, there are effectively five muscle pairs. In our model, the force Fm for m = 1, 2, . . . , 5 provided by each muscle pair is modeled by a circular spring, i.e., Fm = \u2212\u03b1m m \u2212 \u03b2m \u0307m (11) where m = rm \u03b8\u0302m , rm is the radius of the spring, \u03b8\u0302m is the angle between corresponding body segments, \u03b1m is a proportional gain, and \u03b2m is a derivative gain. For simplicity, we will choose rm = 1 for each muscle pair. In this case, F1 corresponds to the soleus\u2013tibialis anterior, F2 to the short heads of the quadriceps\u2013 hamstrings, F3 to the paraspinal\u2013abdominal muscles, F4 to the quadriceps\u2013hamstrings, and F5 to the gastrocnemius, as shown in Fig. 2. Thus 1 = \u03b8\u03021 = \u03b81 2 = \u03b8\u03022 = \u03b82 \u2212 \u03b81 3 = \u03b8\u03023 = \u03b83 \u2212 \u03b82 4 = \u03b8\u03024 = \u03b81 \u2212 \u03b83 5 = \u03b8\u03025 = \u03b82 (12) with \u03b81 , \u03b82 , and \u03b83 as shown in Fig. 1. Nominal gains for the muscle pairs are as given in Section III, i.e., \u03b1 = [\u03b11 , \u03b12 , \u03b13 , \u03b14 , \u03b15 ]T = [500, 300, 300, 300, 300]T and \u03b2 = [\u03b21 , \u03b22 , \u03b23 , \u03b24 , \u03b25 ]T = 0.25\u03b1. We can now derive the form of the muscle input to the system by writing the generalized torques in the \u03b8 space. Let F = [F1 , F2 , F3 , F4 , F5 ]T = [ 1 , 2 , 3 , 4 , 5 ]T and \u03b8 = [\u03b81 , \u03b82 , \u03b83 ]T "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002061_tmag.2004.825468-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002061_tmag.2004.825468-Figure7-1.png",
        "caption": "Fig. 7. Surface force densities for both variants at same time step.",
        "texts": [
            " The rotor speed 20 Hz is not found in the global force because of the geometrically averaging of the x- and y-components. In a next step, (4) is used to calculate the surface force density on the stator teeth. The force density is only computed toward the air gap since the forces between the lamination and the copper winding are much smaller. The main excitation will appear in radial direction toward the rotor. Usually, the normal forces are about 10 to 100 times or even more than the tangential ones, as described in Section V before. Fig. 7 shows the surface force density-distribution for the same time step for both variants. In case of the centrical variant, the forces that occur on the one side of the stator are compensated on the opposite side. If compared with the force excitation for the excentrical case, the forces no longer have the same value on the opposite sides. Consequently, they are not compensated. The stator teeth are excited asymmetrically with the rotor speed and higher orders of this. Fig. 8 shows the force excitation along the edge of one stator tooth for both cases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003471_iros.2007.4399451-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003471_iros.2007.4399451-Figure2-1.png",
        "caption": "Fig. 2. Schematic of the Generic Range Finder as a set of beams",
        "texts": [],
        "surrounding_texts": [
            "The beam sensor senses along a beam, V(s), starting from the sensor origin up to L, the range of the sensor, and it returns the distance of the first hit point along the beam. The intersection of the beam with the unknown physical space is denoted by Vu(s). In the simplified sensor model, all gridcells, along the beam that are in front of the hit point are sensed free, i.e., pij |V (s) = 1, and the cell corresponding to the hit point is sensed as obstacle, i.e., pij |V (s) = 0 and the pij\u2019s values for the cells behind the hit point remain unchanged [?]. The expectation computation in the MER expression is over the set of all possible sensing outcomes for a given sensing action, thus their corresponding probability and the corresponding entropy reduction needs to be determined. It turns out that the set of all possible sensing outcomes for V (s) can be grouped into a finite number of events, determined by simple geometrical computations. The geometry of a sensing action is illustrated in Fig. ??. Vu(s) is divided into a set of intervals. The ith interval of Vu(s) \u22c2 A(q), is denoted as IRi, correspondingly |IRi| is the number of gridcells in this interval, and IOi is the ith interval of Vu(s) that does not intersect A(q), correspondingly the number of grid-cells in this interval is denoted as |IOi|. The number of intervals depends on the geometry of the robot, and for a general mobile-manipulator with m convex links, the number of intervals is m. All possible sensing outcomes are now grouped into the following m + 2 events: Eventc : The hit point lies inside A(q), i.e., hit point lies in one of the IRi\u2019s. The robot configuration q would be in collision, were this event to happen, and H(Q|eventc) = 0. Eventi : i = 0, . . . ,m-1 : The hit point lies inside IOi+1. Eventm : There is no hit point in Vu(s). For simplicity we use pij = p for all cij . Please note that this is not a restriction, the expression is simply more elaborate to write otherwise. The marginal expected entropy reduction for configuration q with H(Q) = H0 turns out to be: E\u2206 s H(Q)) = m \u2211 i=0 PiHi \u2212 H0 = m \u2211 i=1 [Hip \u2211i j=1 |IOj |+|IRj |(1 \u2212 p|IO(i+1)|)] \u2212 H0p |IO1|, (7) where Pi = P (Eventi), and Hi = H(q|Eventi), and is easily computed by inserting p(q|Eventi) in (??), with p(q|Eventi) = { 0 if Eventc p(q) p \u03a3i j=1 |IRj | otherwise, Note that \u03a3i j=1|IRj | is the number of cells sensed free in A(q) \u22c2 V(s), were Eventi to happen. As one can see, for a given q, A(q) is easily determined using forward kinematics, and |IOi|, |IRi| are easily determined by simple geometrical computations and ray casting. The marginal entropy reduction for a configuration q is therefor linear in of number cells in the beam, and hence is efficiently computed. Note that since occlusion does affect MER for OCC-grid model, therefore it prefers sensing positions \u201ccloser\u201d to the set of sensed configurations."
        ]
    },
    {
        "image_filename": "designv11_28_0003508_978-1-84628-469-4_13-Figure13.7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003508_978-1-84628-469-4_13-Figure13.7-1.png",
        "caption": "Figure 13.7. Fuzzification of and ee",
        "texts": [
            " A nonlinear boundary does not add much control performance since it is the width of the boundary layer that influences the controller performance, not the form of the boundary layer [9]. From authors\u2019 point of view, FSMC has little practical value, if not being totally useless. Sliding mode control is a kind of time sub-optimal control. The well-known solution for time optimal set point control of a system with bounded control action is a bang-bang controller across a nonlinear switching curve. For two-dimensional systems, the nonlinear switching curve often has the form depicted in Figure 13.7 instead of a linear switching line. Figure 13.6 also shows there can be a switching band around the switching line to alleviate chattering. Figure 13.4 also illustrates how the control surface may look with a nonlinear switch function. In a Takagi-Sugeno (TS) type FLC, the rule output function typically is a linear function of controller inputs. The mathematical expression of this function is similar to a switching function. This similarity indicates that the information from a sliding mode controller can be used to design a fuzzy logic controller, resulting in a Sliding Mode Fuzzy Controller (SMFC)",
            " The th rule for a Sliding Mode Fuzzy Controller is expressed as follows:i IF e is and e is , THENiA iB )( i ii i cee ksatu Notice that there are still as many inputs to the fuzzy controller as the number of state variables. The structure of the fuzzy controller does not reduce the rule base size. However, this kind of SMFC can achieve more complicated switching functions with less rules than an ordinary FLC does. Also notice that the rule output function is not necessarily a saturation function; it could be a Sign function or hyperbolic tangential function. The fuzzification of and e are illustrated in Figure 13.7. e An FSMC is intended to approximate a nonlinear sliding surface, not a nonlinear switching function. Within an FSMC, the switching function is still a linear function as in Equation (13.2). However, an SMFC can approximate a nonlinear switching function easily with just a few rules. Moreover, for a twodimensional system, the switching line can be either a function of , or a function of since it is a one-dimensional function. A much smaller number of rules are needed to approximate this one-dimensional function",
            " This is how a Sliding Mode Fuzzy Controller reduces the rule base size. e . e To illustrate how the rule base size is reduced, we use a two-dimensional system. Under the typical Sliding Mode Fuzzy Controller, with each input fuzzified into three fuzzy subsets as shown in Figure 13.8, there are nine partitions of the state space, and nine rules are needed. However, with the following simplified rule: IF is , THENe iA )( i ii i cee ksatu The rule base size may be less than nine. To approximate the switching curve in Figure 13.7, may need more fuzzy subsets. It has been show that five membership functions for are enough to approximate the switching curve in Figure 13.7. The control surface of such a five rule FSMC and the corresponding sliding surface is shown in Figure 13.8. e e A sliding mode fuzzy pitch controller and a sliding mode fuzzy heading controller have been designed for the OEX series AUVs. The inputs to the sliding mode fuzzy heading controller are heading error and heading error rate. The output is rudder deflection. The inputs to the pitch controller are pitch error and pitch error rate. The output is stern plane deflection. Figure 13.9 shows the performance of the heading controller in open water trial"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003749_s10015-009-0654-5-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003749_s10015-009-0654-5-Figure7-1.png",
        "caption": "Fig. 7. Task of opening the case of an audio-visual system component. a Audio-visual system component. b Case-opening task sequence",
        "texts": [
            " Move-to-touch skill Fig. 3. Rotate-to-level skill layer. The project layer might also be developed as a hierarchy, but we will not discuss this here. 3.2 Stratifi cation of maintenance tasks We now consider typical tasks involved in the repair of the system components of consumer audio-visual equipment as an example of stratifi cation. The maintenance tasks for an electrical appliance are performed as shown in Fig. 6. The task sequence {task( ( 2) 1, i2)} of the case opening task( ( 3) 1) is shown in Fig. 7. If there are two Phillips screws in side (R), task( ( 2) 1, 1) is composed of two tasks of loosening each of the two Phillips screws using a Phillips screwdriver, which can be described as task( ( 1) 1, 1, 1) and task( ( 1) 1, 1, 2), and the skill sequences {task( ( 0) 1,1,1, i0)} and {task( ( 0) 1,1,2, i0)} are shown in Fig. 8. These skill primitives are described in detail in Nakamura and Kitagaki.5 The loosening tasks at the rear and side (L), called task( ( 2) 1, 3) and task( ( 2) 1, 5), respectively, are similar to task( ( 2) 1, 1) at side (R)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003165_detc2007-34101-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003165_detc2007-34101-Figure1-1.png",
        "caption": "Figure 1: A typical geared rotor system",
        "texts": [
            "org/about-asme/terms-of-use Do W1 Mesh force on gear and pinion yg, yp Displacements in y direction of gear and pinion, respectively \u03b8g, \u03b8p Angular rotations of gear and pinion, respectively Subscripts/Superscripts g gear p pinion b bearing h gear mesh Acronyms DSLR Dynamic to Static Load Ratio DTE Dynamic Transmission Error STE Loaded Static Transmission Error A typical generic geared rotor system, which consists of a spur gear pair mounted on flexible shafts, supported by flexible bearings is shown in Figure 1. The basic elements of such a system are flexible shafts, rigid disks, flexible bearings with clearance nonlinearity, and two gears with flexible teeth and backlash nonlinearity. Assuming that the axial motions of shafts are negligible, each node in a finite element model of a shaft will have five degrees of freedom. Then each finite shaft element has ten degrees of freedom. The rigid disks and gear blanks are modeled as five degrees of freedom rigid elements, whereas flexible bearings are modeled as two degrees of freedom elements having nonlinear stiffness values"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003717_08ias.2008.78-Figure19-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003717_08ias.2008.78-Figure19-1.png",
        "caption": "Fig. 19. Phasor diagram and symbol definitions of a PM reluctance motor.",
        "texts": [
            " Fortunately, at high speed, the motor would be operating at the field-weakening region with lower flux density. The overall mechanical and core losses should be reasonably low in the entire operating region of the motor. Losses of few hundred watts are reasonable for a motor with a rating of a few tens of kilowatts. The HSUB machine in a motor mode can be operated as a synchronous motor without an encoder, or as a brushless dc motor with a rotor position encoder. Fig. 18 shows the current and voltage traces of the prototype motor operating in the brushless dc motor mode. Fig. 19 is a phasor diagram of the phase variables of a PM reluctance machine. The symbol V is phase voltage; I, phase current; E, phase back-emf; suffix d, direct axis; q, quadrature axis; and \u03b4, load angle. The assumptions of sinusoidal time and space variables are used in the phasor diagram. The 3-phase power, P, going into the motor is derived through the products of the voltage projections and the currents. P = 3 (V cos\u03b4 Iq \u2212 V sin\u03b4 Id). (1) The V cos\u03b4 and the V sin\u03b4 terms of Eq. (1) can be rewritten according to Fig. 19. This gives P = 3 [(E + IdXd) Iq \u2212 IqXq Id]. (2) Substituting Id = (V cos\u03b4 \u2212 E)/Xd, and Iq = (V sin\u03b4)/Xq into (2) gives P = 3 [VEsin\u03b4/Xd + 0.5V\u00b2sin2\u03b4(1/Xq \u2212 1/Xd)]. (3) The first term inside the brackets of (3) represents the synchronous power corresponding to the PMs that is proportional to sin\u03b4. The second term is a typical reluctance power that varies according to sin2\u03b4 and results from the difference of the reciprocals of the quadrature-axis and direct-axis reactances. The torque capability of the motor measured at zero speed shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000019_28.90359-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000019_28.90359-Figure9-1.png",
        "caption": "Fig. 9. Motor response to a ramp speed control: (a) General case; (b) minimum oscillation.",
        "texts": [
            " In order to obtain a relatively smooth start, a ramp speed command is imposed: e, = at2/2. The general solution for the rotor angle with the ramp command is (28) at2 aBt (aB2 /K , i s ) - aJ/2 e , = e , , + - - - + 2 K,is K,& . (29) The rotor speed is obtained by differentiation of (29): For the initial conditions of e,,,=,) = Or, and e,(,=,) = 0: (31) ( a J / 2 ) - (aB2/K,i^,) K t i s c, = + er0 BC2 aB c, = Both C, and C2 are functions of the initial angle Or,. sponse is From (30), the steady-state component of the speed re- aB 8,,, = U,, = at - -. K,is (33) As shown in Fig. 9, if there were no transient component, the motor speed_would follow the ramp command with an offset of aB/K , is. The transient component occurs within an exponential envelope, as shown for a general case in Fig. 9(a), where the peak value of the envelope at t = 0 is (34) The peak value of the transient is seen to be a function of C, and consequently of the initial rotor angle e,,. To obtain the minimum transient 2 aB2 J (35) c2 = - K, iS (B2 + 4 J 2 4 ) and aB p . = - K,i, rmin Thus, the peak transient component can be made equal to the steady-state offset. In most drives, the coefficient B of friction is relatively small. The acceleration CI can be made small enough that the start is relatively free of oscillation as shown in Fig. 9(b). From (27), (31), and (35), the initial rotor angle that gives the minimum transient is e,, = -L[Z 2 K , is K , is - J ] . (37) With a small value of acceleration a, this angle is near zero. Fig. 10 shows experimentally measured starting speed responses for three different values of initial rotor angle. In I010 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 21, NO. 5, SEPTEMBERiOCTOBER 1991 each case, a = 0.5 Hz/s for 2 s followed by os = 1 Hz for t > 2s. The transient for the best initial alignment of O r , = 0 is seen to be relatively small"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000112_s0301-679x(02)00022-1-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000112_s0301-679x(02)00022-1-Figure2-1.png",
        "caption": "Fig. 2. An elastic body in contact, domain designation, and the coordinate system (a). Domain description. (b). An asperity in thermoelastic contact.",
        "texts": [
            " The rough surfaces studied in this work are numerically generated based on specified root-mean square roughness, Rq, which is one of the commonly used parameters, and the autocorrelation function characterized by its correlation length and aspect ratio, or the Peklenik number. Appendix A explains the generation method in detail. Fig. 1 shows a sample of the generated surfaces. When two infinitely large elastic bodies with nominally flat surfaces are in contact, the surface of each of these bodies is subject to a combined action of contact pressure and interfacial friction. Fig. 2 (a) illustrates such a body with a top surface, , including a computational surface region, S, and an infinitely large boundary surface, B. and B encircle the solid region, , that receives the heat input from the top surface . This body may have layers on the surface, or a composite structure formed by the mixture of at least two different materials. The contact between the two elastic bodies may be simply described as a rough-elastic surface in contact with an ideally smooth and rigid one. Fig. 2(b) presents the contact and deformation of an asperity of the rough surface subject to a normal load and frictional heating, under which the asperity should experience an elastic depression, uP ij, along the pressure direction and a thermal expansion, ut ij, in the opposite direction. Detailed derivations have been reported in a previous publication [6] and some of the equations are repeated here for clarity. For any surface point (i,j) S, where S includes contact regions, C, the thermo\u2013mechanical contact conditions can be expressed as uP ij ut ij sij a 0, Fij 0, (i,j) C (1a) or uP ij ut ij sij a 0, Fij 0, (i,j) C (1b) and (i,j) S Fij F0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002110_2005-01-1927-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002110_2005-01-1927-Figure2-1.png",
        "caption": "Figure 2. AGCS system layout",
        "texts": [
            " Comparison between the conventional active chassis control system and AGCS Item Conventional active chassis system AGCS Control concept phenomenon control cause control of phenomenon Control direction same direction with acting load excessive energy perpendicular direction with acting load small energy Control feel may be unnatural is natural The kinematics arrangement of the suspension link changes toe angle, which is largely affecting running stability, as the running condition changes. The AGCS system of Hyundai Motors is a device to optimize the toe angle of a rear wheel by controlling the position of a rear suspension link. It consists of actuators, control lever(these are mounted in rear subframe) and ECU as shown in Figure 2. ECU is adjusting actuator stroke based on the vehicle speed and steering angle. Then the control lever is rotating downward or upward around hinge. It moves the inboard mounting point of the rear wheel assist link to maintain optimal bump toe-in value. Sensor part has vehicle speed sensor and steering angle sensor. Vehicle speed sensor reads the vehicle\u2019s speed, and the steering angle sensor reads the driver\u2019s steering amount. Control part commands the actuator by estimating lateral acceleration acting on the vehicle based on the data from the vehicle speed sensor and the steering angle sensor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003276_s00158-008-0298-4-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003276_s00158-008-0298-4-Figure9-1.png",
        "caption": "Fig. 9 Diagram of the plate displacement problem. Corners of larger lower plate clamped. Corners of smaller upper plate pinned to lower plate by stiff bars to prevent complete delamination. Force applied at center of upper plate (displacement controlled)",
        "texts": [
            " A smoother response may be possible if more target points are added, although a smooth downward sloping response may not be obtainable by varying the adhesive energy alone. 4.4 Plate delamination design problem The applicability of the proposed approach to more complex 3D problems is illustrated with the following plate delamination problem. This problem is similar to those studied by Bhate and Dunn (2007), although design optimization is applied. A smaller elastic plate is initially fully adhered to a flexible substrate, shown in Fig. 9. The substrate is pinned at the corners, and the upper plate is rigidly connected at the corners to the substrate to prevent full delamination in the case of a weak adhesive. A vertical displacement is applied to the center of the upper plate. The plates are modeled by a regular mesh of triangular three-node 9-DOF ANDES shell elements (Militello and Felippa 1991). The upper plate is discretized into 800 elements and the lower is discretized into 2,400 elements. Between corresponding shell elements on the upper and lower plates are six-node 18-DOF 3D interface elements, formulated in an analogous way to the beam interface element in the Appendix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003260_1.2957632-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003260_1.2957632-Figure2-1.png",
        "caption": "Fig. 2 Desired tasks for dual arm manipulation, whe",
        "texts": [
            " This is a natural choice for the dampening factor because the Lagrange multiplier vector is nonzero only in the neighborhood of singularities. In the following section, the effectiveness and implementation method of the proposed singularity-robust inverse kinematics will be shown through the numerical simulation. 3 Simulation As a numerical simulation, the dual arm manipulator system is adopted to show the effectiveness of the suggested singularityrobust inverse kinematics algorithm for two tasks with priority order. The desired tasks are deburring and conveyance of workpiece, as shown in Fig. 2. The left arm grips a workpiece to be deburred, and the right arm is equipped with a tool for a deburring task. At the same time, the conveyance task of workpiece is implemented as a secondary task. The primary task requires three degrees of freedom for the implementation of a 150 deg deburring task including tool orientation in local x-y coordinates, and the secondary task requires two degrees of freedom for a conveyance task from \u22120.2,0.2 to 0.6, 0.6 in global X-Y coordinates; in other words, desired tasks can be defined as follows: 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001181_10402000208982542-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001181_10402000208982542-Figure1-1.png",
        "caption": "Figure 1 shows a cylinder loaded and rolling against a plane, lubricated with a paraffinic mineral oil. The cylinder and plane circumferential speeds are varied to generate the desired slide-roil ratio. For convenience, the cylinder surface is named the top boundary, and the upper plane surface the bottom boundary. Lubricant property data are shown in Table I. Other operating parameters are listed in Table 2.",
        "texts": [],
        "surrounding_texts": [
            "An Analysis of Elastohydrodynamic Lubrication with Limiting Shear Stress: Part II - Load lnfluenceG\nYONGBIN ZHANG and SHIZHU WEN Tsinghua University\nNational Tribology Laboratory 100084, Beijing, People's Republic of China\nThis paper studies the load-carrying capacity of elastohydro-\ndynamic lubrication (EHL) film subjected to isothermal condition\nincorporating the interfacial limiting shear stress. The slide-roll\nratio varied fiom 0.0 to 2.0 and light, modest and heavy loads\nwere respectively employed. A special attention was concentrated\non the total lubricant flow entrained into the contact when d~ffer-\nent loads were used. It was indicated that a considerable and even\nalmost complete global film loss under a heavy load in EHL con-\ntacts can be resultingfiom the reduction of the total lubricant flow\nentrained into the contact due to the interjiacial limiting shear\nstress effect.\nKEY WORDS\nElastohydrodynamic Lubrication; Limiting Shear Stress; EHL Film Load-Carrying Capacity\nINTRODUCTION\nIn the first part (Zhang and Wen, 2001), the fluid-contact interfacial limiting shear stress effect was found to be significant in\nFinal manuscript approved December 10,2001 Review led by Tibor Tallian\nelastohydrodynamic lubrication. This effect generates EHL phenomena such as film slippage, flattened pressure profile and collapsing film. The concepl of interfacial limiting shear stress is capable of interpreting the experimentally observed elastohydrodynamic film collapse and failure, which are poorly explained by present EHL theories.\nThe collapse and failure of EHL film with increased load is not explained by conventional isothermal and thermal EHL theories (Lee et al., 1973;Czichos,1974). The lubrication law for collapsing EHL film is obviously distinct. The temperature effect on lubricant viscosity is unable to change the film thickness variation with load described by conventional EHL theory (Cheng and Stemlicht, 1965). Since the EHL film thickness is determined by the net lubricant flow through the contact, and this flow equals the total lubricant flow entrained into the contact minus the lubricant side flow, therefore a reduction of global EHL film thickness can only originate from the reduction of the total lubricant flow into the contact area and from lubricant side leakage. Too simple assumptions of no lubricant side leakage and perfectly smooth surfaces are most probably the reason why conventional EHL theory fails to predict the experimental results. The lubricant side leakage in three dimensional rough concentrated contacts was shown by Chang et al. (1994) to cause EHL film breakdown. Evans and Snidle (1996) proposed that the lubricant side leakage can result in film disappearance in rough EHLcontacts. The lubri-\nNOMENCLATURE w z - ~ = width of the zone where slip case C3 occurs (cf. Zhang and\nb\n\"m,\n\"c PI, S\nSc SfcoeJ Xfcoef\nU h W\n= half Hertzian width, = minimum film thickness = central film thickness = maximum Hertzian pressure, 2wlnh = slide-roll ratio, 2(uo - uh)/(uo + [I,,) = slide-roll ratio which makes the film start to slip\n= friction coefficients on the top and bottom boundaries, respectively = cylinder and plane circumferential speeds, respectively = load per unit axial length\nWen, 200 1 )\n= coordinate = lubricant parameter, a / [5 .1~10-~ (ha, + 9.67)] or\ncoordinate = dimensionless width of the zone where slip case C3 OCCUTS,\nw 2 . p\n= lubricant viscosity-pressure index = lubricant shear strength-pressure proportionality = lubricant viscosity and density at ambient pressure,\nrespectively = ambient lubricant shear strength\nD ow\nnl oa\nde d\nby [\nU m\ne\u00e5 U\nni ve\nrs ity\nL ib\nra ry\n] at\n1 4:\n31 1\n8 N\nov em\nbe r\n20 14",
            "Y. ZHANG AND S. WEN\ncant side leakage was found by Johnson and Higginson (1988) to be increased by lubricant viscoplastic behavior.\nThe (total) lubricant flow entrained into the contact is determined by the inlet condition, i.e. the inlet Couette flow and the inlet Poiseuille flow. It has been assumed that the inaccuracy of an EHL theory in calculating this flow mainly arises from incorrect inlet viscosity prediction. However, the influences on the inlet viscosity of temperature and of non-Newtonian lubricant behavior were found to have modest effects on the total flow into EHL contacts (Cheng and Sternlicht, 1965; Conry et al., 1987). The lubricant side leakage thus seems to be the main mechanism for the rapid film loss with heavy loads in real EHL contacts.\nIn the first part (Zhang and Wen, 2001), it was found that the total lubricant flow into EHL contacts can be severely reduced by interfacial film slippage, at large slide-roll ratios which reduces the inlet entrainment speed and increases the inlet pressure gradient.\nIt was also shown in the first part that film slippage occurrence in the inlet zone drastically reduces the central and minimum film thicknesses. EHL film thickness and total lubricant flow into EHL contacts are very sensitive to the extension of the domain in the inlet zone where film slippage occurs.\nLn the present paper, lubricant side leakage is not considered. Total lubricant flow entrained into the EHL contacts is examined assuming a limiting interfacial shear stress. The contact is ideally smooth, one-dimensional and isothermal. The film pressures and film thickness distributions under different loads are derived by using the analysis developed in the first part. This yields insight into the load-carrying capacity of EHL films.\nMETHOD\nThe theory and numerical approach developed in the first part are used in this work. Thus, it is assumed that the fluid is predominantly viscous and the elastic component of the fluid deformation at the existing rate of deformation is negligible. It is recognized that, under sufficiently a heavy load the fluid in the EHL contact is strongly solidified so that the elastic component of the rate of its shear deformation can not be neglected. The loads in the present analysis range from 20 kN/m to 2500 kN/m, giving the maximum Hertzian pressures from 0.18 GPa to 2.04 GPa. The\nDeborah numbers/qfi/(GI) in the present study for the loads 300 kN/m, 900 kNm, 1500 kN/m and 2500 kN/m (or the maximum Hertzian pressures 0.7 IGPa, 1.22 GPa, 1.57 GPa and 2.04 GPa ) are 0.006, 1.023, 28.05 and 1930.0, respectively. In the present analysis, i t is believed that the fluid model utilized in the first part is applicable for the whole contact area when the load ranges below 300 kN/m, whereas that model can not be applied to all the fluid in the contact when the load exceeds 900 kN/m. For the fluid which is subjected to very high pressure so that it is highly solidified and its Deborah number exceeds unity, the model should incorporate the elastic component shear deformation rate. The developed theory in the first part thus seems inadequate for the present work where a load higher than 900 kN/m is employed. Nevertheless, the inlet fluid in this work is subjected to pressures no higher than 0.7 GPa and its Deborah number is less than 0.006 even at the heaviest load (2500 kN/m). Since the total lubricant flow into EHL contacts and the average EHL film thickness are determined by the inlet condition and the fluid model used here is applicable for the inlet fluid , the proposed theory in the first part is still utilizable in this work. For the fluid which is both viscous and elastic, the model which only considers the viscous component of the rate of the fluid shear deformation (but neglects the elastic component) gives a higher shear stress for a given shear strain rate than the model which incorporates both the viscous and elastic components of the rate of the fluid shear deformation. The use of the developed theory in this work is expected to lead to an exaggerated prediction of interfacial film slippage when the load exceeds 900 kN/m. The resulting film pressure profile is expected to be overly flattened. The local film thickness is expected to show some error, of tolerable magnitude.\nThe film slippage, film pressures, film thickness distributions, friction coefficients and mass flows in the contact shown in Fig. I were obtained for widely varied load and a slide-roll ratio varied from 0 to 2.0.\nLoad Influence On Film Slippage\nIn an EHL contact, heavier load generates a higher film pressure and the viscosity of lubricant heavily depends on pressure. In the presence of film slippage, a higher-viscosity lubricant sustains a larger shear stress for a given shear strain rate, and thus a heavier load more readily causes interfacial slippage of an EHL film, as a result of the shear stress reaching the limiting shear stress at the lubricant-contact interface. It was experimentally observed that a pressure increase increases the shear strength of lubricant (Bair and Winer, 1979), assumed here to represent the interfacial limiting shear stress. Table 3 shows the limiting values of slideroll ratio at which interfacial slip starts, for varying loads.\nD ow\nnl oa\nde d\nby [\nU m\ne\u00e5 U\nni ve\nrs ity\nL ib\nra ry\n] at\n1 4:\n31 1\n8 N\nov em\nbe r\n20 14",
            "An Analysis of Elastohydrodynamic Lubrication with Limiting Shear Stress: Part I1 - Load Influence\n-\nLubricant Density, po 866.0kp/m3 Lubricant Viscosity, qo Ambient Lubricant Shear Strength, t,,, 20.0 MPa Lubricant Viscositv-Pressure Index. a I 21.9 GPa-' Lubricant Shear Strength-Pressure Proportionality, a,, Lubricant Exponent, z 0.036 0.666\nCylinder Radius, R Rolling Speed, ?l. Elastic Modulus, E, , E,\n20 mm 2.0 m/s 193.0 GPa . - I\nPoisson's Ratio, v,, v, 0.28\nDefine:\nn,Gl El R\nwhere Ys is the dimensionless width of the zone with slip case C, (cf. Zhang and Wen, 2001 ), i.e. the ratio of the dimensional width of that zone to the Hertzian zone width. Since the shear stresses at both of the lubricant-contact interfaces for slip case C3 are reduced by the limiting shear stress so that the pressure gradient is reduced to zero (i.e. a complete pressure gradient loss occurs) in that zone, this pressure gradient loss causes the extension of the zone with slip case C, to have a significant effect on film thickness. Ys is used to indicate the severity of film slippage, Fig. 2 shows that when the other operational parameters remain constant, a load increase greatly reduces the value of Y S , even though as shown by Fig. 3 the dimensional width of the zone with slip case C, pronouncedly increases with load. This result is due to the fact that the Hertzian zone width increases more rapidly with load than the dimensional slip zone width. The load increase thus constricts (rather than extends) the film slippage domain, and therefore has less effect on elastohydrodynamic film thickness reduction than it would if the film slippage domain (the value of Ys ) were increased. Nevertheless, a heavier load causes increased loss of the central and minimum film thicknesses due to film slippage for a given slide-roll ratio as indicated in Fig. 8. Thus, for a heavier load the film thickness appears more sensitive to the extension of the film slippage domain. The extension of the film slippage\n1.91 x lo-\"\n0.00 0. 50 1. 00 1. 50 2.00 The slide-roll ratio S\nFig. 2-Values of Y, for different loads and slide-roll ratios.\ndomain results in the limitation of interfacial shear stress over an increased region in lower film thickness. However, the constriction of the film slippage domain by load increase reduces the rate of reduction of film thickness with increasing load. As shown by Fig. 8 for predominant and simple slidings (i.e. S>1.0), the central and minimum film thicknesses show load sensitivity much greater than predicted by conventional EHL theory as long as the maximum Hertzian pressure is below 0.7 1 GPa, whereas the variation of the central and minimum film thicknesses with load approximately follows conventional EHL theory when the maximum Hertzian pressure exceeds 0.7 1 GPa.\nAs seen in Fig. 3, a heavier load generates a wider film slippage domain and a higher lubricant slipping velocity. The slipping velocity curve on the axis s shows a nearly constant maximum for large slip. For large slide-roll ratios, the influence of load on the slipping velocity is weak.\nD ow\nnl oa\nde d\nby [\nU m\ne\u00e5 U\nni ve\nrs ity\nL ib\nra ry\n] at\n1 4:\n31 1\n8 N\nov em\nbe r\n20 14"
        ]
    },
    {
        "image_filename": "designv11_28_0003305_rob.20214-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003305_rob.20214-Figure3-1.png",
        "caption": "Figure 3. The Packbot Scout equipped with the Claymore mine top , and the Direct Fire Weapon Effects Simulator. In front, the remote control for payload operation.",
        "texts": [
            " Many current conflicts, however, take place in urban environments, and a corresponding redirection of armed force training is ongoing. All tests were carried out in facilities regularly used for military training. Deserted and partly demolished industrial and residential buildings offered an environment similar to those expected during combat operations Figure 2 . During the tests no adap- tations or adjustments were done to the environment. The test period spanned from autumn to spring and temperatures from \u221215\u00b0C to +15\u00b0C. The iRobot Packbot Scout9 Figure 3 used in the study was equipped with a number of accessories. The same Direct Fire Weapon Effects Simulator DFWES that is used for combat training was mounted on the robot Saab BT46 . The system includes a laser mounted on the firearms, and a sensor suit worn by the soldiers. Adding the fire simulation system enabled the soldiers to engage the robot with their firearms during training. Two more payloads were developed; a flashlight 8The maneuvers took place in Fagersta 1\u20134 Nov. 2005, Enk\u00f6ping 8\u20139 Nov",
            " Multimodal feedback visual, audio, and other such as tactile feedback of motor loads would likely increase the operators driving performance significantly. The troops have hearing protection that electronically blocks loud noise. The headset can receive in-line audio from radios or other electronic systems and, thereby, enable the use of audio feedback even under noisy circumstances or stealth operations. Two-way audio is a standard feature on many EODrobots which would be of tactical value also in 34Dual tracked arms in the front which are part of the robot\u2019s propulsion system Figure 3 . Journal of Field Robotics DOI 10.1002/rob MOUT. The robot was considered to be too noisy for stealth operation. In addition, booting the OCU operating system causes it to beep. In comparison to the robot, the off-the-shelf laptop with external joystick did not suit the application as well. The weakest point of the entire robot system was the USB-connection for the joystick. It was no more rugged than that found on a common laptop computer, which became especially critical since a reboot was required to regain contact with the joystick if the cable was momentarily disconnected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002660_iros.2006.282408-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002660_iros.2006.282408-Figure2-1.png",
        "caption": "Fig. 2. Model of a planar humanoid robot in midair.",
        "texts": [
            " A humanoid robot maintains its balance through proper control of the reaction at the supporting foot. Note, on the other hand, that this reaction depends on the wrench imposed on the foot through motion of all links of the humanoid. Hence, control of the imposed wrench is of primary importance. To ensure such control, we envision the adaptation of the Reaction Null-Space method introduced in the previous section. We will use a simple three-link planar model, the foot having the meaning of \u201cbase\u201d (see Fig. 2). The joint at the foot is the ankle joint (angle \u03b81), the other joint is called \u201chip joint.\u201d The notation in the model is as follows: m0 Mass of the foot link m1 Mass of the first link (leg) m2 Mass of the second link (upper body) lb Distance from CoM of the foot link to the first joint lg1 Distance from the first joint to CoM of the first link lg2 Distance from the second joint to CoM of the second link l1 Length of the first link \u03a3i Inertial coordinate frame \u03a3f Foot coordinate frame \u03b80 Angle from the inertial coordinate frame to the foot coordinate frame \u03b81 Angle of the ankle joint \u03b82 Angle of the hip joint I0 Inertia moment of the foot link I1 Inertia moment of the first link I2 Inertia moment of the second link r0 Position vector from inertial coordinate frame to foot coordinate frame The equation of motion of the three link model can be written as follows:[ Hf Hfl HT fl H l ] [ x\u0308 \u03b8\u0308 ] + [ cf cl ] + [ gf gl ] = [ 0 \u03c4 ] + [ RT fp JT ] [ f n ] (7) where H l \u2208 R2\u00d72 Inertia matrix of the leg and upper body links Hf \u2208 R3\u00d73 Inertia matrix of the foot Hfl \u2208 R3\u00d72 Inertia coupling matrix cl \u2208 R2 Velocity dependent nonlinear terms of the links cf \u2208 R3 Velocity dependent nonlinear terms of the foot link gl \u2208 R2 Gravity terms of the links gf \u2208 R3 Gravity terms of the foot \u03c4 \u2208 R2 Joint torque x\u0308 \u2208 R3 Acceleration of the foot \u03b8\u0308 \u2208 R2 Joint angular acceleration We assume that an external wrench [fT n]T is acting at the upper body link at a point displaced by a units from the CoM of this link outward"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001067_095441002760179771-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001067_095441002760179771-Figure1-1.png",
        "caption": "Fig. 1 Tooth pro\u00aele in the radial direction",
        "texts": [],
        "surrounding_texts": [
            "Curvic couplings (see F ig. 1) were \u00aerst introduced in 1942; Curvic2 is a trademark of the Gleason Works, USA [1]. Previous numerical analysis on Curvic couplings has been carried out by Pisani and Rencis [2] in two and three dimensions. They compared the results from the \u00aenite and boundary element methods of a single tooth non-contact model, and then used the corresponding stress concentration factor in an axisymmetric non-contact \u00aenite element (FE) analysis in order to evaluate the nominal hoop stress in the Curvic coupling. This paper uses the ABAQUS [3] commercial FE package to provide a validation of the FE contact method for use with Curvic couplings by a comparison with the results from a photoelastic test . The photoelastic experimental technique is dependent on the stress The M S was received on 28 M arch 2002 and was accepted after revision for publication on 16 April 2002. * Corresponding author: School of M echanical, M anufacturing, M aterials and M anagement, University of Nottingham, University Park, Nottingham NG7 2RD, UK. G01102 # IMechE 2002 Proc Instn Mech Engrs Vol 216 Part G: J Aerospace Engineering at The University of Iowa Libraries on July 1, 2015pig.sagepub.comDownloaded from optic law, which was formulated by Maxwell in 1852. The current investigation involves the analysis of a simple Curvic coupling using the three-dimensional photoelastic frozen stress technique (see F igs 2 and 3) to analyse a non-Hertzian contact problem. Some of the photoelastic results in the \u00aegures presented were obtained using an automatic micropolariscope. Fessler and Ollerton [4] used the frozen stress technique to investigate the contact stresses in bodies that would produce Hertzian contact areas, in this case toroids. These experiments showed that accurate results for non-Hertzian \u00aenite bodies could be achieved with the differences between theoretical and experimental results being small. The frozen stress photoelastic technique has been used for non-Hertzian initia lly conforming surfaces by Fessler and F ricker [5]. F essler [6] gives an overall assessment of frozen stress photoelastic analysis along with the type of results that can be obtained. Automatic photoelastic stress analysis allows the removal of one of the main disadvantages of the photoelastic technique, which is the time consuming analysis of the results, speci\u00aecally the fringes, from an experiment. The automatic micropolariscope (AMP) used in this investigation was developed by Marston [7] and was described in detail by Fessler [8]. A study of the subsurface stresses of a contact geometry and friction was carried out by Burguete and Patterson [9] using an automated polariscope. They concluded that the strength of the stress singularity at the edge of contact for a wedge in contact with a plane is affected by the wedge angle. A methodology for determining the coef\u00aecient of friction, m, associated with photoelastic materials was presented by Burguete and Patterson [10] for a range of surface roughness and lubricants. In this paper, a representative range of values for m \u02c6 0, 0:1 and 0.2 is used. Proc Instn Mech Engrs Vol 216 Part G: J Aerospace Engineering G01102 # IMechE 2002 at The University of Iowa Libraries on July 1, 2015pi .sagepub.comDownloaded from Although FE analysis is nowadays well established and extensively used in engineering analysis, its reliability and accuracy in three-dimensional contact problems with friction needs veri\u00aecation. This is particularly important in the analysis of three-dimensional Curvic couplings where contact may occur across 250 or more separate contact surfaces and it is impractical to use a very re\u00aened mesh at the contact surfaces. This paper presents a veri\u00aecation of threedimensional FE results by comparing them to experimental photoelasticity results. The FE analysis is concerned with elastic contact conditions with friction. Elastoplast ic analysis of curvic joints under a blade release condition has been dealt with elsewhere [11]."
        ]
    },
    {
        "image_filename": "designv11_28_0002768_9780470116883.ch2-Figure2.9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002768_9780470116883.ch2-Figure2.9-1.png",
        "caption": "Figure 2.9 Interface at a surface between two different materials.",
        "texts": [
            " For such source-free domains, the curl of the magnetic field H is equal to zero, rx~H \u00bc 0 \u00f02:127\u00de Since any zero-curl vector can be represented in terms of the gradient of a scalar function, the magnetic field intensity for such cases may be written as ~H \u00bc rjm \u00f02:128\u00de where the minus sign is taken to provide a convenient analogy with the case of electrostatic potential. The potential equations must be complemented by appropriate interface and boundary conditions [1]. Figure 2.8 shows an interface between materials 1 and 2. A closed contour parallels the interface within material 1 and returns in material 2, very nearly paralleling its path in material 1, as shown in Figure 2.9. The magnetic flux flowing through the contour is given by the contour integral of the vector potential A. Namely, the flux f can be calculated by integrating the local flux density B over the surface bounded by the contour, that is, f \u00bc Z S ~Bd~S \u00f02:129\u00de Substituting B in terms of the vector potential A, it follows f \u00bc Z S rx~Ad~S \u00f02:130\u00de Applying the Stokes theorem, the integration can be performed over the close contour c as follows: f \u00bc I c ~Ad~s \u00f02:131\u00de The surface spanned by the contour can be made arbitrarily small by keeping the two long sides of the contour arbitrarily close to each other while remaining at opposite sides of the material interface",
            " The flux enclosed by the contour can, therefore, become arbitrarily small as well, so that it vanishes in the limit of the vanishing area. This can happen in the case when the tangential component of A has the same value on both sides of the interface. Consequently, the appropriate boundary condition in the limit becomes ~nx\u00f0~A1 ~A2\u00de \u00bc 0 \u00f02:132\u00de A corresponding condition for the electric scalar potential can be obtained from Faraday\u2019s law relating the line integral of electric field to the time derivative of magnetic flux. Since the flux vanishes for the contour shown in Figure 2.9, the contour integral of the electric field must also vanish, that is,I c ~Ed~s \u00bc qf qt \u00bc q qt I c ~Ad~s \u00bc 0 \u00f02:133\u00de Expressing the electric field in terms of its potentials results in the following integral relationship: I c ~Ed~s \u00bc I c rjd~s q qt I c ~Ad~s \u00f02:134\u00de Since the contour integrals of both E and A vanish, eqn (2.134) can only be satisfied if I c rjd~s \u00bc 0 \u00f02:135\u00de Equation (2.135) implies the continuity of the scalar potential across the material interface as j1 \u00bc j2 \u00f02:136\u00de This interface condition is particularly useful in solving electrostatic problems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000554_robot.2001.933186-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000554_robot.2001.933186-Figure1-1.png",
        "caption": "Fig. 1: Model of the snake-like robot and coordinates located on the robot",
        "texts": [
            " This simulator makes possible to analyze the creeping locomotion with the normal-direction slip, adding to the glide along the tangential direction. Through the developed simulator, we investigate the snake-like robot creeping locomotion which is generated only by rolling each of the joints from side to side, and discuss the optimal creeping locomotion of the snake-like robot, which is adaptable to a given environment. 2 Simulator of a Snake-like Robot for Creeping Locomotion Analysis The snake-like robot, shown in figure 1, is formed from serially-connected links. Each link is swung by electrical motor. The creeping locomotion of the snake-like robot is generated by swinging the joints from side to side to cause the forward (or propelling) force, which comes out from interaction of the robot with the environment through friction. In order to analyze the motion of the snake-like robot in the 0-7803-6475-9/01/$10.000 2 01 IEEE 3656 case of considering the normal slip, the robot dynamics and friction with the environment must be modeled. In this section, we first model the robot and environment dynamics, and then develop a simulator for analyzing the creeping locomotion of the snake-like robot. 2.1 Motion Equations of the Robot As shown in figure 1 (b), we locate each coordinates on the joints of the robot. The displacement of the joints and the displacement of the gravity center of the links, thus can be given by where t, is length of link i , tc, is the distance of gravity center of link i from joint i, and i = 0 ,1 ,2 , . . . , n - 1. Moreovcr, n~ is the displacement of head. The velocity and acceleration of the joints and those of the gravity center of the links can be derived through time-differentiation. For simplicity, we set sk = sin(&) and ck = cos(4k) in the formulation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002986_fuzzy.2006.1681916-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002986_fuzzy.2006.1681916-Figure3-1.png",
        "caption": "Figure 3. Illustration of the control strategy",
        "texts": [
            " To control the 3D displacements of the helicopter we propose four independent control loops: collective pitch ( ( )zU 11 \u03a6= ); cyclic pitch - ( )\u03b8,22 xU \u03a6= , ( )\u03c8,33 yU \u03a6= ; tail rotor pitch - ( )\u03c644 \u03a6=U . The proposed control strategies are resulting from a two-rule-based fuzzy logic controller which was used for real experimentations on cartpole and Pendubot systems [4, 5, 11]. The controllers used for the collective pitch and the tail rotor pitch are one-input, simplified versions of the controllers proposed for the cyclic pitch. C. Two-rule-Sign-Based Controller for the Cart-Pole System To introduce the developed strategy for the cyclic pitch we first consider a cart-pole system (Figure 3). In our approach only a few particular states of the controlled system are considered \u2013 when the sign of the applied force is well defined. Indeed in the case of the Figure 3.a and Figure 3.b the control force should be applied in the left or right direction, respectively. At the same time the more the pole has fallen, the larger of magnitude of the control should be. For the other states of the system it is not so easy to determine the sign of the applied force. Hence, there are systems states where the two goals (cart and/or pole) are in conflict, and system states where they are not in conflict. Our approach to deal with this problem is the construction of a sign-based knowledge base which allows us to bring the system in one of the states defined above. The Figure 3.c shows another initial state in which the horizontal force has to be initially positive to avoid the pole falling down. The consequence of this action is that a state similar to that depicted in the Figure 3.b will result. Therefore, the control strategy is to give more importance to the \u00ab pole-state \u00bb than to the \u00ab cart-state \u00bb. The pole state (cart state) is described using a joint variable (PS, CS) which is made up of two atomic variables, the angular error ( E\u03b8 ) (cart position error - x ) and its rate of change ( RE\u03b8 ) (rate of change of position error - dx ). Each of these atomic variables is associated with two fuzzy sets that are labeled positive and negative. Let \u03b8 be the angle the pole makes with the vertical axis",
            " Let \u03a3 denote one of chosen atomic variables ( E\u03b8 , RE\u03b8 , x , dx ), then, for any\u03be \u2208R , its related fuzzy sets are given by: ( ) ( ) ( ) ( ) \u03a3 \u03a3 \u03a3P N P k \u03be \u03be \u03be \u03be + = = + 1 1 2 , tanh (2) Hence, any real value of \u03a3 is given a non zero grade of membership to both input fuzzy sets. Let SS denotes be the joint variable describing the cart state (CS) or the pole state (PS) which is made up of the pair{ }DXX , { }( )\u03b8\u03b8 RE, . Also, define the fuzzy sets SSP and SSN for SS, using the algebraic product, such that: *)(**)(*)*,( *)(**)(*)*,( deDEsNeESNdeeSSN deDESPeESPdeeSSP = = (3) Then, describing only the two systems states where the two goals are not in conflict (Figure 3 a and b), the following rule base can be proposed: R1: IF \" PS is PSP \" ALSO IF \" CS is CSP \" THEN force is Positive (4) R2: IF \" PS is PSN \" ALSO IF \"CS is CSN\" THEN force is Negative where the logical connective \" ALSO \" is used to explicitly give more importance to the joint variable PS than to the joint variable CS. In this paper \" ALSO \" is a quasi-linear mean operator [12]. The rule firing strengths are thus given by: ( ) ( ) SSP PSP e de CSP x dx SSN PSN e de CSN x dx = + \u2212 = + \u2212 \u03bb \u03b8 \u03b8 \u03bb \u03bb \u03b8 \u03b8 \u03bb ( , ) ( , ) ( , ) ( , ) 1 1 (5) where the weighting parameter \u03bb is drawn from the unit interval"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003165_detc2007-34101-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003165_detc2007-34101-Figure3-1.png",
        "caption": "Figure 3: Dynamic model of a spur gear mesh interface",
        "texts": [
            " To simplify the analysis considerably, linear approximations A and/or B can be accepted, which yields a displacement relation as follows: ( ) i b i b i b i b i b i b q -b , q b q 0, b q b q b , q b b f >   = \u2212 < <   + < \u2212  (3) A typical spur gear mesh is represented by a pair of rigid disks, which are coupled by a nonlinear spring that can be modeled by a nonlinear displacement function fh(p) and a viscous damper with a damping coefficient of Cm , both acting along the pressure line, as shown in Figure 3. Friction forces at the mesh point can be assumed to be negligible. Thus the transverse vibrations along the pressure line are uncoupled from those perpendicular to the pressure line. The damping coefficient is assumed to be time-invariant. 3 Copyright \u00a9 2007 by ASME l=/data/conferences/idetc/cie2007/71790/ on 04/15/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Considering the mesh model shown in Figure 3, the relative displacement between two gears along the pressure line can be written as: p g p p g g tp = y y r \u03b8 r \u03b8 e (t) \u2212 + \u2212 \u2212 (4) where rp and rg are the base circle radii of pinion and gear, respectively, and p\u03b8 and g\u03b8 denote angular rotations of pinion and gear, respectively. The loaded static transmission error et(t) which includes the excitation effect of time variation of mesh stiffness can be written in terms of its Fourier components as: t 1 e ( ) cos( ) sin( ) n m p p m p p m t a mN t jb mN t =  = \u2126 + \u2126 \u2211 (5) where j is unit imaginary number"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003133_j.autcon.2007.02.002-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003133_j.autcon.2007.02.002-Figure6-1.png",
        "caption": "Fig. 6. The turn point needs to be varied in accordance with the type of path: th (c), respectively.",
        "texts": [
            " When turning to move from a current path to a new path, the starting point of the turn needs to be varied in accordance with the type of path. For explanatory convenience, the notations when a vehicle turns are shown in Fig. 5. In the figure, r denotes the radius of a turning curvature, \u03b1 is half of the interior angle of two straight lines consisting of three way points, Op\u22121, Op, and Op+1. A turn point, \u03b5, is given as the distance between the start point for the turning and the next way point, Op. Note that in this paper a turn point does not mean position but a distance. Fig. 6 shows that a turn point varies with the type (or shape) of the path. Specifically, (a) needs a longer distance (or turn point) to track a given new path than (b) and (c), and (b) needs a longer distance than (c), where the forward and rotational velocities are all the same. If a fixed turn point is used for the three cases, an undesired underdamped or overdamped response(s) may appear. This also results in collisions as shown in Fig. 2. The third is the damping degree of a control response. In what follows, we propose a tuning method of feedback control gains, which considers the above-mentioned physical limitations of the vehicle, the turn point, and the damping degree"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000562_irds.2002.1041666-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000562_irds.2002.1041666-Figure1-1.png",
        "caption": "Figure 1: Passive one-legged hopper",
        "texts": [
            " Introduction ilfter the Raibert\u2019s excellent works [l], one-legged hopping robots attached with only the leg spring, have been widely studied both experimentally [2, 3, 4, 51 and theoretically [S, 7, 81. In addition to the leg spring, hip spring also plays important role for animal running 191. It enables the leg to be swung passively. Tompson and Raibert showed that spring-driven oneleggcd hopping robot shown in Figure 1, can hop without any inputs, provided if the initial conditions are appropriately cho- sen [lo]. Therefore, this model is a good template model for the purpose of studying energy-efficient running. Since this model is shown to be marginally stable and eventually falls without controls, some suitable controller should be applied to ensure the stability. Ahmadi and Buehler applied Raibert\u2019s celebrated Foot Placement Algorithm [l] to this passive hopping robot, in which the Neutral Point should be preapproximated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000571_robot.2002.1013603-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000571_robot.2002.1013603-Figure1-1.png",
        "caption": "Figure 1: Graspless klanipulation",
        "texts": [
            " Introduction Graspless manipulation [ 11 (or nonprehensile manip ulation [2]) is a method to manipulate objects without grasping. It includes tumbling, pushing, sliding, and so on (Figure 1). In graspless manipulation, robots do not have to support all the weight of the objects. That is a potential advantage of graspless manipulation over conventional pick-and-place. Thus graspless manipulation is important as a complement of pick-and-place for the dexterity of robots. Graspless manipulation is obviously inferior to pickand-place in terms of operation reliability. Therefore it is important to evaluate the stability of manipulated objects for planning and execution of graspless manip ulation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001370_s0167-8922(08)71076-9-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001370_s0167-8922(08)71076-9-Figure5-1.png",
        "caption": "Figure 5. Position o f Trigger Polnts on Disc.",
        "texts": [
            " A s the d i sc r o t a t e s i t f i r s t t r i gge r s the f l a s h u n i t , which exposes a quarter frame of f i lm i n a camera attached t o the microscope, and then ac t iva t e s a stepper motor t o wind t h e f i lm on. This produces a s e r i e s of images of the contact covering one r o t a t i o n of the d i s c . In prac t ice the images a r e arranged t o t r i gge r a t a cosine spacing r a the r than equiangular spacing round the d i sc so as t o correspond t o equal s teps i n spacer-layer th ickness , a s shown i n Figure 5. The displacement of f r inges r e su l t i ng a t d i f f e ren t speeds w a s determined s i m p l y by l ay ing s t r i n g s of images f r an halfway round a d i sc on a l i g h t box and moving them l a t e r a l l y so as t o align them w i t h a corresponding s t r i p taken from the s t a t i c contac t . The op t i ca l elastohydrodynamic t e s t r i g used was conventional, but arranged, using a s e r i e s of belts and pul leys , t o operate i n t he r o l l i n g speed range 0.0001 t o 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001966_j.future.2004.11.004-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001966_j.future.2004.11.004-Figure1-1.png",
        "caption": "Fig. 1. Model of the manipulator.",
        "texts": [
            " (23) aking the product on the right-hand side of (22) into ccount, the matrix (23) can be expressed as the product f an m \u00d7 n matrix with an n \u00d7 m matrix: ( x) = \u2202Lr\u22121 f h( x) \u2202 x \u00b7 [ g1( x), . . . , gm( x)]. (24) Now, we will focus our attention to the computaion of the Jacobians \u2202Lk f h( x)/\u2202 x of Lie derivatives. ssume that we have already applied the procedure xplained in Section 4.1. The Taylor coefficients xi, yi, ( x0) = (r \u2212 1)! \u00b7 Yr\u22121 \u00b7 [ g1( x0), . . . , gm( x0)]. (28) . Manipulator example Consider the manipulator shown in Fig. 1. This maipulator is used for educational purposes. The angle f the beam is denoted by \u03d51. This angle can be inuenced by input torque u1. Beam and load are conected by a cable. The length l2 can be controlled by second input torque u2. The equations of motion an be found in [8,23]. The associated MIMO sysem (12) has the dimension n = 6 with the state vector = (l2, \u03d51, \u03d52, l\u03072, \u03d5\u03071, \u03d5\u03072)T and m = 2 inputs u1 and 2. For the two-dimensional output y, we use the Carteian coordinates of the load, i.e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001313_imtc.2002.1007183-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001313_imtc.2002.1007183-Figure1-1.png",
        "caption": "Fig. 1 Kinematics scheme of a three-wheeled AGV. The angular velocity o refers to the driving wheel. The attitude 8 is meant to be the angle between the absolute reference system xOy and the mobile reference system P r y . The position Pr is defined by the vector (x,y,6) Mich also takes the attitude of the mobile robot into account.",
        "texts": [],
        "surrounding_texts": [
            "ferent parameters, and thus maximising accuracy, is then s h w a Final@, an experimental a m p l e using a mock-up of an industrial robot is given.\nKevworcik - AGY, calibration, odometric navigation, inertial navigation.\nList of symbols (XJ) estimated position Wt) R driver wheel radius ICR Instantaneous Centre of Rotation cl0 steering angle when the ICR is at infinity a, steering angle with respect to CY,, n, number of counts fiom the driving encoder TOT number of counts kom the driving encoder in one tum 60) vehicle attitude with respect to the fixed reference 80) encoder estimated attitude to the fixed reference @e) gyro estimated attitude to the fixed reference biz distance between the rotation axis of the driver wheel and the axis of the back wheel h c h leads the manoeuvre during clochse steering bL distance between the rotation axis of the dnver wheel and the axis of the back wheel which leads the manoeuvre during counter-clockwise steering V(t) gyro voltage output Tc sampling period G() gyro characteristic DF() Data Fusion algorithm measured driver wheel angular velocity\n,E,& uncertainty in position and attitude estimation\nI. INTRODUCTION\nAutonomous Guided Vehicles are used in many environments such as factories, ports, hospitals, farms, etc., yet there are still significant difficulties in measuring vehicle attitude and position. The measurement systems presently used can be divided into direct, relative and absolute guidance. Though the systems belonging to the fust category, such as wiremagnet guidance, are the most reliable, they present the con-\nsiderable problems in path planning. If the path has to be changed, it takes several hours to install the cable inside the floor, and the guidance system must be stopped during installation. The relative or dead-reckoning methods have the considerable advantage of being totally self-contained inside the robot, of being relatively easy to use and of guaranteeing a high data rate. However, these systems integrate \u2018relative\u2019 increments based on direct integration, and consequently the number of errors increases in time. Absolute guidance systems make use of external references to achieve an absolute measurement with respect to the environment where the robot is moving. They are more complicated with respect to the relative ones, achieve a slower rate, and present the problem of visibility of the targets needed during the robot path. On the other hand, they measure the robot\u2019s position and attitude with respect to absolute references (targets), therefore their errors are always bounded.\nFrom the above considerations it is clear why many of the systems currently used combine data between a relative system and an absolute one [1,2,3,4]. The main challenge with this sort of data fusion is to reduce the number of absolute targets as much as possible by increasing the autonomy of the relative system. In this way it becomes possible to implement absolute architecture in factories where the targets cannot be installed nor seen by the robot throughout the path, or simply their configuration does not allow for the needed accuracy. A relative system, which depends on the instruments used and the recursive algorithm calibration, must be highly accurate in order to achieve this same goal. Since calibration can be affected by time, temperature, load being carried, etc., it would be very useful to be able to carry out a self-calibration procedure during its normal operations, i.e. without having to stop the factory\u2019s activity.\nThis paper presents a technique to self-calibrate an inertialodometric guidance system applied to a three-wheeled robot by using data measured by an absolute system. The inertialodometric guidance is made up of a gyroscope and a couple of encoders. It is important to note that the technique developed here is easily extendible to other robot configurations and that inertial-odometric navigation is among the systems which are most widely used and studied. The fusion technique between the different instruments is beyond the scope\n0-7803-7218-2/02/$10.00 02002 EEE",
            "of the present paper, but information regarding it can be found in [4,5] or other publications.\nOther techniques to calibrate an AGV navigation system have been presented in the past, but they either focus on different navigation systems [2,4], cannot be used on-line [3] or do not consider all the navigation parameters [6].\nThe calibration technique is discussed in 8 3 and the results that can be achieved experimentally by using the proposed technique are then shown in 0 4.\nII. AGV KINEMATICS EQUATIONS OF INERTIALODOMETNC NAVIGATION\nThis section shows the kinematics of a three-wheeled vehicle like the ones that are usually used in industrial environments. It is assumed that two encoders are used on the driver wheel: one to measure the steering angle, the second to measure the angular velocity.\nThe kinematics behaviour is always controlled by two wheels. Therefore, one wheel bears slippage if it is not perfectly aligned with one of the other two. The discrete form of the inertial-odometric navigation equations is the following:\n2n nTOT 2a x,+~ = x, + - .n, . R . cos(a, + a,). cos(&,) y,+, = y , + -. nk . R . cos(ak +a,). sin(&)\n2a 1 Sf+,, = 6: + -. n, . R . sin(a, + a,). - nTOT b\nnTOT\n8g1 = 6,\" + r, . G(V,G)\n' k + l =DF(6f+1,6EI)\n(1)\nEquation 1 is the characteristic which makes it possible to estimate the AGV's position and attitude. The role of the different parameters are described below and shown in figure 2.\n- a, o and are directly measured by the encoders mounted on the driver wheel and the gyroscope; therefore, they represent the inputs in the measurement system;\nIn theory, parameter b can change as a function of the back wheel which is leading the manoeuvre. This depends on the load supported by each wheel and thus on the load centre of mass or the trajectory curvature and change if the robot is steering clockwise or counter-clockwise. For this reason a distinction is made between bR and bL in the procedure described in \u00a7 3.",
            "III. CALIBRATION PROCEDURB\nIn this section, the procedure proposed to estimate the characteristic parameters is described. The following is not a recursive procedure; therefore, no initial guess is needed. Four steps are needed to fully characterise the measurement model. First, the steering angle when $e ICR (Instantaneous Centre of Rotation) is at infinity is estimated. Since it is the first parameter to be estimated, a null technique is implemented in order to both reduce the estimation uncertainty and ignore the other parameters. Then, the estimate found for this angle is used to determine the driver wheel radius by following a rectilinear path. The vehicle base between the wheels is estimated by blocking the steering motor at an angle equal to the maximum angle allowed. At the same time, the odometric measurement of the attitude derivative between the initial and the final point, whose attitude is known by the absolute measurement, is integrated The gyro calibration is achieved in the same phase as the vehicle base estimation by equating the attitude derivative computed by the gyroscope with the attitude derivative computed by the odometric system and scaling the whole characteristic by using absolute attitude measurements. It is therefore possible to note that, thanks to the null technique, only the gyroscope offset accuracy has an effect on the parameter accuracy (note that the gyroscope short-term bias stability is always very high). 3.2 Radius The driving wheel radius is estimated during the second phase. Maintaining the steering angle found for when ICR is at infinity, a rectilinear path is followed until enough distance (according to absolute system position accuracy) is achieved. The absolute navigation system estimates the position at the beginning (xr,yI) and at the end (x2,y2) of this phase (see figure 4). The radius is calculated from the following:\n(3)\n3.1 Steering angle when the ICR is at inJinity\nThe steering angle when the ICR is at infinity is evaluated by the robot itself by setting a regulation loop for the gyro output to zero (see figure 3). In this way position PI is reached when 6z1 = Sf is valid. The angular value read in position PI should correspond to the zero steering angle.\nThe following is the procedure for estimating the driving wheel radius. 1. The steering angle is maintained at the zero previously\nfound. 2. Position PI is estimated by using the absolute navigation\nsystem. 3. The robot follows a rectilinear path until position P2 is\nachieved.\nThe following is the procedure for estimating the zero steering angle. 1. The gyro offset is read before starting the motors. Refer-\nring to figure 4 it is position Po. 2. The driver motor speed @ is increased while regulating\nthe gyro output to zero (i.e. at the offset value) by using the steering motor.\n0 0 I\nX\nY 6\n4.\n5. Position P2 is estimated by using the absolute navigation system; The radius is estimated by equation 3.\n3.3 Distance between the wheel rotation axes\nA curvilinear path is followed to estimate the distance between the rear and driving wheel axes of rotation at infinity ( parameter b). In this way, the odometric navigation integrates the attitude change (equation 1, row 3) and equates it to the absolute change estimated by the absolute navigation system (& in position P2 and 83 in position Pj, see figure 4). From integration of equation 1, row 3, the parameter b is the only unknown parameter since & and R have already been estimated\n2 -. 2a n k . R.sin(a, +a,) Fig. 3 Regulation of the gyroscope output to zero in order to estimate the zero steering angle.\n- k=k,, nTOT L -\nThe uncertainty in estimating the steering angle when the 8 3 -4 ICR is at iniinity is the following:\n(4)"
        ]
    },
    {
        "image_filename": "designv11_28_0003998_iros.2009.5353991-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003998_iros.2009.5353991-Figure2-1.png",
        "caption": "Fig. 2. The manipulator carrying a payload.",
        "texts": [
            " Assume that the inertia ratios \u2016\u2206d\u2016 and \u2016\u2206m\u2016 satisfy conditions (11) and (24), respectively. Then, the forceresponse of the combined manipulator and payload under the impedance controller with the inner/outer loops (14)-(18) converges to the target impedance (13), while the control input remains bounded. This section describes experimental results obtained from implementation of the proposed impedance control scheme using a robotic manipulator at the robotics laboratory of the Canadian Space Agency (CSA), see Fig. 2. The inertial properties of the manipulator links have been identified [22] as listed in Table I. A dummy box which weights 16 kg, is mounted on the manipulator wrist. The payload inertia is calculated to be Ip = diag(0.33, 0.62 , 0.71) kgm2. The target inertia of the impedance controller is set to be three times higher than the actual mass and inertia of the payload. The force/moment interaction between the manipulator and the payload were measured by a six-axis JR3 force/moment sensor. The impedance controller scheme (14)-(18) was developed using Simulink and matrix manipulation was performed by using the DSP Blockset of Matlab/Simulink [23]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002564_11505532_12-Figure12.1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002564_11505532_12-Figure12.1-1.png",
        "caption": "Fig. 12.1. The setup",
        "texts": [
            " The system behaviour considered in this paper is closely related to the phenomenon observed by Huijgens and this relation is emphasized. This paper is an extended version of our previously published conference paper [11]. The paper is organized as follows. First we formulate the problem statement. Next we analyze the behaviour of the uncontrolled system. The controller is proposed and then investigated in Section 12.4. Section 12.5 deals with the local stability analysis of Huijgens phenomenon. Conclusions are formulated in the last section. Consider the system schematically depicted in Fig. 12.1. The beam of mass M can move in horizontal direction with viscous friction with damping coefficient d. One side of the beam is attached to the wall through a spring with elasticity k. The beam supports two identical pendula of length l and mass m. The torque applied to each pendulum is the control input. The system equations can be written using Euler-Lagrange equations: ml2\u03c6\u03081 + mlx\u0308 cos\u03c61 + mgl sin \u03c61 = u1 ml2\u03c6\u03082 + mlx\u0308 cos\u03c62 + mgl sin \u03c62 = u2 (12.1) (M + 2m)x\u0308 + ml 2 i=1 \u03c6\u0308i cos\u03c6i \u2212 \u03c6\u03072 i sin \u03c6i = \u2212dx\u0307\u2212 kx, where \u03c6i \u2208 S1 are the angles of the pendula, x \u2208 R 1 is the horizontal displacement of the beam, and u1, u2 are the control inputs",
            " In our clock model we combine together two simple ideas: first, the oscillations of the clock pendulum should be described by equations of the free pendulum with a given level of energy; second, the model should take into account an escapement mechanism to sustain this level. Then, the simplest model of the pendulum clock is given by the following equation: ml2\u03c6\u0308 + mgl sin\u03c6 = \u2212\u03b3\u03c6\u0307[H(\u03c6, \u03c6\u0307)\u2212H\u2217], \u03b3 > 0. This equation has an orbitally stable periodic solution which corresponds to the motion of the free pendulum with the energy equal to H\u2217. This limit cycle attracts almost all initial conditions as can be seen from the following relation for the Hamiltonian function H(\u03c6, \u03c6\u0307): H\u0307 = \u2212\u03b3\u03c6\u03072(H \u2212H\u2217). The model of the two clocks hanging from a beam as shown in figure 12.1 can thus be derived as the system (12.1) with ui = \u2212\u03b3\u03c6\u0307i[H(\u03c6i, \u03c6\u0307i)\u2212H\u2217], i = 1, 2. (12.7) From the equations of this model it follows that the system has at least two invariant sets \u21261 := {\u03c6\u03071 = \u2212\u03c6\u03072, \u03c61 = \u2212\u03c62, x = 0, x\u0307 = 0} and \u21262 which is a some subset of the set {\u03c6\u03071 = \u03c6\u03072, \u03c61 = \u03c62}. Computer simulation shows that both of them can be stable provided the constant H\u2217 is relatively small, while for large values of H\u2217 the system can demonstrate erratic behaviour. Thus at least three different synchronization regimes can be observed for such a system depending on the system parameters and/or initial conditions: anti-phase synchronization, in-phase synchronization and another oscillatory regime which is neither in-phase nor antiphase synchronization (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001813_146441904323074558-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001813_146441904323074558-Figure1-1.png",
        "caption": "Fig. 1 (a) Externally pressurized herringbone bearing with grooves and (b) notation for an eccentric bearing",
        "texts": [
            " With the need for still higher aerostatic bearing speeds, as well as improvement in stiffness, and in the light of past research on aerodynamic bearings, the present investigation is primarily concerned with determining the effect of herringbone grooves on the performance of externally pressurized bearings. This type of bearing is referred to as a grooved hybrid bearing (GHB) as it combines aerostatic and aerodynamic design principles. The analysis follows that of reference [5], with minor adaptations to suit practical machine tool spindle air bearing designs. For completeness, the main assumptions and equations describing static and dynamic equilibrium of the bearing are repeated here. The bearing con guration analysed is shown in Fig. 1a. It is supplied with externally pressurized air through one of the two rows of ori ces placed symmetrically with respect to a radial plane through the bearing centre. The ori ces are assumed to feed recesses of known depth and diameter positioned at entry to the bearing gap, and the axial positions of the ori ces and recesses are constrained to be inboard of the grooves. Grooves may be cut into the shaft of the journal and arranged so that shearing action produced by the shaft rotation pumps air towards the geometric centre of the bearing against the aerostatic pressure gradient",
            " The radial and tangential components of the bearing load are found by integrating the lm pressure over the bearing area Fr Ft \u00bc \u02c6 \u2026L 0 \u20262p 0 paP \u00a1 cos y\u00a4 sin y\u00a4 \u00bc R dy\u00a4 dz Substitution of equations (4) and (20) for P and performance of the y\u00a4 integration yields in dimensionless variables fr ft \u00bc \u02c6 \u00a1p Re Im \u00bc \u20261/2 0 G dz (26) The dimensionless forces in equation (26) are de ned by fr \u02c6 Fr epaLD ft \u02c6 Ft epaLD (27) The resulting bearing load \u00b7W and attitude angle j may now be calculated \u00b7W \u02c6 W epaLD \u02c6 f 2 r \u2021 f 2 t \u00a1 \u00a21/2 (28) j \u02c6 tan\u00a11 ft fr \u00b4 (29) Figure 1b illustrates the relationship between Fr and Ft. When the bearing is operating in a stable manner, the frequency number s is zero. To determine the threshold of instability, s is varied until ft \u02c6 0 [10], as cited by Fleming [5]. The neutral stability condition of the bearing is then found by equating the central force due to the whirling bearing mass to the radial force Meo2 pn \u02c6 Frn (30) A dimensionless bearing mass may be de ned by \u00b7M \u02c6 Mpa 2Lm2 C R 5\u0301 (31) In terms of previously calculated quantities \u00b7Mn \u02c6 144frn s2 (32) Pan [10], as cited by Fleming [5], shows that \u00b7Mn is an upper limit of \u00b7M for stability when qft /qs is negative at s \u02c6 sn; conversely, \u00b7Mn is a lower limit for stability when qft/qs is positive at s \u02c6 sn",
            " A number of parameters were xed to suit a particular size and design Proc. Instn Mech. Engrs Vol. 218 Part K: J. Multi-body Dynamics K01903 # IMechE 2004 at HOWARD UNIV UNDERGRAD LIBRARY on March 10, 2015pik.sagepub.comDownloaded from of spindle, and only the effect of the more important grooverelated parameters on bearing stiffness and whirl stability at high speed was determined. The bearing chosen for this study had a length\u2013diameter ratio L/D \u02c6 2, with a double row of ori ces positioned at a distance from the end of the bearing Lf /(L/2) \u02c6 0:75, as shown in Fig. 1a. In the following analysis, L/2 becomes L because, owing to symmetry, only half of the bearing was considered. The herringbone groove angle bd was xed at 30\u00af, and the groove width fraction a at 0.5. These values approximate the optima found by Vohr and Chow [2] for maximizing the radial load capacity of aerodynamic bearings. Their studies also showed that load capacity was insensitive to these parameters over a wide range of values. The ratio of the groove clearance to the land clearance was varied from H \u02c6 1 (plain aerostatic bearing) to H \u02c6 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001300_robot.2001.933158-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001300_robot.2001.933158-Figure4-1.png",
        "caption": "Fig. 4 Incompletely restrained wire-suspended mechanism",
        "texts": [
            " To control the suspended object by pulley position pi and wire length l i , we need a calculation method of trajectories for pulley positions and wire length considering dynamics of the suspended object, which is the inverse dynamics problem. In this section, we present the calculation method of inverse dynamics for general incompletely restrained wire-suspended mechanisms to get the trajectories of pulley positions and wire length. We here consider mechanisms which has n(< 6) wires, and n manipulators shown in Fig.4. Each manipulator has a pulley on its tip pi where wire is draw- ing. The other end of the wire is connected with an end-effector (object). The inverse dynamics problem is to calculate control variable (input torque of manipulator ~i and winding torque of wire Ni) for given trajectory of end-effector X . Thus, we here assume that the trajectory of endeffector is given by X, X , X. We firstly solve the wire force vector represented by A(X) [ \u201d 1 = y ( X , X , X ) (1)\u2019 f, where n must be n 2 3 to have solution of wire force vector[8]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003384_wcica.2008.4593288-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003384_wcica.2008.4593288-Figure9-1.png",
        "caption": "Fig. 9. Force/moment analysis of mating when the search strategy ends in a right-side \u2018deflected alignment\u2019 trap region",
        "texts": [
            " These possibilities are brought by special shapes of connectors and multiple pegs and holes. On the other hand, only a simple two-classes pattern recognition is required to classify different cases in a same class of trap regions. We realize our identification method from careful force analysis. It should be pointed out that this analysis method can be easily extended to other connectors with more pins although only a typical 3-pin connectors are investigated here. An example of the force analysis is shown by Fig. 9. After the search strategy ends in a right-side \u2018deflected alignment\u2019 trap region, a trial of mating will result in a contact state, whose full view is given by Fig. 9. Owing to the special structure of the female connector, there is a contact point between the convex part of the female connector and the rear part of the header. From the experimental observations, the zaxial contact force mainly comes from this contact point, which is denoted by zf . }{ rF denotes the frame of the wrist of the robot arm where the force sensor is mounted. In the analysis, we are concerned about the moment xm , which exhibits distinct characteristics in the two different subclasses of deflected alignments. The moment xm is consisted of two main components, which are caused by the y-axial force yf and the z-axial force zf respectively. The moment xm can be computed by zzyyx dfdfm . (1) Note that even there is no certain contact point shown in Fig. 9, the arm of force zd of the resultant z-axial force zf will be located in the negative direction of the ry axis. Similarly, in the case of left-side deflected alignment, the equation of moment xm can be given by zzyyx dfdfm . (2) Because all the forces and moments can be measured online, the relation among yf , zf and xm can be formulized by zzyyx fdfdm \u02c6 (3) where xm\u0302 denotes the estimated moment xm . Given a set of n training samples )}(),(),({ kmkfkfT xzy , coefficients yd and zd are typically determined by the least square estimation (LSE) method through minimizing the performance n k xx kmkmJ 1 2)(\u02c6)( "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002724_978-1-4684-1033-4_13-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002724_978-1-4684-1033-4_13-Figure3-1.png",
        "caption": "FIGURE 3. ISOGRID GEOMETRY",
        "texts": [
            " In fact, designs that permit some degree of elastic postbuckl ing deformation in these modes may be tolerated in service for some appl ications. General instability involves the complete structure, however. It almost always corresponds to total collapse and is usually accom panied or closely fol lowed by substantial permanent damage. General instability is the major influence on the cyl inder design, therefore. For this reason, the cylindrical shells and wide columns were designed to buckle in the general instability mode. Isogrid geometry and associated parameters are defined in Figure 3. General instability for CFCAI compressed cylindrical shells was analyzed using two levels of sophistication. The preliminary design analysis that was used for trade studies was based upon the following equation from Reference 2: t 2- C E - f3 o oR (I) NCR is the value of compressive stress resultant to cause buck 1 ing, E is the elastic modulus of the skin, t is the skin thickness and R is the shell radiu~ of the skin midsurface. C was taken to be 0.397 as recommended in Reference 1; this is the result of applying a Rknockdown\" factor of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003643_bio.1108-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003643_bio.1108-Figure1-1.png",
        "caption": "Figure 1. Schematic diagram of the flow-injection system: (a) rutin (or sample) solution; (b) carrier solution (water); (c) luminol and CoTSPc solution; (d) hydrogen peroxide solution. P, peristaltic pump; V, six-way injection valve; F, flow-cell; PMT, photomultiplier tube; HV, negative voltage; COM, computer.",
        "texts": [
            " CoTSPc was synthesized and purified as previously described (26): a a mixture of monopotassium salt of 4-sulfophthalic acid, ammonium chloride, urea, ammonium molybdate and metal salt was heated for several hours at 180\u00baC, then the crude product treated with HCl and NaOH successively and the residue washed with absolute ethanol. Finally it was refluxed for a few hours in absolute methanol to get a blue product. The identity of the product was confirmed by HPLC and by its UV\u2013vis and IR spectra. All CL measurements were made with the IFFM-D mode Flowinjection chemiluminescence analysis system (Xi\u2019an Remax Electronic Instrument Limited Co., Xi\u2019an, China). A schematic diagram of the flow system for the determination of rutin is shown in Fig. 1. It has two peristaltic pumps and an injection system synchronized by microprocessors. Polytetrafluoroethylene (PTFE) tube (0.8 mm i.d.) was used to connect all components in the flow system. The sample was injected into the carrier stream (water) via the six-way injection valve. A Y-shaped mixing element, positioned just before the flow cell inlet, was used for mixing the two streams. The flow cell was a coil of glass tubing (2 mm i.d., total length 100 mm), located in front of the detection window of the photomultiplier tube (PMT). For maximum light collection, the coil was backed with a mirror. The CL emission was converted by PMT to current signals and the output was fed to luminescence analyzer, recorded with a computer via an A/D convert card and special software. The CL spectrum was recorded with a Hitachi F-2500 mode spectrofluorimeter (Tokyo, Japan) combined with a flow-injection system. All CL measurements were made with the FIA manifold shown in Fig. 1, which comprised two peristaltic pumps, transporting a carrier stream of aqueous solution, into a channel where the rutin solution (or sample solution, 150 \u03bcL) was injected, and mixed with the stream of the luminol\u2013CoTSPc and hydrogen peroxide solutions. The flow-rate was controlled to 2.6 mL min\u22121. The concentration of rutin was quantified based on the maximal CL intensity changes (\u0394I), \u0394I = I0 \u2212 Is, where I0 is the background signal of the luminol\u2013CoTSPc\u2013hydrogen peroxide system without sample, and Is is the CL intensity with the rutin sample"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000297_s0736-5845(01)00037-0-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000297_s0736-5845(01)00037-0-Figure5-1.png",
        "caption": "Fig. 5. Initial location of brake plate.",
        "texts": [
            " From our experiments it was found that this additional calculation is not necessary to determine an arm configuration that enables the placing the wheel in an adequate position inside the field of view of the two cameras. Previous experimental work performed by Korde et al. [18] has been directed toward verifying the effectiveness of using algebraic constraints to relate estimates of the view parameters obtained before the camera-reorientation event with those following it. The evidence found in those experiments motivated the implementation of the strategy with the wheel-loading experiment, depicted schematically in Fig. 5. For this experiment, the receiving brake plate was placed at different, distant locationsFas much as 1:5 mFso that the cameras must be reoriented in order to include it within their fields of view. Every new location of the brake plate was defined in such a way that the visual features attached to it were visible to all the participating cameras following appropriate pan/tilt, but it was otherwise arbitrary. The experiment was aimed at achieving the same level of precision as obtained for the case where the cameras were fixed and the manipulator\u2019s workspace was limited [19]",
            " The first two steps constitute the execution of a preplanned sequence of joint rotations of the manipulator and the subsequent, initial estimation of the view parameters based on samples of the internal configuration of the manipulator and the corresponding image-plane location of the visual features attached to the manipulated object (wheel). The procedure for performing the estimation of view parameters is explained in [19]. The third step is performed after the brake plate is moved far from the physical region where the original sampling was performed in the preplanned trajectory, as shown in Fig. 5. The next step consists of finding the value of the view parameters denoted as %C; which are based on the features attached to the brake plate, or nonmanipulable body (a body not held by the robot that performs the task). This set of view parameters, independent from C; is used to specify camera-space maneuver objectives which determine an adequate approach trajectory of the manipulated object toward the nonmanipulable one, as explained by Skaar et al. [20] and Chen [19]. The fifth step consists of finding an approximate value of the view parameters Cn 1 ;y;Cn 4 by considering the known angular rotation of the cameras as described by Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001226_bit.260251217-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001226_bit.260251217-Figure4-1.png",
        "caption": "Fig. 4. Calibration curves for inorganic phosphorus obtained with a continuous flow system usiig immobilized enzyme columns. The symbols refer to (0) column type I (enzyme immobilized and preserved in phosphate buffer), (0 ) column type I1 (enzyme immobilized in phosphate buffer and preserved in phosphate buffer with lOpM FAD, 0.07mM TPP, and 3mM calcium chloride, and ( A ) column type I11 (enzyme immobilized and preserved both in phosphate buffer with 10pM FAD, 0.07mM TPP, and 3mM calcium chloride). The operational activity of immobilized enzyme was determined (A) on the same day after immobilization and (B) three weeks after immobilization, using the system shown in Figure 1.",
        "texts": [
            "0, containing the ingredients after the immobilization reaction. Column type I11 contained glass beads onto which pyruvate oxidase had been immobilized and preserved by the standard method as described in the Materials and Methods Section. The efficiencies of the different types of column were determined by the feeding of a phosphorus standard solution. When examined on the same day after the immobilization of the enzyme, column type 111 was found to keep the highest activity among the columns [Fig. 4(A)]. Examinations made three weeks later revealed that the activities of the column types I1 and I11 were almost the same as those of column types I1 and I11 examined on the same day after the immobilization of the enzyme, but the activity of column type I decreased considerably [Fig. 4(B)]. All of the data that follow were obtained with column type 111. The contents of inorganic phosphorus in the pyruvate oxidase preparations from Toyojozo Co. and BMY and a peroxidase preparation were determined by the Hitachi 726 method. While inorganic phosphorus was not detected in the peroxidase, large quantities of inorganic phosphorus were found in all the sources of pyruvate oxidase studied (Table I). The calculated amounts of inorganic phosphorus these enzyme preparations would bring into an assay tube are shown in the last column of Table I",
            " Under these circumstances, the determination of inorganic phosphorus using pyruvate oxidase in the form of solution was virtually impossible. By contrast, when the enzyme was immobilized and preserved even in a buffer that contained inorganic phosphorus, only the enzyme protein was immobilized onto alkylamine glass beads; inorganic phosphorus contained in a buffer was easily removed from immobilized enzyme by washing. We found that when pyruvate oxidase was immobilized and preserved according to the standard method, immobilized pyruvate oxidase showed the highest activity and the best stability (Fig. 4), and the use of immobilized pyruvate oxidase in column form made the determination of inorganic phosphorus in serum possible. Since phosphate buffer could not be used for the debmination of inorganic phosphorus, triethanolamine buffer was employed. In this case, the enzyme column was found to retain 80% of its original activity even after 900 runs for one month, as shown in Figure 7. An immobilized enzyme column allows the substrate to react with many enzyme molecules in a limited space, ensuring a rapid reaction to occur within seconds"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003133_j.autcon.2007.02.002-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003133_j.autcon.2007.02.002-Figure5-1.png",
        "caption": "Fig. 5. Notations when a vehicle turns.",
        "texts": [
            " The first one is the physical limitations of the vehicle. For example, the control references, \u03c9z\u2032r and \u03c9y\u2032r, in Eqs. (22) and (23) should to be chosen so as to not exceed their maximum rotational velocities, \u03c9z\u2032max and \u03c9y\u2032max, and to ensure the safety level shown in Fig. 2. The second is the turn point. When turning to move from a current path to a new path, the starting point of the turn needs to be varied in accordance with the type of path. For explanatory convenience, the notations when a vehicle turns are shown in Fig. 5. In the figure, r denotes the radius of a turning curvature, \u03b1 is half of the interior angle of two straight lines consisting of three way points, Op\u22121, Op, and Op+1. A turn point, \u03b5, is given as the distance between the start point for the turning and the next way point, Op. Note that in this paper a turn point does not mean position but a distance. Fig. 6 shows that a turn point varies with the type (or shape) of the path. Specifically, (a) needs a longer distance (or turn point) to track a given new path than (b) and (c), and (b) needs a longer distance than (c), where the forward and rotational velocities are all the same",
            " If a fixed turn point is used for the three cases, an undesired underdamped or overdamped response(s) may appear. This also results in collisions as shown in Fig. 2. The third is the damping degree of a control response. In what follows, we propose a tuning method of feedback control gains, which considers the above-mentioned physical limitations of the vehicle, the turn point, and the damping degree. Using the proposed method, the horizontal motion control is first described and then is generalized to vertical motion and 3-D motion controls. From Fig. 5, we can calculate the interior angle of two straight lines, \u03b1, by the law of cosines as: a \u00bc 1 2 cos\u22121 b2 \u00fe c2\u2212a2 2bc where, a= |Op+1\u2212Op\u22121|, b= |Op\u2212Op\u22121|, and c= |Op+1\u2212Op|. Also, we have the relationship between r and \u03b5 as: e \u00bc r tana : \u00f024\u00de Our purpose is to obtain an appropriate turn point \u03b5 according to the path type. However, this is not trivial work because r= vr /\u03c9z\u2032 changes during path-following control. While it is possible to control a vehicle to maintain constant rotational velocity for turning control, this method needs two times the number of switching controllers",
            " In this paper, we use the regulation nature of a linear feedback controller not only for straight line tracking but also for turning control. e three paths form an acute angle (a), a right angle (b), and an obtuse angle Here, we introduce themaximum yawing velocity,\u03c9z\u2032max. Note that this is a constant value. Then, Eq. (24) can be rewritten as: e \u00bc l rmin tana \u00f025\u00de where, \u03bc is a real number and rmin=vr /\u03c9z\u2032max. A vehicle can start path-following control if | pV\u2212Op| 2\u2264\u03b52 is satisfied, where, pV is the current position of the vehicle, andOp is the position of the next way point (see Fig. 5). Next, we present the tuning method. Let \u03b7ymax and \u03b7\u03c8max be the maximum values of \u03b7y and \u03b7\u03c8, respectively. The values of \u03b7y and \u03b7\u03c8 at a turn point can be regarded as \u03b7ymax and \u03b7\u03c8max because they grow smaller when path-following control starts. Thus, from Eqs. (19) and (20), the feasible region of feedback control gains is defined by: k\u03b7\u03c8 V pk\u03b7y \u00fe q \u00f026\u00de where, p=\u2212 |\u03b7ymax| / |\u03b7\u03c8max|, q= |\u03c9z\u2032max| / |\u03b7\u03c8max|, and \u2212q /p and q are the maximum values of k\u03b7y and k\u03b7\u03c8 , respectively. Note that |\u03b7ymax| depends on \u03b5 and \u03b1 since |\u03b7ymax|=\u03b5cos(\u03c0 / 2\u22122\u03b1), when 0b\u03b1b\u03c0, and therefore it is known that the feasible region also changes in accordance with a path type"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003373_acc.2008.4586837-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003373_acc.2008.4586837-Figure3-1.png",
        "caption": "Fig. 3: The rotor dynamic system.",
        "texts": [
            " Moreover, suppose, (A\u2212LC,G,H \u2212NC, 0) is strictly passive and G being full column rank. Then, (x, e) = (0, 0) is a globally asymptotically stable equilibrium point of the interconnected system (8), (13) for any \u03d5(\u00b7) satisfying Assumptions 1 and 2 (i.e. system (8), (13) is absolutely stable). In this section, we apply the controller design proposed in the previous section to tackle a motion control problem for mechanical systems with non-collocation of friction and actuation. As a typical example, we consider a rotor dynamic system as depicted schematically in Figure 3, which is a model of an experimental setup as presented in [20]. The system consists of an upper disc actuated by a drive part (power amplifier, motor) and a lower disc. The upper disc is connected to the lower disc by a steel string, which is a lowstiffness connection between the discs. In the experimental setup, a (lubricated) brake mechanism applies a friction torque Tfl to the lower disc. Moreover, the friction torque Tfu acting on the upper disc is due to friction in the bearings at the upper disc and electromagnetic effects in the drive part"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001248_robot.1997.606865-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001248_robot.1997.606865-Figure2-1.png",
        "caption": "Figure 2: HEC Kohonen nodes with path polygons fit to 80% confidence level contour.",
        "texts": [
            "0\u2019 rotation, halved when a local maximum is reached, until a local maximum is found at a step size of 0.125 feet and 0.125O.) Future work will compare computational complexities and general success of both models. We speculate, however, that the computational complexity is less for the HEC Kohonen because there are fewer elements to examine than ELDEN\u2019s cell-based model. A comparison is forthcoming. 3.5 Motion Planning and Self-Referencing Using the two conventions of polygon estimation shown in Figure 2, we start at a 90% confidence level contour and approximate a polygon centered at node k in Euclidean space, and oriented along the major and minor axes of the cluster\u2019s eigenvector matrix @k. These polygons can represent the C-space p a t h polygons. We then use t-vectors (another compact and multifunctional model) to construct the Essential Visibility Graph (EVG) for planning motion on a global level [B]. If a complete plan of motion is not realized, we gradually decrease the confidence level contours, thereby shrinking the path polygon sizes [l]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000683_890127-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000683_890127-Figure3-1.png",
        "caption": "Fig. 3 -",
        "texts": [
            " Data were transmitted to a mini-computer through an AID converter, and piston lateral movement and inclination of piston etc. were analyzed. Tf = N/Acc N ; measured noise Acc; measured cylinder acceleration - (1) liner transfer liner force system of transfer between slap noise vibration system of between and impact Measuring function vibration and liner piston 890127 3 Using Eq.(l) and Eq.(2), the transfer function (Th) between the piston slap noise and piston slap force (abbreviated to \"slap noise transfer function l' hereafter) was calculated: The device which excited the cylinder liner is shown is Fig. 3. This device was completely isolated from the engine. A piezoelectric force transducer was used for measuring the exciting force, as can be seen in Fig. 3. Using measured exciting force and cylinder liner vibration acceleration, the transfer function (TI) between cylinder liner vibration acceleration and exciting force was calculated as follows: TI = AccfF F ; Measured exciting force Th = Tf * Tl (2 ) (3) ANALYTICAL METHOD Fig. 4 - Measuring system of noise Analysis flow for the simulation of piston slap noise is shown in Fig. 5. First, many boundary conditions must be decided. Boundary conditions, such as the friction factor at the pin portion, the friction factor between the top ring and the piston, oil coefficient due to squeeze effect and due to wedge effect , were obtained from a data base built from measured data"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000552_ip-smt:20020588-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000552_ip-smt:20020588-Figure4-1.png",
        "caption": "Fig. 4 <I Two-turn coil in the laced clement space b Two-:um coil in the edge element space",
        "texts": [
            " In the facet element space the right-hand side vector 6 is defined as follows: 0 = Ne;, ( 2 ) where i, is the vector of facet values of J a n d the matrix N, transfomis the facet J values into currents associated with the edges. The vector i/ is expressed in terms of loop currents i,. i.e.: il = k,i, (3) IEE Prv.-Sci. Mmh. Tc~cI?mL V d 149, Nu. 5. S ~ ~ r o n l ~ o . ZW2 Here k, is the matrix which describes the winding distribution in the facet element space. The element in the ith column and 4th row of k, is equal to the total number of loop Li conductors that penetrate through the facet Fn. Fig. 4u shows the facct Fcj in the region of a twotun1 coil. In the calculation of k/iq, we suggest that the windings be described by a set of closed oriented plane curves. Thus the coil in Fig. 4. is replaced by a piirallelogram loop and by four-triangular loops. First we determine the points of intersection of the facet F, with curves L, (j= 1,2. ..., mi). The set of these points is divided into subsets: {s;,,+}, {s;.,-}. If the scalar product ( r , , j ( t + A t ) - ~ ; , , ( t - At))F, , at the point of intersection is positive then this point belongs to {s;,,;+}. Otherwise the point belongs to {si.,-}. The entry kj,<] may be expressed as follows: = N.,+ - Nl.y- (4) where N;.,,, N;,<,- are the number of elements of subsets {si,+) and {",
            " The FE equations have the following matrix form: klAk,R = -k lA i , ( 5 ) Here A is the matrix of permeances associated with edges, k,, is the FE representation of operator grad, R is the vector of nodal values of 0 and i,,, is the vector of edge value of T (curlT=J). The vector i,,, may be expressed as: Here the matrix k,,, describes the winding distribution in the edge element space. The element k,,,, in the uth row and ith i,, = k,& ( 6 ) 187 column of k,,, can be calculated by means of the following procedure. First we determine the points of intcrsection of the surfaces SjJ ( j= l,2, ..., m;) with the uth edge Que, (Fig. 4h). The set of these points is divided into subsets leiu+}- {e,.t,-}. If the scalar product of Q.fu and S., at the point of intersection is positive then this point belongs to {e;..+). Otherwise the point belongs to { e , , - ] . The value of k,,z;.z, is equal to the difference between the number of elements in the subsets. From (5 ) the vector of fluxes associated with edges may be expressed as @ = A(k , ,R + im). The matrix k: transforms this vector into the vector of flux linkages, Le.: d + Y = k:@ (7 ) Q = k:Nzk,i, (8) 'P = kiN,k,cp (9) The matrix k,,, can also be used to define the vector fl in (1)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003382_rspa.2008.0142-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003382_rspa.2008.0142-Figure2-1.png",
        "caption": "Figure 2. An inclined rectangular duct with rigid base and sides and a thin elastic plate as the top surface. Fluid supplied far upslope fills the channel and flows downslope under the influence of gravity alone.",
        "texts": [
            " We analyse the linear stability numerically in \u00a74. A brief comparison of this theory with a qualitative experiment is presented in \u00a75. In \u00a76, we consider the particular geological application of ropy pahoehoe lava. Finally, in \u00a77, we summarize our most significant findings. Appendix A furnishes the derivation of the Fo\u0308ppl\u2013von Ka\u0301rma\u0301n equations in the present context and outlines their limits of validity. Appendix B briefly discusses the supplementary problem in which the elastic skin is replaced by a very viscous fluid one. As shown in figure 2, we consider a duct of infinite length and rectangular cross section (having width 2y0 and depth 2ay0, where a is the aspect ratio) inclined at angle q to the horizontal. The duct is described by a Cartesian coordinate system with x\u0302 directed downslope, y\u0302 across the slope and z\u0302 perpendicular to the slope; the origin is located on the centre line. The bottom, z\u0302ZKay0, and sides, y\u0302ZGy0, are rigid; the top, z\u0302Zay0C z\u0302\u00f0x\u0302; y\u0302; t\u0302\u00de, is an isotropic Hookean elastic plate of thickness 2d/2y0, Young\u2019s modulus E and Poisson ratio n, where z\u0302 is the out-of-plane displacement of the initially flat plate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000030_978-1-4757-3403-4_13-Figure13.1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000030_978-1-4757-3403-4_13-Figure13.1-1.png",
        "caption": "Figure 13.1 Schematic representation of the two-link planar arm with the planned Cartesian path.",
        "texts": [
            " This is basically due to the following reasons: (i) the efficiency of the gradient method ofTRJ algorithm to reach a local solution compared to the relatively heaviness of the genetic algorithm to reach an estimated global solution; (ii) the fast computation of the penalty terms using the quadrature points in the TRJ algorithm compared to the slower branch-and-bound interval procedure of the proposed algorithm. The example proposed concerns a two-link (m = 2) mechanical arm with revolute joints. The problem is the minimum-time planning under torque and velocities constraints of a trajectory whose Cartesian path is, for example, schematically shown in Fig. 13.1. T,~ The distal end of the second link is required to exactly cross some given via points (8 = 10, so that n = 11) on the Cartesian path. These via points are expressed as Cartesian coordinates of the arm base frame (first two columns in Table 13.1). By solving the inverse kinematics problem the Cartesian via points are con verted into joint via points, and reported in the last two columns of Table13.1. Note that the second and the penultimate knot points have not been imposed, being associated to the two free joint displacements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003240_robot.2007.363872-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003240_robot.2007.363872-Figure5-1.png",
        "caption": "Fig. 5. (a) In 2D, the same virtual link represents two configurations: a concave triangle and a convex triangle. (b) In 3D, the same virtual link represents many configurations with different dihedral angles \u03c1 between the sub-chain\u2019s plane and its parent\u2019s plane.",
        "texts": [
            "right be c\u2019s children, and c.len be the length of c\u2019s virtual link. Let p be c\u2019s parent and s be c\u2019s sibling. 1: Update c.arr from p.arr and s.arr. 2: Randomly sample c.len from c.arr. 3: Set c.arr to [c.len, c.len]. 4: if c has children then 5: Sample(c.left). 6: Sample(c.right). 7: end if 2) Sample dihedral or concave/convex orientation: Each sub-chain and virtual link forms a triangle. In 2D, two different configurations have the same virtual link length: a concave orientation and a convex orientation (see Figure 5(a)). In 3D, a virtual link length can represent many configurations depending on the dihedral angle between its triangle and its parent\u2019s triangle (see Figure 5(b)). Thus, we also sample the orientation of the virtual link. 3) Calculate joint angles: Consider the joint angle \u03b8 between links a and b. Links a and b are connected to a virtual link c to form a triangle. Let la, lb, and lc be the lengths of links a, b, and c, respectively. The joint angle can be computed using the law of cosines: \u03b8 = acos( l2a + l2b \u2212 l2c) 2lalb ). (2) Given two configurations, qs and qg , a local planner attempts to find a sequence {qs, q1, q2, . . . , qg} of valid configurations to transform qs into qg at some user-defined resolution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002754_3-540-26415-9_114-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002754_3-540-26415-9_114-Figure5-1.png",
        "caption": "Fig. 5. Simplified model",
        "texts": [
            " In order to compensate the fall during the transfer we design a criteria of stability, next section will present this criteria. Compensation of the fall during the transfer relay on a stability criteria, the AD have to produce the trajectory and force compensation helpful for the user in case of instability. In the following sub section we will introduce a stability criteria of the patient. This stability criteria is based on the establishment of the Zero Moment Point (ZMP) [13] on a simplified model of the patient. The patient is a 7 bar mechanism studied in the sagittal plane (xo, yo) (see Fig. 5), mi is the mass of the ith segment, M is the total mass of the patient, Xzmp is the position of the ZMP along the xo axis in the frame Ro. Using the Newton-Euler formulation at the ZMP we get the equation of the position of the ZMP during the transfer: Xzmp = HZ + M(Y\u0308GXG \u2212 X\u0308GYG) + i=n\u2211 i=1 migXGi M(Y\u0308G + g) (1) Xzmp = Y\u0308GXG \u2212 X\u0308GYG + gXG Y\u0308G + g (2) The stability criteria of the patient is done by using the ZMP equation, the patient posture is defined stable if Xzmp is included in the foot\u2019s area. In case of instability the AD had to produce the assisting force to remain the ZMP into the foot\u2019s area. In the next sub section will present the assisting force model. The goal of the assisting force is to ensure the postural stability of the patient. The force interaction F between the patient and the AD is defined into the hand position of the patient at the point H (see Fig. 5). By included F into the Newton Euler formulation (eq. 1) we get an other expression of the Xzmp : Xzmp = M(Y\u0308G + g)XG \u2212 MX\u0308GYG \u2212 FXYH + FY XH M(g + Y\u0308G) \u2212 FY (3) With the stability criteria : a \u2264 Xzmp \u2264 b (4) According to eqs. 3 and 4 if the patient is in an instable posture the AD had to provide the assisting force to remains the patient into a safe posture. To solve this problem we express the force interaction F under a non linear problem under constrained, by finding the minimal effort F Elderly People Sit to Stand Transfer Experimental Analysis 959 to the following formulation: Minimize F = \u221a FX 2 + FY 2 subject to: [ YH \u2212YH \u2212(XH + a) (b + XH) ][ FX FY ] \u2264 [ M((g + Y\u0308G)(XG \u2212 a) \u2212 X\u0308GYG) M((g + Y\u0308G)(b \u2212 XG) + X\u0308GYG) ] (5) With this model of assisting force we need kinetics information of the patient"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002754_3-540-26415-9_114-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002754_3-540-26415-9_114-Figure1-1.png",
        "caption": "Fig. 1. Description of the assistive device",
        "texts": [
            " This device provide support during the walk and also during the sit to stand transfer, it is primarily intended for elderly patients who have falling background [12]. We focus on postural stability especially during the verticalisation, postural observation and estimation is implemented on the assistive device in order to monitor the patient and modify its posture. This paper presents experimental results done with elderly and a postural stabilization criteria during the transfer. The assistive device (AD) is a two degree of freedom mechanism mounted on an active mobile platform (see Fig. 1). During the transfer assistance the handles of the AD pull slowly the patient to the up position. This is obtained by using two parallel and independent mechanisms combined in a serial way. The trajectory of the handles relay on a trajectory generator, it allow the patient to get off its retropulsion configuration to an antepulsion configuration. Force sensors are added on each handle to measure force interaction between the user and the device. Details on the design the AD and its trajectory generator can be found in [12]",
            " Obviously, patient who could not stand up with an external help could not use the device to stand up. Patient who could stand up without a help could stand up thanks to the AD. Due to their physical condition and age the patient could not produce many trial, nevertheless concerning the force measurement we can observe a repeatability of the measurement on each user. The global shape is the same for each trials of the same patient but it is not the same between the patients. Concerning the sit to stand transfer the effort along the y axis (Fig. 1) do not evolve in the same way, see Fig. 2. For the patient 1 its seems that the patient lift up the right handle (Fy > 0) whereas for the patient 2 (if we do not consider the first trial Fy \u2248 0) the force interaction Fy is still evolve in the negative value meaning that the patient is still pushing during the transfer with a maximum force Fy = \u2212140 N around 19 % of his weight. The opposite direction of the effort Fy between the left and the right handle indicate that the patient 1 is tipping over on his left side"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000750_1.1570951-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000750_1.1570951-Figure8-1.png",
        "caption": "FIG. 8. Closed-loop control of nozzle-to-workpiece distance. ~a! Experimental setup; ~b! experimental results.",
        "texts": [
            "7 mm of the workpiece surface so that the penetration depth would be kept constant. Besides the slight changes in the focal position, the experimental variation plotted in Fig. 6 is mainly due to the influence of the nozzle-to-workpiece distance on the PCS signal. The data show that the theoretical result matches well with the experimental data. The data in Fig. 6 shows that the PCS signal decreases with increasing nozzle-to-workpiece distance, so the plasma charge current can be used to realize closed-loop control of the nozzle-to-workpiece distance. Figure 8 shows experimental results for closed-loop control of the nozzle-toworkpiece distance for bead-on-plate welding of a bent plate. As the welding began, the focal point was located on the workpiece surface, meaning that the focal position was zero and the nozzle-to-workpiece distance was 10 mm. The welding conditions were laser power of 1.5 kW and welding speed of 1.2 m/min. Two weld beads were obtained with and without the closed-loop control, as shown in Fig. 8~b!. For weld A, the nozzle-to-workpiece distance varied during welding because the nozzle height was constant but the workpiece was bent before welding, which changed the focal position so that the welding process was unstable. Weld A shows the variation of the welding mode from deep penetration welding ~DPW! to heat conduction welding ~HCW! due to the variation of the focal position.20,21 However, with the PCS signal used to keep the nozzle-to-workpiece distance constant, the weld bead formation for the same welding conditions was stable so as to form the very uniform weld B shown in Fig. 8~b!. Figure 9 shows the experiment setup to evaluate plasma control with an external magnetic field.22 The plasma plume was driven to the left by the ampere force induced by the plasma charge current and the external magnetic field, which increased the absorption efficiency of laser energy in the keyhole. Figure 10 shows the experimental method used to clarify the effect of the external magnetic field on the plasma control. The exciting current for the magnetic field was 3 A and the external voltage added between the nozzle and the workpiece was 25 V"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002197_1.1867270-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002197_1.1867270-Figure1-1.png",
        "caption": "FIGURE 1. (a) Electromagnetic Momentum Generator Scheme. (b) Electromagnetic Inertia Manipulation Thruster.",
        "texts": [
            " ELECTROMAGNETIC INERTIA MANIPULATION CONCEPTS A non-exhaustive review of several electromagnetic devices was pursued that can be viewed as producing inertia modifications of the related material system. Within the scope of this work, the list is restricted to those concepts having been proposed and described in peer-reviewed literature, being functionally able to generate \u201cforceproducing\u201d effects, as required for propulsion purposes. They are: Brito\u2019s EMIM Thruster, Corum-Slepian\u2019s EM Drive, and Woodward\u2019s Mach-Slepian Device. By Minkowski\u2019s formalism (Brevik, 1979), a non-vanishing momentum of electromagnetic origin is shown to arise for the particular device depicted in Fig. 1. It is always possible to represent the Electromagnetic Momentum Generator (EMMG) as a single particle located at the \u201cmatter\u201d system center of mass (or any \u201cstructural\u201d point). When the ON condition is set, the whole system must include the EM fields being created under such a condition, so that a mass tensor is readily found as related to the whole system (Brito, 1998), given by ( ) ( )M I p v= + + \u2227m m / c0 EM * EM 0 2 . Since, by assuming a closed system, the 4-momentum must be conserved, the thrust in 3-space becomes ",
            " If the capacitor has a simple parallel plate configuration, the induced B flux is perpendicular to the E field between the plates and the fields have the same frequency and a convenient relative phase, then the magnetic part of the Lorentz force, due to the polarisation current induced by the variation of the E field, will generate a stationary force like that described by Eq. (7). According to Woodward, such a stationary force, however, can only arise in this sort of systems without violating 4-momentum conservation if Mach effect mass fluctuations actually take place, physically coupling the system with the chiefly distant matter in the universe. To test the concept, Woodward assembled the device shown in Fig. 3, basically a Corum-Slepian device he renamed Mach-Slepian. Although geometrically different from the Electromagnetic Momentum Generator (Fig. 1), the Mach-Slepian device shares a common concept for the creation of \u201ccrossed\u201d electric and magnetic fields domains. Experimental results have been reported in peer-reviewed literature for Brito\u2019s and Woodward\u2019s devices. The authors are not aware of publications regarding Corum\u2019s experimental data. The experimental setup basically consists of mounting the device as a seismic mass atop a thin vertical cantilever beam (a resonant blade), sitting on a vibration-free platform. Piezoceramic strain transducers are used to detect the seismic mass displacements through output voltages proportional to the strain level in a broad dynamic range, achieving very high sensitivities"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003508_978-1-84628-469-4_13-Figure13.6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003508_978-1-84628-469-4_13-Figure13.6-1.png",
        "caption": "Figure 13.6. A nonlinear switching curve and its corresponding control surface",
        "texts": [
            " A nonlinear boundary does not add much control performance since it is the width of the boundary layer that influences the controller performance, not the form of the boundary layer [9]. From authors\u2019 point of view, FSMC has little practical value, if not being totally useless. Sliding mode control is a kind of time sub-optimal control. The well-known solution for time optimal set point control of a system with bounded control action is a bang-bang controller across a nonlinear switching curve. For two-dimensional systems, the nonlinear switching curve often has the form depicted in Figure 13.7 instead of a linear switching line. Figure 13.6 also shows there can be a switching band around the switching line to alleviate chattering. Figure 13.4 also illustrates how the control surface may look with a nonlinear switch function. In a Takagi-Sugeno (TS) type FLC, the rule output function typically is a linear function of controller inputs. The mathematical expression of this function is similar to a switching function. This similarity indicates that the information from a sliding mode controller can be used to design a fuzzy logic controller, resulting in a Sliding Mode Fuzzy Controller (SMFC)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002038_iros.2004.1389945-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002038_iros.2004.1389945-Figure5-1.png",
        "caption": "Figure 5. Virtual mss-spring-damper model.",
        "texts": [
            "*+\"') 0 =-(\"a - \",) Here, va ,vL is the right and lefl velocity p is represented by Eq.(3) using the Jacobian malnx. The L is distance between two wheels. The velocity Figurei. Cantigurauonof mobile robot Impedance control is the algorithm that adjusts the position to the force feed back and maintains constant force, modeling interconnections between uncertain environments and the robot as impedance [9]. The Virtual Impedance method[lO,ll] is that the general impedance algorithm is applied lo the travel of the mobile robot and collision avoidance field. As seen in Fig.5, the virtual impedance method is a form of generating virtual force according to the information Gom distance and velocity, the modeling robot and a reference point, and relation between the robot and the obstacles as a spring and a damper. This method is generally used as LAP(Loca1 Avoidance Planner). That is to say, when GPP(Globa1 Path Planner) generates trajectory X(t), X(r ) consists of a reference point, and we can calculate acceleration x of the robot allowing deviation from the given trajectory to generate virtual force according to the distance between the robot and an object at the given reference point [ 121"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001951_physreva.15.408-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001951_physreva.15.408-Figure2-1.png",
        "caption": "FIG. 2. Coordinate system for the smectic C phase: xy is the smectic plane. The director in the undistorted sample, Uo, lies in the xz plane at an angle + (the tilt angle) to z. Pg) is the azimuthal angle of the (reoriented) director U, and n, P are the polar and azimuthal angles of the magnetic field H. The shaded area describes the base of the cone of the allowed orientations of the director.",
        "texts": [],
        "surrounding_texts": [
            "PHYSICAL REVIEW A VO LUME 15, NUMBER 1 JAN UAR Y 1977\nMagnetic instabilities of smectic-C liquid crysta&s\nE. Meirovitch and Z. Luz Department of Isotope Research, The Weizmann Institute of Science, Rehovot, Israel\nS. Alexander The Racah Institute of Physics, The Hebrew University, Jerusalem, Israel\n{Received 3 June 1976)\nWe have investigated elastic deformations by external magnetic fields in flat samples of smectic -C with fixed boundary conditions. In the calculations the internal parameters {tilt angle, density, interlayer distance) are assumed to be fixed, distortions of the smectic layers are neglected, and only reorientations of the director about the normal to the smectic layers are allowed. The problem is solved exactly assuming a one-dimensional variation of the order parameter. Stability conditions and explicit expressions for the orientation of the director as a function of position are derived for general orientations of the magnetic field. Solutions of the variational problem can be classified according to the maximum deviation angle, 4, of the director. In general there are several separated allowed regions of 4. When Freedericksz transitions occur, they are usually\ndiscontinuous first-order transitions. The properties of the solutions are discussed and some special examples are considered in detail. Transitions are investigated both as a function of the magnitude and of the orientation of the magnetic field. Expressions for the free energy are also derived.\nI. INTRODUCTION\nThe elastic theory of smectic C liquid-crystal phases\"' has been discussed by the Orsay group. ' It was shown there that nine elastic constants are needed to describe the system when one assumes that the interlayer spacing and the tilt angle are constant. Rapini4 has used this theory to discuss the behavior of single-crystal layers of smectic C in magnetic fields. He has shown that the analog of a Freedericksz transition should be observable in this phase. Essentially these transitions involve the rotation of the director on the cone, determined by the normal to the smectic layers and the tilt angle.\nThe calculation of Rapini is patterned on the nematic case. It is, in fact, equivalent to the determination of a criterion for the stability of the initial state when a magnetic field is applied along suitable symmetry directions. We will show that this procedure is, in general, inadequate. A smectic C can have several locally stable configurations in a magnetic field. In such a situation the configuration resulting continuously from the initial state when the field is applied may remain locally stable (against small deformations} in spite of the fact that configurations of lower energy are available to the system. This gives rise to the usual difficulties in interpreting experimental results when first-order transitions are involved.\nInstead of checking for the stability of an assumed state, we look explicitly for the solutions of the Euler-Lagrange equations resulting from the requirement that the sum of the magnetic and elastic energies should be extremal. The mathe-\nmatical procedure in treating nematic slabs with oblique boundary conditions is analogous to that used by Onnagawa and Miyashita. '\nWe follow Rapini in restricting ourselves to flat smectic layers and boundary conditions determining the orientation of the director at the two boundaries of a parallel slab. Explicitly, we only discuss Rapini's type-N geometry (see Fig. 1} with layers parallel to the surface of the slab, but the general case only differs in that it involves different combinations of the elastic constants.\nFor simplicity, we assume that the magneticsusceptibility tensor is axially symmetric with its unique axis defining the local orientation of the director V. Experimentally this seems to be very nearly the case, ' and the generalization of our results is straightforward. We discuss the solution\n15 408",
            "15 MAGNETIC INSTABILITIES OF SMKCTIC-C LIQUID CRYSTALS 409\nas a function of the orientation of the magnetic field in the coordinate frame determined by the boundary conditions. For most orientations metastable states exist and first-order transitions have to be considered.\nIt should be noted that the extension of these results to a situation with curved layers is not immediate. It can be seen from the structure of the elastic energy' that the orientation of the director is coupled to the local curvature. When the layers are not flat, this gives rise to volume-anisotropy terms which complicate the calculation, and are neglected in our calculation.\n\u2014,'X,H' sin'c. sin P\nx [cos(Q \u2014P }+cote. cot(]', (2.2}\nwhere X, is the anisotropic part of the magnetic susceptibility (assumed to be positive);\nXg X[) XL (2.3)\nThe total free energy per unit area of the slab (in units of ,y jP\u2014sin'c.sin'P) can then be expressed as\nII. THEORY\nThe geometry, coordinate system, and notation used in the calculations are described in Figs. 1 and 2. We consider a parallel slab of thickness 2L with boundaries and smectic layers parallel to the xy plane. The director U is tilted by the tilt angle P, and has an azimuthal angle P(U(P, Q)). As boundary conditions we assume Q(0) = $(2L) = 0, i.e., at the boundaries U, is in the xy plane. The magnetic field has polar angles n, P [H=H(o. ,P }]. The only variable is then the azimuthal angle P, which is a function of the position in the slab [Q = P(z)]. The elastic free-energy density becomes'\n(2.1)\nand the magnetic free-energy density is\n2 dzE 2 dg\n\u2014[cos(Q \u2014P )+ cotn cot&]'],\n(2.4)\nwhere E is the sum of the elastic and magnetic free-energy densities, and\n$'=B,/(sin'o, sin'gy, H') . (2.5)\nd 2 = [cos(O \u2014P)+ cote. cot(]' dg\nThe Euler-I. agrange equation obtained by requiring that Eq. (2.4) be extremal, is\n, \u2014[cos(Q \u2014P ) + cote cot/] sin(Q \u2014P ) = 0,,d'P dg2\n(2.6)\nwhich has a first integral;\n\u2014[cos(Q \u2014P )+ cote cot(]' =\u2014G(4, Q) . (2.7)\nThe constant of integration was obtained by observing that dQ/dz = 0 when Q takes on its maximum value 4. From symmetry, this maximum is at z =L, i.e. , halfway between the plates.\nFrom Eq. (2.V) we now obtain an expression for the second integral of the Euler equation;\n(2 8)\nwhere (from Eq. 2.5)\nh = (HLsinn sing)(y, /B, )' ' (2.9)\nis determined by the parameters of the problem. For given h the energy is thus extremal when the maximum tilt angle C is such that\ndQk(4 ) [G( )gg (2.10)\nOnce we know the solution of Eq. (2.10) we can de-",
            "E. MEIROVITCH, Z. LUZ, AND S. ALEXANDER\ntermine z as a function of P from\nz(Q) 1 dP L h 0 [G(4, p)]'~' (2.11)\nFor given Q we can substitute Eq. (2.8) into Eq. (2.4) to obtain an explicit expression for the average free energy per unit volume E of the slab,\nSince h is obviously real, one notes that Q is restricted to those ranges for which\nI L dzl(z) dz =\n0\ndzdF (Q) d@\ndz dP \u2014.\nG(e, y)-0; 0-y/C-l. (2.12) (2.13)\nThese restrictions and their dependence on P, o. and P are discussed in Sec. III.\nIt is convenient to compute the energy as a function of C in the form\n]\u201e,(G(4, Q) \u2014[cos(P \u2014P )+ cotn cot)]'] t\n(2.14)\nThis coincides with the true free energy when the extremum condition [Eq. (2.10)] holds. In practice, it is convenient to solve Eq. (2.10) graphi cally; we compute the integral h(C) as a function of 4 numerically. Solutions are then given by the points where h(4) has the specific value h. The free energy for these solutions is then proportional to E, computed from Eq. (2.14}. When several solutions exist for given h (i.e. , 8 and L} it is possible to compare their energies. Some examples are discussed in Sec. IV.\nOur derivation yields only a small number of stationary configurations for a given field, namely, those given by the implicit expression (2.11), where 4 satisfies Eq. (2.10). The lowest-energy configuration is always of this type. In general, however, these are not all the solutions of the Euler-Lagrange equation [Eq. (2.6)]; stationary configurations of higher energy do exist. There are two points where our derivation can be generalized.\n(i) In choosing the integration constant in the first integral [Eq. (2.7)] we assumed that there is a maximum angle 4 for which (dP/dz)o = 0. This excludes twisted configurations (analogous to cholesterics) which are of course possible but always have a higher elastic energy without any decrease in magnetic energy.\n(ii) A similar generalization is possible in passing to the second integral [Eq. (2.8)]. In the form given we have assumed that dP/dz has a unique sign, so that P(z) is a monotonic function of z from Q = 0 to 4 [condition (2.12)]. Additional, nonmonotonic, solutions can be obtained if one allows more than one extremum (dQ/dz = [G(4, p)]'~'= 0] where one can pass between two monotonic branches (dQ/dz = [G(4, Q}]'~') of the solution. Such solutions necessarily have nodes (@= 0,z w 0, 2L). Thus, one has solutions of the type we have considered between any two nodes. The requirement that dQ/ dz should be continuous at the nodes then implies:\n= [cos(4, -P )+ coto. cot&] = const. ,2 noae\n(2.15)\nwhere the i, are the extremal values of Q in the different intervals. This, together with the integral condition (2.8) for the interval between any two adjacent nodes, determines the solutions.\nIII. NATURE OF THE SOLUTIONS\nBefore presenting some results of numerical calculations for specific values of P and\na = \u2014cotn cot&, (3.1)\nP(P) = [cos(P -P ) \u2014a]', where\nG(4 (jb)=P(4) \u2014P(Q) .\n(3.2)\n(3.3)\nThe condition (2.12), 0~ P/4 1, then implies\nP(@)\u2014P(0) P(4) has extrema when\ndP(4) d = -2[cos(P \u2014P) -a] sin(P \u2014P) = 0 . (3.5)\nFor ~a ~&1 there are two minima [cos(Q -P) -a= 0] and two maxima [sin(P -P)=0]. Examples of the function P(P) for two special values of ~a~&1, are shown in Fig. 3. When\n~ a ~ & 1, there is only one maximum and one minimum.\nThe allowed ranges of 4 follow immediately from Eq. (3.4), and the requirement that Q vary contin-\nI\nwe want to discuss the general features of the function h(4) defined in Eq. (2.10). As noted in (2.12), we require G(C, Q)& 0 for Q varying continuously from zero to C, thus limiting the allowed ranges of C.\nTo determine these ranges and the limiting values of k(C) at the ends of the allowed regions, consider the function"
        ]
    },
    {
        "image_filename": "designv11_28_0000844_kem.245-246.351-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000844_kem.245-246.351-Figure6-1.png",
        "caption": "Fig. 6 a) Break disk; b) Example of thermal fatigue cracks developed on a break disk.",
        "texts": [
            " Another important feature is that thermal fatigue cracks may be long but with a small depth. Mechanical fatigue cracks that develop at stress concentrations in crankshafts are approximately semi-circular, as can be seen in [5]. Thus, if those cracks in journals of Fig. 3 were mechanical fatigue cracks its depth would have caused the crankshafts to fracture. As they are thermal fatigue cracks (superficial cracks) they can be long and shallow and therefore the crankshaft does not fractured. An example of this phenomenon of thermal fatigue cracks is that which occurs on disk brakes. Fig. 6 shows a damaged disk brake. Fatigue cracks are long, with a small depth, and the position is parallel to the heat front (caused by the brake pads). Escobar [9], in his MSc Thesis found some cracks at the lobes of two camshafts. After an extensive examination he concluded that those cracks were thermal fatigue cracks caused by an improper grinding process. The cracks were small cracks, with low depth, and all in the direction parallel to the grinding wheel, identical in form to those on the crankshaft journals"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002507_robio.2006.340096-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002507_robio.2006.340096-Figure4-1.png",
        "caption": "Fig. 4. Control Torques for (a) side-view and (b) top-view.",
        "texts": [
            " This is achieved through the so-called proximal point function proxC(x), which equals x if x E C and equals the closest point in C to x if x f C. The set C must be convex. Using the proximal point function we transform the force laws into implicit equalities (see [8]) --y E Nc, (A,) -\\ > A, = proxc, (AV, -rr,,), (46) where r, > O forI = N, T. C. Joint Actuators Each cardan joint has 2 DOF that are controlled by two joint actuators. The actuators are modeled as controlled torques applied around the axes of rotation for the joint. Fig. 4 illustrates how the direction of positive rotation is defined. Define a positive control torque Tv, to give a positive rotational velocity around eBi+1 and a positive control torque Th, to give a positive rotational velocity around eBi, both with respect to 3 y link i. The total torque 1rC, RER3 applied to link i is 1rci= [ Thi \u00b0] -RBi 1 [0 Th(i_l) 0]T +-RBi+ [Tvi \u00b0 \u00b0] [Tv(i l) O 0]T for i 1,... n,n, where the relative rotation matrix is R -1 (Rsi ) Rs1 (48) and Tho Tvo = Thn = Tv, = 0. The vector of the torques applied to all links -rc E R6n is 1C = [1x3 TC1 01x3 rC2T 01x3 rk]jT* (49) In this chapter, we will define the joint angles and show how to control them for snake robot locomotion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003977_s12213-008-0010-1-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003977_s12213-008-0010-1-Figure4-1.png",
        "caption": "Fig. 4 Motion pattern of the versatile microrobot",
        "texts": [
            " We can easily attach additional microprocessing if we put on another microrobot with a microtool such as a feeder of biological samples. This flexibility meets the requirements of various users. The use of small devices avoids reparation of instruments and easily implements additional manipulation with low cost. 3.1 Structure and drive sequence Over the last several years, we have developed the versatile microrobot for microscopic manipulations [16]. Figure 3 shows the structure of the versatile microrobot. The motion pattern of the versatile microrobot is depicted in Fig. 4. The specification of the robot is listed in Table 1. We have developed a microprocessing system organized by versatile microrobots and have confirmed the feasibility of the microrobot from several experimental demonstrations [17]. However, we have some problems with this system. When the robot needs to remain stably on a steel surface for a long time, we need to keep applying a current to the electromagnets. We also have to compensate for the versatile microrobot's motion even if we need only orthogonal motions [18, 19] although the versatile microrobot can move in an XY direction and rotate independently"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001877_10599490523940-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001877_10599490523940-Figure1-1.png",
        "caption": "Fig. 1 The V-groove butt joint design",
        "texts": [
            "175 mm diameter ball tip; \u2022 Electrode workpiece distance equal to 2 mm; and \u2022 Welding speed equal to 40.6 cm/min. Five different groove designs were used in this study to obtain a full penetration and a consistent weld metal profile. As such, current levels and wire feed speed were adjusted for each groove design. Different base metal dilution ratios were simulated by changing the included angles of the V-groove butt joint design. The included angles of 0, 25, 50, 75, and 90\u00b0 were prepared as shown in Fig. 1. The test pieces were cleaned and clamped with bolts (tightened to 50 ft-lb) onto a fixture that provided the back purge for the weld root with argon. The welded samples were tested under three different conditions: (a) as-welded; (b) heat treatment to T6 temper; and (c) naturally aged for 30 days at room temperature. The T6 temper was accomplished by heating the sample to 460 \u00b0C (860 \u00b0F) for 10 min, quenching into water, Leijun Li, Kevin Orme, and Wenbin Yu, Department of Mechanical & Aerospace Engineering, Utah State University, Logan, UT 84322- 4130"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002193_0471758078.ch2-Figure2.16-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002193_0471758078.ch2-Figure2.16-1.png",
        "caption": "FIGURE 2.16. Homogeneous catalysis electrochemical reactions. Reaction scheme and typical cyclic voltammetric responses. The reversible wave pertains to the mediator alone. The dotted curve is the response of the substrate alone. The third voltammogram corresponds to the mediator after addition of the substrate.",
        "texts": [
            " As with the other reaction schemes involving the coupling of electron transfer with a follow-up homogeneous reaction, the kinetics of electron transfer may interfere in the rate control of the overall process, similar to what was described earlier for the EC mechanism. Under these conditions a convenient way of obtaining the rate constant for the follow-up reaction with no interference from the electron transfer kinetics is to use double potential chronoamperometry in place of cyclic voltammetry. The variations of normalized anodic-to-cathodic current ratio with the dimensionless rate parameter are summarized in Figure 2.15 for all four electrodimerization mechanisms. In the simplest catalytic reaction scheme (Figure 2.16) a fast and reversible couple, P/Q serves as catalyst (mediator) for the reduction (taken as an example, transposition to oxidation being straightforward) of the substrate A. Instead of taking place at the electrode surface, electron transfer to A occurs via 0 0.1 0.2 0.3 0.4 0.5 0.6 \u22128 \u22126 \u22124 \u22122 0 2 4 6 8 y x* p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fv=RT p and x is defined as: the reduced form of the mediator, Q, generated at the electrode surface at a potential that is less reducing than the potential at which the direct reduction of A occurs. As depicted for cyclic voltammetry in Figure 2.16, catalysis comes out as an increase in the mediator wave, accompanied by a loss of reversibility. The species resulting from the reduction of A, B may undergo a large variety of reactions of the same type, as described previously in the case where the A/B reaction takes place at the electrode surface. Homogeneous Electron Transfer as the Rate-Determining Step The simplest case, which we consider first, is when the reaction Q\u00fe A* ke P\u00fe B is the rate-determining step of the catalytic process. The cyclic voltammetric responses are then functions of two dimensionless parameters, a kinetic parameter, le \u00bc \u00f0RT=F\u00de\u00f0keC0 P=v\u00de, and an excess factor, g \u00bc C0 A=C0 P, where C0 P and C0 A are the bulk concentrations of the mediator and substrate, respectively",
            " In the converse case, where substrate diffusion is rate limiting, the position of the peak potential toward the standard potential of the P/Q couple allows a simple determination of the rate constant using equation (2.21). For intermediate situations, the ratio of the peak currents in the presence or absence of substrate, ip=i0p, which is a function of the two parametersle and g, may be used to determine the value of the rate constant according to the procedure outlined in Figure 2.19. Homogeneous Catalytic EC Mechanism There is a large variety of homogeneous catalysis mechanisms according to the nature of the steps that follow the homogeneous electron transfer step (Figure 2.16). Their reaction schemes are parallel to the reaction schemes of the direct electrochemical mechanisms, the initial electrode electron transfer being replaced by the homogeneous electron transfer from the electrogenerated mediator Q to the substrate A. Among them, the homogeneous catalytic EC mechanism, where a first-order irreversible reaction follows the homogeneous electron transfer step (Figure 2.16), is of particular interest since it forms the basis of the application of homogeneous catalysis to the determination of the lifetime of short-lived intermediates. The three homogeneous steps may be characterized, in addition to g, by three dimensionless kinetic parameters: le \u00bc RT F keC0 P v ; l e \u00bc RT F k eC0 P v ; lC \u00bc RT F kC v Insofar as the intermediate B obeys the steady-state approximation, as is usually the case in practice, there are two limiting situations as to the nature of the rate-limiting step according to the value of the parameter l e=lC \u00bc k eC0 P=kC, which measures the competition between the followup reaction and the backward electron transfer (see Section 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001214_acc.1988.4789927-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001214_acc.1988.4789927-Figure1-1.png",
        "caption": "Figure 1: Two Link Planar Manipulator",
        "texts": [
            ",t) - B pxp (20) (21) (22) Here PL is the solution of (16), and a is defined by (17). The positive function I (*1 is derived from the following diffetential equation: \u00a3A Ct) - -reA (tt), S Ct1)> 0 (23) where r is a positive constant. This adaptive robust control algorithm, originated from the design in 1151, is able to render the state x of the system (10) to converge to zero. Moreover, it assures that remains bounded. VCW!fLLJf D3SZS Po A flC-LMM PLASR -aw The robust control schemes presented in the last two sections will be applied to the twolink planar manipulator shown in Fig. 1 as an illustrative exa le. (18) Here the unknomn constant t can be physically related to the bound of the uncertainty. Next, we assu that the function p (-,0, is concave and continously different?aale (see [15] for details) . The adaptive algorithm is then t K aPA(P,e(t),e(t),e{t9t IiPLX 11f, -W )(t) > 00t 84 (19) In the figure, subscript i (i - 1,2) denotes the lower arm (link-1) or the upper arm (linkl2). These two links are assumed to be rigid with lengths l}. Their masses are assumed to exist as point masses at their distal ends, and will be denoted by mk for link-i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001980_1.2196418-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001980_1.2196418-Figure2-1.png",
        "caption": "Fig. 2 2R planar manipulator used for computer simulations",
        "texts": [
            "org/about-asme/terms-of-use Downloaded F Jp k = =1 k x Ts \u2212 xd Ts 2 + v Ts \u2212 vd Ts 2 + a Ts \u2212 ad Ts 2 16 The robot used for computer simulations is described in Secs. 6.1\u20136.3. F D F D 418 / Vol. 128, JUNE 2006 rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 08/16/2017 6.1 Two-Link Arm Robotic Manipulator. The following two-link arm robot will be used as a model to simulate the behavior of a real robotic manipulator on the computer. The generalized coordinates qT= q1 q2 are chosen to be the angles defined in Fig. 2. A mathematical dynamical model of the robot can be obtained by using the Newton-Euler method or any method from the analytical dynamics 11 M q = m1lc1 2 + m2 2l1lc2c2 + l1 2 + lc2 2 + I1 + I2 lc2 2 m2 + l1lc2m2c2 + I2 lc2 2 m2 + l1lc2m2c2 + I2 lc2 2 m2 + I2 17.1 V q, q\u0307 T = C q, q\u0307 q\u0307 T = \u2212 m2l1lc2s2q\u03072 2 \u2212 2m2l1lc2q\u03071q\u03072 m2l1lc2s2q\u03071 2 17.2 Fi q\u0307i = 0,i + 1,ie \u2212 1,i q\u0307i + 2,i 1 \u2212 e\u2212 2,i q\u0307i sign q\u0307i i = 1,2 17.3 where s1=sin q1 , c1=cos q1 , and so on is the typical notation in robotics. Also, a detailed friction model suitable for industrial controller design 10 is considered in 17"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000861_pime_proc_1990_204_081_02-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000861_pime_proc_1990_204_081_02-Figure10-1.png",
        "caption": "Fig. 10 Bearing nomenclature and wetted Urn extent",
        "texts": [
            "comDownloaded from 85 THERMAL BEHAVIOUR OF A TWIN AXIAL GROOVE BEARING UNDER VARYING LOADING DIRECTION The temperature field in the film can be obtained from the solution of an energy balance: = - z , U + - h3 { G x ( $ ) ~ + Gz($-)~) (6) PV( T ) and The derivation of equation (6) is explained in reference (28) and embodies a balance between heat removal by convection and generation by shearing. It does not account for heat transfer through the journal and bush and is therefore most applicable to thick-film lubrication and where the thermal conditions are not extreme. In cavitated parts of the film, equation (6) can be simplified since pressure gradient terms are negligible and so it reduces to U h aT pc, - - = z, u 2 ax (7) Figure 10 illustrates the bearing geometry, loadcarrying film and pertinent nomenclature along with the unwrapped film which shows clearly the corresponding load-carrying and cavitated parts. The numerical model for calculating the extent of the wetted film under isothermal conditions is well documented in reference (1) and therefore this will not be explained in detail here. When thermal effects are accounted for, temperature prescriptions are necessary and for the loaded part of the film, to which equation (6) is applicable and where half the bearing only is considered, centre-line symmetry is satisfied by setting aT/az = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003934_robot.2008.4543374-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003934_robot.2008.4543374-Figure1-1.png",
        "caption": "Fig. 1. Model of planar underactuated biped robot with semicircular feet and torso",
        "texts": [
            " Luo are with the Bio-Mimetic Control Research Center, RIKEN, 463-0003 Nagoya, Japan {asano,luoz}@bmc.riken.jp Z.W. Luo is also with the Department of Computer Science and Systems Engineering, Graduate School of Engineering, Kobe University luo@gold.kobe-u.ac.jp stability of the dynamic gait and feedback structure of the mechanical energy inherent to the walking system. II. DYNAMIC GAIT GENERATION WITH CONSTRAINT ON IMPACT POSTURE A. Model of underactuated biped with torso This paper deals with a planar underactuated biped model with semicircular feet and a torso as shown in Fig. 1. A bisecting hip mechanism (BHM) [5] is used to stabilize the torso passively in an upright pose. Through the synergistic effect of BHM, we can efficiently generate a dynamic bipedal gait without having to maintain the torso\u2019s posture actively. Semicircular feet are also very effective for generating an efficient dynamic gait [6][7]. Two joint torques between each leg and torso can be exerted. Let \u03b8 = [ \u03b81 \u03b82 \u03b83 ]T be the generalized coordinate vector; the dynamic equation of the biped model is then M (\u03b8)\u03b8\u0308 + h(\u03b8, \u03b8\u0307) = Su + JT H\u03bbH , (1) where Su = \u23a1 \u23a3 1 0 0 1 \u22121 \u22121 \u23a4 \u23a6[u1 u2 ] , (2) and JT H\u03bbH \u2208 R 3 denotes the constraint force of the BHM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000891_tgrs.1985.289468-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000891_tgrs.1985.289468-Figure1-1.png",
        "caption": "Fig. 1. Geometrical configuration.",
        "texts": [
            ". INTRODUCTION IN PREVIOUS works the eddy currents distribution was calculated within a conducting plate when the excitation was a circular current loop parallel to the plate [1] and when the circular loop was perpendicular to the plate [2]. In this work a circular loop of radius R is located above the plane Osy separating the two media and is placed in an arbitrary position according to the geometric configuration of Fig. 1. Three regions are defined and the magnetic permeability and conductivity of region 2 are constant. The projection of the circular loop on the dividing plane O\u00b0y between region 1 and 2 is an ellipse. The axis 0., coincides with the minor axis and the axis Oy coincides with the major axis of the ellipse. The field in region 1 is the sum of the field of the circular loop and the field of the eddy currents which are induced within the conducting medium. The eddy current distribution within the material is calculated as a function of the variables x, y, z, t and with the angle sp as a parameter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003278_0022-2569(71)90371-5-Figure4.6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003278_0022-2569(71)90371-5-Figure4.6-1.png",
        "caption": "Figure 4.6 Displacement curve for R C R C R mechanism ($4 vs. 0~),",
        "texts": [],
        "surrounding_texts": [
            "I tO0\n50\ng o\n.\n-IO0\n-150\n-200\n- - 9 z z\n8~2\ni ': ! i ! i i iO I 0 0 150 2 0 0 250 3 0 0 350 4 0 0\ne, d e g\nF i g u r e 4 . 3 D i s p l a c e m e n t c u r v e f o r R C R C R m e c h a n i s m (8~ vs. ~),).\n2oc ~50\nIOC ~\n5C\ng -50\n-IOC 8a4 O 4\n-15\u00b0 l\n- z o o L , ' i i I !,, i ! 5 0 ~00 150 200 2 5 0 3 0 0 3 5 0 4 0 0\n8 d , d e g\nF i g u r e 4 .4 D i s p l a c e m e n t c u r v e for FICRCR m e c h a n i s m (04 vs. 8,).\nF r o m equat ion (14), S., = :c w h e n H~ ~ 0 or w h e n\nX cos e., - Y sin 8., = 0.\nSquaring and adding equat ions (16) and (I 8) to e l iminate 8~ g i v e s\nX e + y e = Z ' - ' .\n18)\n1 9 }",
            "J.M. Vol. 6 No. 3 - D",
            "Briefly, expanding and simplifying equation (19) and using equation I5~ to eliminate 0~ and 0-, gives\nO1\"\ncos\"0~ = 1 i 20!\n0 a : = n w i2 1 )\nwhere n = 0, 1, 2 . . . . Equation (21) may also be obtained for S~ = :c by using equation (7) and by equating H4 to zero.\nIt follows if these conditions are satisfied that the two couplers c~..,3, c~34 of the corresponding spherical five-link mechanism are in line. For the spatial R C R C R mechanism as the couplers a.,_:~ and a:~4 become parallel, the offsets S~ and $4 tend to infinity. This type of result was obtained by Dimentberg[3] for the spatial four-link RCCC m e c h a n i s m .\nAcknowledgemen t -The authors wish to acknowledge the financial ass is tance of the Science Research Council (Grants B/SR/4354 and BS/SR/8420).\nReferences [1] D U F F Y J., A Derit'ation o f Dual Displacement Equations jor Fic'e, Six and Seven Link Spati,~d Mech-\nanisms Using Spherical Trigonometry (3 parts), Liverpool Polytechnic 1969. [2] Y A N G A. T,. Displacement analysis of spatial five-link mechanisms using 13 \u00d7 3) matrices with dual\nnumber elements . Trans. A S M E, J. Engng Ind. 191B. February 1969. [3] D I M E N T B E R G F. M., A General Method for the Investigation o f Finite Displacements o j Spati~[\nMechanisms ~znd Certain Cases o f Passive Joints. Purdue Transla t ion No. 436. Purdue Universi ty Libraries. [4] W A L L A C E D., Displacement analysis o f spatial mechanisms wit/1 more than fi)ur links, Doctoral dissertat ion. Columbia Universi ty , New York. 1968. Univers i ty Microfilms. Ann Arbor, Michigan. U.S.A. [5J Y U A N M. S. C. and F R E U D E N S T E I N F.. Displacement Analysis o f the RRCCR Fi~'e-Link Spatial Mechanism. Part of Doctoral dissertat ion. Columbia Univers i ty , New York. [6.7] D U F F Y J. and H A B I B - O L A H I H. Y., Displacement Analysis o f Spatial Fit'e-link 3R-2C Mecttanisms (Parts 2 and 3) to appear inJ . Mechanisms. [81 Y A N G A, T., Application o f Quaternion Algebra and Dmd Numbers to the Analysis oj'Spati.[ Mechanisms. Doctoral dissertat ion. Columbia Univers i ty . New York (1963). Universi ty Microfilms Ann Arbor, Michigan. U.S.A. [9] Y A N G A. T. and F R E U D E N S T E I N F., Application of dual number quaternion algebra to the analysis of spatial mechanisms. Trans. A S M E J . AppL Mech. 86E, (I 964).\nAppendix 1 Primary and secondary equations, definitions Expansion o f equation ( l ) into primary and secondary equations\nPrimary equation:-\nA (0r) sin 0q+ B(Or) cos 0,, - C(Or) = cos c~u cos c~x - sin cq~ sin c~j~. cos 0j.\nSecondary equation:-\nAz(O~) sin 0~ + B._(Or) cos 0,, + C,_,(O~) = S~ sin 2 ~ sin-' ~ - sin 0~.\n(1.1)\nt l .2)\nExpansion o f equation (2) into primary.' and secondary equations\nPrimary equation:-\nsin ce~j cosec a~q[A(0r) cos 0 q - B(Or) sin 0q] sin 0~\n+ sin c~#[cot cq~{A (0r) sin 0q + B (0.) cos 0,,} + tan c~oC(0r)] cos 0~\n= cos ~ k - - cos cq~[A (0r) sin 0,,+ B(Or) cos 0,,-- C(Or)] (1.3)"
        ]
    },
    {
        "image_filename": "designv11_28_0000683_890127-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000683_890127-Figure1-1.png",
        "caption": "Fig. 1 - Measuring system of transverse movement",
        "texts": [
            " Using electro-hydraulic exciter, the piston and the cylinder liner were excited at the same time by shaking the link attached to the connecting rod in a lateral direction. The cylinder liner vibration acceleration was measured by attaching an acceleration transducer to the cylinder liner at the piston thrust side. The noise arround the engine was measured by microphone. The following transfer function, between the piston slap noise and the cylinder liner vibration acceleration (Tf) was calculated: Gap sensors were attached on the thrust and anti-thrust side of a piston to permit data to be taken from the engine through the link device, as shown in Fig. 1. Data were transmitted to a mini-computer through an AID converter, and piston lateral movement and inclination of piston etc. were analyzed. Tf = N/Acc N ; measured noise Acc; measured cylinder acceleration - (1) liner transfer liner force system of transfer between slap noise vibration system of between and impact Measuring function vibration and liner piston 890127 3 Using Eq.(l) and Eq.(2), the transfer function (Th) between the piston slap noise and piston slap force (abbreviated to \"slap noise transfer function l' hereafter) was calculated: The device which excited the cylinder liner is shown is Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003230_14644193jmbd103-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003230_14644193jmbd103-Figure3-1.png",
        "caption": "Fig. 3 Track geometry",
        "texts": [
            " Using these vectors, the tangents t\u0304i 1 and t\u0304i 2, and the normal n\u0304i to the surface at the contact point are defined, respectively, in the body coordinate system as t\u0304i 1 = \u2202u\u0304i P \u2202si 1 , t\u0304i 2 = \u2202u\u0304i P \u2202si 2 , n\u0304i = t\u0304i 1 \u00d7 t\u0304i 2 (2) This parameterization can be used to describe the wheel and rail surfaces. For example, the surface geometry of the rail r can be described in the most general form using the two surface parameters sr 1 and sr 2, where sr 1 represents the rail arc length and sr 2 is the surface parameter that defines the rail profile, as shown in Fig. 2. The surface parameter sr 1 is defined in the rail body coordinate system, whereas the surface parameter sr 2 is defined in a profile coordinate system X rpY rpZ rp shown in Fig. 3. The location of the origin and the orientation of the profile coordinate system, defined, respectively, by the vector Rrp, and the transformation matrix Arp, can be uniquely determined using the surface parameter sr 1. Using this description, the global position vector of an arbitrary point on the surface of the rail r can be written as follows rr = Rr + Ar(Rrp + Arpu\u0304rp) (3) where Rr is the global position vector of the origin of the rail coordinate system X r Y r Z r , Ar is the transformation matrix that defines the orientation of the rail coordinate system, and u\u0304rpis the local position vector that defines the location of the arbitrary point on the rail surface with respect to the profile coordinate system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001553_tmag.1983.1062845-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001553_tmag.1983.1062845-Figure6-1.png",
        "caption": "Fig . 6 . V e c t o r p o t e n t i a l as a f u n c t i o n o f time i n two p o i n t s o f t h e r o t o r : - r o t o r s u r f a c e ,",
        "texts": [],
        "surrounding_texts": [
            "\"t\" equal to those at \"t + T\" one period later. The obtained solution [AI is used as initial values to solve the non linear algogithm ( 6 ) .\nThe degree of calculation precision depends on the proper choice of the time step and the subdivision of the considered domain.\nThe flow chart of the solution procedure is shown in figure 1.\n! I\nFig. 1. Flow chart of the solution procedure\nNUMERICAL APPLICATION\nThe described numerical model is used to determine eddy currents and losses in a simple electromagnetic structure constituted by a three phase a.c. machine with a solid cylindric rotor (figures 2 and 3).\nFirst calculations have been done with stationary rotor and the stator fed by sinusoi'dal currents. Both linear and saturated magnetic circuit cases are considered. The flux plots corresponding to these cases are shown in figures 2 and 3 .\nThe eddy current density space distributions on the rotor surface and 1 mm inside are shown in figure 4. for a given instant.From this figure two remarks can be noticed. The first is that.the eddy currents are smaller on the rotor surface in the saturated case than in the linear one. The second remark is that the last phenomenon is inversed 1 mm inside the rotor body. This can be explained by the fact that the current penetration in the saturated case is greater (see figures 2 and 3 ) , and the magnetisation level is lower,.because the permeability is smaller in such case.\nFig. 2 : Flux plot in the studied example linear magnetic circuit\nFig. 3 . Flux plot in the studied example saturated magnetic circuit",
            ". s a t u r a t e d X . s a t u r a t e d o . l i n e a r A . l i n e a r\nI n a second s t ep , ca l cu la t ions have been done fo r\nt h e r o t o r s u r f a c e - 1 mm i n s i d e t h e r o t o r\nb o t h l i n e a r and s a t u r a t e d cases, w i t h r o t a t i n g r o t o r with a speed W/p (p is t h e number o f p o l e p a i r ) and t h e s t a t o r f e d by s inuso i ' da l cu r ren t s p roduc ing a r o t a - t i n g f i e l d w i t h s p e e d 2 w / p . P h y s i c a l l y , e d d y c u r r e n t s a n d v e c t o r p o t e n t i a l s i n t h e r o t o r b o d y must p u l s a t e with w . This is confirmed by f i g u r e 5 .\nF ig . 5 . Vec to r po ten t i a l as a f u n c t i o n o f t i m e o n the rotor s u r f a c e - l i n e a r case ___\nI n t h i s f i g u r e , t h e t e e t h h a r m o n i c s are a l s o shown. A series d e c o m p o s i t i o n o f t h e v e c t o r p o t e n t i a l i n a p o i n t o f t h e r o t o r h a s g i v e n h a r m o n i c s o f t h e o r d e r 1 1 , 1 3 , 23 and 25 ; t h e number o f s l o t s p e r p h a s e p e r p o l e i n t h e p r e s e n t case is 2. It may b e n o t e d t h a t t h e s e t e e t h harmonics become s m a l l e r i n s a t u r a t e d case as Shawn i n f i g u r e 5 ; t h i s i s due t o lower teeth permeance. Moreo v e r , t h e . e f f e c t o f t h e t e e t h h a r m o n i c s becomes less i m p o r t a n t i n s i d e t h e r o t o r body ; t h i s is shown i n f i g u r e 6.\n- 1 mm i n s i d e r o t o r body.\nTo examine the more g e n e r a l case where t h e s t a t o r c u r r e n t s are no t s inuso lda l , ca l cu la t ions have been do - n e w i t h s t a t o r c u r r e n t s p r o d u c i n g two d i f f e r e n t r o t a - t i n g f i e l d s w i t h s p e e d s 2 W / p and 4 W / p . I n t h i s case as t h e r o t o r s p e e d i s W / p t h e e x p e c t e d p u l s a t i o n s i n t h e r o t o r a r e W /p and 3 w / p . Such a r e s u l t is brought i n t o e v i d e n c e i n f i g u r e 7.\nlo-\nF i g . 7 . V e c t o r p o t e n t i a l as a func t ion o f t ime on t h e r o t o r s u r f a c e due t o n o n - s i n u s o y d a l s t a t o r c u r - r e n t s :\n- l i n e a r c a s e - - s a t u r a t e d c a s e ----- - s a t u r a t e d c a s e -----",
            "CONCLUSION\nA dynamic model for eddy current calculation in saturated electric machines is developed and discussed in the paper. The solution of the magnetic diffusion equation through the use of an air-gap macro element has permitted the determination of eddy currents accounting for machine rotation in the presence of the magnetic saturation. The obtained results show the model possibilitiesto consider saturation and space variable reluctance effects on eddy current distribution.\nNOMENCLATURE\nA potential vector $ magnetic reluctivity V linear velocity Jo excitation current density\n1\n[A] vector of nodal values of \"A\" [I] vector of nodal values of current [A]\" vector of nodal values of \"AI1 at a given instant t z n.At [A], vector of nodal values of \"A\" for the ith N.R. iteration A t time step [SIn assembling main matrix (in case of rotation) at a [SN] derivative matrix of [SI with respect to diffegiven instant t = ndlt\nrent unknown nodal values of A\nREFERENCES\n[l] P. Silvester, M.V.K. Chari, \"Finite element solution of saturable magnetic field problems\", Trans. IEEE, vol PAS. 89, pp. 1642-1651, 1970.\n[2] E.F Fuchs and E.A. Erdelyi, \"Nonlinear salient pole alternator subtransient reactances and damper winding currents\", Trans. IEEE, vol. PAS-93, pp. 1871- 1892, 1974.\n[3] A. Foggia, J.C. Sabonnadigre and P. Silvester, \"Finite element solution of saturated travelling magnetic field problems\", Trans. IEEE, vol. PAS-94, pp. 566-871, 1975.\n[4] A. Razek, J.L. Coulomb, M. Feliachi and J.C. Sabonnadi&re, \"The calculation of electromagnetic torque in saturated machines within combined numerical and analytical solutions of the fields equations\", Trans. IEEE, vol. MAG-17, pp. 3250-3252, 1981 -\n[5] A. Razek, J.L. Coulomb, M. Feliachi and J.C. Sabonnadi&re, \"Conception of an air-gap element for the dynamic analysis of the electromagnetic field in electric machines\", Trans. IEEE, vol. MAG- 18, pp. 655-659, 1982.\n[6] F. Bouillault et A. Razek, \"Prise en compte du mouvement dans la d6termination numerique des courants de Foucault dans une structure 6lectromagn6tique\", Rev. Phys. App., t 18, pp. 103-106, 1983.\n[7] F. Bouillault and A. Razek, \"Numerical calculation of eddy currents in mobil electromagnetic systems\", Conf. ?roc. U.P.E.C., Guilford, 1983."
        ]
    },
    {
        "image_filename": "designv11_28_0000418_095440603767764426-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000418_095440603767764426-Figure4-1.png",
        "caption": "Fig. 4 Zero-pitch reciprocal screw con guration at y1 \u02c6 08 and y1 \u02c6 1808",
        "texts": [
            " Mechanical Engineering Science C14402 # IMechE 2003 at Library - Periodicals Dept on March 21, 2015pic.sagepub.comDownloaded from matrix S of joint axes can be simpli ed as 0 0 1 0 0 0 0 +1 0 +d 0 0 +1=2 0 + 3 p =2 0 +\u2026d=2 \u2021 a\u2020 0 0 +1 0 +\u2026d \u2021 a\u2020 0 + 3 p a +1 0 0 0 +d 0 0 0 1 0 3 p a 0 2 6666666666664 3 7777777777775 \u202625\u2020 The zero-pitch reciprocal screws are $r \u02c6 \u20301, 0, \u00a1 1= 3 p ; 0, d , 0\u0160T or \u2030 3 p =2, 0, \u00a1 1=2; 0, 3 p d=2, 0\u0160T \u202626\u2020 This reciprocal screw is a transversal one that intersects all six joint axes. This gives two corresponding constraint con gurations in Fig. 4, which exhibits the constraint wrench affecting the con guration of the linkage. Similarly, the screw matrix S of joint axes at the con guration of y1\u02c6 908 or 2708 becomes 0 0 1 0 0 0 +1 0 0 0 +d 0 0 +1 0 +\u2026d \u2021 a\u2020 0 0 +1=2 0 + 3 p =2 0 +\u2026d \u00a1 a\u2020=2 0 0 +1 0 +d 0 + 3 p a 0 0 1 0 3 p a 0 2 6666666666664 3 7777777777775 \u202627\u2020 Their reciprocal screw axis of pure force constraint yields $r \u02c6 \u20301, 0, 1= 3 p ; 0, d \u2021 a, 0\u0160T or \u2030 3 p =2, 0, 1=2; 0, 3 p \u2026d \u2021 a\u2020=2, 0\u0160T \u202628\u2020 This is also a transversal one intersecting all revolute joint axes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002325_j.triboint.2006.09.003-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002325_j.triboint.2006.09.003-Figure2-1.png",
        "caption": "Fig. 2. Sketch section of contact deformation under a normal load.",
        "texts": [
            " It consists of four elements: four wire races, some balls, a cage and two frameworks. Moreover, the pitch circle diameters of this kind of bearings are available from 150 to 3000mm [2]. The balls were distributed homogeneously in the circumference of the framework. The framework itself is constructed from aluminum alloy, while the wire is made of bearing steel GCr15 having HRC 55 of hardness. When a normal force acts on two general convex bodies in contact, the contact point expands into a contact area, as shown in Fig. 2. The contact area whose size depends on external loads, mechanical properties and topographies of surfaces [9] is elliptic according to the Hertz contact theory (see Fig. 3). Contact deformation mainly comes from two contact areas: the ball-wire and the framework-wire. The ball-wire race contact belongs to the non-conforming contact whose typical sizes of the contact region range from 0.1 to 1.1mm [10,11]. Moreover, the minor axis of the contact ellipse is in the rolling direction, while the major axis of that is in the lateral direction [12]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003978_6.2009-6139-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003978_6.2009-6139-Figure4-1.png",
        "caption": "Figure 4: Detailed Turn Diagrams. The Turn-short (a) and Route-Tracking (b) methods as described in this section.",
        "texts": [
            " The aircraft turns toward the next assigned waypoint when it calculates an aspect angle of greater than 90 degrees (the waypoint is behind the aircraft) and the aircraft is within the declared tolerance distance for that waypoint.  Turn-Short. In this situation, the aircraft is required to begin turning before reaching a waypoint. Ideally, the turn is executed so that the aircraft tracks the intended flight path. Based on the current aircraft speed American Institute of Aeronautics and Astronautics 5 and anticipated bank angle, Eq. 6 is used to compute the ideal turn circle radius. The start of the turn is then calculated using Eq. 8, where (d) is the distance to the next waypoint, as shown in Fig. 4. American Institute of Aeronautics and Astronautics 6  Heading Constraint. A fly-past type waypoint can also have a constraint on the direction of approach to that waypoint. There may be a requirement to fly over a point from a given direction in order to aid subsequent navigation or place a sensor at a given location. This method was originally presented by this author in Ref. 4. Equation 10 shows the calculation of a constrained heading turn, where is the bearing of the current waypoint from the vehicle and is the desired heading when crossing the waypoint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001128_38.20335-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001128_38.20335-Figure2-1.png",
        "caption": "Figure 2. The distance between two objects.",
        "texts": [
            " Here, a segment must be tested against all environmental objects and all other segments unless they are neighboring segments. The neighboring segments cannot collide with each other because of the motion restrictions of the joints. To simplify the calculation, we use the distance between the centers of objects minus the sum of the radii of their hull sphere. While the values are positive, we can take the increment to the smallest of them and continue the next step. Otherwise collision is possible. Then the possible intersections must be detected. The smaller increment will be chosen to get accuracy (see Figure 2). Using this distance function, we can usually eliminate most objects. After this elimination there are only local objects to consider, which will often be only one object. To calculate the possible intersection of two objects, we can now use their geometrical models. But in the most likely case it is sufficient to use a simplified model, such as the hull volumes. Three simple geometries are useful: the convex hull, the hull sphere, and the hull cylinder. The choice of one of them depends on the geometry of each object (see Figure 3)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002372_1.2167651-Figure12-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002372_1.2167651-Figure12-1.png",
        "caption": "Fig. 12 The planar and the spherical right-angle triangle forming in the SBL",
        "texts": [
            ", the condition a b3+b1 in the planar version which can be considered as 3+ 1 in the spherical version. The difficulty in our analogy arises when the planar conditions are in the nonlinear form that they usually originated from in the planar trigonometry. The only nonlinear condition in Table 1 is a= b1 2\u2212b3 2. This condition cannot be used in the spherical SBL by direct substitution of the geometrical parameters. In other words, condition = 1 2\u2212 3 2 is not a valid spherical equivalent for the planar one. To solve this problem, considering Fig. 12 a it is seen that condition a= b1 2\u2212b3 2 is related to the case that OAOA is a right-angle triangle and b1 is the hypotenuse. Meanwhile, in the spherical SBL, a trigonometric analogy leads us to the case that should be a right-angle spherical triangle with 1as the hypotenuse Fig. 12 b . In the spherical trigonometry the equivalent relation to that of the planar case is as follows 11 : cos 1 = cos cos 3 \u2192 = arccos cos 1 cos 3 24 So the only correction need for obtaining tabular form of all possible coupler curves in spherical SBL driving from Table 1 is substituting the condition a= b1 2\u2212b3 2 with its spherical equivalent, =arccos cos 1 / cos 3 . In Table 2 all the possible coupler curves, singular points, and related conditions are classified. The present work was an investigation on the path generation in the planar and the spherical SBLs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000904_1077546303009005006-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000904_1077546303009005006-Figure1-1.png",
        "caption": "Figure 1. Coordinate system.",
        "texts": [
            "comDownloaded from lis and centrifugal terms, is the damping matrix, and is the vector of gravitational forces and moments. Also, the equation of motion of an underwater vehicle can be represented in the earth-fixed reference frame in terms of position and attitude through the Euler transformation as (3) where , , , and . The inertia matrix , including hydrodynamic added inertia, is symmetric and positive definite. The Coriolis and centrifugal matrix, also including added inertia effect, , satisfies the skew symmetric relationship . The damping matrix is positive definite. The coordinate system is shown in Figure 1. A more detailed discussion on mathematical models of underwater vehicles can be found in Fossen (1994). ) % ( % & * ((% %# + Direct adaptive control laws are derived in the following subsections employing two different types of neural network. As mentioned in the previous section, it is difficult to obtain a mathematical model of an underwater vehicle. Not only is it difficult to obtain the exact values of hydrodynamic coefficients, but the coefficients change with the configuration of the underwater vehicle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002301_105994905x75484-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002301_105994905x75484-Figure7-1.png",
        "caption": "Fig. 7 Schematic diagram of TIMETAL 21S plug-and-nozzle assemblies for the Trent 800 engine on the Boeing 777 (Ref 10)",
        "texts": [
            " Using TIMETAL 15-3 instead of commercially pure titanium saves approximately 64 kg (140 lb) per Boeing 777 aircraft (Ref 10). Tubing wall thicknesses are typically 0.5 mm (0.020 in.) or 0.8 mm (0.032 in.). The ducts carry air at temperatures of up to 232 \u00b0C (450 \u00b0F) (Ref 1). More recently, TIMETAL 15-3 has been considered for use in portions of the ducting system of the Airbus A380 (Fig. 6) (Ref 11). For plug-and-nozzle and other types of exhaust systems, TIMETAL 21S is now used in lieu of much heavier nickel alloy systems on several aircraft models. Examples for the Boeing and Airbus aircraft are provided in Fig. 7 and 8, respectively. Using TIMETAL 21S instead of nickel-base alloys saves approximately 82 kg (180 lb) on each Rolls Royce Trent engine (or 164 kg [360 lb] total) on the Boeing 777 aircraft (Ref 3). TIMETAL 21S is also used in the exhaust systems of several military aircraft programs. 706\u2014Volume 14(6) December 2005 Journal of Materials Engineering and Performance In the past decade, strip alloys have proven useful in several aircraft applications, including TIMETAL 15-3 for pneumatic ducting and TIMETAL 21S for engine exhaust systems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000652_0470867906-Figure7.4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000652_0470867906-Figure7.4-1.png",
        "caption": "Figure 7.4 Visualisation of the mechanics",
        "texts": [
            " When the damper characteristic is changed over, the spring compression exhibits a significantly more desirable behaviour. As discussed above, it is also necessary to concern ourselves with the visualisation of the mechanics and the software. For the mechanics this quickly becomes an ad hoc solution, unless CAD data is available from the development of the mechanics, which can be drawn upon for a suitable representation. The solution shown here shows a graphic representation of a quarter of a car, which is \u2018driven\u2019 by the simulation data, see Figure 7.4. This functions both as direct output during simulation and also for a subsequent consideration of the extracted data. By contrast, a general solution can be found for the software. As already indicated it is a question of considering the software using a type of debugger and controlling its processing, see Figure 5.7. In contrast to the tools normally used, this is a debugger that considers the processing of software on virtual hardware. Naturally, if this is to run properly an exact synchronisation between hardware and software is crucial"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003560_978-1-4020-9137-7_13-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003560_978-1-4020-9137-7_13-Figure1-1.png",
        "caption": "Fig. 1 Aerosonde UAV",
        "texts": [
            " Three fuzzy modules are designed for autonomous control, one module is used for adjusting the roll angle value to control UAV\u2019s flight heading, and the other two are used for adjusting elevator and throttle controls to obtain the desired altitude and speed values. The performance of the proposed system is evaluated by simulating a number of test flights, using the standard configuration of MATLAB and the Aerosim Aeronautical Simulation Block Set [11], which provides a complete set of tools for rapid development of detailed six-degree-of-freedom nonlinear generic manned/unmanned aerial vehicle models. As a test air vehicle a model which is called Aerosonde UAV [10] is utilized (shown in Fig. 1). Basic characteristics of Aerosonde UAV are shown in Table 1. The great flexibility of the Aerosonde, combined with a sophisticated command and control system, enables deployment and command from virtually any location. GMS aircraft instruments are deployed in order to get visual outputs that aid the designer in the evaluation of the controllers. The paper is organized as follows. Section 2 starts with the basic flight pattern definition for a UAV and then explain a sample mission plan which includes SID (Standard Instrument Departure) and TACAN (Tactical Air Navigation) procedures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001422_bf00532523-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001422_bf00532523-Figure1-1.png",
        "caption": "Fig. 1. The (/~co ~, q)-plsne with domMn \"7\" and the eigenvslue curves of an elastic system subjected to follower forces (flutter system)",
        "texts": [
            " (54) From (54) follow the same values #~ok as above and the eigenflmetions sk (as far as these exist). Let functions ~# and sk be normalized so that holds. Together with (55), (56) leads to l f s ~ dx - ~], o i.e., orthonormality of the adjoint eigenfunetions. (57) H. H. E. Leipholz: Assessing Stability of Elastic Systems 353 First, let it be shown that condition \"ogj 4= ~o~ for ] 4= i\" is indeed being satisfied in domain \"y\" of the (/~c@, q)-plane defined by 7, = (0 =< q < q*, o =</zo~ 2 < ~ ) (5s) and shown in Fig. 1 : In this figure, the most severe ease of an elastic systenl with follower forces i.e., a flutter system, has been assumed. Such system is known to be one having for specific values of q coalescing eigenva2ues, as follows from the trace of its eigencurves. Hence, domain \") / ' is bounded from above by the load value q = q* at which eigenvalues coalesce for the first time. For q = 0, problem (53) changes into --#og~,lo q- D8[~70 ] := 0, U[~0]z = 0. (59) This set of ,equations describes the free vibrations of the unloaded system. Hence, operator D[O, ~] has become the selfadjoint operator D~. The eigenvalues #o~1~,o ,2 k = 1, 2, 3, ..., of D~ are all distinct from each other and are those points on the #~2 axis in Fig. 1 in which the eigencurves of problem (53) intersect this axis. But, operator DIg, ~7] is supposed to depend continuously on q. Hence, the eigenvalue curves of D[q, ~]] expand continuously into the first quadrant of the (#(o 2, q)-plane from the points (q 0, #~@ 2 = = #cue,0) on the #c@-axis. Due to this continuity of the eigenvalue curves, there is a domain in the (/~(@,q)-plane, say, domain \"7/\" in which for fO 2 a value q < q* there are discrete eigenvalues tt k, as shown in Fig. 1. Secondly, it will be proved tlaat in domain \"y\" the sets of eigenfunetions ~Tk and ek are complete: For q = 0, one is dealing with problem (59). For this problem Ds ~ / ) s , ~0 = e0, (60) due to selfadjointness, and l g J ~0,~0,/dx = ~j . (61) 0 Moreover, since (59) is a free..vibration-problem, there exists the bounded, positive definite symmetric function of Green, n~mely, G0 = w ~0.~(x) ~0)(~) z , (62) k /Z(~)O,k to which Mereer's theorem can be applied yielding 1 -- So, So < ~ . (63) #~o0,k I t is assumed that in domain \"y\" not only the eigenvalues corresponding to a specific value of q are all distinct, but that also the trace of the eigencurves is so that for # ~ = O(q), = NS'(q)[ < r#cog,~, (64) where/\" is an appropriate constant and p % 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003740_1.2975154-Figure22-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003740_1.2975154-Figure22-1.png",
        "caption": "FIG. 22. B vector field in three dimensions toward the axis of the helicoidal magnet. The three numeric values of Bx, By, and Bz are relative to the axis point at x=\u22120.5220 m.",
        "texts": [
            " The more regular trend of Bx with respect to those highly periodic of By and Bz confirms the general tendency of the field to be less [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: 131.230.73.202 On: Thu, 18 Dec 2014 07:41:10 [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: 131.230.73.202 On: Thu, 18 Dec 2014 07:41:10 modulated versus X than the other directions Y and Z. Finally, in Fig. 22 a vectorial representation of B along the axis of the magnet is illustrated. This diagram has been drawn with the data used to obtain the graphics in Fig. 21. Observing this B representation, the helicoidal configuration of the field also along the magnet axis is highlighted. In the early part of this paper we have presented a study regarding the volume magnetic charge density M considered in the \u201cmagnetic charge model\u201d for predicting the field of helicoidal magnets. The magnetization M within the structure has been fixed as uniform and helical"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002641_tmag.2006.872518-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002641_tmag.2006.872518-Figure5-1.png",
        "caption": "Fig. 5. Laminated core: (a) real model, (b) solid core model.",
        "texts": [
            " 2) DC Steady State Eddy Current Analysis: The dc steady state eddy current analysis with method ( : electric scalar potential), taking account of the rotation of the rotor by the Lagrange coordinate system [2], is carried out. In this method, the dc steady state flux and eddy current distributions can be obtained without time iteration, but the coefficient matrix becomes asymmetric. Therefore, the ILUBiCGSTAB method is used as the solver of the linear equations. 3) Modeling of Laminated Core: The laminated core is approximated by the solid core model with anisotropic permeability and conductivity [3] as shown in Fig. 5. The subscripts and denote the values in parallel and perpendicular directions to the lamination, respectively. The superscript (*) denotes the real values of the material constants and the physical quantity. In the solid core model, the magnetic resistance of the gap between the steel sheets and the eddy currents parallel to the lamination are taken into account. However, is neglected because and are much different in the two cases and the steel sheet seems to be enough thin. Then, the material constants of the solid core model are given by the following equations using the space factor : (7) (8) (9) (10) 4) Iron Loss Calculation: In this paper, the iron losses of the rotor and the shaft are evaluated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002061_tmag.2004.825468-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002061_tmag.2004.825468-Figure1-1.png",
        "caption": "Fig. 1. Lamination of the induction machine\u2014two pole pitches.",
        "texts": [
            " For linear interpolation of the time-dependent variables, the first order time-step algorithm is applied, and can be written as a function of time: (2) (3) is the weighting parameter and set to according to the Galerkin scheme [3]. With the Maxwell stress tensor (4) an expression for the local surface force density is given [4]. The index stands for the normal components of the vectors and . is the normal vector of the boundary surface from region 2 to 1. and are the magnetic-coenergy densities of these regions. For the regarded application, investigations have shown that an induction machine with stator slots and rotor bars provides a very good variant [5]. The lamination is shown in Fig. 1. Although only two pole pitches are depicted, the machine is modeled as a 360 -model since the number of elements is small for 2-D calculation in general. The models have about 25 000 first-order triangular elements and 12 500 nodes. In Fig. 2, closeups of the air gaps of the centrical and the excentrical model are opposed. To the left, the centrical model is depicted. The air gap has a constant value of mm. Next to it, the excentrical model is shown. The air gap differs between and mm. The maximum air gap is depicted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003063_2008-36-0068-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003063_2008-36-0068-Figure1-1.png",
        "caption": "Figure 1 geometry of (a) small-end and (b) pin-boss",
        "texts": [
            " The same process of step 1 for the small-end is applied to the pin-boss until a converged solution is obtained. This procedure is repeated successively between small-end and the pin-boss until the pin rotation speed from the two rounds of iteration is close enough. Geometry of and load on the small-end and pin-boss The engine used in this study is a 15 litter in-line 6 cylinder diesel engine. Both the small-end and the pin-boss are truncated so they both pose trapezoidal shapes, as are shown in Figure 1. The small-end has a bush inserted while the pin-boss is bushless. There is an oil jet from the oil circuit beneath the piston rings spraying oil on to the small-end and the pinboss. In addition, there is also an oil drilling from the big-end supplying extra oil to the small-end. The bore of the small-end bush has two axial tapers at the two sides, designed to reduce possible excessive contact between the bush and the pin. The pin is free to rotate inside the bush and the pin-boss. Two load-speed cases were considered: maximum torque (1200rpm) and rated speed (1800rpm)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002852_iros.2006.281799-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002852_iros.2006.281799-Figure8-1.png",
        "caption": "Fig. 8 Joint velocity when a joint is locked at minimum sudden change",
        "texts": [
            " For this case, the sum of the sudden change in joint velocity for the two manipulators is 81rad/s. When joint 2 of the master and slave manipulators fails and is locked at t=2.25 s, the sudden change of surviving joint 3 for the two manipulators reaches maximum value A=0.2rad/s and A=0.4rad/s respectively. In contrast, when joint 2 of the master and slave manipulators fails and is locked at t=3.35 s, the sudden changes in surviving joint 3 for the two manipulators reaches minimum value A =0.066rad/s and A =0.012rad/s respectively. These simulation results reveal that the sudden Fig. 7 and Fig. 8 are the simulation results of the fault tolerant operations for the arbitrary initial position and orientation on condition that a joint fails and is locked at the moment of maximum and minimum sudden change in joint velocity respectively. Fig. 7 shows that, if joint 2 of the two manipulators fails and is locked at the moment of their own maximum sudden change in joint velocity, the velocity of surviving joint 3 for master and slave manipulators will jump from -0.38rad/s to -0.58rad/s and from 0.02rad/s to 0.42rad/s respectively. This case will cause a large vibration to manipulators and reduce their operational accuracy, In contrast, if the joints of two manipulators fail and are locked at the moment of minimum sudden change in joint velocity, the velocity of surviving joint 3 of master and slave manipulators only change from -0.03 irad/s to 0.035rad/s and from 0.292rad/s to 0.304rad/s as Fig. 8 shows. It means that for this case the velocity fluctuation of surviving joints is smaller and the manipulators operate more stably. Thus, we can conclude that reducing the sudden change in joint velocity can obviously raise the stability of fault tolerant operations for two coordinating manipulators. Using the fault tolerant planning algorithm proposed in this paper, we can obtain the optimal initial posture with minimum sum of the sudden change in joint velocity, (1.148,0,0.815)m , 041 -194.8 042 -1410 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001806_1.2199857-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001806_1.2199857-Figure5-1.png",
        "caption": "Fig. 5 Physical interpretation of \u2020C3\u2021, \u2020C4\u2021",
        "texts": [
            " 6 by using nC1 and nC2, we obtain 0 nC2 nC2 \u2212 nC1 1 9 As shown in Fig. 4 b , both nC1 0 and nC2 0 are satisfied if the line of action passes through strictly inside of the contact segment between the objects 1 and 2. C3 Let vG be the velocity vector of objects at the ECOF of the system of two objects xG. From Eq. 7 , since vG is antiparallel to f1+ f2, the slip may not occur between the object 2 and the pusher if the direction of vG is included strictly inside of the friction cone between the object 2 and the pusher Fig. 5 a . 424 / Vol. 128, JUNE 2006 rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 08/16/2017 C4 Let nF1 and nF2 be the moment which the pusher exerts to the object 2 at each end of the contact segment. Rewriting Eq. 8 by using nF1 and nF2, we obtain 0 nF2 nF2 \u2212 nF1 1 10 As shown in Fig. 5 b , both nF1 0 and nF2 0 are satisfied if the line of action passes through strictly inside of the contact segment between the objects 2 and the pusher. 4.3 The Set of Pusher Velocity. We now propose the algorithms to obtain the set of the stable pusher\u2019s motion. First, we show the method for obtaining the region stable pusher\u2019s COR. In this method, by discretizing the COR space, we check whether the objects are stably manipulated or not for the given position of the COR. Algorithm 1\u2014The set of pusher COR"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002015_j.mechmachtheory.2004.03.003-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002015_j.mechmachtheory.2004.03.003-Figure4-1.png",
        "caption": "Fig. 4. Free-body diagram of the crank.",
        "texts": [
            " (16), the tangential speed component at the planet gear roller and ring gear roller at the contact point P2i3 can be determined as V * 2i3 \u00bc V * P32i u* t 2i3 u *t 2i3 \u00bc \u00bdx4R4 cos\u00f0h4 ha\u00de \u00fe x3R3i cos\u00f0h3i \u00fe ha\u00de r3 sin ha i * cos ha j * \u00f017\u00de The model of kinetostatic analysis considering friction of the roller drives is developed in this section. It is assumed that the gravity forces are relative small and can be neglected, and the centers of mass are located at the geometrics center of the components. The free-body diagram of the crank is as shown in Fig. 4, and a known input torque T * in is applied to the crank. Vectors R * 34 and R *0 34 point from O3, the planet gear center, to points P43 and P 0 43 (they are the contact points of the crank and planet gear), respectively. F * 14 is the vector of the force exerted by frame 1 on crank 4, additionally, there is a frictional torque t * 14. Similarly, F * 34 \u00f0F *0 34\u00de and t * 34 \u00f0 t *0 34\u00de are, respectively, the force and frictional torque exerted by the planet gear on the crank at the contact point P34 \u00f0P 0 34\u00de",
            " Frictional torques t * 34, t *0 34 and t * 14 can be expressed as t34 \u00bc l34F34Rb3D34 \u00f018\u00de t034 \u00bc l34F 0 34R 0 b3D 0 34 \u00f019\u00de t14 \u00bc l14F14Rb4D14 \u00f020\u00de where Rb3 \u00f0R0 b3\u00de and Rb4 are the radii of the roller bearings placed between the crank and planet gear and the frame, respectively, and l34 and l14 are the friction coefficients of the roller bearings. Furthermore, D34, D0 34 and D14 represent the direction indicators that can be expressed as: D34 \u00bc x3 x4 jx3 x4j, D 0 34 \u00bc x0 3 x4 x0 3 x4j j and D14 \u00bc x4 jx4j, respectively [23]. As shown in Fig. 4, the three scalar equations of motion that are applied to the crank body can be written as F34x \u00fe F 0 34x \u00fe F14x \u00bc m4a4x \u00f021\u00de F34y \u00fe F 0 34y \u00fe F14y \u00bc m4a4y \u00f022\u00de \u00f0R34xF34y R34yF34x\u00de \u00fe R0 34xF 0 34y R0 34yF 0 34x \u00fe t34 \u00fe t034 \u00fe t14 \u00fe Tin \u00bc I4a4 \u00f023\u00de where m4 is the mass of the crank, I4 is the moment of inertia of the crank about the center of mass, and a4x and a4y represent, respectively, the magnitudes of the X and Y components of the center of mass acceleration of the crank. Furthermore, R34x and R34y can be expressed as: R34x \u00bc R4 cos h4 Rb3 cos h34 and R34y \u00bc R4 sin h4 Rb3 sin h34, and h34 (h34 \u00bc tan 1 F34y=F34x), is measured counterclockwise from the X axis to the common normal at the contact point P34"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003144_e2008-00551-0-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003144_e2008-00551-0-Figure1-1.png",
        "caption": "Fig. 1. Model geometry.",
        "texts": [
            " This study is a continuation of earlier works by the author [8,10,13] and explores how the sequence of activated actuators affect on noise control of a aluminium L-jointed plates with piezoelectric actuators and sensors. The estimated parameter was the level of sound radiation from two L-jointed plates excited through a single piezoceramic element by voltage harmonically varied in time. The system considered in the study was built up of two perpendicularly, rectangular aluminium plates and was line jointed by angle-aluminium, (see fig. 1). The excited plate, with piezoceramic elements, was fixed along one edge. Actuators and sensors 20\u00d7 20\u00d7 1mm made from PIC-140 material were mounted symmetrically on the plate (see Fig. 1). The plate was actuated by single PIC \u2013 actuator (marked A1), while the remaining actuators (marked A2, A3, A4) were used to control plate vibrations. The piezoceramic sensors were marked S1, S2, S3, S4. Inner surfaces of piezoelectric actuators adhering to the plate were grounded and the potential on the upper electrode was applied. The parameters of the aluminium plates and piezoelectric PIC140 assumed for the numerical procedures were: a) aluminium: density = 2704 kgm\u22123, elasticity modulus = 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000603_2001-01-1007-Figure22-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000603_2001-01-1007-Figure22-1.png",
        "caption": "Fig. 22 Statistical prediction of the magnitude and position of the half order component of the gas pressure torque and its correlation with the corresponding harmonic component of the crankshaft\u2019s speed",
        "texts": [
            " In order to show how the statistical model of the half harmonic order of the gas pressure torque could be used to identify non-uniformities and detect the responsible cylinder the following case is considered. The engine runs at a constant speed of 1200 rpm with cylinder #4 almost disconnected (IMEP4 = 0.06\u00b10.02 MPa) while the IMEP of the other cylinders is equal to 0.84\u00b10.04 MPa. These data are close to the experimental results shown in Fig. 19. The calculations for this case are summarized in Tab. A3 in the Appendix and the results are presented in Fig. 20 to Fig. 22. Figure 20 presents the average values of the half order component of the gas pressure torque 5.0T , calculated from the measured cylinder pressures for 10 successive engine cycles. With dotted lines are indicated the limits of variation of the average torque predicted by the statistical model. As it may be seen the measured values are well included in the predicted domain. Figure 21 presents the phases of the vectors interpreting the half order component of the gas pressure torque and the dotted lines indicate the limits of variation predicted by the statistical model. Again, the measured values are fairly well included in the predicted domain. Figure 22 presents the mean value of the random vector interpreting the resultant torque of the half order harmonic component of the gas pressure torque, its phase and its ellipse of dispersion. Based on the fact that the corresponding speed vector lags the torque vector by about 90\u00b0 (see Fig. 4) the possible directions of the vector interpreting the half order component of the crankshaft\u2019s speed may be determined. Similar calculations may be performed, assuming that other cylinders are not contributing to the total engine torque"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003505_robot.2007.363143-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003505_robot.2007.363143-Figure7-1.png",
        "caption": "Fig. 7. The Zero Moment Point.",
        "texts": [
            " This constraint can be derived as an equality constraint by substituting (2) into (3) to express \u03b8\u0308 in terms of x\u0308, then replacing x\u0308 with the left hand side of (20) to yield: r1 \u00d7 f1 + r2 \u00d7 f2 = I [ \u03b8s \u03b8ss ] K\u22121 ( fw m +g ) (25) = [v1 v2] \u00b7 ( fw m +g ) where v1 and v2 are the two scalar components of the vector {I [ \u03b8s \u03b8ss ] K\u22121}, and the sum of the ground forces is fw = f1 + f2 (26) Rearranging (25) yields: f1 + f2 +mg = mx\u0308 (27) r\u03041 \u00d7 f1 + r\u03042 \u00d7 f2 + r\u03043 \u00d7mg = 0 (28) where r\u03041 = r1 + r\u03043 (29) r\u03042 = r2 + r\u03043 (30) r\u03043 = [\u2212v2 v1] (31) Equation (28), in comparison to (21), represents the moment equation of an equivalent system that has a zero moment of inertia, and a virtual point that we call ZMP (zero moment point) where the moments of all external forces applied on the system, including the gravity force, are zero. Note that the moments is, generally, not zero around the center of mass because of the angular acceleration of the rigid body along the path. Thus, satisfying a zero moment around the ZMP is a necessary condition on the ground forces so that the vehicle tracks the desired path. The ZMP is located at \u2212r\u03043 from the center of mass, as is shown in Figure 7. Note that r\u03043 reflects the body\u2019s inertial parameters as well as the path curvature. The forces acting upon the equivalent system, however, have not changed, and so (20) still holds. Our goal now is to find the set of admissible accelerations that are produced by the ground forces that satisfy the friction constraints and the equality constraint (28). The set of admissible accelerations would yield the desired dynamic stability margins. The set of admissible accelerations is a convex polygon in the plane of f1 and f2 since both are constrained by a set of linear inequality and equality constraints [5]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000249_elan.1140030605-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000249_elan.1140030605-Figure7-1.png",
        "caption": "FIGURE 7. Enzyme distribution in the enzyme layer when the enzyme concentration is given by Equation (4), for the following n values: (a) 1, (b) 2, (c) 4, (d) 6, (e) 10.",
        "texts": [
            ", [M,,] 2 KmM and [S] 2 KM5), Equation 2 is simplified and rewritten as follows: D M d2[Mred1 A 2 + k,,[E] = 0 (3) In our earlier paper [ 161, [El was considered to be a constant value throughout the EL. However, here we assume that [El is given by a function of x and is described as follows: I - X \" [El = [El, exp {(a) } (4 ) where [El, is the total enzyme concentration at the surface in the EL., and a is the parameter having the dimension in length. Plots of [EY[E],versusx/lwhena/l = 0.5, as shown in Fig. 7, demonstrate that the larger the index number n, the more abruptly the enzyme concentration increases a t x = I - a. I Solution Enzyme layer x= 0 X+ x = I Making the substitution of Equation 4 into Equation 3 leads to D, 9 + ka[E], exp { ( ~ r } I - x = 0 ( 5 ) Dimensionless numbers concerning [Mred] and x are defined as C = [hfred]/Km andX = ( I - x)/u, respectively, and u2 is the ratio of the enzyme reaction to the mediator diffusion, as defined by h d J M Therefore Equation 5 becomes 0.5 I 0 0 5 The total concentration of the mediator is assumed to be constant throughout the EL"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001695_peds.2003.1282961-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001695_peds.2003.1282961-Figure3-1.png",
        "caption": "Fig. 3. Itnplemrntation of the SVM unit",
        "texts": [
            " SVM Sigiial Gerierator Uiiit In SVM signal generator unit, three (two non-zero and one zero) voltage vectors are employed in each sampling period to synthesize a desired resultant space voltage vector V,, which could produce accurate control of the stator flux linkage, and the torque. F ig3 illustrates the implementation of the SVM strategy, where VQ - V7 are the space voltage vectors generated .by VSI, T, the sampling period, TO- Tz are the duration of each voltage vector in one sampling period, and y is the space position angle of the flux linkage increment vector dy,, which is the same as the angle of V,. Based on the vector diagram in Fig.3, the implementation of SVM could be expressed as the following equations: dvs= T,xV, = TlxV,+ T>xV~+ ToxVo T/ = IV,lxsin (60\"-y) / IV//xsin (120\") (7) (8) T2 = IV,lxsin ( y ) / IV2(xsin (120') (9) Any desired resultant voltage vector could be produced for accurate control of torque and tlux linkage to minimize the ripples, and meanwhile, the switching frequency is almost fixed by using the SVM unit as well. D. Workirig Mode of F l i i ~ Linkage Vector The essential relationship of different t lux linkage vectors for the SVM DTC drive system is illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000855_jra.1986.1087062-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000855_jra.1986.1087062-Figure4-1.png",
        "caption": "Fig. 4. Idealized model of a two-link robot.",
        "texts": [
            ", and aci all involve derivatives relative to the base frame. However, when the above equations are 184 IEEE JOURNAL OF ROBOTICS AND AUTOMATION, VOL. RA-2, NO. 4, DECEMBER 1986 evaluated, the vector operations can be carried out using the basic vectors of any convenient frame as shown earlier. As another example, for the evaluation of (41) we write Example (Equations of motion for a two-link robot arm): As a simple example we will consider the dynamics of the two-joint linkage with the coordinate frames shown in Fig. 4. The parameters of the coordinate frame transformations are defined as follows: Pi is the angle of rotation about the zi-] axis and yi is the angle of rotation about the xi-axis. The joint variable 8i is the rotation about the zi-axis. For a change of coordinate frames involving a rotation about zi-l through an angle p i , which is followed by a rotation about xi through an angle yi and a joint rotation about zi through an angle 8i, we have TABLE I ORIENTATION ANGLES FOR THE COORDINATE FRAME TRANSFORMATIONS Transformation PI Yi e, 0 to 1 0 0 1 to 2 0 - 90 02 81 cos Bi cos Pi- sin Bi cos yi sin Pi cos 8i sin Pi+ sin Oi cos yi cos Pi sin 8i sin yi sin yi sin Pi -sin yi cos Pi cos yi =I- sin 8i cos pi- cos 8i cos yi sin pi - sin 8; sin Pi+ cos 0; cos y; cos Pi cos Bi sin yi "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003554_978-3-540-30301-5_4-Figure3.22-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003554_978-3-540-30301-5_4-Figure3.22-1.png",
        "caption": "Fig. 3.22 The Nabtesco RV drive",
        "texts": [],
        "surrounding_texts": [
            "The purpose of a transmission or drive mechanism is to transfer mechanical power from a source to a load. The design and selection of a robot drive mechanism requires consideration of motion, load, and power requirements and the placement of the actuator with respect to the joint. The primary considerations in transmission design are stiffness, efficiency, and cost. Backlash and windup impact drive stiffness especially in robot applications where motion is constantly reversing and loading is highly variable. High transmission stiffness and low or no backlash result in increased friction losses. Most robot transmission elements have good efficiencies when they are operating at or near their rated power levels but not necessarily when lightly loaded. Larger than necessary drives add weight, inertia and friction loss to the system. Underdesigned drives have lower stiffness, can wear rapidly in continuous or in high duty cycle operation or fail due to accidental overloads. Joint actuation in robots is generally performed by drive mechanisms which interface the actuator (mechanical work source) to the robot links through the joints in an energy-efficient manner. A variety of drive mechanisms are incorporated in practical robots. The transmission ratio of the drive mechanism sets the torque, speed, and inertia relationship of the actuator to the link. Proper placement, sizing, and design of the drive mechanisms set the stiffness, mass, and overall operational performance of the robot. Most modern robots incorporate efficient, overload damage resistant, back-driveable drives. Direct Drives The direct drive is kinematically the simplest drive mechanism. In the case of pneumatic or hydraulic actuated robots, the actuator is directly connected between the links. Electric direct-drive robots employ hightorque, low-speed motors directly interfaced to the links. The complete elimination of free play and smooth torque transmission are features of a direct drive. However, there is often a poor dynamic (inertia ratio) match of the actuator to the link requiring a larger, less energy efficient, actuator. Part A 3 .7 Band Drives A variant of direct drive is band drive. A thin alloy steel or titanium band is fixed between the actuator shaft and the driven link to produce limited rotary or linear motion. Drive ratios in the order of up to 10 : 1 (10 actuator revolutions for 1 revolution of the joint) can be obtained. Actuator mass is also moved away from the joint \u2013 usually toward the base, to reduce robot inertia and gravity loading. It is a smoother and generally stiffer drive than a cable or belt drive. Belt Drives Synchronous (toothed) belts are often employed in drive mechanisms of smaller robots and some axes of larger robots. These function much the same as band drives, but have the ability to drive continuously. Multiple stages (two or three) of belts are occasionally used to produce large drive ratios (up to 100 : 1). Tension is controlled with idlers or center adjustment. The elasticity and mass of long belts can cause drive instability and thus increased robot settling time. Gear Drives Spur or helical gear drives provide reliable, sealed, low-maintenance power transmission in robots. They are used in robot wrists where multiple axes intersect and compact drive arrangements are required. Largediameter, turntable, gears are used in the base joints of larger robots to handle high torques with high stiffness. Gears are often used in stages and often with long drive shafts, enabling large physical separation between ac- tuator and driven joint. For example, the actuator and one stage of reduction may be located near the elbow driving another stage of gearing or differential in a wrist through a long hollow drive shaft (Fig. 3.1). Planetary gear drives are often integrated into compact gearmotors (Fig. 3.20). Minimizing backlash (free play) in a joint gear drive requires careful design, high-precision and rigid support to produce a drive mechanism which does not sacrifice stiffness, efficiency and accuracy for low backlash. Backlash in robots is controlled by a number of methods including selective assembly, gear center adjustment, and proprietary anti-backlash designs. Worm Gear Drives Worm gear drives are occasionally used in low-speed robot manipulator applications. They feature rightangle and offset drive capability, high ratios, simplicity, good stiffness and load capacity. They also have poor efficiency which makes them non-back-driveable at high ratios. This causes the joints to hold their position when unpowered but also makes them prone to damage by attempts to manually reposition the robot. Part A 3 .7 Proprietary Drives Proprietary drives are widely used in standard industrial manipulators. The harmonic drive and the rotary vector (RV) drive are two examples of compact, low-backlash, high-torque-capability drives using special gears, cams, and bearings (see Figs. 3.21 and 3.22). Harmonic drives are frequently used in very small to medium-sized robots. These drives have low backlash, but the flexspline allows elastic windup and low stiffness during small reversing movements. RV drives are usually used in larger robots, especially those subject to overloads and shock loading. Linear Drives Direct-drive linear actuators incorporate a linear motor with a linkage to a linear axis. This linkage is often merely a rigid or flexure connection between the actuator forcer and the robot link. Alternatively, a packaged linear motor with its own guideways is mechanically connected directly to a linear axis. Direct linear electromagnetic drives feature zero backlash, high stiffness, high speeds, and excellent performance but are heavy, have poor energy efficiency, and cost more than other types of linear drives. Ball Screws Ball\u2013screw-based linear drives efficiently and smoothly convert rotary actuator motion into linear motion. Typically, a recirculating ball nut mates with a ground and hardened alloy steel screw to convert rotary motion into linear motion. Ball screws can be easily integrated into linear axes. Compact actuator/drive packages are available, as well as components for custom integration. Stiffness is good for short and medium travel, however it is lower for long motions because the screw can only be supported at its ends. Low or zero backlash can be obtained with precision-ground screws. Speeds are limited by screw dynamic stability so rotating nuts enable higher speeds. Low-cost robots may employ plain screw drives featuring thermoplastic nuts on smooth rolled thread screws. Rack-and-Pinion Drives These traditional components are useful for long motions where the guideways are straight or even curved. Stiffness is determined by the gear/rack interface and independent of length of travel. Backlash can be difficult to control as rack-to-pinion center tolerances must be held over the entire length of travel. Dual pinion drives are sometimes employed to deal with backlash by providing active preload. Forces are generally lower than with screws due to lower ratios. Small-diameter (low teeth count) pinions have poor contact ratios, resulting in vibration. Sliding involute tooth contact requires lubrication to minimize wear. These catalog stock drive components are often used on large gantry robots and track-mounted manipulators (Fig. 3.23). Other Drive Components Splined shafts, kinematic linkages (four-bar, slidercrank mechanisms, etc.) chains, cables, flex couplings, clutches, brakes, and limit stops are some examples of other mechanical components used in robot drive mechanisms (Fig. 3.8). The Yaskawa RobotWorld assembly and process automation robots are magnetically suspended, translate on air a planar (two-DOF) bearing, and are powered by a direct electromagnetic drive planar motor with no internal moving parts (Fig. 3.12)."
        ]
    },
    {
        "image_filename": "designv11_28_0003675_s12239-008-0038-1-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003675_s12239-008-0038-1-Figure1-1.png",
        "caption": "Figure 1. Coordinate transformation from the coordinate of the tri-axial force sensor to the housing coordinate.",
        "texts": [
            " The overall experimental setup, including triggering, motion control of the linear actuator, recording of the experimental data and oscilloscope displays were carried out by a master program of Labview program (Lee, 2007). In order to calculate the internal friction coefficient under any CV joint conditions, one needs to find a universal equation to cover all articulation angles and rotational phase angles. This is accomplished by introducing a coordinate transformation matrix based on Euler angles representing articulation angle , and rotational phase angle . The components and directions of the three force components measured with the tri-axial force sensor installed inside the CV joint are depicted in Figure 1. Force component Fx represents the normal force P and is directly related to the applied torque. Force components Fy and Fz represent the axial and vertical friction forces respectively, which are the source of the total combined friction force Q. Using the defined coordinates of the tri-axial forces, one can obtain the individual Euler transformation matrix as illustrated in Figure 1. By multiplying each individual transformation matrix in sequence, a global transformation matrix that relates the measured internal forces to the global forces in accordance with the housing coordinate can be obtained. Thus, one can readily get the following equation which calculates the net friction coefficient along the housing groove at any rotational and articulation position in the CV joints. (1) 3.1. Slip to Roll Ratio Characterization efforts to investigate the friction mechanisms in a CV joint were endeavored"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002381_msf.505-507.631-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002381_msf.505-507.631-Figure3-1.png",
        "caption": "Fig. 3 sequence of constructing VR CNC",
        "texts": [
            " Both movable and fixed components can be built in CAD software that can output either STL (stereo lithographic) or VRML (Virtual Reality Modeling Language) format in which the adopted VR software EON studio is able to import. The CNC components will then be organized into nodes in EON studio such as model mesh, material, motion, light source, etc. These nodes will be displayed in \u201cComponent-Nodes\u201d window and the behavioral relationship among the components can be assigned in the \u201cRoute\u201d window. The sequence in constructing the VR CNC is shown in Figure 3. Motion control of a real CNC was fulfilled through control of the servomotor, driving system and feedback system. Similarly, the virtual CNC machine table could be actuated according to the NC codes such as G00 and G01 for linear motion, G02 and G03 for circular motion. Virtual CNC controller. The VR CNC controller is composed of Human Machine Interface (HMI), NC codes parser, and interpolation algorithm. Visual Basic 6.0 was used in developing the VR CNC controller. The VR controller HMI interface, as shown in Figure 4, was developed underlying Microsoft Visual Basic 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002313_dia.2005.7.927-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002313_dia.2005.7.927-Figure1-1.png",
        "caption": "FIG. 1. Schematic diagram of sensing element based on a coiled Pt-Ir wire: 1, electrically insulating sealant; 2, Teflon-covered platinum wire; 3, outer membrane; 4, cotton fiber with enzyme gel; 5, stripped platinum wire; 6, enzyme layer.",
        "texts": [
            "21 The coil-type glucose biosensors were prepared by winding the top 10 mm of a 90\u2013100- mm-long Teflon-covered platinum-iridium wire (diameter 0.125 mm, Pt:Ir 9:1) along a 30- gauge needle to form a coil-like cylinder. Before the wire was coiled, the Teflon coating was stripped from the top 10 mm and polished using a swab with polish paste. The resulting cylinder unit had an outer diameter of 0.55 mm, an inner diameter of 0.3 mm, a length of approximately 1 mm, and an approximately 0.07- mm3 inner chamber for extra enzyme storage (Fig. 1). This chamber was filled with cotton and sonicated for cleaning. Two microliters of aqueous solution containing 10\u201320 mg/mL of glucose oxidase, 30\u201340 mg/mL of bovine serum albumin, and 0.6% (vol/vol) glutaraldehyde was pipetted on the platinum-iridium coil and left to dry for 1 h at 24 1\u00b0C. The result- ing immobilized enzyme layer was fairly uniform and without visible cracks as observed under a 4 dissection microscope. A 2.5% (wt/vol) polymer tetrahydrofuran solution, including 40% epoxy adhesive and 60% PU, was directly formed upon the enzyme layer using multiple dip-coatings and then dried at room temperature for 30 min"
        ],
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    },
    {
        "image_filename": "designv11_28_0001963_0954407041581101-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001963_0954407041581101-Figure1-1.png",
        "caption": "Fig. 1 HPS/EPS steering system lay-out",
        "texts": [
            " However, even in less favour-Fs f (Cb)=power steering force ISW moment of inertia of the steering wheel about able conditions, such as parking, modern vehicles require very little effort to turn the steering wheel. The currentrotation axis Kt torsion bar/torque sensor torsional stiffness state of the art records three solutions adopted by automotive car makers for vehicle steering: (a) steer-by-M rack and front wheels reduced inertia r pinion radius wire; (b) hydraulic power steer; and (c) electric power steer. The last two have the same mechanical lay-outx dSW\u03a9r=rack displacement (depicted in Fig. 1) but differ by the elements of the power assistance unit.dSW steering wheel rotation angle t dWheel /dSW=steering ratio q Cb /Kt=torsion bar/torque sensor torsion angle 1.1 Steer-by-wire system The most advanced (and still not industrialized) systemThe MS was received on 9 April 2003 and was accepted after revision for publication on 7 May 2004. is the steer-by-wire. No mechanical links are present. * Corresponding author: Dipartimento di Ingegneria Meccanica, Tor The required steering-wheel position is translated intoVergata University, Via del Politecnico 1, 00133 Rome, Italy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000515_robot.2001.933195-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000515_robot.2001.933195-Figure5-1.png",
        "caption": "Figure 5: Roll Angle Criterion",
        "texts": [],
        "surrounding_texts": [
            "' h e microrover Micro5 observes and senses the environnient by on-board stereo cameras. An elevation map is built by coordinate traiisforniatioii based on range image data. An elevation map consists of many square grids. Each grid G(z, y) has the height information z at that point (z,y). z = h(G) = h ( z , y) (1) An elevation map shows a terrain da ta in front of a rover. The conventional elevation map has based on the implicit assumption that a rover can be described as a point. Here a new map concept[l5] is used to include the effect of the size of the rover as shown in Fig.3. A rover occupies some grids on an elevation map, and so a virtual map considering the position information and the attitude of a rover is introduced. The authors call this map an Extended Elevation Map (EEM). The information about the traversability is added to each grid on EEM. By using EEM, path planning can be conducted in such a way as if the rover were a point while the size of the rover is automatically taken into account. 371 2 3 Traversability 3.2 Judgment of Traversable Area 3.1 Rover Geometry The performance of a rover inoviiig in an unstiuctured environment depends upon the geometry, such as, susperision, size, the number of wheels etc. \u2018I\u2019o consider the size of a. planetary rover, a model is introduced as shown in Fig.4. Rover geometry is expressed by three parameters : roll angle, pitch angle, and height. r, l h e maximum roll angle umnZ is equivalent to the capability to go over obstacles. The pitch angle ,Bvaaz iiieaiis the ma.ximurn negotiable angle over which a rover ca.n move. The height hmin means the inininium distance between the body of a rover a.nd the ground to avoid hitting the ground. Though this model shows the case of a five-wheel rover, it is easy to adapt such a inodeling to any other rover with different geometry. (a) rover geometry {A *-. --. \u2018lhversable area means the area where a rover can stay stably. Now suppose that the position of the four wheels of Micro5 are FE, FL> BR, a.nd BL respectively. And then the position of the center of gra.vity and the orientation(azi1nuth angle) of a. rover on EEM i s t o be expressed by (x, y, 6\u2019) respectively. Traversability probability is determined by the following three coliditions : roll angle criterion, pitch angle criterion, and height criterion. 3.3 Roll Angle Criterion Suppose that the height of a right wheel and the height of a left wheel are expressed by normal distributions N ( ~ R , CR\u2019), N ( ~ L , u ~ ) respectively. Here h denotes the average value of height and c denotes the variance for sensor noise respectively. Then the height difference between the right and the left wheels is given by A h = N ( h ~ - h ~ , u ~ 2 + u ~ 2 ) . The stability coiidition for a rover roll angle i s defined at5 Probability distribution which satisfies the equation (2) means the probability Pr, for roll angle criterion as shown in F\u2019ig.5. Yr,F and Pr,B indicate the probabilities for front wheels and rear wheels respectively. 3.4 Pitch Angle Criterion Suppose that the height of a front wheel and the height of a rear wheel are expressed by normal distributions N ( l z ~ , CF\u2019), N ( ~ B , ag\u2019) respectively. Then the difference between the height of a front wheel and a rear wheel is given by N ( ~ F - h ~ , UF\u2019 + u ~ \u2019 ) . The stability condition for a rover pitch angle is defined as Probability distribution which satisfies equation (3) means the probability Prp for pitch angle criterion. Here PrpR and P r p ~ indicate the probabilities for right wheels and left wheels respectively. 371 3 3.5 Height Criterion Suppose that Gi(i = 1 ' ' N ) denotes the grid which the rover occupies and Gi(zi,yi) denotes its coordinate. Prhi denotes the probability that G'i is a traversable area. The height hi(za,yi) of the plane is expressed by normal distribution N ( h p , U,\"). So the height h*(z i , yi) at the grid Gi(zi , yi) is expressed by Therefore the condition for the height criterion is, hi - h*(Xi,Yi) > 0 (5) Probability distribution which satisfies equation (5) means the probability Prhi for height criterion. The probability P T ~ ( z , y, 8) for height criterion is expressed by N prh(x , 'Y) 0) = Prhj (6 1 j=1 3.6 Traversability Probability Traversability probability is calculated by the following equation. 4 Path Planning Extended grids on EEM are searched in the pro- posed path planning algorithm. Here suppose Chat a rover can move in eight kinds of directions ( 0 = . j ( j = 1 , 2 , . . . ,8). In the case of a. 2-1/2 dimensional environment like the surface of Mars, moving distance and time should be considered for a microrover to make a pat,li, since the slope of the terrain can dramatically affect the performance. A cost function is required for estimating the time and power of the motion over a 2-1/2 dimensional terrain. So the path from a start poiiit to a goal is determined in such a way that the following cost fuiiction be minimized while traversability is satisfied. The cost function E consists of two energy functions, motion energy Eho,. for horizontal movement and potential energy Eve,. for vertical movement. where Ehor = Ever = 5 Simulation Results In order to confirm the validity of the proposed method, the proposed a path-planning algorithm in a terrain environment is simulated. Table 2 shows the parameters used for this simulation. Figure 7 show the probability distributions for traversability. Figure 8 shows tha t a. reasonable path can be planned by the proposed algorithm. 371 4 6 Conclusion A new path planning for a planetary microrover has been presented in this paper. The validity of the proposecl method is confirmed by computer simulations. This paper also have presented the newly developed microrover. Experiments of Micro5 in Mars-like terrain are under going. References [ 11 G . Giralt , \u201d Remote Intervent,ion Robot Autonomy and Real World Application Cases,\u201d Proc. of IEEE Int. Conf. on R&A, pp.541-547, 1993. [2] R.Chatila, R.Alami, S.Lacroix, J.Perret, C.Proust, \u201dPlanet Exploration by Robots : From Mission Planning to Autonomous Navigation,\u201d Proc. of ICAR\u201993, pp.91-96, 1993. [3] J.L.Loch, R.Desai, \u201cMoose on the Loose: Toward Extended Mission Autonomy for Robotic Exploration of Planetary Surfaces,\u201d Proc. of ICAR\u201993, pp.97-101, 1993. [4] R.Simmons, E.Krotkov, \u201dAutonomous Planetary Exploration: From Ambler to APEX,\u201d Proc. of IC.4R\u201993, pp.429-434, 1993. [5] E.Gat, R.Desai, R.Ivlev, J.Loch, and D.P.Miller, \u201dBehavior Control for Robotic Exploration of Planetary Surfaces,\u201d IEEE Trans. on R&A, Vol.10, No.4, pp.490-503, 1994. [6] http;//mpfwww.jpl.nasa.gov/ [7] C. R. Weisbin, D. Lavery, G. Rodriguez, \u201dRobotics Technology for Planetary Missions Into the 21st Century,\u201d Proc. of i-SAIRAS\u201997, pp.5-IO, 1997. [8] D.Gaw, A.Meyste1, \u201d Minimum-Time Navigation of An Unmanned Mobile Robot in A 2-1/2D World With Obstacles\u201d, IEEE Int. Conf. on R&A, pp.16701677, 1986. [9] Z.Shiller, H.H.Lu, \u201dRobust computation of path constrained time optimal motions,\u201d Proc. of IEEE Int. Conf. on R&A, pp.144-149, 1990. [lo] T.T.Lee, C.L.Shih, \u201cRobust Path Planning in Unknown Environments via Local Distance Funct,ion,\u201d Proc. of i-SAIRAS\u2019SO, pp.251-254, 1990. [Ill D.P.Miller, M.G.Slack, R.J.Firby, \u201dPath planning and execution monitoring for a planetary rover,\u201d Proc. of 1EEE Int. Conf. on R&A, pp.20-25, 1990. [la] R.Morlanss, A.Liegeois, \u201c A D.T.M based Path Planning Method for Planetary Rovers,:\u2019 issions, Technologies et Conception des Vehicles Mobiles Planeraires, pp.499-507, 1992. [13] L.Matthies, E.Gat, R.Harrison, B.Wilcox, R.Volpe, T.Litwin, \u201dMars Microrover Navigation : Performance Evaluation and Enhancement,\u201d Proc. of IROS\u201995, pp.433-440, 1995. [14] M.Hebert, T.Kanade, I.Kweon, \u201d3-D Vision Techniques for Autonomous Vehicles\u201d, ICMU-RI-TR-8812, CMU 1988. [15] LNakatani, T.Kubota, T.Yoshimitsu, \u201dPath Planning for Planetary Rover Using Extended Elevation Map\u201d, Proc. of i-SAIRAS\u201994, pp.87-90, 1994. [16] Y.Kuroda, K.Kondo, K.Nakamura, Y.Kunii, T.Kubota, \u201dLow Power Mobility System for Micro Planetary Rover \u201dMicr05\u201d ,\u201d Proc. of i-SAIRAS\u201999, pp.77-82, 1999. 371 5"
        ]
    },
    {
        "image_filename": "designv11_28_0003001_icarcv.2006.345243-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003001_icarcv.2006.345243-Figure2-1.png",
        "caption": "Fig. 2. Definition of the parameters for parallel parking right backward.",
        "texts": [
            " Two major constraints are: \u2022 Limitations to the steering angle given by the mechanics of the tractor: \u2212\u03c6max \u2264 \u03c6 \u2264 \u03c6max \u2022 Jack-knifing limitations to the angle between tractor and trailer: \u2212jkmax \u2264 \u03b82 \u2212 \u03b81 \u2264 jkmax Further constraints which consider practical aspects of parking a real vehicle in real traffic situations will be considered in a later section. Without loss of generality the description of the parallel parking maneuver is given for parking right backward. Typically the depth of the parking box is at about 1 1 2 of the breadth of the vehicle. Reducing the vehicle to a bicycle model we ask for the minimum longitudinal distance sx for a given lateral depth sy (see figure 2). However, there are further questions which are important when thinking about parallel parking in the scope of the development of a respective parking assistant. They will be discussed in section IV. The principle question of this section is that of the existence of a minimum parking distance and of a strategy to get it. It can be seen immediately that by allowing \u2022 cusps (driving back and forth), \u2022 turns (driving backward entire circles) any distance sx is achievable. Reasonable and efficient maneuvers for parallel parking therefore have to be restricted: \u2022 The unique sense of driving is backward into the parking box. \u2022 The angular maximum deviation of tractor and trailer from their initial and final direction must not exceed 90\u25e6. With this restrictions and for a given sy > 0 it can be concluded that also sx > 0. We can further conclude that between the initial configuration and the final configuration there is an intermediate configuration where truck and trailer are in a straight line again (see figure 2). We call this the inflecting configuration, which has a relative angle \u0393 with respect to the initial or final configuration. The angle \u0393 is also called gain. During the exercise of particular parallel parking maneuver the configuration forming a straight line can reappear several times. In the case of repeated inflecting configurations we only consider the biggest of the occurring angles as \u0393. By a sequence of refinement steps the minimum parking maneuver is constructed. Given some reference point of the vehicle (e"
        ],
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    },
    {
        "image_filename": "designv11_28_0002671_tsmcb.2006.870636-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002671_tsmcb.2006.870636-Figure10-1.png",
        "caption": "Fig. 10. Force distribution of the agent that is about to roll over (a) CCW and (b) CW.",
        "texts": [
            " This is the main different feature between our and Shiller\u2019s derivations. The projections of the   xbF(k \u2212 \u2206k2) ybF(k \u2212 \u2206k2) zbF(k \u2212 \u2206k2) 1   =   1 0 0 \u2212 \u2206k2\u2211 n=1 v(k \u2212 n) \u00b7 Ts \u00b7 cos (\u03b83DM\u2212Pitch(k \u2212 n)) 0 1 0 0 0 0 1 \u2206k2\u2211 n=1 v(k \u2212 n) \u00b7 Ts \u00b7 sin (\u03b83DM\u2212Pitch(k \u2212 n)) 0 0 0 1     x\u2032bF(k \u2212 \u2206k2) y\u2032bF(k \u2212 \u2206k2) z\u2032bF(k \u2212 \u2206k2) 1   (24) external forces on vectors +Xb, +Yb, and +Zb are then obtained by applying the dot products to both sides of (30) as follows: fXb =mgkXb +ma (31) fYb =mgkYb +mv\u03c9 (32) N =mgkZb . (33) The force distribution of the agent is depicted in Fig. 10(a) and (b) when the agent is about to roll over CCW and CW, respectively. In the case of rolling over CCW, the moment on the agent created by the total normal force N and the friction force fYb , which are applied only to the left track, should satisfy the constraint NWb/2 \u2265 \u2212fYb h in order to prevent the agent from rolling over. Here,Wb and h are the width and the height of the center of mass of the agent, respectively. In the same way, the moment on the agent should satisfy the constraint NWb/2 \u2265 fYb h in order to prevent the agent from rolling over CW"
        ],
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    },
    {
        "image_filename": "designv11_28_0003366_icma.2007.4303842-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003366_icma.2007.4303842-Figure1-1.png",
        "caption": "Fig. 1 Sketch of the models",
        "texts": [
            " A set of parameter combination has been chosen and tested on different slopes. Results showed that the model with this set of parameters has relatively large basin of attraction and can endure larger disturbance than ever discovered. Based on the results, we expand the straight leg model to kneed leg model, and discussed the effects of foot radius on the basin of attraction. II. MODELLING 1-4244-0828-8/07/$20.00 \u00a9 2007 IEEE. 1908 Consider a planar straight leg model on a floor with a small downhill angle \u03b3 , as shown in Fig. 1 (left). The model consists of a pair of rigid legs with round feet, interconnected through a frictionless hinge. We assume that there is no slip between the foot of stance leg and the rigid floor. The impact between the foot of swing leg and floor is modeled as fully inelastic, an instantaneous, which means that no slip and no bounce occur, and an exchange between the stance and the swing leg at the impact time. Due to the oversimplification of the kneeless model, a foot-scuffing will occur at mid stance and will be neglected in simulation",
            " Each foot is a part of a circle and has a radius of r . The global parameters include the gravity acceleration g and the slope angle \u03b3 . The inertia coordinate is fixed on the slope and the x -axis is parallel to the incline, thus the gravity has components on both directions of the coordinates. To show the detail, this part is zoomed out and rotated an angle of \u03b3 . This model has two degrees of freedom and the variables are set to be 1\u03b8 and 2\u03b8 . The model with knees has more parameters than the straight leg model, as shown in Fig. 1 (right). Subscript \u201ct\u201d, \u201cs\u201d and \u201cL\u201d indicate \u201cthigh\u201d, \u201cshank\u201d and the whole \u201cleg\u201d, respectively. Thus, the whole leg has a mass of Lm , a length of Ll , and a moment of inertia of LJ . The thigh has a mass of tm , a length of tl , and a moment of inertia of tJ . The parameters of shank can be computed by the parameters of the whole leg and the thigh. The knee of the stance leg is always locked. The knee of the swing leg becomes free when this leg just becomes swing leg from stance leg. At this time the model has three degrees of freedom"
        ],
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    },
    {
        "image_filename": "designv11_28_0000963_0142331203tm0099oa-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000963_0142331203tm0099oa-Figure1-1.png",
        "caption": "Figure 1 System with two-stage gearbox",
        "texts": [
            " According to Chen and Patton (1999), model-based fault diagnosis can be de ned as the determination of faults in a system from the comparison of system measurements available with a priori information represented by the system\u2019s mathematical model, through generation of residual quantities and their analysis. A residual is at UCSF LIBRARY & CKM on April 9, 2015tim.sagepub.comDownloaded from a fault indicator or an accentual signal, which re ects the faulty situation of the monitored system. All design factors are speci ed in design drawings. The design factors connected to gear dimensions are transformed into dynamic model parameters, as given, e.g., in Figure 1 for a two-stage gearing system with electric motor and driven machine. The system consists of model parameters such as: rotor inertia, Is; gear inertia of rst stage, I1p, I2p; gear inertia of second stage, I3p, I4p; driven machine inertia, Im; gearing stiffness kz1, kz2 and shaft stiffness k1, k2, k3; and damping coefcient of a exible couple, C1. The manifestation of gear dimensions (model parameters) in diagnostic signals is vibration components coming from the natural vibration of a gearbox system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002167_1-4020-4611-1_8-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002167_1-4020-4611-1_8-Figure6-1.png",
        "caption": "Figure 6. Optical fibre biosensor setup. (a) Optical fibre bundle; (b) thermostated reaction vessel; (c) reaction medium; (d) sensing layer; (e) stirring bar; (f) septum and needle guide for sample injection; (g) PVC jacket; (h) screw-cap for securing the sensing layer.",
        "texts": [],
        "surrounding_texts": [
            "Except the physical entrapment of horseradish peroxidase in a polyacrylamide gel used by Freeman and Seitz 23 , immobilization of the Chemiluminescence-based Sensors 166 luminescence enzymes was mainly performed via a covalent coupling on a synthetic membrane. Commercially available membranes, supplied in a preactivated form, were used by several authors: Immunodyne from Pall, Immobilon-AV from Millipore or UltraBind from Gelman Sciences."
        ]
    },
    {
        "image_filename": "designv11_28_0003483_acc.2008.4586679-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003483_acc.2008.4586679-Figure5-1.png",
        "caption": "Fig. 5. Extension of Dubins shortest path",
        "texts": [
            " Theorem 4: For a given initial configuration Ci = (0, 0, \u03b1), and a final configuration Cf = (d, 0, \u03b2), it is possible to construct a Dubins path of length L(\u03b2) > L\u2217(\u03b2) if d \u2265 d\u2217 = 2(1 + \u221a 6). Proof: For d \u2265 d\u2217, p\u039b \u2265 4. Now let \u03b4L = mod (L(\u03b2) \u2212 L(\u03b2)\u2217, 2\u03c0). Extending the path length by 2\u03c0m,m \u2208 N, is trivial (e.g. make m loops around a point on the original path). So let us assume that \u03b4L < 2\u03c0. Now first consider the case when 0 < \u03b4L \u2264 2\u03c0 \u2212 4. For this case the suggested path modification is shown in Fig. 5 at the left. We modify the linear portion of the original path (segment p). To extend the path length, we can make a left turn of length v followed by a right turn of length 2v and finally a left turn of length v. Let the distance between the centers of the circles C1, C2 be d12. Then the length of curved portion is 4v, with v = arcsin(d12/4). Hence the increase in path length is given by f(d12) = 4 arcsin(d12/4) \u2212 d12. f(\u00b7) achieves its maximum value fmax = 2\u03c0\u22124 at d12 = 4 and is monotonically increasing in the interval d12 \u2208 [0, 4). Hence for \u03b4L \u2264 fmax this maneuver suffices. For the case when \u03b4L \u2208 (fmax, 2\u03c0), the maneuver shown in Fig. 5 at the right can be used to achieve the required path length. It consists of a left turn of length \u03c0/2, followed by a straight line of length d14, followed by a right turn of length \u03c0 followed by a straight line of length d24 = d14 followed by a left turn of length \u03c0/2. Hence to achieve the required increase in path length \u03b4L, d14 = d24 = (\u03b4L \u2212 (2\u03c0 \u2212 4))/2. Remark 1: Note that d\u2217 is not the tightest possible lower bound but one where extending the original path is fairly straightforward. We now propose a decentralized algorithm (shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003554_978-3-540-30301-5_4-Figure3.1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003554_978-3-540-30301-5_4-Figure3.1-1.png",
        "caption": "Fig. 3.1 The PUMA 560 robot",
        "texts": [
            " The physical size of this envelope and the loads on the robot within this envelope are of primary consideration in the design of the mechanical structure of a robot. Robot work envelope layouts must include considerations of regions of limited accessibility where the mechanical structure may experience movement limitations. These constraints arise from limited joint travel range, link lengths, the angles between axes, or a combination of these. Revolute joint manipulators generally work better in the middle of their work envelopes than at extremes (Fig. 3.1). Manipulator link lengths and joint travel should be chosen to leave margins for variable sensor-guided controlled path motions and for tool or end-effector changes, as offsets and length differences will often alter the work envelope. Load capacity, a primary robot specification, is closely coupled with acceleration and speed. For assembly robots, mechanism acceleration and stiffness (structure and drive stiffness) are often more important design parameters than peak velocity or maximum load capacity, as minimizing small pick-and-place motion cycle time, while maintaining placement precision, is generally a top priority",
            " Because power is force times velocity, we obtain the fundamental relationship that the ratio of input to output forces is the reciprocal of the ratio of input to output speeds. Another way of saying this is that, in the ideal machine, the mechanical advantage of a machine is the inverse of its speed ratio. The kinematic skeleton of a robot is modeled as a series of links connected by either hinged or sliding joints forming a serial chain. This skeleton has two basic forms, that of a single serial chain called a serial robot (Fig. 3.1) and as a set of serial chains supporting a single end-effector, called a parallel robot, such as the platform shown in Fig. 3.2. Robots can be configured to work in parallel such as the individual legs of walking machines (Figs. 3.3 and 3.4) [3.3], as Part A 3 .3 Platform Base Fig. 3.2 A parallel robot can have as many as six serial chains that connect a platform to the base frame Fig. 3.3 A photograph of the adaptive suspension vehicle (ASV) walking machine Fig. 3.4 The adaptive suspension vehicle walking machine well as the fingers of mechanical hands (Figs",
            " They are used in robot wrists where multiple axes intersect and compact drive arrangements are required. Largediameter, turntable, gears are used in the base joints of larger robots to handle high torques with high stiffness. Gears are often used in stages and often with long drive shafts, enabling large physical separation between ac- tuator and driven joint. For example, the actuator and one stage of reduction may be located near the elbow driving another stage of gearing or differential in a wrist through a long hollow drive shaft (Fig. 3.1). Planetary gear drives are often integrated into compact gearmotors (Fig. 3.20). Minimizing backlash (free play) in a joint gear drive requires careful design, high-precision and rigid support to produce a drive mechanism which does not sacrifice stiffness, efficiency and accuracy for low backlash. Backlash in robots is controlled by a number of methods including selective assembly, gear center adjustment, and proprietary anti-backlash designs. Worm Gear Drives Worm gear drives are occasionally used in low-speed robot manipulator applications"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003103_s1560354708040084-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003103_s1560354708040084-Figure5-1.png",
        "caption": "Fig. 5. Surface of the region Fz(0.17, 0.2, \u03c91, C1, C2) > 0. Note that the units are not isotropic. The unilateral condition is valid inside the dark region. The minimal region where the unilateral contact is valid is inside the shown elliptic region. This region corresponds to |C1| < 0.4556, |C2| < 0.0414 and |\u03c91| < 0.8634.",
        "texts": [
            " UNILATERAL CONTACT CONDITIONS In this paragraph the unilateral contact condition between the disk and the plane will be investigated in more details in order to determine the limits for values of integration constants C1 and C2. Now, if the expressions for angular velocities (8), and (10) are substituted into the expression for vertical reaction force (5) one obtains the unilateral contact expressed in the form Fz(h, \u03b1, \u03c91, C1, C2). As can be shown for the fixed values of h and \u03b1 the boundary of this region is represented by a one-sheeted hyperboloid surface in (\u03c91, C1, C2) space. The example is shown in Fig. 5. In this space the cross-sections of the boundary are for constant C2 an ellipses while for constant C1 or \u03c91 they are hyperboles. In the latter case, for \u03c92 1 = [ 3 + 16h2 + 12h\u03b1(2 \u2212 h\u03b1) ] /(15 + 16h2)(h + \u03b1) hyperbolas degenerate to the pair of intersection lines. On the basis of these lines one may obtain the coordinate system which transforms the hyperboloid to the canonical form and then determines the minimal region where unilateral contact is fulfilled (see Fig. 5). Of particular interest is the case C2 = 0. For \u03b1 = 0 the condition reduces to the elliptic region given by h(15 + 16h2) 3 + 16h2 \u03c92 1 + 144h (3 + 16h2)(3 + 8h2) 3 2 C2 1 < 1. (21) REGULAR AND CHAOTIC DYNAMICS Vol. 13 No. 4 2008 The \u03c91 ellipse axis of (21) becomes smaller with increasing h with limit 0 at infinity. The C1 has a minimal value h = \u221a 6 \u221a 3 \u2212 6/8 \u2248 0.2620 for where C1 \u2248 \u00b10.852 and \u03c91 \u2248 \u00b10.9717. In particular for h = 0 the region is infinite and at h \u2248 0.37375 it is circular (Fig. 6 left)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002724_978-1-4684-1033-4_13-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002724_978-1-4684-1033-4_13-Figure6-1.png",
        "caption": "FIGURE 6 WIDE COLUMN DESIGN",
        "texts": [
            " RIB CRIPPLING NCR = 16,792Ib.!in. PCR = 1.055 x 106 lb. a SK I N = 33,200 PSI a RIB = 83,000 PSI TABLE 3. BUCKLING PREDICTIONS FOR THE CYLINDRICAL SHELL 225 226 L. W. REHFIELD, R. B. DEO AND G. D. RENIERI A wide column design was selected having the same isogrid triangle geometry, stiffener and skin thickness and the same critical strain levels as the 20 inch diameter cylinder. Rib depth was increased to obtain a reasonable longitudinal buckle half wave length. The resulting design is shown in Figure 6. A trade study which led to the selection of rib depth is summarized in Figure 7. General instability load is plotted versus rib depth (d) for various half wave lengths (A). A half wave length of 5.25 inches and rib depth of 0.31 inch were selected which result in the same skin and rib strains (E) at the time of general instability for the wide column as for the cylinder (Ecolumn/Ecyl inder = 1.0). The 5.25 inch buckle half wave length was to be achieved in test by properly restraining the panel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002116_6.2004-1738-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002116_6.2004-1738-Figure1-1.png",
        "caption": "Figure 1 Geometry, boundary and loading conditions of the Kapton square membrane in the experimental test [6]",
        "texts": [
            " Analysis results are compared with the data. The results of this study provide a useful understanding, as well as alternative approach for the analysis of ultra-light, tensioned gossamer space structures. Copyright \u00a9 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. The specimen is a Kapton square membrane with the following dimension: 500mm x 500mm x 25\u00b5m (thickness). Its two adjacent corners hung on the tester frame and the other two corners under tension loads, as shown in Figure 1 [6]. For finite element simulation, due to symmetry, only a quadrant of the membrane is modeled. Symmetry boundary conditions are applied on two sides of the quadrant. In order to capture fine details of wrinkling, about ten thousands elements and nodes are used in the finite element models used. Gravity loads are considered negligible, because the membrane thickness is extremely thin. Hence, wrinkling deformation of the membrane is solely due to the uniformly distributed traction load at the corner, where a truncation with a dimension of 25 mm has been modeled",
            " However, a more exhaustive study would be necessary to further refine the imposition of point imperfections such that an even closer simulation of the experiment can be achieved. DISTRIBUTEED IMPERFECTION The distributed imperfections, on the other hands, have many imperfect nodes that are adjacent to each other. Here, distribution based a select membrane buckled mode shape is used to simulate the test results. This is shown in Figure 4, which is the quadrant model of the membrane specimen shown in Figure 1. The above stated membrane buckled mode shape was obtained by Su et al [7]. The linear buckling mode was computed by significantly reducing the membrane bending stiffness in the eigenvalue buckling solution. This is used here to study the distributed imperfection, where the magnitudes are uniformly scaled down to not exceed a tenth of the membrane thickness. This buckling mode has been selected due to its similarity with regards to wrinkle location and direction to the experiment result. Using the above imperfection, finite element simulation of wrinkle formation has been made"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003230_14644193jmbd103-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003230_14644193jmbd103-Figure6-1.png",
        "caption": "Fig. 6 The components of the truck",
        "texts": [
            " The vehicle consists of two trucks and a car body. Each truck consists of two wheelsets, two equalizer bars, a frame and a bolster as shown in the figures. The equalizer bars are connected to the wheelsets by journal bearings. The frames are connected to the equalizer bars by spring-damper elements, which represent the primary suspension. The bolster is connected to the frame by a revolute joint. The car body is connected to the bolster by spring\u2013damper elements, which represent the secondary suspension, as shown in Fig. 6. The vehicle is assumed to travel on a tangent track. The dimensions, material and inertia properties of this vehicle, shown in Table 1, are similar to the data reported in previous investigations [3]. The track model is constructed using a track preprocessor that generates a standard data file required by the main multi-body system computer code SAMS/Rail used in this study. In this numerical study, the following two simulation scenarios are considered using the vehicle model in order to compare between the planar and spatial contact models"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003497_biorob.2008.4762844-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003497_biorob.2008.4762844-Figure2-1.png",
        "caption": "Fig. 2. Isometric view of WL-16RV.",
        "texts": [
            " In this research, we aim to develop a new stabilization control under unknown external disturbance caused by passenger\u2019s static motion. This disturbance compensation control consists of the following four key points: \u2022 Calculation of the target external force \u2022 Target ZMP deviation computation \u2022 Waist trajectory computation \u2022 Combination with dynamic disturbance compensation control A. Calculation of the Target External Force To measure forces and moments caused by a passenger\u2019s motion, we use a 6-axis force/torque sensor placed between the passenger\u2019s seat and the pelvis (Fig. 2). Fig. 3 shows one example of external forces measured by the force/torque sensor. The vertical axis specifies dimensionless quantity divided external force strength by a robot\u2019s waist weight. In this research, the waist particle weight is 61.6 kg. As shown in Fig. 3, the measured force vibrates, so the modification value also vibrates to compensate for external forces, and a biped robot becomes unstable. We solved the problem by using an average force between N control cycles as the target force as follows: t target tt N F F dt N \u2212 = \u222b (1) where targetF is the target external force, and tF is the measured external force at time t "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000449_isie.2001.931878-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000449_isie.2001.931878-Figure5-1.png",
        "caption": "Fig. 5. Rcpresentation of the relation between (a) w-plane and (b) &-plane, and (c) symmetric property of J+( ' ) and J,e(2) at the axis of zz = In rd.",
        "texts": [
            " For this consideration, the work space is transformed to the cylindrical coordinate space for convenience as follows 680 ISIE 2001, Pusan, KOREA An imaginary eddy current density J:?) 15 ' L introduced ' so as to make the net eddy current satisfy the boundary condition. Hence, the net eddy current J,J obtained by substrating J:?) from J::) is zero at r' = r d , namely, the edge of the disk, as (13) ( r d , 4') tJr, (1) (rd, 4') - e$'(rd, 4') = 0 . The procedure to obtain the imaginary eddy current density distribution J:? is understood from Fig. 5. All the points in the moving frame can be expressed by using the complex variables w so that they have the relation In order to use the mapping method, zc is defined as lnw. w is transformed to zzyz coordinate. Then, the relation is By setting x2 = lnr ' and y2 = #', the w domain is transformed into zc domain. All the points , 0 5 r' 5 Td and 0 5 #' 5 2.n, in Fig. 5(a) are mapped onto the region of x, 5 lnrd and 0 5 yz 5 2n as shown in Fig. 5(b). In another word, all the area inside the circle is mapped onto the left area of the linear strip. The circle whose radius equals to r d corresponds to the dotted line at x, = Inrd. n o m the fact that the linear strip can be fold a t the axis of the dotted line, it can be said that all the points inside the circle are symmetric to those outside the circle at the axis of x, = lnrd. Our idea to find the imaginary eddy current density distribution is to assume that it is symmetric to the primary eddy current density distribution J:!' at the axis of z, = In r d , as shown in Fig. 5(c). Therefore, J:? can be expressed by $I. From Fig. 5(c), we know the relation w = r'ezd' . (14) z, = In w = In T' + 4'i . (15) (2) (1) Jrl ( x , , ~ , ) = Jrl (2ln7-d - x , , ~ , ) . (16) Mapping the point (21n~d - xr, y,) again onto the wplane by using (15), we have the relation Equation (17) indicates that the imaginary eddy current density at the arbitrary point (r',q!~') equals to the primary eddy current density at the point ( $, 4'). Finally, the radial component of the net eddy current density has the form 68 1 TSTE 2001, Pusan. KOREA \u2018I:4BLE 1 PARAMETERS Description Variable Value Unit width of the pole U 20 rrwn height of the pole b 20 mm Another thing to note here is that the above analysis result is performed with ignoring that the induced magnetic flux by the net eddy current and valid for the low angular velocity region alone"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001258_robot.2002.1013416-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001258_robot.2002.1013416-Figure1-1.png",
        "caption": "Figure 1: A two-link plana robot manipulator.",
        "texts": [
            "1 Using indirect CCT method: Cartesian coordinates as intermediate coordinates By using the indirect CCT method, we will introduce the linear R2x2 Cartesian coordinate system as the intermediate coordinate system (which is a coordinate basis). The relationship between the cylindrical coordinates and the linear Cartesian coordinates is given by x = ?-cos$ 9 = ?-sin4 ( 5 ) It is easy to show that (6) + = =cos4i+sin$Q r$ = ~g=-sint$3i:+cosf$g = 0 (2) 2.2 Cylindrical basis: a non-coordinate basis The derivation below is based on the 2-link pla- nar manipulator shown in Figure 1. To map the stiffFor the dimensional space, we choose ness control between the cylindrical space and the joint space, we need to realize two space and linear Cartesian space, and (2) linear Carte sian space and joint space, as shown in Figure 2. the basis {+,e} of the cylindrical coordinates. The relationship between the Cartesian and the cylindrical bases is defined by (1) r  \u0302 = cos83i:+sin8$ I - 6 = -sinf?i?fcos6$ (3) 3.1.1 Between the cylindrical space and the linear Cartesian space w h e r e f = & a n d $ = a ",
            ";;;I 8MTf = [(T 8M f ) (;T 8MT f ) 3 is found to be an asvmmetric matrix bv carrving out the partial derivatives. Note that % &nd @$-are 2-D tensors or 3-D matrices. Note that in a conservative system, the stiffness matrix in the Cartesian space, K,, is always symmet- the choice of coordinates and can assume totally different physical forms even though the same stiffness control system is considered. 3.1.2 Between the linear Cartesian space and joint space From the geometry of the 2-link manipulator, as shown in Figure 1, the differential displacements dx, in the linear Cartesian space and d9 in the joint space are related by the Jacobian matrix Je as follows d~ = JedB (10) where -lis& - l ~ s ( 9 1 + 62) -k@(01 + & ) I (11) By using the principle of virtual work and the chain rule, we can derive the congruence transformation and its inverse between the linear Cartesian space and the joint space: Ke = J~IK,Je+K, K, = J i T (KO - K,) JS1 (12) where K, matrix is defined as K, = mf = [ a , 1 [ (Kf) (%I , Or where Kg,ll = - ( h s + h s 2 ) f X - ( h s 1 + b 1 2 ) f y , Kg,12 = -12~12 fx -12 512 f, Kg,21 = -bc12fX -12 512fy and Kg,22 = 4 2 ~ 1 2 fz - l2sl2fv"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000426_s0020-7403(02)00136-4-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000426_s0020-7403(02)00136-4-Figure7-1.png",
        "caption": "Fig. 7. The deformation of the V-belt around the driven pulley under di erent angular speeds.",
        "texts": [
            " The increase of angular speed decreases the distribution of the normal and tangential tractions on the contact surfaces. Fig. 6 shows the deformation of the V-belt cross section along the radial direction for angular speeds 1500 and 6000 rpm at di erent positions as shown in Fig. 3. The radial deformation of the V-belt cross section at the position b3 is larger than other positions due to larger belt tension existed. Further, the deformed cross section of the V-belt becomes concave because of the belt tension and the friction forces on the contact surfaces between the V-belt and the pulley 2anges. Fig. 7 shows the deformation of the V-belt around the driven pulley of the V-belt drive system at angular speeds != 1500 and 6000 rpm. Since the belt tension increases gradually from the entry point to the exit point for the driven pulley of the V-belt drive system, the deformation along the inward radial direction increases as the angular position =* increases. Besides, Figs. 6 and 7 show the outward radial deformation due to the e ect of the centrifugal force as the angular speed increases from != 1500 rpm to "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002325_j.triboint.2006.09.003-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002325_j.triboint.2006.09.003-Figure4-1.png",
        "caption": "Fig. 4. Force diagram of a ball.",
        "texts": [
            " E \u00bc E1E2 \u00f01 v21\u00deE2 \u00fe \u00f01 v22\u00deE1 , (4) Fig. 3. Hertzian contact ellipse. Re \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R01R 00 1R02R002 \u00f0R01 \u00fe R02\u00de\u00f0R 00 1 \u00fe R002\u00de s , (5) b a \u00bc \u00f01=R001\u00de \u00fe \u00f01=R002\u00de \u00f01=R01\u00de \u00fe \u00f01=R02\u00de 2=3 , (6) e \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 b a 2 s . (7) By neglecting Coulomb friction, we assumed that deformation was mainly produced by the external preloading force acting on the ball-wire race. Fig. 4 shows the force diagram of a rolling element. According to Fig. 4, the equations of equilibrium below can be formed to calculate the force of the individual contact point: Z\u00f0F 1 F2\u00desin a F a \u00fe Gi\u00f0 \u00de \u00bc 0, (8) \u00f0F 1 \u00fe F2\u00decos a cos\u00f0c\u00de\u00bd \u00fe cos\u00f02c\u00de\u00fe; ;\u00fecos\u00f0\u00f0Z 1\u00dec\u00de \u00fe cos\u00f0Zc\u00de 0, \u00f09a\u00de \u00f0F 1 \u00fe F2\u00decos a sin\u00f0c\u00de\u00bd \u00fe sin\u00f02c\u00de\u00fe; ; \u00fe sin\u00f0\u00f0Z 1\u00dec\u00de \u00fe sin\u00f0Zc\u00de 0, \u00f09b\u00de where c is the rolling element location distribution angle: c \u00bc 2p Z . (10) When the bearing is subjected to no external loads, the only resultant force is that produced by its own mass. Since the outer framework is fixed, the inner one at contact point no"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000246_bf00312219-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000246_bf00312219-Figure10-1.png",
        "caption": "Fig. 10a-i. Functional model of the pleural wing joint if the first subunit of the tergo-pleural muscle is active; downstroke; the nob stands in position 5 (a-e); the upper end of the pleural wing joint is turned outwards (d-f, > L); the angle between the pleural wall and the insertion region of the first subunit of the tergo-pleural muscle is increased (a-e ~/); the groove of the tooth of the ventral radial vein contacts the anterior peak of the pleural wing joint (a, tl, g); the groove is in contact with the middle peak (b, e, h); the groove is in contact with the posterior peak (e, f, i); for the component parts see Fig. 8",
        "texts": [
            " The positions A, B and C are adjusted by the relative strength of the contraction of basal muscles 1 and 2 and antagonistic pterale III muscle 1. During the first half of downstroke the groove of the tooth connects with one of the peaks of the pleural wing joint. Diagrams of the functional movements of the gearbox are shown in Figs. 8-10. The operational parts of the wing joint and thoracic structures are shown in Fig. 8. In Fig. 9 the first subunit of the tergo-pleural muscle is not contracted. In Fig. 10 the first subunit is active and the tooth has been moved so that its groove connects with one of the peaks. The first and second subunit of the tergo-pleural muscle act as a tension muscle, supporting pleuro-sternal muscle 1. The two subunits put the pleural wall under additional tension (cf. Heide 1971) when the gears are in action. Contraction of the first subunit pulls its kidney-shaped insertion region (Fig. 8 ir) inwards; the nob (n) on the pulling wire (pw) is puUed from position 3 (Fig. 8 3) to position 5 (Fig",
            " 8 g l -3) outwards (Figs. 9, 10, d, e, f, > 1). Figure 9 g-i shows the two possible ways of interaction of the tooth if the gears are not activated: (1) during flight the tooth moves into the anterior groove described above (Fig. 9h); (2) it lies behind the gearbox of the pleural wing joint (Fig. 9i). This position is used when the indirect flight muscles are active and the wings are not coupled to the wing-base-driving sclerites (Nachtigall 1968) or when the wing lies in the resting position (Fig. 4a). Figure 10g-i shows the different positions of the wing leading edge when the groove of the tooth connects with one of the peaks of the pleural wing joint (Fig. 4b-d). When the tergo-pleural muscle is not active during flight, the wing base moves up and down over the turning axis (Fig. 5 ta), consisting of the anterior and posterior turning point. The movement of the foUowing wing-driving struc- tures can be seen in Fig. 1 l a : poster ior tergal lever (Fig. 11 a ptl); the heads of the costal (hco) and the radial re in (hr) interact ing with pterale II (pt H) ; interaction of the anter ior upper branch of pterale I (pt I) , the anterior tergal lever (atl) and pterale I I ; the pleural wing jo int with its gearbox, consisting of three upper peaks (g l -3 ) ; the tooth of the ventral radial rein (tvr) with the groove of the tooth and the pleural wall (p/)",
            " the jo int of the anterior peak of pterale II with the pleural wing joint) is replaced by the groove of the tooth of the ventral radial rein connecting with one of the peaks of the pleural wing joint , thereby forming a new poster ior turning point. _ 3 _ ~ - t v r + - 50 \u00b0 . . . . . . . . . \" , \u00bb \" !13 \"'--. \u00a2 b First possible use. The pleural wing joint acts like a torsion rod (see Fig. 7 t); the gearbox is used (\u00ae). The groove of the radial tooth (tvr) contacts one of the three peaks (tvr+g, position 2, see Fig. 10). 1-5: positions of the wing during downstroke; wing-beat amplitude increased now to 110 \u00b0. Dotted+ broad-striped areas, power input from the downstroke muscles, the elastic pleural wall is pushed farther outward (white + heavily striped areas) and the active pleurosternal muscle 1 stretched still more creating more potential energy. After the click: loss of contact between the groove of the tooth with a peak (position 4) and release of this energy results in the pleural wall turning farther inward OCinely lined area)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000383_12.22507-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000383_12.22507-Figure1-1.png",
        "caption": "Figure 1. Diagram of Single Impact Jet Apparatus",
        "texts": [
            " Curves showing the relationship between jet and equivalent drop sizes have been published'5'6 and the claim that jet impact can \"simulate drop impact to a reasonable accuracy\" has also been substantiated by an independent programme financed by the U.S. Office ofNaval Research . 2. JET APPARATUS AND DAMAGE ASSESSMENT 2.1 Single impact apparatus In this jet technique a lead slug is fired with a 0.22\" calibre air-rifle into the rear of a water-filled stainless steel chamber. The forward motion of the sealing neoprene disc extrudes the water at high velocity through the orifice section at the front of the chamber. Figure 1 illustrates the jet production apparatus. The most important part of the design is the nozzle section of the chamber from which the jet emerges. The jet velocity is approximately 3-5 times the projectile velocity. The main requirement is to produce coherentjets with a smooth, slightly curved front profile. The system is calibrated by selecting a suitably dimensioned chamber and measuring the jet velocity variation with firing pressure116'4. The velocity measurement is usually made by taking the time for the jet to travel between two fibre optics at 6mm and 14mm stand-off distance from the nozzle orifice",
            " It is important therefore in simulating drop damage with a jet to know what is the \"equivalent drop size\". The equivalence has been obtained by projecting specimens (typically PMMA or alumina) at suspended drops using a gas gun and comparing the damage with that produced by jets at the same velocity. Earlier equivalence curves have been recalibrated and extended to lower velocities. (Figure 10) 3. RESULTS 3.1 High-speed photography of jets The jets produced by MIJA can be examined through high speed photography. Figure 1 1 shows the smooth frontedjet profile and figure 12 showsjet induced shock waves in PMMAwhich verify the cohereni nature of the liquid at the head of the jet. SPIE Vol. 1326 Window and Dome Technologies and Materials II (1990) / 287 '4 a) I) 04oE V . O8mm mmrn 20 is 10 S 0 0 100 200 300 400 500 600 . \u20141 Jet velocity /m s Figure 10. Equivalent drop size curve Figure 1 1.Typical liquid jet from MIJA Figure 12.Impact ofjet on PMMA Downloaded From: http://proceedings.spiedigitallibrary.org/ on 05/14/2015 Terms of Use: http://spiedl.org/terms 3.2 Multiple impacts on one site The MLJA system has the capability ofproducing large numbers of impacts with a narrow spread of velocity and equivalent drop size. As mentioned previously this allows the damage produced by an impact at a given velocity to be magnified as seen in figure 13 and figure 14 on ZnS which show repeated impact on one site"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003102_00207170701447379-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003102_00207170701447379-Figure2-1.png",
        "caption": "Figure 2. Schematic diagram of test rig.",
        "texts": [
            " On the other hand, from inequality (108), it ends up with e2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e22 4e1e3 q =2e1 < \" < e2 \u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e22 4e1e3 q =2e1, \u00f0109\u00de where e1 \u00bc d11d31 0:25d221 \u00f0110a\u00de e2 \u00bc d11d32 0:5d21d22 \u00f0110b\u00de e3 \u00bc d11d33 0:25d222: \u00f0110c\u00de The stability region for \" can be found directly from inequality (109). For the AMB control system studied in this paper, it is found, by inequality (109), that the state feedback loop is stable in Lyapunov sense if the singular perturbation parameter is within the range 0< \"<0.1435. The suspension model of the AMB system, as shown in figure 2, and its parameters are tabulated in appendix A. A test rig is established with a Data Acquisition Board MSP-77230 including a pair of 12-bit A/D and 16-bit D/A converter with cycle periods of 10.5 ms and 1.5ms respectively. The simulation system DS1104 of dSPACE is established to connect Simulink/Matlab and the test rig. The deviation and current are recorded directly from the senor outputs experimentally. That is, the available measurements are the incremental displacement and incremental coil current, available from an eddy-current gap sensor and a simple circuit with a resistor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001054_s0376-7388(00)00612-8-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001054_s0376-7388(00)00612-8-Figure1-1.png",
        "caption": "Fig. 1. Schematic representation of yeast propagation and immobilization within the annular passages of the hollow fibres prepared from no. 4 dope solution (A and B: yeast injection ports).",
        "texts": [
            " Saccharomyces cerevisiae (ATCC 4126) was chosen for immobilization in this study. The composition of medium was glucose 20 g/l, yeast extract 6.0 g/l, NH4Cl 2.5 g/l, K2HPO45.5 g/l, citric acid 3.0 g/l, NaCl 1.0 g/l, MgSO4\u00b77H2O 0.25 g/l and CaCl2\u00b72H2O 0.15 g/l. This medium was filtered through a 0.2 mm nylon microporous membrane and was used for yeast propagation. The yeast of about 5 g/l was injected into the annular passage of the annular hollow fibre prepared and then was sealed in the annular passage using a quick setting epoxy resin as shown in Fig. 1. The nutrients were circulated in the shell side. The operating pressure in the lumen side was controlled at 380 mmHg using B-720 Buchi vacuum system so that the nutrients were permeated through the outer layer, the cell layer and the inner layer into the lumen side as the pressure in the shell side was maintained at atmosphere. The operating temperature was kept at 30\u25e6C and the cultivation time was 24 h. Samples of annular hollow fibres with immobilized cells were immersed in a 2.5% glutaraldehyde solution overnight (\u223c12 h) at 4\u25e6C, completely rinsed with distilled water, and then progressively dehydrated with 20\u201390% ethanol, in increments of 10%, by holding them at each concentration for 30 min",
            " The open cavities would improve free convective transport of spores into the finger-like cavities. This would simplify the inoculation procedure and the cells could establish itself within the voids and the annulus of the membrane, thus creating a good cell layer [14]. Experiments for immobilization of yeast have been conducted by introducing convective flow for transport of nutrients. Schematic representation of immobilization and propagation of the yeast in the annular passages of the hollow fibre is shown in Fig. 1. The annular hollow fibres chosen for the immobilization were made from the polymer dope 4 as the outer layer of the hollow fibre prepared has shown high water permeability. Fig. 7 illustrates the yeast immobilized in the annular passages of the annular hollow fibre prepared from. The initial loading concentration of yeast was 5 g/l. The nutrients permeated through the outer layer, cell layer, and inner layer to the lumen side. The operating pressure was controlled at 380 mmHg vacuum at lumen side"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003471_iros.2007.4399451-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003471_iros.2007.4399451-Figure1-1.png",
        "caption": "Fig. 1. Schematic of a beam sensor and associated geometric information for MER computation",
        "texts": [],
        "surrounding_texts": [
            "The beam sensor senses along a beam, V(s), starting from the sensor origin up to L, the range of the sensor, and it returns the distance of the first hit point along the beam. The intersection of the beam with the unknown physical space is denoted by Vu(s). In the simplified sensor model, all gridcells, along the beam that are in front of the hit point are sensed free, i.e., pij |V (s) = 1, and the cell corresponding to the hit point is sensed as obstacle, i.e., pij |V (s) = 0 and the pij\u2019s values for the cells behind the hit point remain unchanged [?]. The expectation computation in the MER expression is over the set of all possible sensing outcomes for a given sensing action, thus their corresponding probability and the corresponding entropy reduction needs to be determined. It turns out that the set of all possible sensing outcomes for V (s) can be grouped into a finite number of events, determined by simple geometrical computations. The geometry of a sensing action is illustrated in Fig. ??. Vu(s) is divided into a set of intervals. The ith interval of Vu(s) \u22c2 A(q), is denoted as IRi, correspondingly |IRi| is the number of gridcells in this interval, and IOi is the ith interval of Vu(s) that does not intersect A(q), correspondingly the number of grid-cells in this interval is denoted as |IOi|. The number of intervals depends on the geometry of the robot, and for a general mobile-manipulator with m convex links, the number of intervals is m. All possible sensing outcomes are now grouped into the following m + 2 events: Eventc : The hit point lies inside A(q), i.e., hit point lies in one of the IRi\u2019s. The robot configuration q would be in collision, were this event to happen, and H(Q|eventc) = 0. Eventi : i = 0, . . . ,m-1 : The hit point lies inside IOi+1. Eventm : There is no hit point in Vu(s). For simplicity we use pij = p for all cij . Please note that this is not a restriction, the expression is simply more elaborate to write otherwise. The marginal expected entropy reduction for configuration q with H(Q) = H0 turns out to be: E\u2206 s H(Q)) = m \u2211 i=0 PiHi \u2212 H0 = m \u2211 i=1 [Hip \u2211i j=1 |IOj |+|IRj |(1 \u2212 p|IO(i+1)|)] \u2212 H0p |IO1|, (7) where Pi = P (Eventi), and Hi = H(q|Eventi), and is easily computed by inserting p(q|Eventi) in (??), with p(q|Eventi) = { 0 if Eventc p(q) p \u03a3i j=1 |IRj | otherwise, Note that \u03a3i j=1|IRj | is the number of cells sensed free in A(q) \u22c2 V(s), were Eventi to happen. As one can see, for a given q, A(q) is easily determined using forward kinematics, and |IOi|, |IRi| are easily determined by simple geometrical computations and ray casting. The marginal entropy reduction for a configuration q is therefor linear in of number cells in the beam, and hence is efficiently computed. Note that since occlusion does affect MER for OCC-grid model, therefore it prefers sensing positions \u201ccloser\u201d to the set of sensed configurations."
        ]
    },
    {
        "image_filename": "designv11_28_0001913_jmes_jour_1979_021_072_02-Figure16-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001913_jmes_jour_1979_021_072_02-Figure16-1.png",
        "caption": "Fig. 16. Model squeeze-film bearing, simplified plan view",
        "texts": [],
        "surrounding_texts": [
            "Ten static eccentricity ratios were chosen for investigation. These were 0, 0.2, 0.4, 0-6 and 0.8 along the horizontal axis (for the measurement of Crr) and vertical axis (for Css). The PRBS input signal is uniquely defined by the following three parameters (16): (i) signal amplitude, (ii) sequence length, and (iii) clocking frequency. A series of tests was performed at the natural frequency of the journal on its beam (26 Hz) to determine the force/displacement characteristics of the system. It was found that an input forcing amplitude of k 7 N gave a good compromise between the need to obtain measurable deflections (approximately 0.025 mm) whilst avoiding nonlinear behaviour (less than 10 per cent of radial clearance). Much lower force levels could be used, down to (say) kO.7 N, but a t this stage of development it was felt that the creation of artificially low signal-tonoise ratios would only hinder the interpretation of results. Journal Mechanical Engineering Science Q IMechE 1979 Vol21 No 6 1979 at UNIV OF VIRGINIA on June 9, 2016jms.sagepub.comDownloaded from Using the real-time spectrum analyser, the effects of varying sequence length and clocking frequency were studied. Given that the dynamics of interest lie within the range from d.c. to 100 Hz, a sequence length of 127 bits/period and clocking frequency of 333 Hz were found suitable. The bandwidth of such a sequence is approximately 160 Hz. It was observed that, when testing the system using the spectrum analyser, up to 100 spectral averages were required to produce a visually \u2018clean\u2019 spectrum. Hence, it was decided to average responses over 100 PRBS periods. (It should be noted that the periodic noise associated with ordinary journal bearings due to surface roughness and out-of-roundness was not encountered here.) Before performing the actual tests, it was necessary to evaluate the shaker system and also quantify the effect of shaft dynamics on the total response. The journal was adjusted and locked in a concentric position in the clearance in the absence of any oil. Using the spectrum analyser, the spectrum of the PRBS source signal was measured together with that of the forcing function applied to the journal. The spectra obtained are shown in Fig. 3, and it can be seen that the forcing signal maintains the bandwidth of the source signal. During the same test, the spectrum of the rotor displacement was also obtained (Fig. 4). The solid line is the theoretical frequency response of the shaft, computed using a damping factor of &=0.05. This Vol 21 No 6 1979 Journal Mechanical Engineering Science Q IMechE 1979 at UNIV OF VIRGINIA on June 9, 2016jms.sagepub.comDownloaded from is, at most, 5 per cent of the damping expected from the squeeze a m . The final estimates of oil-film damping could be corrected to allow for the effect of shaft damping. However, the effect on the predicted frequency responses would be negligible. Consequently, shaft damping was ignored. The static eccentricity ratio was selected and oil (Shell Tellus 37) was pumped through the bearing at 35 kN/mz inlet pressure and with sufficient flow to provide a full 360\" film of oil. The inlet and outlet thermocouples were monitored until a steady operating temperature of approximately 20\u00b0C (viscosity 77 z 70 cP) was reached. On the basis of a previous digital-computer simulation of the system, the sampling frequency was chosen to be 3.33 kHz, or ten times the PRBS clocking frequency. The journal was perturbed about its equilibrium position using the chosen input sequence. After allowing starting transients to decay, the forcing signal and corresponding journal displacement were recorded over 100 PRBS periods. The tape speed (30in/s) was determined by the need to provide sufficient bandwidth to record and reproduce the 3.33 kHz synchronizing pulse. The tape was played back through the analogue-todigital converter, using the recorded timing pulse to trigger the sampling process. In this way, the start of a new PRBS period was detected and averaged in synchronism with the previous sequence. Synchronization was thus ensured, irrespective of variations in tape speed. Averaging was performed over the duration of 100 pseudo-random sequences. A punched paper tape, containing the averaged records of input force and output displacement, and consisting of 1269 samples per record, was produced for subsequent processing. Before a discrete-time model could be fitted to the input and output records, two operations had to be performed on the raw data-removal of the d.c. level and generation of a record of journal velocity. Despite analogue balancing of the two signals prior to analogue-to-digital conversion, both sampled records still displayed a slight d.c. offset. This was removed digitally by computing the mean of each record and subtracting it from each sampled value. The use of the state variable form of the model equation requires a sampled record of journal velocity in addition to one of displacement. Differentiation of signals should be approached with caution, and it is usual to apply low-pass filtering prior to differentiation to avoid unreliable results. However, since the oil-film itself acts as an effective low-pass filter and the sampling rate was sufficiently large to avoid aliasing, the displacement signal was differentiated without arbitrary modification. An algorithm based on Stirling's interpolation formula (17) was used to perform this differentiation. The pre-processing leaves three zero-mean records of input force, output velocity and output displacement. Each record now consists of 1263 samples, six having been lost during differentiation. The three records (say XI&), xz(k) and u(k), where k = 1,1263) are loaded into appropriate arrays, as shown in Appendix 1. A digital computer program then implements equation (9) to produce a least-squares estimate of the matrix a, whose elements correspond to the discrete arrays I: and C, as shown in Appendix 1. By manipulation of equation (7), an estimate of the dynamical parameter matrix, A, is obtained. 5 EXPERIMENTAL RESULTS The estimates of the squeeze-film damping coefficients, C,, and Css, obtained from the discrete-time modelling are shown plotted against static eccentricity ratio in Fig. 5 . Also displayed are the theoretical values of these coefficients predicted from short-bearing theory (equation (2)). These estimates were used in conjunction with equation (10) to predict the frequency-response function of the squeeze-film damper along the horizontal and vertical axes, as shown in Figs 6a and b. Also displayed are the expected frequency responses predicted by short-bearing theory together with the spectral estimates of the respective displacement signals. Since it has been demonstrated that the input forcing spectrum is effectively flat up to 100 Hz, then these spectral estimates represent a good approximation to the empirical frequencyresponse functions relating journal displacement to applied force."
        ]
    },
    {
        "image_filename": "designv11_28_0000243_1.1537264-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000243_1.1537264-Figure2-1.png",
        "caption": "Fig. 2 Drive unit",
        "texts": [
            " Since density of silicon nitride (Si3N4) is about forty percent of that of bearing steel, the mass of a ceramic (Si3N4) ball is also about forty percent of that of a steel ball having the same diameter. Since Young\u2019s modulus of silicon nitride (Si3N4) is 1.5 times higher than that of steel, the stiffness of the ceramic ball linear bearing is 1.2 times higher than that of the steel ball linear bearing. 2.2 Sound and Vibration Measurements. A drive unit, which was developed for sound and vibration measurement of linear motion rolling bearings @7#, is shown in Fig. 2. The drive unit consists of a motor, a coupling, support bearings, a sliding screw, sliding guides, a pusher, and a concrete bed. The profile rail of a test linear bearing is fixed on the concrete bed by bolts. The carriage of the test linear bearing is driven through a coupling, support bearings, a sliding screw, sliding guides and a pusher using a motor. Therefore, when the motor rotates at a constant speed, the carriage of the test linear bearing can be driven at a constant linear velocity. The measurements of sound and vibration of the test linear bearings were carried out in a soundproof room"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002667_acc.2006.1657387-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002667_acc.2006.1657387-Figure2-1.png",
        "caption": "Fig. 2. l \u2013 l control configuration",
        "texts": [
            " Substituting (30) into (26) and (27) and using the result in (29) and simplifying results in: \u03b4e 12 = 0 (31) Thus the orientation of vehicle 2 will converge to that of vehicle 1. The stability of the zero dynamics can only be proved for the linear and circular motions. These types of motions are sufficient for the applications suggested in the introductions. However, simulations show the stability for broader situations where the radius of curvature of the desired motion does not change too rapidly. A controller must be designed to stabilize the distance of vehicle 3 from the two neighboring vehicles (Fig. 2). Distances are measured from the centers of mass of vehicles 1 and 2 to an arbitrary point on vehicle 3, which is offset by d from its center of mass. The feedback controller inputs are the driving force and the steering torque of vehicle 3, F3 and T3. The desired distances ld13 and ld23 to vehicles 1 and 2, respectively, are to be maintained. Thus the outputs of the control system are: [l13, l23]. The configuration variables that define the dynamics of vehicle 3 are: [x3, y3, \u03b83]. The configuration variable-output relations of this control system are obtained by writing the acceleration equation for the l \u2013 l configuration, which are solved for the second-order derivative of l13 and l23",
            " Therefore, two asymptotically stable first order surfaces are assumed (\u03bb1,2 > 0): s = [ s1 s2 ] = [ (l\u030713 \u2212 l\u0307d13) + \u03bb1(l13 \u2212 ld13) (l\u030723 \u2212 l\u0307d23) + \u03bb2(l23 \u2212 ld23) ] (41) Since the matrix form of the input-output equations for the l \u2013 l controller is similar to that of the l \u2013 \u03c8 controller, the same form of control law as introduced in (14) stabilizes the outputs in the presence of parameter uncertainty and disturbance. The determinant of b\u0302 in (40) must be calculated to investigate any singularities: det(b\u0302) = d m\u030211m\u030233 s(\u03b33 \u2212 \u03b32) (42) Using (34) and (35), one can show that the determinant is nonzero at all times except when (\u03b82 + \u03c823)\u2212 (\u03b81 + \u03c813) = n\u03c0. This happens when the origin of the coordinate systems of vehicles 1 and 2 and the control point of vehicle 3 are collinear (Fig. 2). This configuration is avoided by defining proper formation parameters. The controller nonlinearity gains, k1 and k2, are determined by assuming the bounds for the parameter uncertainty and disturbances similar to (15) to (17), and using (19). These gains guarantee that si.s\u0307i \u2264 \u2212\u03b7i|si|. Therefore, the outputs, l13 and l23, reach the surfaces despite the existence of parameter uncertainty and disturbance. \u03b7i > 0 determines the speed of the reaching phase. After the outputs reach their corresponding surfaces, they slide to their desired values, ld13 and ld23, as is observed from (41) for s1 = s2 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002193_0471758078.ch2-Figure2.21-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002193_0471758078.ch2-Figure2.21-1.png",
        "caption": "FIGURE 2.21. Homogeneous catalytic EC mechanism. Passage from control by forward electron transfer to control by follow-up reaction upon increasing the mediator concentration. g \u00bc 5, k e=kC \u00bc 1000 M 1, RTke=Fv \u00bc 100 M 1.",
        "texts": [
            " It is thus possible to derive from the experimental data the value of the following group of constants: \u00f0ke=k e\u00dekC \u00bc KekC, where Ke is the equilibrium constant for the uphill electron transfer reaction \u00f0RT=F\u00de ln Ke \u00bc E0 A=B E0 P=Q. If the standard potential of the A/B couple, E0 A=B , is known independently, we obtain the rate constant kC for decomposition of the transient intermediate B. If not, kC can be obtained when the following conditions are achieved. Upon increasing the mediator concentration, while keeping the excess factor, g \u00bc C0 A=C0 P, constant, the system tends to pass from kinetic control by the forward electron transfer step to control by the follow-up reaction (Figure 2.21). An ideal situation would be reached if the available concentration range would allow perusal of the entire intermediary variation between the two limiting situations. More commonly encountered situations are when it is possible to enter the intermediary zone coming from the forward electron transfer control zone or, conversely, to pass from the intermediary zone to the follow-up reaction control zone. In both cases the values of ke and Ke=kC can be obtained. Since in most cases, the electron transfer reaction is very uphill, k e is at the diffusion limit, allowing then the derivation of kC and E0 A=B",
            " As discussed earlier, the determination of lifetimes of unstable intermediates by direct electrochemical methods such as cyclic voltammetry is limited to the submicrosecond range (Section 2.2.1). This lower limit may be pushed down to the subnanosecond range by application of an indirect method based on redox catalysis (Section 2.2.6). The catalytic increase of the current at the level of the catalyst P/Q wave is a source of kinetic information on the homogeneous electron transfer and on the follow-up reaction. In the framework of the homogeneous catalytic EC mechanism (three first steps of Scheme 2.13) there are, as discussed in Section 2.2.6 and summarized in Figure 2.21, two limiting cases (reductions are taken as example, transposition to oxidations being straightforward). One of these is when the catalytic response is governed by the forward electron transfer and therefore by the dimensionless parameter le \u00bc RT F keC0 P v \u00f02:25\u00de If the system were to remain in this situation, no kinetic information concerning the follow-up reaction would be available. In the other limiting case, the catalytic response is governed by the follow-up reaction, while electron transfer acts as a preequilibrium"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003807_ls.55-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003807_ls.55-Figure1-1.png",
        "caption": "Figure 1. (a) Coordinate systems for lubricating and solid domains. (b) Profi led shapes on stationary pad.",
        "texts": [
            " Load carrying capacity, coeffi cient of friction, temperature distribution and pressure variations as functions of various operating parameters have been presented in this paper. It is observed that in the presence of roughness on the surface of pad, the performance (increase in load carrying capacity and reduction in coeffi cient of friction) of pad thrust bearings enhances signifi cantly. A schematic diagram (with coordinate system and profi led shapes on stationary pad) of pad thrust bearing is provided in Figure 1. The Lobatto quadrature technique as developed by Elrod and Brewe2 is used in this model. Momentum and energy equations for Newtonian and non-inertial laminar lubricating fi lm for infi nitely wide pad thrust bearing are written below as (list of notations are provided in the Nomenclature): Momentum equation: \u2202 \u2202 \u2202 \u2202 \u2202 \u2202 p x z u z =     \u03b7 (1) Energy equation: \u03c1 \u03b7C u T x z k T z u z p \u2202 \u2202 \u2202 \u2202 \u2202 \u2202 \u2202 \u2202     =     +     2 (2) In this analysis, the following lubricant\u2019s viscosity model has been adopted: \u03b7 \u03b7 \u03b3= \u2212 \u2212( ) 0 0e T T (3) Copyright \u00a9 2008 John Wiley & Sons, Ltd",
            "1002/ls In order to compute pressure distributions in bearing in x direction by incorporating variation of viscosity, generalised Reynolds equation is developed using the lineal mass fl ux as follows: Lineal mass fl ux: m udz h h \u03c1 = \u2212 + \u222b 2 2 (10) The generalised Reynolds equation is obtained by taking the divergence of lineal mass as: \u2207\u22c5          = m \u03c1 0 or \u2202 \u2202 \u2202 \u2202 \u2202 \u2202 \u2202 \u2202x h p x u u h x x h u up L U L U\u03be \u03be \u03be 3 1 0 6 2    = +( ) \u2212 \u2212( )    (11) where \u03be \u03be \u03be \u03be \u03be p = + \u2212 ( ) 0 2 1 2 0 0 4 3 . In order to achieve effi cient and accurate computations, the temperature variation across the fi lm thickness in the energy equation is represented by Legendre polynomial of order 2. To get numerical values of temperatures at four Lobatto points (A, B, C and D) as indicated in Figure 1a, four equations are required. Two equations are obtained from boundary conditions (temperatures at pad and runner surfaces), and the remaining two equations are developed by taking zeroth and fi rst moments of energy equation across the fi lm thickness. The simplifi ed forms of the resulting equations are provided as follows: Zeroth moment of energy equation: c T x c T x c T x c T x k C h T p U 1 0 2 1 3 2 4 3 22\u2202 \u2202 \u2202 \u2202 \u2202 \u2202 \u2202 \u2202 \u2202 \u2202 \u2202+ + + =         \u2212 \u03c1 \u03b6 T C h c L p\u2202\u03b6 \u03c1           +     1 2 2 5 (12) First moment of energy equation: c T x c T x c T x c T x k C h T p U 6 0 7 1 8 2 9 3 22\u2202 \u2202 \u2202 \u2202 \u2202 \u2202 \u2202 \u2202 \u2202 \u2202 \u2202+ + + =         + \u03c1 \u03b6 T T T C h c L U L p\u2202\u03b6 \u03c1     \u2212 +       +     1 2 2 10 (13) Expressions for the coeffi cients (c,s) appearing in equations (12) and (13) are provided in the Appendix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002015_j.mechmachtheory.2004.03.003-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002015_j.mechmachtheory.2004.03.003-Figure3-1.png",
        "caption": "Fig. 3. Relative speeds at conjugated joints.",
        "texts": [
            " Based on the chain rule of differentiation, we have x3 \u00bc dh3 dt \u00bc dh3 dh4 dh4 dt , and the angular velocity of the planet gear and segment O2iO3i can be expressed as follows. xi \u00bc hix4 \u00f0i \u00bc 3; a\u00de \u00f06\u00de By differentiating Eqs. (2) and (3) with respect to the angle of the crank h4 twice, gives h03 \u00bc Rah2a R3h23 cos\u00f0h3 ha\u00de R4 cos\u00f0h4 ha\u00de R3 sin\u00f0h3 ha\u00de \u00f07\u00de h0a \u00bc R3h23 \u00fe Rah2a cos\u00f0h3 ha\u00de R4 cos\u00f0h3 h4\u00de Ra sin\u00f0h3 ha\u00de \u00f08\u00de where h0i \u00bc dhi dh4 \u00f0i \u00bc 3; a\u00de, and the angular acceleration of the planet gear and segment O2iO3i can be written as ai \u00bc hia4 \u00fe h0ix 2 4 \u00f0i \u00bc 3; a\u00de \u00f09\u00de As shown in Fig. 3, the relative speed at contact point P5i3 of the disc pin and disc pin hole can be considered to be belonging to the planet gear V * P35i and to the disc pin V * P5i3 , respectively, which can be written as V * P5i3 \u00bc x * 5 R * P5i3 \u00f010\u00de V * P35i \u00bc x * 3 R * 3c \u00f011\u00de Assuming both the planet gear and the disc pin are rigid bodies, the normal speed component between the planet gear and disc pin at the contact point is 0. Hence, the normal speed component with respect to the disc pin hole V *n P35i and to the disc pin V *n P5i3 are the same; that is, V n P35i \u00bc x3R3c cos bc, V n P35i \u00bc x5R5i3 cosbP and x3R3c cos bc \u00bc x5R5i3 cos bP . As shown in Fig. 3, since R3c cos bc \u00bc R5i3 cosbP , therefore x3 \u00bc x5 \u00f012\u00de From Eqs. (10) and (11), the relative tangential speed component between the planet gear and disc pin at the contact point P5i3 can be obtained as V * 5i3 \u00bc V * P5i3 V * P35i \u00bc x * 3 R * 5i3 R * 3c \u00f013\u00de Once the location of the instantaneous center is found, the position vector from O4 to the instantaneous center can be expressed as: R * 4c \u00bc R * 5i3 R * 3c, and the angular speed ratio can be written as x4 x3 \u00bc R4c R4 R4 \u00f014\u00de Substituting Eqs. (12) and (14) into Eq. (13), yields V * 5i3 \u00bc \u00f0x4 x5\u00de R4 sin h4 i * R4 cos h4 j * \u00f015\u00de As shown in Fig. 3, the relative speed at contact point P2i3 of the ring gear roller and planet gear roller can be expressed as V * P2i3 \u00bc x * 4 R * 4 \u00fe x * 3 R * 2i3 \u00f016\u00de where R * 2i3 is the vector from the planet gear center O3 to the contact point P2i3, and it can be expressed as: R * 2i3 \u00bc \u00f0R3i cos h3i r3 cos ha\u00de i * \u00fe \u00f0R3i sin h3i r3 sin ha\u00de j * . Based on Eq. (16), the tangential speed component at the planet gear roller and ring gear roller at the contact point P2i3 can be determined as V * 2i3 \u00bc V * P32i u* t 2i3 u *t 2i3 \u00bc \u00bdx4R4 cos\u00f0h4 ha\u00de \u00fe x3R3i cos\u00f0h3i \u00fe ha\u00de r3 sin ha i * cos ha j * \u00f017\u00de The model of kinetostatic analysis considering friction of the roller drives is developed in this section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000027_978-94-015-9514-8_47-Figure11-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000027_978-94-015-9514-8_47-Figure11-1.png",
        "caption": "Figure 11. Sarrus-chain complexes",
        "texts": [],
        "surrounding_texts": [
            "In their work on foldable structures Pellegrino and You [8] have proposed combining movable rings to higher complexes. On the basis of the above-described cylindric or prismatic Sarrus- chains such combinations become possible in great generality and variety. However, due to their lower manufaturing costs, highly symmetric linkages are preferred in applications, as far as possible. But, there might be cases in which an unfolding structure of a given overall form is demanded. Fig.II shows three examples of Sarrus-chain complexes: The first complex is a combination of eighteen Sarrus-chain modules which consist of three combined Sarrus linkages; the second complex uses twelve Sarrus-chain modules which consist of four Sarrus linkages; and the third complex finally uses six Sarrus-chain modules which are made of six Sarrus linkages. According to the symmetries these Sarrus-chain complexes can be \" bundled\" to a small size. References I. Kempe. A. B.: On Conjugate Four-piece Linkages. Proc. Lond. Math. Soc.1s.VoI.9, (1878).133-147. 2. Darboux. G.: Recherches sur un systeme articule. Bull. Sci. Math . 2s, Vol. 3, (1879). 151-192. 3. Baker. J. E. ,.Yu, H. Ch.: Re-Examination of a Kempe Linkage. Mechanism and Machine Theory . Vol.l8 No.1. (1983) .. 7-22. 4. You. Z .\u2022 Pellegrino. S.: Foldable Bar Stuctures, Int. 1. Solids and Structures .. VoI.34. (1997) . 1825 -1847 5. Roschel. 0. : Zwangltiufig bewegliche Polyedermodelle I, Math. Pannonica , 611 , (1995) 267-285. 6. Roschel, 0.: Zwanglaufig bewegliche Polyedermodelle II. Sci.Malh.Hungarica, Vo1.32. (1996). 383-393. 7. Sarrus. P.: Note sur la transformation des mouvements rectilignes alternatifs. en mouvements circulaires; et reciproquement. C.R.Acad.des Sciences. Paris. (1853). 1036-1038. 8. Pelegrino. S .\u2022 You. Z. Foldable ring structures. Space structures 4. Ed. by G.A.R .. Parke and C.M. Howard. Vol.I. (1993), Thomas Telford. London. 783-792."
        ]
    },
    {
        "image_filename": "designv11_28_0003061_978-3-540-72434-6_75-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003061_978-3-540-72434-6_75-Figure1-1.png",
        "caption": "Fig. 1. The experimental setup of gear train system",
        "texts": [
            " The output of the j-th neuron in the hidden layer can be obtained by = 2 j jO exp(-net /2 )\u03c3 (20) where \u03c3 is the smoothing parameter of gauss function. The output of PNN can be expressed by 30 k j jk j 1K 1 net O w N = = \u2211 , k=1,2,3 (21) where wjk is the weighting coefficient between the j-th neuron in the hidden layer and the k-th neuron in the output layer, and also indicates the fault sets of the training samples. Then, the output Ok of the PNN can be obtained by = =k r k r net max net , O 1 , r=1,2,3 (22) The experiment equipment of gear train system is shown in Figure 1. It consists of a motor, a converter and a pair of spur gears in which the transmitting gear has 46 teeth and the passive gear has 30 teeth. The vibration signals are measured in vertical direction from two accelerometers that mounted on the bearing housing of gear train system. When the BPNN accomplish training, using the six statistical parameters and normalized by membership function to compute with the trained weighting coefficients wij and wjk and obtained output values. Each value represents a kind of gear fault and the output value represents the degree of certainty for corresponding fault"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002796_pime_proc_1973_187_147_02-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002796_pime_proc_1973_187_147_02-Figure2-1.png",
        "caption": "Fig. 2. Deformation and stresses under a rolling cylinder",
        "texts": [
            " (3) where W is the normal load/unit width of the roller and b is the half-width of the band of contact. It was found that this theory greatly undere3timates the frictional loss. Greenwood et al (IS) then argue that the hysteresis loss cannot be described in terms of the total elastic energy input/unit volume, as assumed in equation (3), because each element of material passes through a complex stress cycle as it moves under the rolling body. The stress distribution on any element is conveniently described, as shown in Fig. 2, by three independent stresses-a shear stress t = T ~ ~ , a second shear stress s = +(uu-ux) at 45\" to t and a two-dimensional hydrostatic stress u' = +(ux+u,). Greenwood et aZ. consider a material with Poisson's ratio v = 0.5, which is incompres- sible under hydrostatic stress. The changes in strain energy are then only associated with changes in s and t . The stress cycle through which any element of material passes can now be represented on an s, t stress diagram as shown in Fig. 3a. By considering incremental changes in energy, it was then shown that the total energy loss/unit volume for an element at a depth y for one passage of the contact is given by : where G is the shear modulus and lo is the total length of E = (a/8G)Zo2 ",
            " The authors themselves indicate that \u2018the rate of lubricant supply had a significant influence upon the incidence of failure. . .\u2019 Certainly the lubricant (surface environment) is not influencing sub-surface behaviour to the depths reflected in the authors\u2019 data. Again, a consideration of surface as well as of sub-surface effects in the development of wear particles might produce a fuller picture of those factors important in the generation of a wear particle. In reference to the authors\u2019 numerical technique, some additional discussion appears to be warranted. Fig. 2 implies that the stresses and contact length 2b were calculated for a cylinder on a flat plate when the experiments were conducted with two discs. This geometric change could significantly change the values of stress, the loss of coefficient a, and the internal heat generation function q. If uniform heat flow in the radial direction is assumed, the equation for heat conduction is not as the authors suggest (the equation for one-dimensional orthogonal heat flow) but rather is q = - K - - d y ( . z ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000290_s0957-4158(00)00026-x-Figure17-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000290_s0957-4158(00)00026-x-Figure17-1.png",
        "caption": "Fig. 17. Reconstruction of 3D co-ordinates of a marker from two camera images.",
        "texts": [
            " This option, however, creates very large number of ghost markers causing problems in 3D trajectory generation. Normally, there is no need to use this option unless some awkward test conditions arise, in which case user interference is generally required for manual elimination of ghosts. Once the correspondences between the camera images have been established at every \u00aeeld, combined image co-ordinates of the same marker are used to reconstruct its 3D co-ordinates. A marker's 3D co-ordinates can be reconstructed if its image co-ordinates are available in at least two calibrated cameras. Fig. 17 illustrates a marker with world co-ordinates (X, Y, Z ) and its image co-ordinates ur, vr and us, vs in camera-r and camera-s, respectively. Knowing the DLT calibration parameters, arij and asij, of both cameras, Eq. (7) can be written twice, which provide four equations in terms of three unknowns (X, Y, Z ) as before. Each equation in the set represents one of the four planes (P1, P2, P3, P4) shown in Fig. 17, and the target marker redundantly satis\u00aees all the four plane equations. However, due to the errors involved, any three of the four equations will give a di erent solution. Therefore, the redundancy can be utilised by minimising the error in the least squares sense. Degree of redundancy increases when the marker is seen by more than two cameras, hence providing more reliable solution. For a marker seen by n-number of cameras, Eq. (7) written n-times will then give the following set of linear equations: B\u03022n 3X\u03023 1 D\u03022n 1 9 Where; X\u0302 X, Y, Z T, and the elements of B\u00c3 and D\u00c3 consist of image coordinates and calibration parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001477_ip-nbt:20040839-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001477_ip-nbt:20040839-Figure2-1.png",
        "caption": "Fig. 2 Underside of the mobile platform Piezo discs are divided into three electrodes per disc",
        "texts": [
            " The mobile platform is driven by the slip\u2013stick principle [5\u20137], which enables positioning in the submicrometre range. The functional material for the actuators is piezoelectric ceramic The authors are with the Division Microrobotics and Control Engineering, University of Oldenburg, Oldenburg 26111, Germany r IEE, 2004 IEE Proceedings online no. 20040839 doi:10.1049/ip-nbt:20040839 Paper first received 30th January and in revised form 11th June 2004 IEE Proc.-Nanobiotechnol., Vol. 151, No. 4, August 2004 145 in the shape of piezodiscs. The discs are segmented to create three electrodes per disc (Fig. 2). With that configuration it is possible to move the mobile platform in three DOF. The performance of the platform has been described in [8, 9]. The mobile platform has some advantages in comparison with other known mobile platforms driven by the slip-stickprinciple [6, 7, 10\u201313]. The platform is less damaging to the surface, because instead of sliding on the surface, the spheres roll on it. It also reduces the necessity of a very smooth surface usually required for the slip\u2013stick drive [14]. This enables the robot to drive on a variety of surfaces, including a regular microscope stage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002145_1-4020-3363-x_33-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002145_1-4020-3363-x_33-Figure6-1.png",
        "caption": "Figure 6. Schematic representation of calorimetric column with immobilised cells.",
        "texts": [
            " (1) for boundary conditions r = 0 : dci dr = 0 (2) r = R : ci = cib the observed overall particle reaction rate per unit volume of particle, vobs, can be calculated vobs = \u2212 ADei\u03bd i V dci dr r=R = \u2212 3Dei\u03bd i R dci dr r=R (3) where A, V, and R are particle surface area, volume, and radius, respectively. The calculation of the temperature change in the column necessitates linking Eq. (3) to balance equations for the column. According to the calorimeter configuration the column should be described as a continuous packed bed reactor in which the layer of immobilised cells is sandwiched by two layers of inert glass beads as depicted in Figure 6. Balance equations were derived from following assumptions: the reactor is differential, plug flow occurs in the reactor, interstitial velocity of flow is high enough to prevent the effect of external diffusion, heat loss through the reactor wall is negligible so that the reactor is considered to be adiabatic [49]. Mass balances: w dcib dz = ( )1\u2212\u03b5 vobs\u03bd i (4) Heat balance: w\u03c1CP dT dz = ( )1\u2212\u03b5 vobs( )\u2212\u2206 r H (5) Symbols in equations are: cib \u2013 bulk concentration, w \u2013 superficial liquid flow rate, z \u2013 axial coordinate in the column, \u03c1 and Cp \u2013 liquid density and specific heat capacity, Hr\u2206 - molar reaction enthalpy, \u03b5 \u2013 bed void fraction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003038_camp.2007.4350364-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003038_camp.2007.4350364-Figure1-1.png",
        "caption": "Fig. 1. The direction of the displacement. d is the new candidate direction, t is the site of the target, and Ot is the angle between the agent reference axe y and direction to t",
        "texts": [
            " The mathematical definition of the fitness function has been formulated by considering obstacles, prey, and predators as entities that generate an electrostatic field that is attractive (+) or repulsive (-) depending on the actors (see Table below): predator preys obstacle lair predator + prey + The analytical form of the fitness functions are given below: Fpred() i iiaFp(0)-a2 E aFobj (0)1-a3 EFpobj (0) i j7Xi wi'th a, + a2 + a3 = 1. Fprey (0) = biF (0) -b2 EFobj (0) b3E Fpobj (0) A. Genetic algorithm outline The GA has been designed to approximate the solution of the general optimal problem stated above [12]. The planner, on the basis of the information given by the sensors agents, provides the new direction of the displacement, in terms of angles from its own reference system (see Figure 1). Steps followed are: a) the generation of a starting population of solutions represented as a string of bits where each string represents an angle; b) the application of the crossover operation, with probability Pc, on randomly chosen solutions (Single Point Crossover); c) the bit-mutation, with probability Pm, to change one or more bit randomly; d) the computation of the fitting function; e) the selection the new population of solution using the binary tournament selection. Steps a)-e) are repeated a given convergence criteria is not satisfied. In our case the probability of crossover and mutation are Pc = 0.9 and Pm = 0.01 respectively. Candidate solutions represent the angle 0, in the interval [-T, + ] (see Figure 1). They are mapped in 16- bits word using the function: R(O) (= \u00b1 T2)(2 1) with bi + b2+ b3 1 where: Fp(O) hi x (2 -0 Op) and F1(0) h2 X (7 - 01Q) are attractive fields. Fob (0) >Zk (r )2 and F0b' (0 )Z C,k are Coulomb's fields where ri is the distance between the predator i (or the prey in the case of the function Fobj) and the obstacle j along the k direction , and R5k is the distance between the predator i (or the prey in the case of the function Fpobj) and the j predator along the k direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003409_rspa.2007.0106-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003409_rspa.2007.0106-Figure1-1.png",
        "caption": "Figure 1. The pre-bifurcation state in a prestressed annular thin film subjected to a uniform displacement field on the outer boundary (rZR2) and azimuthal shearing on the inner rim (rZR1). The radial and orthoradial stress distributions shown in (a) are both tensile but, as indicated in (b), one of the two principal stresses s1 and s2 can become compressive in a certain part of the annular domain.",
        "texts": [
            " The attractive feature of the boundary-layer method adopted is that approximations for the critical wrinkling load and the asymptotic structure of the corresponding localized eigenmodes are obtained naturally along the way. Comparisons with direct numerical simulations are included in \u00a74, and we conclude in \u00a75 with a summary and brief discussion. The model adopted in this paper was introduced and discussed in Coman & Bassom (2007c), so here we restrict ourselves to highlighting only the main features. The general setting is depicted in figure 1a: a clamped annular film of inner radius R1, outer radius R2 and thickness h (h/R2/1) is stretched by imposing the uniform displacement field U0O0 around the outer edge while the inner boundary is rotated through some (small) angle by the application of a torque M. Classical plate theory is used to describe the statics of the thin film and the notation used is standard. Assuming an axisymmetric deformation prior to the onset of instability, the pre-bifurcation state of stress is easily deduced by solving the system of equations for plane stress elasticity",
            " In particular, lh M\u00f01Kn2\u00de pEhU0R2 and m2h12 U0R2 h2 ; \u00f02:2\u00de where E is the appropriate Young\u2019s modulus. We see that l is a dimensionless quantity proportional to the ratio between the shear stress and the initial tension in the annulus, while m measures the dominance of membrane action over bending effects. The assumptions used tacitly in the asymptotic analysis included in \u00a73 are: (i) hZOS(1) and (ii) m[1. The second assumption is quite natural as mfR2/h and reflects our interest in the thin-film limit of the configuration described in figure 1a. We mention in passing that Dean\u2019s original work and a related numerical contribution by Bucciarelli (1969) dealt with the complementary case m/0. If sh s(r, l, h, n) denotes the second-order plane stress tensor that characterizes the pre-bifurcation state due to the applied loads, it is known that this tensor has exactly one negative eigenvalue within the annular region h!r! rh 4h4\u00f01Kn\u00de2 Cl2 1Kh2 2 4\u00f01Cn\u00de2 ( )1=4 ; \u00f02:3\u00de as long as lO 4h2 ffiffi n p 1Kh2 hl0: \u00f02:4\u00de The expression that appears on the right-hand side of the inequality (2.4) represents the loading parameter threshold that marks the onset of compressive stresses in the film; in the case of a true membrane (i.e. mZN), this corresponds Proc. R. Soc. A (2007) to the critical wrinkling load. For the sake of completeness, a sketch of the prebuckling principal stress distribution in the annular domain is included in figure 1b. Solutions of the eigenproblem (Pm) are sought in the form w\u00f0r; q\u00deZW \u00f0r\u00deexp\u00f0inq\u00de W \u00f0r\u00dehW1\u00f0r\u00deC iW2\u00f0r\u00de \u00f02:5\u00de with the understanding that the real part of (2.5) represents the physical quantity, and where n2N is the mode number (the number of identical halfwaves of the wrinkling pattern). Using the normal-mode ansatz (2.5), it is found that the complex amplitude WhW(r) satisfies the differential equation W 000 0CA\u00f0r\u00deW 000 CB\u00f0r\u00deW 00CC\u00f0r\u00deW 0CD\u00f0r\u00deW Z 0; \u00f02:6\u00de where A\u00f0r\u00deh 2 r ; B\u00f0r\u00dehK 2n2 C1 r2 Cm2 AC B r2 ; C\u00f0r\u00deh 1 r 2n2 C1 r2 Km2 AK B r2 C iln r2 and D\u00f0r\u00deh 1 r2 n2\u00f0n2K4\u00de r2 Cm2 n2 AK B r2 C iln r2 : Equation (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001281_robot.1990.125991-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001281_robot.1990.125991-Figure3-1.png",
        "caption": "Figure 3. An Adept robot in a polyhedral environment. All links are modeled as line segments. Link I ran touch the two obstacles a t the back.",
        "texts": [
            " The stick-figure approximation of robot links is as follows. The links are approximated by a union of cylinders. Then obstacles are grown in all directions by the radius of the cylinders, and the robot links are shrunk t o the cylinder axes. The intersection detection is done between the cylinder axes and the unions of the triangles approximating the surfaces of' the grown obstacles. Link 3.2: III. EXAMPLE 1,ink 4 : The above derivaliou is applied to a 4 degrtics of freedom Adept robot in a block world as shown in Figure 3. Each link and the long object in the gripper is represented with a line segment. Link 3.1 is the vertical arm casing with a fixed It:ngtti, anti L i n k 3.2 is the verlically moving a rm of a variable length. Note ( I 3 is a sliding joint variable. Given a triangular face of an obstacle whose vertices are ( ~ ~ , y , , z ~ ) for 1'=1,2,3, the riiatrix equation (4) for each link becomes Link 1 : I,ink 2: I,irik 3.1: !Icos(Hl) + II2co~(HI+H,) L Isin( 0 I ) + L 2sin( H + H,) ti, ~ L , 1 where t l , and 1,: denote thc length and height of I-th link, and p is the elevation angle (froill the horizontal plane) of Link 3 ",
            "1: ti , = ( I l + cos ' ( k ( Y ~ S ( O l + k ) + k ) + k 0, = k ( : o s ( O ] + k ) + kcos( (I l+tI ,+k) + k l Link 3 . 2 : I,ink -1: 0 , = k O l O , + 1 cos [ kcos( 0 + k ) + k cos(Hl + H, t k ) + k B,+ k k1 H, = k - ~ , - ~ , + t a n - ' 1 kcos( f i1+k)+kcas(H1+H2+k)+k + C O S - ' a = ksin(H,+H,+k) + ksin(H,+k) + kH3 + k b = kcos(H,+H,+k) + kcos(Hl+k) + kH3 + k. The constants k ' s involve dot and cross products of z,, y,, z, and arctangents and square roots of the products. The exact expressions of the boundary equations are shown in Appendix. The CO for 8 , and 0, for the setting in Figure 3 are shown in Figure 4. They are computed at an angular resolution of 2 degrees, and it took 4 seconds on a 3 MIPS VAX machine t o generate them. IV. CONCLUSIONS The boundary equations of configuration obstacles for stick-figure manipulators in three-dimensional polyhedral environments are presented. For a manipulator whose kinematics is represented in DenavitHartenberg notation, it is shown tha t the boundary equations for the n - th joint variable can be solved explicitly in terms of the previous joint variables"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002957_tmag.2006.871448-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002957_tmag.2006.871448-Figure1-1.png",
        "caption": "Fig. 1. One of the typical structures of the 4QT electrical machine.",
        "texts": [
            " Index Terms\u2014Electrical machine, finite-element method, four-quadrant transducer, inductance. I. INTRODUCTION A four-quadrant transducer (4QT) is a hybrid electric vehicle (HEV) power train concept [1]\u2013[4]. Basically, the idea of the 4QT system is to transfer the requirements for speed and torque of the wheels of a vehicle to a high-efficiency operating point of the internal combustion engine (ICE) in the most efficient way. One of the typical structures of the 4QT electrical machine is shown in Fig. 1. It comprises three parts: the stator with the three-phase windings, the outer rotor with the radially-magnetized permanent magnets on both sides, and the inner rotor with the three-phase windings fed via slip rings. The stator and outer rotor operate as one machine called stator machine (SM), and the outer rotor and inner rotor operate as another machine called double rotor machine (DRM). A prototype machine was manufactured. The inductances were measured and calculated. The influence of the saturation and saliency on the inductances is investigated in this paper. For permanent-magnet synchronous machines, d axis is the axis of the magnetic pole, i.e., the axis of a permanent magnet in Fig. 1, and q axis is the axis between two magnetic poles, i.e., the axis between two permanent magnets. In Fig. 1, the d or q axis of the SM coincides with that of the DRM, and they are labeled \u201cd\u201d and \u201cq.\u201d The saliency means the difference between the d- and q-axis permeance from the aspect of structure. It has great influence on the inductances and torque of the machines. There is obvious saliency for the SM, but there is little saliency for the DRM due to the close permeability of the permanent magnets (NdFeB) and air. Digital Object Identifier 10.1109/TMAG.2006.871448 D- and q-axis inductances are important parameters for permanent-magnet synchronous machines, and some determination methods have been developed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000319_1.1519275-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000319_1.1519275-Figure5-1.png",
        "caption": "Fig. 5 Calculation of tensile stress: \u201ea\u2026 Location of critical point; \u201eb\u2026 Determination of x dimension from a tooth layout",
        "texts": [
            " In this paper, we choose the load that will keep the critical tooth tensile stress or tooth contact stress the same for different gear designs. The gear stress calculation formulas are adopted from Dudley\u2019s work @26#. In this work, a gear tooth is modeled as a stubby cantilever beam. Lewis formula is used for the calculation of tensile stress for gear tooth. The critical point in the root fillet of the gear can be determined by inscribing a parabola into the tooth profile which is tangent to root fillet at point a. The parabola has its origin where the load vector cuts the center line. It is shown in Fig. 5~a!. The Lewis formula is expressed as st5 Lt W~2x/3! (6) In Eq. ~6! Lt is the transverse component of the applied load. W is the tooth width. x is shown in Fig. 5~b!. The stresses on the surface of the gear teeth are determined by Hertz\u2019s formula. The compressive stress at the pitch line of a pair of spur gears can be expressed as: sc5A 0.70 ~1/E111/E2!cos f sin f A Lt Wd S mG11 mG D (7) In Eq. ~7!, f is pressure angle. E1 and E2 are the modulus of elasticity of pinion and gear respectively. Lt is the transverse com- 798 \u00d5 Vol. 124, DECEMBER 2002 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 09/09/20 ponent of the applied load. d is the pitch diameter of the pinion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001600_05698198308981480-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001600_05698198308981480-Figure1-1.png",
        "caption": "Fig. 1-Ringon-block wear tester",
        "texts": [
            " All of these results demonstrate that lubricant chemical effects on the fatigue life of test specimens and bearings can be significant and have a pronounced influence on metal fatigue. Water, base stock, and lubricant additive-material interactions create a complex problem for bearing manufacturers when these environmental factors are encountered. EXPERIMENTAL PROCEDURE The experimental plan involved using the ring-on-block tester to evaluate the chemical reactivity of lubricant for. nlulations through weight loss measurements. A schematic of the tester is given in Fig. 1. A more detailed discussion of the ring-on-block tester and test specimens is given in ASTM test method D-2782. The author's tester, however, was modified to maintain accurate control of the oil inlet temperature and the internal electrical heating element was replaced with an external heatingjacket. The external heating jacket was installed around the lubricant reservior tank for the purpose of providing uniform heating and eliminating possible degradation effects on lubricants from single-element heating"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002844_kem.306-308.211-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002844_kem.306-308.211-Figure3-1.png",
        "caption": "Fig. 3 Finite element model of connecting rod and design variables",
        "texts": [
            " \u2211 \u2212 \u2211 \u2212 \u2212= = = vn i i vn i ii yy yy R 1 2 2 12 ))(( ))(\u02c6)(( 1 x xx (6) where )(\u02c6 i y x is the corresponding predicted value for the observed value )( i y x at validation points and y is the mean of the observed value and v n is the number of validation points. Connecting rod is the core component of internal combustion engine to transmit the gas pressure acting on the piston to crankshaft. From the kinematical viewpoint, it transfers reciprocal motion of piston to circular motion of crankshaft. Thus, connecting rod is subjected to both compressive and tensile loads alternately. Since this loading condition produces the alternating stress, design of connecting road is required to consider fatigue life. As shown in Fig. 3, connecting rod consists of three parts as small end, rod, and big end. Design variables and parameters are described in configuration of connecting rod. Young\u2019s modulus, yield stress, and poission\u2019s ratio are )GPa(200 , )MPa(814 , and 33.0=\u03bd , respectively. As boundary condition, all degrees of freedom on bottom of big end are fixed. Loading condition is concerned with fundamentals of engine operation; maximum compressive load exerts at the top or bottom during power stroke and maximum tensile load exerts at the top of exhaust stroke"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002301_105994905x75484-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002301_105994905x75484-Figure5-1.png",
        "caption": "Fig. 5 Schematic diagram of TIMETAL 15-3 pneumatic environmental control system on the Boeing 777 (Ref 10)",
        "texts": [
            " Note that lower-temperature aging cycles are less affected than higher-temperature aging cycles. There is also a significant effect of heat-up rate. The inherently slow heat-up rate (such as in a vacuum furnace) used during the manufacture of parts typically results in an acceptably aged structure. The early promise of cold-formable alloys as a panacea for all fabricated titanium sheet metal structures has not been fully realized. Nevertheless, there are several applications in which the attributes of cold-formable alloys have proven to be useful in modern aerostructures. As shown in Fig. 5 and 6, TIMETAL 15-3 strip is now used Journal of Materials Engineering and Performance Volume 14(6) December 2005\u2014705 in the environmental control system ducting of several aircraft models, including the Boeing 777 and Airbus A380. TIMETAL 15-3 ducting has been used in the Boeing 777 since 1992 (Ref 1). Using TIMETAL 15-3 instead of commercially pure titanium saves approximately 64 kg (140 lb) per Boeing 777 aircraft (Ref 10). Tubing wall thicknesses are typically 0.5 mm (0.020 in.) or 0.8 mm (0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001403_027836498900800504-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001403_027836498900800504-Figure10-1.png",
        "caption": "Fig. 10. Singular configuration for the 2D parallel manipulator.",
        "texts": [
            " Thus we will consider any subset of 1, 2, 3 segments and determine the condition for which any such subset has a rank less than 1, 2, 3. The cases of I and 2 segments are rather trivial: for one line we have only to verify that this line exists, and for two lines, that the lines are distinct. This is clearly the case if we except the configuration where the base and the mobile are collinear. We will consider now the whole system of three bars. By reference to Figure 6 we can see that the only possibility for a system of three coplanar bars to be a 2-rank Grassmann variety is obtained when the three lines cross the same point (Fig. 10). In particular, if the mobile and the base are homothetic, we get a Fig. 9. 2D parallel manipulator. rather disturbing singular configuration when the base and the mobile are parallel, whatever their relative position is. This is easy to verify by building a paper model. Another design is straightforward to avoid the above singular configuration (Fig. 11). We can see here that whatever the position of the mobile is, the three segments cannot cross the same point. 5. Study of the TSSM We will deal now with the case of the TSSM (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002896_b605399h-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002896_b605399h-Figure1-1.png",
        "caption": "Fig. 1 (A) Schematic of a segmented microtubule on a kinesin surface. The spherical cobalt ferrite particles are conjugated to the biotinylated (BTU) segment of the microtubule via a neutravidin linkage. (B) Schematic of the magnet, flow cell and objective configuration.",
        "texts": [
            ", \u2018\u2018seeds\u2019\u2019) were prepared by centrifuging the 2.3% BTU microtubules to remove any unpolymerized biotin-labeled tubulin, resuspending them in paclitaxel-free buffer, and shearing them by thrice passing through a 30-gauge needle. The resulting seeds were then stabilized by diluting to 32 nM in tubulin in a solution containing 10 mM paclitaxel in buffer.10 The biotinylated microtubules were then magnetically labeled with biotinylatedCoFe2O4 using a neutravidin crosslinker, schematically shown in Fig. 1A, following a previously published method.6 The exact a The Pennsylvania State University, Department of Chemistry, 104 Chemistry Building, University Park, PA 16802, USA. E-mail: mbw@chem.psu.edu; Fax: \u00fe1 814 865 3292; Tel: \u00fe1 814 863 3547 bThe Pennsylvania State University, Department of Bioengineering, University Park, PA 16802, USA. E-mail: wohbio@engr.psu.edu; Fax: \u00fe1 814 863 0490; Tel: \u00fe1 814 863 0492 This journal is c the Owner Societies 2006 Phys. Chem. Chem. Phys., 2006, 8, 3507\u20133509 | 3507 Pu bl is he d on 0 9 M ay 2 00 6. D ow nl oa de d by A st on U ni ve rs ity o n 25 /0 1/ 20 14 1 4: 59 :5 5. View Article Online / Journal Homepage / Table of Contents for this issue number of magnetic particles that are attached is not known, however it is assumed to be proportional to the amount of biotin functionalities on the microtubules\u2019 surfaces. In all alignment experiments, a flow cell (shown in Fig. 1B), prepared by affixing two glass coverslips with double-sided tape, was perfused sequentially with a casein solution (0.5 mg mL 1) for 5 minutes and then a solution of inactive Drosophila melanogastor kinesin, a preparation of hexa-His tagged kinesin that is truncated at amino acid 559, is not motile, and displays irreversible binding to microtubules. After 5 min incubation with kinesin, the magnetic microtubule solution was added, and the flow cell was then exposed to a magnetic field using a 5 mm edge length cube NdFeB permanent magnet (Engineered Concepts, Inc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003211_detc2007-34379-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003211_detc2007-34379-Figure9-1.png",
        "caption": "Figure 9: Correction due to Indentation",
        "texts": [
            " In practice, due to very ssible to use \u03b4 and \u03b1 of previous ation Issue for Hertzian Conta using Rigid Search tact assumption fits Hertz theory, i.e. u curvatures ar con middle. When looking for location of these middles using rigid profiles, locations are found with no indentation. Doing this, the lateral displacement Y of one profile with respect to the other is the input parameter. During elastic dynamical that both profiles can interfere with an indentation \u03b4 (blue body at abscissa Y1 interfering with the green body in the figure 9). Normal contact force depends on \u03b4 and profiles curvatures. If the contact location is looked for using this Y1 abscissa, it'll be found too high (magenta circle), thus, in order to find the p Y2 abscissa such as : Y2 = Y1 \u2013 \u03b4 . sin (\u03b1) In principle iterations should be necess c small time steps necessary to integrate dynamical equations, it is po me step. ti The third step also takes into account the same actual relative wheel/rail situation and consists in looking for possible \u201csecondary\u201d positive indentations at stored locations corresponding to these edges situated on opposite sides of the gutters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000877_bf00384690-Figure1.1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000877_bf00384690-Figure1.1-1.png",
        "caption": "Fig. 1.1. A hydraulic hose reinforced by one steel braid consisting of two families of wires. The latter are interwoven symmetrically along helicoidal lines.",
        "texts": [
            "n general, a reinforced hydraulic hose consists of two rubber cylinders, interconnected by a braid of steel wires (Fig. 1.1). Its function is to convey a fluid with a high internal pressure, say 4-30 MPa. Hence, it must conform to two more or less conflicting requirements, viz. the capability of withstanding the high pressure, yet retaining a certain amount of flexibility. To this end the braid usually consists of two families of wires linked up in ribbons and wound helicoidally along the steel cylinder. The two families are interwoven and add up to a regular and symmetric pattern. The properties of high strength and pliancy make the hydraulic hose suited to the purpose of transmitting hydraulic power between moving machine parts and of conveying control pressure signals along tubes at the bottom of the sea in off-shore plants"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002671_tsmcb.2006.870636-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002671_tsmcb.2006.870636-Figure7-1.png",
        "caption": "Fig. 7. Graphical description of (a) \u03be1(Ddiff(k)), (b) \u03be2(Ddiff(k), \u03b8wall(k)), and (c) \u03be1(Ddiff(k)) + \u03be2(Ddiff(k), \u03b8wall(k)).",
        "texts": [
            " For wall following, the desired rotational velocity of the agent is determined by the control parameters as follows: \u03c9d(k) = (\u03be1 (Ddiff(k)) + \u03be2 (Ddiff(k), \u03b8wall(k))) \u00b7 \u03c9max (16) where \u03c9d(k) is defined within the range from \u2212\u03c9max to \u03c9max, taking into consideration the motor torque constraints. The rotational velocity is positive for a CCW rotation about the Zb axis, and vice versa. The weight functions \u03be1(Ddiff(k)) and \u03be2(Ddiff(k), \u03b8wall(k)) are defined as follows: \u03be1 (Ddiff(k)) = Ddiff(k) Dref (17) \u03be2(Ddiff(k), \u03b8wall(k))= ( 1 \u2212 \u2223\u2223\u2223\u2223Ddiff(k) Dref \u2223\u2223\u2223\u2223 ) \u00b7 ( \u03b8wall(k) 2 3 \u00b7 \u03b8sr ) (18) where Ddiff(k) and \u03b8wall(k) are defined within the range from \u2212Dref to Dref and within the range from \u22122/3\u03b8sr to 2/3\u03b8sr, respectively. The characteristics of the weight functions are illustrated in Fig. 7. As shown in Fig. 7(a), the weight function \u03be1(Ddiff(k)) is determined for the agent to approach the reference line for wall following. That is, the function makes the agent turn toward the reference line at the rotational velocity in proportion to Ddiff . As shown in Fig. 7(b), the weight function \u03be2(Ddiff(k), \u03b8wall(k)) determined by both Ddiff(k) and \u03b8wall(k) is sensitive to \u03b8wall(k) at Ddiff(k) = 0 rather than atDdiff(k) = \u2212Dref orDdiff(k) = Dref . This causes the agent to turn its heading direction to the tangent of the reference line quickly when the agent is located in the neighborhood of the reference line. Therefore, the desired rotational velocity \u03c9d(k) is determined by the sum of both weight functions, as depicted in Fig. 7(c), where the agent approaches the reference line and runs parallel with the line. In this case, the desired velocity \u03c9d(k) is applied to the agent practically for wall following when the wall-following conditions vcmd(k) > 0.9vmax and \u03c1\u2032 \u2264 2Dref are satisfied. The first condition implies that the operator intends to drive the agent quickly, and the second implies that the distance to the wall model is less than the beginning distance 2Dref for wall following. Under such conditions, it is difficult for the operator to drive the agent by his own efforts without colliding with obstacles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000562_irds.2002.1041666-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000562_irds.2002.1041666-Figure2-1.png",
        "caption": "Figure 2: Model definition",
        "texts": [],
        "surrounding_texts": [
            "1 Introduction\nilfter the Raibert\u2019s excellent works [l], one-legged hopping robots attached with only the leg spring, have been widely studied both experimentally [2, 3, 4, 51 and theoretically [S, 7, 81. In addition to the leg spring, hip spring also plays important role for animal running 191. It enables the leg to be swung passively. Tompson and Raibert showed that spring-driven oneleggcd hopping robot shown in Figure 1, can hop without any inputs, provided if the initial conditions are appropriately cho-\nsen [lo]. Therefore, this model is a good template model for the purpose of studying energy-efficient running. Since this model is shown to be marginally stable and eventually falls without controls, some suitable controller should be applied to ensure the stability.\nAhmadi and Buehler applied Raibert\u2019s celebrated Foot Placement Algorithm [l] to this passive hopping robot, in which the Neutral Point should be preapproximated. They realized energy-efficient h o p ping in simulation and experiment [U, 121. On the other hand, FranGois and Samson derived new controller different from Raibert\u2019s [13]. They applied general control method used in nonlinear oscillatory system. That is, first constructing Poincare map (discrete system), then linearizing it around fixed points, and finally applying some linear feedback to get asymptotically stable periodic orbit. However, since the model cannot be integrable, both examples above need approximated models, or approximated periodic solutions, to derive the controllers. The re fore, there remains static error comes from the modeling error. In this paper, inspired from RanGois and Samson\u2019s work [13], we present a novel controller to realize energy-efficient onGIegged hopping. Instead of depending on some pre-planned periodic solutions, or target dynamics, here we utilize the intrinsic dynamics of the original nonlinear hybrid system to make the robot generate natural hopping gaits. A model description is the same as those in [13] and reviewed in Section 2. Since our goal is energy-efficient hopping, wc explore the condition of energy-preservation and continuation in Section 3. Then, we derive a control law to ensure those conditions and show the simulation resuts in Section 4. In Section 5, two parameter adaptation laws, one for asymptotic stabilization to desired periodic gait, and the other for input minimization, are given.\nSimulation results shows that the controllers we invented have much potential for energy-efficient control of legged running robot.\n0-7803-7398-7/021$17.00 02002 IEEE 2625",
            "2 Model description of passive hopping robot\nWe consider exactly the same model of passive hopping robot as [13] in this paper. In this section, the model description is reviewed.\n2.1 M o d e l definit ion and no ta t ion\nWe consider the planar onelegged hopping robot shown in F igu re 2. The robot is attached with not only the leg spring hut also hip spring.\nWe impose the following assumptions on the model as seen in many related literatures.\n(A) The center of mass (COM) of the body is just on the hip joint and COM of the leg lies on the leg\n(B) Mass of the foot (unsprung mass) is negligible\n(C) The springs are mass-less and non-dissipating (D) The foot does not bounce back, nor slip the\nground (inelastic impulsive impact)\nIn addition to these assumptions, we further suppose, just for the simplicity, that the COM of the robot is on the hip joint without loss of generality. Table 1 summarizes the variables appear in this paper. The equations of motion are composed of four phases; stance phase, lift-off phase, flight phase, and touchdown phase. Table 2 defines the phase-indicating suffix of the variables. For example, zlo represents the forward velocity of COM at the lift off. Table\n~ i : + K ~ ( T - T ~ ) - M T O ~ = ~ g ( i - + j ~ , i i + ~ ~ 4 j + $ ( M T ~ O ) = rMgsin0 (1) Jbd + Kh(0 - 6) = 7.\nHere, f is the control force to the leg, while T~ is the control torque to the hip joint, which is applied during stance. The spring is initially loaded with the same value of gravity force ( M g ) .\nAt the flight phase, COM of the robot moves along the ballistic flight path and the angular momentum",
            "of the robot around thc COhf is prcservcd\nI x = o\nHere, 7\u201d represents the control torque to the hip joint, which is applied during flight. By the assumption (D) in Section 2.1, the velocities of the generalized coordinates change instantaneously at the touch-down phase, according to thc following equations.\n(3) h d + = d t d - ?td+ = &d+ COS B t d - X t d + Sin e t d .\nHcre,\nPtd- := COS8td f i t d - S i n 8 t d + T O 8 t d - - . (4)\nAt the lift-off phase, there is no discontinuous changes except for ?lo = 0.\n3 Analysis on the energy preservation and continuation\nFor a passive running robot, the analysis on the energy is important because, during complete passive running, the total mcchanical energy is conserved. According to (3), the energy change between just before touch-down and just after touch-down is cdculated to be\nE t d + - E t d -\n( 5 )\nWe call f i t d - \u201cEnergy Dissipation Coeficien?\u2019 because, if the condition\nb t d - = 0 ( 6 ) holds at touch-down and no input is applied to the robot, then total mechanical energy of the system is preserved during hopping. Of course if we apply some control inputs, then the internal energy is not conserved. But we can say that ( 6 ) is necessary condition for complete passive running. Next, we consider the conditions for the robot to sustain hopping without falling to the ground. We can see the condition is found to be\n?td+ < 0. (7)\nThis is the condition for the axial velocity of the leg just after touch-down to be negative. This is well understood if we recognize from Section 2.2 that the necessary condition for the robot to be in the stance phase is T < TO. Unless this condition holds, the hybrid system cannot switch to the stance phase from the flight phase, and hence, it cannot continue time evolution. Note that (7 ) is not always satisfied.\n4 \u201cNon-Dissipative Touch-Down Control\u201d and quasi-periodic hopping gait\n4.1 Control goal\nDue to the compactness of the phase space, if the continuous time evolution is ensured and the total energy is preserved, the solution of this hybrid nonlinear system lies on periodic orbits on the energyinvariant manifold. This invariant hybrid flow is the gait we are searching for. Therefore, we derive controller to ensure the both condition ( 6 ) and (7), and call this new controller \u201cNon-dissipotiue Touch-down Control \u201d. We can do this by applying control inputs only at the flight phase, and allowing the robot freely to move at stance phase with zero inputs. The reason why we are doing so is that if no energy dissipation occurs at touch-down = 0), there is no interaction between the robot and environment, even we use apply control inputs at flight phase. Thcn, the total mcchanical energy of the robot \u201cincluding power source of the actuators\u201d, is exactly preserved. Energy preserving gait in this sense, is what we want. Sincc we are using the control torque only at the flight phase, we define the control input r as follows.\nf = r8 = 0, (8) 7\u201d =: r. (9)\nOur control problem is to find the control input 7 that makes the robot land at the time To, with ( o l d , 8&) satisfying (6). and (7), for any given lift-off states (i~,,Blo,8lor$ro,~lo). Th ugh this is the deadbeat control to bring T,, &, and & - to the desired valucs,,we have only to choose some T, and B t d , because & - is automatically calculated by ( 6 ) . There are, howcvcr, a large number of such pairs (Tu,&) satisfying (7) . Here, we choose the simplest values as follows.\nFirst, we determine T, so that the vertical velocity at touch-down and lift off is the same in magnitude and opposite in direction,"
        ]
    },
    {
        "image_filename": "designv11_28_0002522_jmes_jour_1975_017_003_02-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002522_jmes_jour_1975_017_003_02-Figure3-1.png",
        "caption": "Fig. 3. Computed oil-film pressure distributions along the circumferential direction from dijjferent theories",
        "texts": [
            "4 x 10-4cm; h,/h, = 2. Boundary condition type A : temperature prescribed on surfaces A,, A,, A,, A, and A, of Fig. 2. Boundary condition type B: temperature prescribed on surfaces A,,, A, and A, as shown in Fig. 2. Convergence factor E = 0.005 for all cases except case 3, when E = 0.04 (iteration of pressure). bearing width-to-length ratio, B/L, of 5 is chosen so that the computed pressures and temperatures along the mid-circumference are comparable to those for the infinitely wide bearing (9-04) as plotted in Fig. 3. The prersure curves of isoviscous cases 1 and 4 agree with the isoviscous curve HZ of Hunter and Zienkiewicz (6). The varying mesh lengths in the %-direction in these two cases do not have any effect on the resulting pressure distributions. The non-isoviscous pressure of case 2 (boundary condition type A) is lower than that of case 3 (boundary condition type B) at inlet, but is higher at outlet. Thus, for large BIL ratios, different types of boundary condition of the oil-film volume do not affect significantly the bearing load-carrying capacity",
            " Compared with case 3, the bearing load-carrying capacity of case 5 is higher when the pressure-viscosity effect is taken into account. The pressure curve of case 5 agrees closely with the non-isoviscous curve H, of Hahn and Kettleborough (9). The small discrepancy between these two curves is due to the fact that, in the case of curve H , the variation of density with temperatures is taken into account i\u2018 -1 a denser grid (10 x 10) is used; moreover, the sic\u2018: rage effect of case 5 (B/L = 5) is probably of some inhence. Also shown in Fig. 3 are the isoviscous and nonisoviscous pressure distributions of cases 6 and 7 for the bearing ratio B/L = 1. It can be seen that the pressures of cases 6 and 7 are respectively lower than those of cases 4 and 5 (B/L = 5). The non-isoviscous temperature contours along the bearing mid-circumference in case 5 are different from those of case I,, as shown in Fig. 4. The discrepancy is more noticeable for part of the oil film close to the bearing surface, where the contours of case 5 extend further towards the inlet"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003948_med.2009.5164659-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003948_med.2009.5164659-Figure1-1.png",
        "caption": "Fig. 1. X-Cell 60 SE Instrumented Helicopter Model",
        "texts": [
            " The method is also unreliable to describe low-frequency modes, primarily due to pilot feedback [7]. Other linear model development was given by [8] by using time-domain identification. The system identification approach requires experimental input output data collected from the flight tests of the vehicle. The flying test-bed must be outfitted with adequate instruments to measure both state and control variables. The paper presents an analytical development of linear model for X-Cell 60 small scale helicopter (Fig. 1) based on combination of first principle results and time domain identification. It is demonstrated that the proposed technique can enhance the accuracy of dynamics model obtained from the first principle prediction. Using the technique, the establishment of global helicopter linear model can be achieved for a practical design of linear control laws. A. Modeling Approach The approach to helicopter modeling can be in general divided into two distinct methods. The first approach is known as first principle modeling based on direct physical understanding of forces and moments balance of the vehicle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002008_j.ics.2004.03.176-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002008_j.ics.2004.03.176-Figure3-1.png",
        "caption": "Fig. 3. A load cell (Fig. 5) is mounted on robotic gripper (this figure) perpendicular to the direction of needle insertion and perpendicular to the gripper\u2019s open and closing motion. The gripper has pincers, which align the needle to the pre-planned trajectory when the pneumatic gripper closes.",
        "texts": [
            " However, in order to maintain direct control of the needle or instrument, the interventionalist is exposed to radiation when performing procedures in close proximity to the CT aperture during CT fluoroscopy. This prototype CT-integrated robot system enables remote needle insertion with tactile feedback during CT fluoroscopy. Remote insertion avoids harmful X-rays and preserves tactile feedback. 2. Methods The preliminary system, shown in Fig. 1, consisted of a six-axis, programmable robot (Kawasaki FS-2 with C-70 controller, Wixom, MI) (Fig. 2), seamlessly integrated with the CT scanner\u2019s (Philips IDT 16 Slice Scanner) 3-D coordinate system [7,8]. The robot was equipped with a pneumatic gripper (Fig. 3) customized to align the surgical needle and to sense resistance force associated with insertion through tissue. A remote needle insertion controller provided variable resistance during the remote simulated insertion of a vicarious needle\u2014based on force feedback from the gripper\u2014while simultaneously commanding the robot to drive the surgical needle along a straight path. The tactile feedback loop is illustrated in Fig. 4. Initial alignment to a planned trajectory was performed in the treatment planning phase"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002600_vppc.2005.1554631-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002600_vppc.2005.1554631-Figure5-1.png",
        "caption": "Fig. 5. Illustration of proper adjustment of ICE start (vehicle begins hybrid drive mode)",
        "texts": [
            " This also gives the possibility to choose ICE and PM motor operating points which can significantly influence on energy losses and fuel consumption [5]. In case of \u201cpure electric starting\u201d, after properly adjusting the vehicle speed, ICE starts. In order to avoid negative angular velocity of crown wheel occurring at this moment, the following conditions should be filled: For *33 \u03c9\u03c9 = , 0 and ,0 21 >> \u03c9\u03c9 ; *3\u03c9 is the minimum adjusting speed of vehicle when ICE is starting and then hybrid drive mode will begin. For planetary gearbox, the following equation is fitting: Fig.5. illustrates this analysis and shows the considering relations in 3D form. It\u2019s easy to note the proper area for ICE starting. When 1\u03c9 is lower than the value ')1( 3\u03c9k+ , 2\u03c9 is negative value. In this case it\u2019s possible to accelerate vehicle, but it\u2019s necessary to change the direction of crown wheel speed. ICE should start when vehicle stops. This kind of vehicle starting way is called hybrid starting. There are some explanations for fig.5: In figure: 0 ;0for * 0for ' 0for ' 1233 233 322 >>= == == \u03c9\u03c9\u03c9\u03c9 \u03c9\u03c9\u03c9 \u03c9\u03c9\u03c9 ; )( 21 \u03c9\u03c9 f= is for the condition const dt d =3\u03c9 , and the line )( 31 \u03c9\u03c9 f= is for the condition const dt d =3\u03c9 ; At the crossing point of three axes, 02 =\u03c9 , 03 =\u03c9 , '21 \u03c9\u03c9 k\u2212= . III. ANALYSIS OF DIFFERENT ICE STARTING WAYS When vehicle operates in pure electric mode, there are three ways for engine starting to change vehicle operating mode from pure electric to hybrid: 1) Using external starter; 2) Short-time mechanical braking of PM motor shaft; 3) Short-time electrodynamics braking of PM motor shaft (generator mode) In cases 2 and 3, the same impact can be obtained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000603_2001-01-1007-Figure11-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000603_2001-01-1007-Figure11-1.png",
        "caption": "Fig. 11. The random vectors representing the resultant of the third order component of the engine torque and the third order component of the engine speed.",
        "texts": [
            ",2,1 , , ikikT = === \u03d5\u03d5 \u03c3\u03c3\u03c3\u03c3 (12) In this case, the components of the resultant torque will have the following statistical characteristics [6]: -mean values: \u2211 \u2211 = = = = N i kkk N i kkk iy ix TT TT 1 1 cos sin \u03d5 \u03d5 (13) -standard deviations:      ++ +     \u2212= \u2211 \u2211 = = \u03a4 N i k N k N i k N T ik ikxk T 1 2 1 2 22 1 2 1 2 22 2cos 2cos \u03d5\u03c3 \u03d5\u03c3\u03c3 \u03d5 (14)      \u2212+ +     += \u2211 \u2211 = = \u03a4 N i k N k N i k N T ik ikyk T 1 2 1 2 22 1 2 1 2 22 2cos 2cos \u03d5\u03c3 \u03d5\u03c3\u03c3 \u03d5 -covariance: ( )\u2211 = \u2212= N i kkTxyk ikk TK 1 222 2 1 2sin \u03d5\u03c3\u03c3 \u03d5 (15) Using these formulae to calculate the statistic characteristics for the major harmonic order k=3, one obtains: 2 3 2 33 3323 323 cos sin 3 3 yx iG s y G S x TTT BNpNT pNT T V T V += \u00d7\u2212= = \u03d5 \u03d5 (16) )]2cos1()2cos1([ 3 22 33 2 2 2 333 \u03d5\u03c3\u03d5\u03c3\u03c3 \u03d5 ++\u2212= TT N T x )]2cos1()2cos1([ 3 22 33 2 2 2 333 \u03d5\u03c3\u03d5\u03c3\u03c3 \u03d5 \u2212++= TT N T y (17) 3 22 3 2 23 2sin)( 33 \u03d5\u03c3\u03c3 \u03d5TK T N xy \u2212= (18) The non-zero value of the covariance shows that the principal axes of the ellipse of dispersion are rotated with respect to the axes of coordinates by the angle \u03b3 :      = \u2212 \u2212\u2212 2 3 2 3 321 2 1 tan yTxT xy K \u03c3\u03c3 \u03b3 (19) and the actual values of the half axes of the ellipse of dispersion are: \u03b3\u03b3\u03c3\u03b3\u03c3\u03c3 \u03b3\u03b3\u03c3\u03b3\u03c3\u03c3 \u03b7 \u03c2 2sincossin 2sinsincos 3 22222 3 22222 33 33 xyyx xyyx K K TT TT \u2212+= ++= (20) This situation is represented in Fig. 11, together with the estimated direction of the third order component of the crankshaft\u2019s speed. For non-major harmonic orders k the phase angle diagrams of the cylinder torques (see Fig. 2) are symmetric and: \u2211 \u2211 = = == N i N i kk ii kk 1 1 0cossin \u03d5\u03d5 (21) Then, 0== yx kk TT , but the standard deviations (equations 14) will always have a finite value. In this case the ellipse of dispersion has its center in the origin of the coordinate system. If 2k is a non-major harmonic order, it has also a symmetric phase angle diagram and 02cos2sin 11 == \u2211\u2211 == N i k N i k \u03d5\u03d5 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002372_1.2167651-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002372_1.2167651-Figure5-1.png",
        "caption": "Fig. 5 Lines L1 and L2 are envelopes of all the possible paths in type 1",
        "texts": [
            " It is seen that for the three cases, the Fig. 8 Double points in type 2 when the 438 / Vol. 128, MARCH 2006 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/201 width of the path is equal to 2b1. This result leads us to construct a triangle such that its three corners lie on the path of point C. From the geometry of SBL, one can see that the dead centers occur when OAA AB 10 . So two lines L1 and L2 are limiting positions of coupler AB and also are envelopes of all the possible paths of point C. From Fig. 5 the slopes of two envelopes are: = \u00b1 arctan b1 b3 2 \u2212 b1 2 , 9 Now let v and w denote the tangent points of line L1 and the paths Fig. 5 . Considering the slope obtained in Eq. 9 and intersecting line L1 with path fR and fL the abscissa and ordinate of points v xv ,yv and w xw,yw are obtained as follows: 2 2 condition b1\u2212b3\u00cfa\u00cfb1 is satisfied Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F xv = 1 b3 b1 2 \u2212 b3 2 + a b3 2 \u2212 b1 2 , yv = b1 b3 a \u2212 b3 2 \u2212 b1 2 . 10a xw = 1 b3 3 \u2212 b3 2 \u2212 b1 2 2 \u2212 b1 2 b3 2 \u2212 b1 2 + b3 2a b1 2 \u2212 b3 2 , yw = b1 b3 3 b3 2 \u2212 b1 2 3 + b1 2 b3 2 \u2212 b1 2 \u2212 b3 2a . 10b The construction of this triangle leads to synthesis of the SBLs to rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/201 generate the desired symmetrical closed paths with four points of accuracy t, w, s, and w or u, v, z, and v see Fig. 5 . 3.1.1 The Piecewise Nearly Straight Closed Path. Another importance of the study of the coupler point path in the SBL is the ability of this mechanism in generating the piecewise nearly straight closed paths. This study is performed with considering the curvature of the path of point C. The curvature of the path in the straight part locally goes to infinity. Since the path is expressed using the implicit Eqs. 5 and 8 , to achieve the local curvature, the following equation is used 11 : x,y = \u2212 fxx fy 2 \u2212 2fxyfxfy + fyy fx 2 fy 2 + fx 2 3/2 11 where f = f x,y is implicit function of x and y, denotes the curvature, fx, fy are first partial derivatives and fxx, fxy, and fyy are second partial derivatives of the function f x,y with respect to the x and y"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003413_fbit.2007.97-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003413_fbit.2007.97-Figure4-1.png",
        "caption": "Figure 4. Simulation of the FE model in ABAQUS",
        "texts": [
            "02 >R (9) The viscoelastic parameters were estimated from the normalized force\u2013displacement profiles in the experiments. These computed parameters were fed into the ABAQUS database for the nonlinear elastic parameters. The initial hyperelastic parameters were estimated from a prior knowledge of the experiments. The parameter reached convergence after two or three iterations, as shown in Figure 3. Table 2 presents the initial and estimated parameters for the neo-Hookean model which was 287.5 \u00b1 53.7 Pa. Figure 4 shows the stress and deformation contours of the developed FE model. Figure 5 shows the predicted forces from the FE simulation with the estimated parameter and experimental results. The force responses of the hyperelastic model and experimental data are almost the same from the value of R2. This paper shows an algorithm for effectively characterizing soft tissue\u2019s material parameters for haptic rendering of medical simulations. The viscoelastic and hyperelastic material parameters were estimated in two stages in the QLV framework"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003696_3.5328-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003696_3.5328-Figure4-1.png",
        "caption": "Fig. 4 X, n- con tours in space of z and e/e for a = 7r/2.",
        "texts": [
            " Finally Ae||, generally of second order but required here to be zero, is given by 0 = a 2 - 3) X)] \u2014^ fl - X - (M - D(M - 1 + X) + M2 L \u00b0\u03022 (M - 2 + 2X) (ca + \u0302 \\], 1 - X < M < rs\u00ab2 \\ r / J 0 - \u00ab2 - 3) 3 - X (4.9a) ^\u00b0 ca)[3X - r / - 3 + X)] [x -L 3 + (A* - l)(/i - 3 + X) -4s\"2 ~ 3 ^ (M _ 4) iCa + ^ J , 3 - X < M < 5 - X (4.9b) Equations (4.7-4.9b) define X and n as functions of z and of \u00a30/r = (e_L)o/r (to first order). For the .special case a = 7T/2, A^i = 0 so that ^0/r = (ejo/r = (e^f/r = e/i, and contours of constant X and /-t are shown in the z \u2014 e/i plane in Fig. 4. The 3-impulse subregion is confined between the two heavy lines, the remaining region requiring two impulses. Note that X is discontinuous across the left-most heavy line. % may be assumed positive except in the leftmost 2-impulse region. For Tr/3 < a < w/2, we may introduce the parameter p .= eQ/ef = (ejo/tei)/ = \"&/(& + ^a) in place of \u00a3O/T. Figure 5 shows the X and JJL contours in the z \u2014 p plane for the case ca = J (a = 75.5\u00b0). After X and JLI have been read, the impulse locations are available from (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002474_1.2718220-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002474_1.2718220-Figure4-1.png",
        "caption": "Fig. 4 Geometry of air foil bearings: \u201ea\u2026 Journal bearing and \u201eb\u2026 thrust bearing",
        "texts": [
            " A turboblower having a 75 kW high-speed motor and its rotor configuration are shown in Fig. 2. The machine has maximum pressure ratio of 1.8, and its operating speed range is 20,000\u201326,000 rpm. The rotor consists of a high-speed motor, a cooling fan, an impeller, and rpm wheel, where a motor element, hatched in Fig. 2, is assembled into the shaft with interference fit. The mass of rotor assembly is 11.5 kg, and the rotor is supported by bump-type 17 air foil bearings. Figure 3 shows the thrust bearing and front journal bearing employed, and the geometric parameters are described in Fig. 4 and Table 1. The foil structures were fabricated by plastic forming of spring-tempered sheet metal JULY 2007, Vol. 129 / 843 07 by ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use u r s F b 8 Downloaded Fr sing molds, and they were fixed by spot welding. Polytetrafluooethylene coating was applied to the top foils and the facing urfaces of rotor were hardened above Hrc=50. The machine is designed to be an environmental-friendly sys- ig. 2 Turbo blower and its rotor: \u201ea\u2026 Layout of the turbo lower and \u201eb\u2026 rotor assembly om: http://gasturbinespower"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003459_iciea.2008.4582679-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003459_iciea.2008.4582679-Figure2-1.png",
        "caption": "Fig. 2 The basic structure of turbomolecular pump with active magnetic bearings.",
        "texts": [
            " In this paper, we designed adaptive variable structure controller for turbomolecular pump with active magnetic bearings. The center of gravity that located below the blades of the turbomolecular pump could be schematized as Fig. 1. There were five degree of freedoms controlling by large, small, and thrust active magnetic bearings in this system; two radial displacements, one axial displacement, and two angles of the mass center were x, y, z, \u03b8x, and \u03b8y, respectively. The basic structure of turbomolecular pump with active magnetic bearings could be represented diagrammatically as Fig. 2. The symbol O meant the mass center of the rotor; a and b meant the distance from the large and small magnetic bearing to the mass center in the z direction, respectively; 1 to 10 meant the magnetic poles for magnetic bearings; F1 to F10 mean the magnetic forces for magnetic bearings; the directions of the five degrees of freedoms and the direction of the magnetic forces also showed in Fig. 2. In this paper, the rotor was assumed to be rigid with asymmetric mass unbalance. The mass unbalance was supposed locating upon the mass center due to the vibration happening above the mass center when the system working. Considering the influence of gyroscopic effects and unbalanced forces on system, the dynamic equations of system about the mass center could be expressed as follows: 7531 22 )sincos( FFFFttmxm \u2212+\u2212+\u2126\u2126\u2212\u2126\u2126= \u03b7\u03b5 8642 22 )cossin( FFFFttmym \u2212+\u2212+\u2126\u2126+\u2126\u2126= \u03b7\u03b5 109 FFmgzm \u2212+\u2212=       \u2126\u2126+\u2126\u2126\u22c5\u2212 \u2212+\u2212 =\u2126+ )cossin( )()( 22 8642 ttmc FFbFFa II ypxr \u03b7\u03b5 \u03b8\u03b8       \u2126\u2126\u2212\u2126\u2126\u22c5+ +\u2212++\u2212 =\u2126\u2212 )sincos( )()( 22 7531 ttmc FFbFFa II xpyr \u03b7\u03b5 \u03b8\u03b8 (1) where the significant m was the mass of the rotating shaft; \u2126 was the rotating speed about the spinning axis; x, y, \u03b8x, and \u03b8y were the radial displacements and the angular displacements of the mass center, respectively; Ir and Ip were the transverse and polar mass moments of inertia of the rotor, respectively; F1 to F10 were the magnetic forces for magnetic bearings; \u03b5 978-1-4244-1718-6/08/$25"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003245_acc.2008.4586956-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003245_acc.2008.4586956-Figure1-1.png",
        "caption": "Figure 1: Rotor bearing system with active disk.",
        "texts": [
            " Algebraic identification has already been employed for parameter and signal estimation in nonlinear and linear vibrating mechanical systems by Beltr\u00e1n-Carbajal et al. [10, 11]. Here numerical and experimental results show that the algebraic identification provides high robustness against parameter uncertainty, frequency variations, small measurement errors and noise. The rotor-bearing system consists of a planar and rigid disk of mass M mounted on a flexible shaft of negligible mass and stiffness k at the mid-span between two 978-1-4244-2079-7/08/$25.00 \u00a92008 AACC. 3023 symmetric bearing supports (see Fig. 1 when a = b). Due to rotor imbalance the mass center is not located at the geometric center of the disk S but at the point G (center of mass of the unbalanced disk), the distance u between these points is known as disk eccentricity or static unbalance (see Vance [12]; Dimarogonas [13]). In our analysis the rotor-bearing system has an active disk mounted on the shaft and near the main disk (see Fig. 1). The active disk is designed in order to move a mass m1 in all angular and radial positions inside the disk, which are given by \u03b1 and r1, respectively. In fact, these movements can be got with some mechanical elements such as bevel gears and ball screw (see Fig. 2). The mass m1 and the radial distance r1 are designed in order to compensate the residual unbalance of the rotor bearing system. An end view of the whirling rotor is also shown in Fig. 3, with coordinates that describe its motion. The coordinate system (\u03b7, \u03be, \u03c8) of this figure is fixed to the active disk, and the coordinate system (X,Y,Z ) is an inertial frame with Z the nominal axis of rotation",
            " The proposed control objective consists of reduce as much as possible the rotor vibration amplitude, denoted in adimensional units by R = p z21 + z23 u (3) for run-up, coast-down or steady state operation of the rotor system, even in presence of small exogenous or endogenous perturbations. In the following table are given the rotor system parameters employed troughtout the paper: Table 1: Rotor system parameters M = 1.2 kg m1 = 0.003 kg a = b = 0.3m \u03b2 = \u03c0/6 rad \u03b1 = 0 rad rdisk = 0.04m u = 100\u03bcm c\u03d5 = 1.5\u00d7 10\u22123 N m/ s D = 0.01m We are proposing to use an active disk for actively balancing of the rotor (see Fig. 1 and Fig. 3). We can see that if the mass m1 is located at the position\u00b3 r\u0304 = Mu m1 , \u03b1\u0304 = \u03b2 + \u03c0 \u00b4 the unbalance can be cancelled. In order to design the position controllers for the balancing mass m1, consider its associated dynamics: z\u03077 = z8 z\u03078 = 1 m1 \u00a1 F \u2212 gm1 sin z9 +m1z7z 2 10 \u00a2 z\u03079 = z10 z\u030710 = 1 m1z27 (\u03c42 \u2212 gm1z7 cos z9 \u2212 2m1z7z8z10) y2 = z7 y3 = z8 From these equations, one can get the following nonlinear controllers with integral compensation to take the balancing mass to the equilibrium position (y\u03042 = r\u0304 = Mu m1 , y3 = \u03b1\u0304 = \u03b2 + \u03c0): F = m1v2 + gm1 sin z9 \u2212m1z7z 2 10 (4) \u03c42 = m1z 2 7v3 + gm1z7 cos z9 + 2m1z7z8z10 (5) with v2 = y\u0308\u22172 (t)\u2212 \u03b321 [y\u03072 \u2212 y\u0307\u2217 (t)]\u2212 \u03b321 [y2 \u2212 y\u22172 (t)] \u2212\u03b320 Z t 0 [y2 \u2212 y\u22172 (\u03c3)] d\u03c3 v3 = y\u0308\u22173 (t)\u2212 \u03b332 [y\u03073 \u2212 y\u0307\u22173 (t)]\u2212 \u03b331 [y3 \u2212 y\u22173 (t)] \u2212\u03b330 Z t 0 [y3 \u2212 y\u22173 (\u03c3)] d\u03c3 where y\u22172(t) and y\u22173 (t) are desired trajectories for the outputs y2 and y3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003776_j.wear.2008.07.008-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003776_j.wear.2008.07.008-Figure10-1.png",
        "caption": "Fig. 10. FE mesh of spur gear in contact including gear data.",
        "texts": [
            " Changes in the bulk geometry may lter the stiffness, k, and following the transient rolling length, L0, ignificantly. e and tractive load, see text for details, (a) constant s < slimit, the markers indicate ween constant and linearly increasing slip at equal accumulated applied slip. 324 J. Dahlberg, B. Alfredsson / Wear 266 (2009) 316\u2013326 .69 in Fig. 7(a): (a) Q/ P = 0.5 and (b) gross sliding with Q = P. t c b i o 5 t w E s F s c w g o 5 a H n n s d n n [ s o 5 s i u s l s t t c a T geometry in Fig. 10 and varied during the engagement according to Fig. 12(a) top. The region close to the pitch-circle is magnified in Fig. 12(a) bottom. In this region the slip increase was approximately linear with gk/aE\u2217 = 0.33 mm\u22121, which with = 0.3 gave a/gR\u2217 = 0.025. Fig. 9. Surface parallel stress component, yy , for sR\u2217/ a = 1 Fig. 3(a) shows that the relation between s and contribute o long transient distances. In particular, low slip and high coeffiient of friction may give long transient distances. Rapid transient ehaviour was notably found for large slip, small and stiff bodies, ",
            " 1(a), than in front of the braking cylinder. This on-symmetry corresponded to and could in principle explain the on-symmetry noted for contact entering and exiting asperities in 14]. At gross sliding, i.e. later during the same rolling sequence, the tress profiles were equal but mirror with respect to contact entry r exit sides, see Fig. 9(b). .5. Case study: Gear contact A spur gear contact close to the pitch-circle was used as a case tudy of transient rolling with linearly increasing slip. The gear data s included with the FE mesh in Fig. 10. The FE model was evalated using MARC [18] and it contained 16296 four-node plane train elements. During rolling, 17\u201318 elements with 41 m side ength on the investigated side contacted elements with 61 m ide length on the opposite side. The model was linear elastic and F F he internal FE slip contact prameter e = 1 m, see Fig. 5(b). The ransient traction profile on the pinion was captured at 6 instants lose to the pitch-circle, see Fig. 11. At this position, P = 895 N/mm nd R\u2217 = 10.8 mm, which with E\u2217 = 113 GPa gave a = 0",
            " 11(f), the contact was at the position where ositive gross sliding started. The tangential load transmitted at nstants from Fig. 11(c)\u2013(f) are plotted against normalized roll disance in Fig. 12 (b). Here, the rolling distance start at the position here Q = 0. The figure also include results from an identical gear imulation with = 0.05 and predictions by Eqs. (16) and (18) with = 0.05; 0.1; 0.3, i.e. a/gR\u2217 = 0.0042; 0.0084; 0.025. The stiff- ess, k, was estimated from the gear contact. The teeth in Fig. 10 ere brought into contact at the pitch-circle. Well in contact, one ooth was displaced perpendicular to the line of action. The average f the tangential displacements just outside each contact rim was sed to determine k = 34 000 N/mm2. The FE results in Fig. 12(b) suggested that the transient change f traction load in the gear contact was faster than predicted by q. (16). The deviation was believed to be a result of non-zero ig. 13. Development of traction at the pinion surface just after the pitch-circle for he case where was changed at the pitch-circle from = 0 before it to = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002785_1.3438180-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002785_1.3438180-Figure5-1.png",
        "caption": "Fig. 5 'Output angular motion-RCCC mechanism",
        "texts": [],
        "surrounding_texts": [
            "'\" o ~o N.~ o <:(\na:: ':~ (!)O wto o\n:~ o o\n00 <:(0 a:: \u2022 ,~ ., (!)\n'\" o o\no o o OJ , o~ o \u2022 g~ -0 ,- o~ 0' o l\" N ,\nWo 0 eo 0\n'~~+----,----,..----,----=------'t~ '0.00 90.00 180.00 270.00 3sd.oo\nI NPUT ANGLE e mEG. )\nFig. :~ Relative coupler motion-RRSS mechanism\nThen the fixed revolute axis is located ao, the point where the normal from the point al meets the revolute axis Uo, and is given by\nao = ao' + (uO'(al - ao'))uo (26)\nThe list of linkage parameters useful for function-generation syn thesis becomes\n(27)\nwhere (3 denotes the twist angle between the revolute axis uoand the output cylindric joint axis, u, = (1, 0, 0)'.\nDisplacement Analysis. For a given input rotation fJ, we wish to determine the output rotation cp, the relative coupler rotation a, and the translations s, Sa, So along the cylindric joint axes Uc, Ua, Ub, respectively. Therefore, we make the following geometric observations.\n(a) The angle between the axes Ua and Ub is constant.\nUb/ = [R(O, UO)]Ubl\nAlternatively, we could very well employ\nUb = [R(fJ, uo)] [R(a, Ua1)]Ubl (32)\nand similarly find expressions for E, F, G in order to solve for O!, the relative coupler rotation. (c) F?'om au?' identification of the RCCC mechanism, we have\nb, = b,\" = [R(cp, U,)]b'l + su, + SbUb\nwhere, with link ED normal to axis U\"\nb\"\nb'l' [R(fJ, uo)](b\" - ao) + ao\nb, [R(a, ua)](b,/ - a) + a + SaU a\n(33)\nThe above equation (33) is linear in s, Sa, Sb, and easily solved RS\n5 = (S, Sa, Sb)' = D-1d\nwhere the direction-cosine matrix D is\nD = rUe, - Ua, Ub]\n(34)\n(28) and the right-hand-side vector is\nwhere,\nThe equation (28) above has two solutions for the angular dis placement cp, which are given by equation (13) except that we have\n(b)\nwhere,\nE\nF\nUa'[T(u,)]Ubl\nua'[P(U,)]Ubl\nThe angle between the axes Ub and u, is constant.\nUb = [R(a, Ua)] [R(O, UO)]Ubl\n(29)\n(30)\nThe solutions for the relative coupler rotation a are given by equation (19) using\nE u,'[T(Ua)]Ub/\nF u,'[P(Ua)]Uo/ (31)\nG u,'[Q(Ua)]Ub/ - UCtUbl\nwhere,\n484 / MAY 1973\nd = [R(a, ua)](b,/ - a) + a - [R(cp, u,)]b\"\nThe linear and angular displacements associated with the RCCC mechanism can thus be found prior to the velocity analysis.\nThe new position X(x) of a coupler point can now be deter mined in terms of its first position X(XI) as\nx = [R(a, Ua)](XI' - a) + a + SaU a (35)\nwhere\nXl' = [R(fJ, UO)](XI - ao) + ao\nVelocity and Acceleration Analyses. The velocity and accelera tion quantities can be obtained by differentiation of the corre sponding displacement equation(s) and solution to the resulting linear equation(s). Thus from equation (28), we obtain\n1>= Ua'[P(Uc)]uo\n1>2u.'[T(u,)] Ub - 2i1a'ilb - Ua'Ub\nu.'[P(U,)]Ub\nwhere, for sake of completeness, we mention\nVOUa,\nUa Aoua,\n(36)\nTransactions of the AS M E\nDownloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/20/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use",
            "In order to obtain the angular velocity a and acceleration a of the coupler link relative to the driving link, we differentiate equa tion (30) to obtain\no ... N\no o .;\no o\n\"'~\n'\"\n.0 z\"'. ...... 0\n___ ~lg:U)\n-, C/)\no '\" '0.00 90.00 180.00 270.00\nINPUT ANGLE e (OEG.)\nN ,\no o\nFiS~. 6 Output linear motion-RCCC mechanism\no\no\nExample 2. Determine the output motion, the motion of the (37) follower link ED, for the crank-rocker RCCC function-generation\nmechanism given as\nwhere\nUb (Va + VO)Ub,\niib (Aa + 2VaVO + AO)Ub,\nVa a[P(u a )], etc.\nWith the above substitution, equations (37) yield\nor\nu,'(aZ[T(u a)] - 2a[P(ua )] - 2VaVO - AO)Ub\nu,'[P(Ua)] Ub\nUc t Ubl1i=o u,'[P(Ua)]Ub\n(38)\nWe may now proceed to determine the translational velocities by differentiating equation (34). We obtain\n(39)\nwhere,\nd = Vo(b. - ao) + Va(b. - a) - V\u00a2b,\nA similar analysis would lead to the explicit expression for translational accelerations.\nwhere,\nand the derivative form of equation (33) is\nb. = A\u00a2b. + SUe + SbUb + 2SbUb (41)\nKnowing the kinematic motion of the coupler link, we may de termine the instantaneous velocity and acceleration of any coupler point X(x) as\nIi = Vo(x - ao) + Va(x - a) + SaUa\nii = Ao(x - ao) + Aa(x - a) + 2VaVo(x - a) (42)\n+ (saUa + 2s aua )\nJournal of Engineering for Industry\nUo (0.0914, 0.9668, 0.2388)'\nao (-0.8561,0.4430, 1.9135)'\nUa, (0.6264, 0.6892, 0.3640)'\na, ( - 0.2240, 0.5701, 1.1573)'\nUbi (- 0.2287, 0.7290, - 0.6452)'\nb, (0, 0.7416, -0.2441)'\nSb, -0.9724\nThe constant angular speed of the input link CA is unit rad per sec.\nFigs. 5 and 6 display the useful analysis solution that is con tinuously realizable from the present position. The alternative solution may be eliminated by checking closeness of the current position to the preceding position with respect to the output angu lar displacement cf>. The other kinematic quantities-\u00a2, fIj, s, S, ii-are then uniquely determined. The velocity and acceleration curves were verified by numerically differentiating the corre sponding displacement curve using central differences and a step size of f) /10,000.\nDiscussion We have deduced the kinematic solutions for the various spatial four-bar mechanisms from direct differentiation of the rotation matrix.\nAs an alternative approach, it is possible to employ in our derivation classical expressions [16-18] for first and second derivatives of a position vector measured in a moving reference frame, e.g., one which is fixed to the input link at point A(a) for the RCCC mechanism. Thus, the velocity of a coupler point x in the inertial reference frame may be written as\nx = a + x. (43)\nwhere, using subscript r to denote motion relative to the moving reference frame rotating with angular velocity Wo,\nx. Xr + Wo X Xr,\nxr x - a,\nDifferentiating equation (43), we get the acceleration as\nMAY 1 973 / 485\nDownloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/20/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use",
            "ii = ii + ii, where, using X to denote the vector cross product,\n(44) the support of this research through Grant NSF-GK-27835. The invaluable assistance of Bell Laboratories is appreciated.\n)(s iir + Wo X Xr + 2wo X lir + Wo X (wo X Xr),\nWo Ouo,\nlir Wa X Xr + saU a,\nXr wa X Xr + Wa X (wa X xr ) + saUa.\nHere the relative angular velocity and acceleration are given by\n(45)\nand can be obtained by taking derivatives of the relative coupler displacement, a.\nThe purpose of the above elaborate use of classical vector mathematics was to demonstrate the fact that the equations (43) and (44) are identical to the equations (42) derived earlier, in consideration of the following and other similar identities; the Coriolis acceleration term, is\n2(wo X li r ) = 2(VoVa(x - a) + saU a ) (46)\nand the relative angular acceleration terms, are\n(47)\nConclusions A simple geometric method has been presented which is useful for obtaining solutions for the kinematic analysis of plane and spatial mechanisms. In most cases the solutions are available in explicit closed-form. Furthermore, the method offers better geometric insight of the constraints governing mechanism motion than that provided by the matrix loop equations. The kine matic quantities sought for each member are dependent upon a particular set of constraints associated with that member. The method described combines the advantages of both vector and matrix methods in determining the kinematic quantities. The system of constraint equations as formulated may, in general, be solved by numerical methods. The simplicity, accuracy, and efficiency of the analytical method makes it extremely useful for optimum synthesis applications, where the analysis solutions must be computed repeatedly.\nIt is earnestly hoped that the aforementioned analogy between the classical vector approach and the method presented would tend to provide better understanding in tackling kinematical as well as dynamical problems.\nAcknowledgments The author is grateful to the National Science Foundation for\n486 / MAY 1 973\nReferences Suh, C. H., \"Differential Displacement Matrices and the G eration of Screw Axis Surfaces in Kinematics, \" Journal of Engineer ~n. for Industry, TRANS. ASME, Series B, Vol. 93, No.1, Feb. 1971 ping 1-10. ' P.\n2 Chen, P., and Roth, B., \"Design Equations for the Finit I. and Infinitesimally Separated Position Synthesis of Binary Links a\ne ~d Combined Link Chains,\" ASME Paper No. 68-Mech-8. n\n3 Shigley, J. E., Kinematic Analysis of M:echanisms, MCGraw. Hill, New York, 1969.\n4 Denavit, J., Hartenberg, R. S., Razi, R., and Uicker, J. J. Jr \"Velocity, Acceleration and Static-Force Analyses of Spatial Link: ages,\" Joumal of Applied Alechanics, TRANS. ASME, Series E, Vol 87 No.4, Dec. 1965, pp. 903-910. '\n5 Bagci, C., \"Static Force and Torque Analysis Using 3 X 3 Screw Matrix, and Transmission Criteria for Space Mechanisms\" Jou1'nal of Enginee\"ing for Indust,\u00b7y, TRANS. ASME, Series B, Vol. 93, No.1, Feb. 1971, pp. 90-101.\n6 Soni, A. H., and Harrisberger, L., \"Die Anwendung der 3 X 3- Schraubungs-Matrix auf die kinematische und dynamische Analyse von raumlichen Getrieben,\" Verein Deutscher Ingeniew'e-Berichte No. 127, 1969, pp. 35-40. '\n7 . Rabinowitz, P., Numerical Methods for Nonlinear Algebrau: Equations, Gordon and Breach Science Publishers, New York, 1970, 199 pages.\n8 Uicker, J. J., Jr., Denavit, J., and Hartenberg, R. S., \"An Iterative Method for the Displacement Analysis of Spatial Mecha nisms,\" Jow'nal of Applied Mechanics, TRANS. ASME, Series E, Vol. 31, No.2, June 1964, pp. 309-314.\n9 Yang, A. T., \"Displacement Analysis of Spatial Five-Link Mechanisms Using 3 X 3 Matrices With Dual-Number Elements\" Journal of Engineering for Industry, TRANS. ASME, Series B, Vol. ni, No.1, Feb. 1969, pp. 152-157.\n10 Dimentberg, F. M., \"The Screw Calculus and Its Applications in Mechanics,\" Izadatel' stvo Nauka, Akademiia Nauk, Moscow, USSR,1965.\n11 Yuan, M. S. C., Freudenstein, F., and Woo, L. S., \"Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates, Part 2-Analysis of Spatial Mechanisms,\" Journal of Engineering for Industry, TRANS. ASME, Series B, Vol. 93, No, 1, Feb. 1971, pp. 67-73.\n12 Sheth, P. N., and Uicker, J. J., Jr., \"A Generalized Symbolic Notation for Mechanisms,\" Jow'nal of Engineering for Industry, TRANS. ASME, Series B, Vol. 93, No.1, Feb. 1971, pp. 102-112.\n13 Gupta, Viney K., and Radcliffe, C. W., \"Mobility Analysis of Plane and Spatial Mechanisms,\" Jow'nal of Engineering for Industry, TRANS, ASME, Series B, Vol. 93, No.1, Feb. 1971, pp. 125-130.\n14 Kaufman, R. E., and Sandor, G. N\" \"Operators for the Kine matic Synthesis of Mechanisms by Stretch-Rotation Techniques,\" ASME Paper No. 70-Mech-79.\n15 Chen, P., and Roth, B., \"A Unified Theory for Finitely and In finitesimally Separated Position Problems of Kinematic Synthesis,\" Journal of Engineering for Industry, TRANS. ASME, Series B, Vol. 91, No.1, Feb. 1969, pp. 203-208.\n16 Pipes, L, A., Matrix Methods for Engineering, Prentice-Hall, Englewood Cliffs, New Jersey, 1963.\n17 Beggs, J. S., Advanced Mechanism, The Macmillan Company, New York, 1966.\n18 Sherby, T. A\" and Chimelewski, J. F., \"Generalized Vector Derivatives for Systems with Multiple Helative Motion,\" Journal oj Applied Mechanics, TRANS. ASME, Series E, Vol. 90, No.1, Mar. 1968, pp. 20-24.\nTransactions of the ASME\nDownloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/20/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use"
        ]
    },
    {
        "image_filename": "designv11_28_0002027_1.2179460-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002027_1.2179460-Figure2-1.png",
        "caption": "Fig. 2 The spherical coordinate frame of a meshing roller",
        "texts": [
            " The rollers are distributed uniformly around the reference circle of the planet worm-gears for meshing with the sun-worm and with the stationary internal gear. The rollers in this paper are in the form of balls. The schematic structure of the toroidal drive is illustrated in Fig. 1. Journal of Mechanical Design rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/27/201 To analyze the meshing contact, the coordinate frame between the meshing roller and the planet worm-gear is introduced. Figure 2 illustrates the sun-worm meshing with a planet worm-gear via a meshing roller to demonstrate the relationship between a roller and the planet worm-gear. The roller coordinate frame S o , i , j ,k of a meshing roller is fixed at the center of the roller, the planet worm-gear rotatable coordinate frame S2 o2 , i2 , j2 ,k2 is fixed at the center of the worm-gear and rotates with the worm-gear. In Fig. 2, is the radius of a meshing ball, P is a point on the surface of the ball, r2 is the radius of the reference circle of the planet worm-gear, and u and v represent the spherical coordinates of the meshing ball in the roller coordinate frame S o , i , j ,k . The equation of the generating surface of a meshing roller can be obtained in the roller coordinate frame S as r = xi + yj + zk x = cos v y = cos u sin v z = sin u sin v 1 where, x ,y ,z represents a point P on the generating surface and r is the vectorial expression of the point of the generating surface. The equation is derived from using radius of the contacting ball roller in Fig. 2. With the coordinate transformation, the above can be rewritten as r2 = x2 i2 + y2 j2 + z2 k2 where x2 = cos v + r2 y2 = cos u sin v z2 = sin u sin v 2 Vector r2 is the vectorial expression of a point P of the generating surface in the planet worm-gear rotatable coordinate frame S2 . There are several latency errors in manufacturing and assembly of a toroidal drive system. In this analysis, three typical latency errors are discussed. They include the worm-gear center-distance offset, the sun-worm lateral misalignment and the worm-gear angular misalignment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002368_j.euromechsol.2005.06.006-Figure13-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002368_j.euromechsol.2005.06.006-Figure13-1.png",
        "caption": "Fig. 13. Deformed mesh after 9 1 2 cycles. The lines in the center of each element are oriented in the preferred direction of n = F e \u00b7 n\u0304 .",
        "texts": [
            ", Ekh and Runesson (2001) and Johansson et al. (2005). The lower side of the square is fixed while the opposite side has a prescribed displacement. The material parameters Hfib = 0.3, \u03b7n = 100, and \u03b7y = 1 are utilized in addition to the fixed parameters that are listed in Table 3. The prescribed displacement is cyclic with amplitude determined by the components lx and ly. The length of the square side is l0 = 10 mm, and the ratio between the horizontal and vertical displacements of the prescribed side is lx/ly = 4 as shown in Fig. 13. Fig. 12 shows the deformed finite element mesh at the first load step. The lines in the center of each element represent the initial orientation n = F e \u00b7 n\u0304 at t \u2248 t0 evaluated as the Gau\u00df-point average in each element. This initial orientation is, in analogy with the previous subsection, determined by the principal direction of E e at the first load step t = t0, whereas n\u0304 evolves according to the evolution rule for t > t0. The initial stiffness is chosen as \u03b1 = 1 and \u03b2 = 0.05 such that A\u0304 = G + 0.05 N at t = t0. Since the spherical part of the metric dominates at t = t0, initial orientations shown in Fig. 12 have no practical influence on the response at t \u2248 t0 . Fig. 13 shows the deformed finite element mesh. The lines in the center of each element represent the mean-value of the orientation n\u0304 over the Gau\u00df-points in each element. It is clear from Fig. 13 that the orientation aligns with the lower and upper sides in the upper and lower parts of the mesh. The cyclic response in the point \u201cP\u201d (Gau\u00df-point average in the element) in Fig. 11 is shown in Figs. 14, 15. The cyclic response of the orientation \u03b8 versus the normalized horizontal displacement ux/l0 of \u201cP\u201d is shown in Fig. 14. Recall that the orientation is defined in Fig. 5(a). Fig. 15 shows the stiffness parameters \u03b1 and \u03b2 versus the normalized horizontal displacement. It is clear that the evolution of the orientation \u03b8 tends to saturate after a few cycles, whereas the saturation of \u03b1 and \u03b2 is small",
            " Hardening in the inelastic stress-strain response can be classified as isotropic (due to the stiffness evolution \u03b2), kinematic (via conventional formulation), and a special form of distortional hardening (due to the stiffness evolution \u03b2 and the orientation n\u0304 ). In the present context, the special form of distortional hardening concerns reorientation of the initially isotropic yield surface and, also, change of proportions between the principal axes of the corresponding ellipsoidal yield surface. The model calibration is outside the scope of this paper. However, by comparing the numerical example in Fig. 13 with graphical images from so-called twin-disc experiments (although they represent completely different loading cases), it seems reasonable to anticipate that parts of the model can be calibrated (inverse analysis assuming strongly inhomogeneous stress and strain states). It is obviously possible to introduce additional material parameters in the model (e.g., in Eqs. (38), (40)2, and (41)2) with the purpose to increase the modeling flexibility. The modeling of deformation induced anisotropy due to substructure evolution does not require the \u201cfictitious configurations approach\u201d"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000449_isie.2001.931878-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000449_isie.2001.931878-Figure8-1.png",
        "caption": "Fig. 8. Experimental setup.",
        "texts": [
            " If the magnetic Reynolds number R, is infinite, which happens when the angular velocity is infinite, the net magnetic flux density Bz equals to zero. These two extreme cases agree well to Wouterse\u2019s result [ 11. Finally, by using Lorentz force law [7], we have the braking torque in the volume under the pole projection area as follows. Tb = -dBZ T\u2018JTtds h . (23) L 3. EXPERIMENTAL VALIDATION OF THE ANALYSIS RESULTS To validate the accuracy of the proposed model, the braking torque is measured experimentally. The experimental setup in Fig. 8 is composed of the rotating disk, the electric motor, the extended array of the electromagnets, and the load cell. The electric motor is used 682 ISIE 2001, Pusan, KOREA to rotate the disk with the constant angular velocity. The electromagnet supplies the magnetic flux which goes through the pole projection area in the disk. The braking torque is generated in the rotating disk and the reaction torque is exerted on the extended array of the electromagnets. The reaction torque is translated to the force which is exerted on the load cell"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003094_j.mechmachtheory.2007.12.001-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003094_j.mechmachtheory.2007.12.001-Figure2-1.png",
        "caption": "Fig. 2. RR-PR-PR Assur group.",
        "texts": [
            " Also B belongs to the circle centered in A, of radius BC. B is the intersection point of the fourth order coupler curve with the circle and eight intersection points exist at most. Due to the fact that this intersection contains two imaginary points as doubles points, there will be at most four real intersection points. Therefore the maximum number of the assembly modes of the RR-RP-RP triad is four. A similar procedure to the one previously described can be used for the position analysis of the RR-PR-PR triad with two external prismatic joints (Fig. 2). The input data for the position analysis are the coordinates of the external joint A (0, 0) and of the auxiliary points D (d, 0) and F (xF, yF) situated on the sliding direction of the external prismatic joints. The dimensions of every link as the lengths lAB, lBC, lBE, the angle a and the distances d1 and d2 are also given. The position of the links is described by the coordinates x and y of joint B and the displacement s. The constraint equations to be solved are given as x2 \u00fe y2 \u00bc l2 AB \u00f018\u00de \u00f0xE x\u00de2 \u00fe \u00f0yE y\u00de2 \u00bc l2 BE \u00f019\u00de \u00f0xC d\u00de2 \u00fe y2 C \u00bc d2 1 \u00fe s2 1 \u00f020\u00de In Eqs",
            " Similarly to the procedure adopted in previous section for eliminating to the unknowns x and y, a polynomial equation of fourth order with only variable s is derived: X4 i\u00bc0 Hisi \u00bc 0 \u00f036\u00de The coefficients Hi (i = 0,1, . . ., 4) depend only on the Assur-group data. Eq. (36) provides four solutions for s in the complex field. For every root sj (j = 1, . . ., 4), the coordinates of the joints B, C and E and the displacement s1 are determined. The real solutions correspond to the assembly modes of triad. The order of the polynomial equation (36) is minimal. This is confirmed by the following consideration: For a given position of the external joints A, D1 and F1 of the triad (Fig. 2), the internal joint E lies on the fourth order curve of the ABCD1 four-bar mechanism of the RRRP type [5,12]. Also E belongs to the straight line parallel to the sliding direction of the external prismatic joint F1. The intersection of the fourth order coupler curve with a straight line will be at four real intersection points at most. Therefore the maximum number of the assembly modes of the RR-PR-PR triad is four. The input data for the position analysis of the RR-RR-PP Assur group (Fig. 3) are the coordinates of the external joints A (0, 0), D (d, 0) and of the auxiliary point F (xF, yF), the dimensions of each link as the lengths lAB, lBC, lCD, the distances di (i = 1, 2, 3) and the angles a and h",
            " Also C belongs to the straight line parallel to the sliding direction of the external prismatic joint D1 and located at distance d4. The point C 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 this triad is two. In this section the proposed procedures are applied to corresponding numerical examples. Example 1. The method presented in Section 2 is applied in the first numerical example for the RR-RP-RP triad with two internal prismatic joints (see Fig. 2). The geometrical data and the position of external joints A, D and F are given in the upper part of Table 1. For the specific geometry here considered, by solving the fourth order polynomial equation (17), two real roots and two complex roots for the displacement s are obtained (see Table 1). For each real value of the displacement s, the coordinates of the internal joint B and the displacement s1 are calculated. The two configurations of the triad corresponding to the real solutions are presented in Fig. 6. Example 2. The geometrical data and the position of the auxiliary points D and F of the RR-PR-PR triad (see Fig. 2) are given in the upper part of Table 2. For the specific geometry here considered, solving the fourth order polynomial equation (36) two real roots and two complex roots are obtained. For each real value of the displacement s1, the coordinates of the internal revolute joints B, C and E are determined. The two assembly modes of the triad are presented in Fig. 7. 1 nd solutions of the RR-RP-RP Assur group d = 40, d1 = 30, d2 = 45, d3 = 35, lAB = 75.4053, xF = 103.9025, yF = 78.9332, a = 50 . s x y s1 195"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003978_6.2009-6139-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003978_6.2009-6139-Figure6-1.png",
        "caption": "Figure 6: Geometric Definitions. The Body axis of the aircraft, inertial axis, and angles describing the position of a sensor come into play when translating between sensor angles and inertial axis locations.",
        "texts": [
            " The sensor is assumed to be a rectangular view defined by a center point (boresight) and a given field-of-view in the horizontal and vertical direction ( . The sensor rotates about the aircraft body axis according to an elevation angle ( ) and an azimuth angle ( ), where sensor elevation is the angle between the sensor boresight and the vehicle x-y plane, and sensor azimuth is the angle between the projection of the sensor boresight onto the vehicle x-y plane and the vehicle x-axis. Figures 6 and 7 show the sensor geometry in detail. Note that Fig. 6 shows the sensor rotation angles, while Fig. 7 describes the sensor field of view and axis system from the perspective of the sensor view plane. When describing the orientation of a rigid body, it is common to find the use of Euler angles, especially in aerospace applications. However, there are a number of disadvantages to the use of Euler angles, including the problems of rotation through \u03b8 = \u03c0/2. To overcome problems with Euler angle computations, quaternions are increasingly used in aerospace modeling",
            " (15) (16) Although the preceding relationships are meant to describe rigid body motion for an aircraft, this section shows the application of quaternions and the DCM to model the view of a sensor. The following process will determine the intercept of a sensor view and the ground plane (N-E plane) of the inertial axis. This model is simplified, assuming a flat earth, but the principle can be applied to more advanced earth models. American Institute of Aeronautics and Astronautics 9 The first step is to establish a quaternion describing the sensor view. Referring to Fig. 6, the sensor is pointing away from the aircraft at a given elevation and azimuth angle. An inertial-axis quaternion can be defined for the sensor using the property of quaternion multiplication 3,6 . By defining sensor-axis Euler angles shown in Eq. 17, a sensor quaternion ( ) can be initialized using Eq. 13. (This is a quaternion describing the sensor pointing angle using the aircraft body axis as its reference frame.) If the aircraft body quaternion is defined as ( ), then Eq. 18 defines sensor quaternion ( ) that is independent of the aircraft body axis by multiplying the sensor quaternion and the aircraft quaternion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003488_robot.2007.363548-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003488_robot.2007.363548-Figure2-1.png",
        "caption": "Fig. 2. Two-four-phase electrostatic motor",
        "texts": [
            " The main purpose of this paper is to provide analysis on the thrust force characteristics of the voltage-induction type electrostatic motor with two-four-phase electrode. To simplify the discussion, first we will analyze the thrust force characteristics of two-four-phase electrode by ignoring electrostatic induction. In the analysis, we assume that electric power to the slider is directly fed by electric cables without using induction. The total characteristics including the effect of induction will be discussed in the latter part of the paper. The schematic diagram of the two-four-phase electrostatic motor (without induction) is shown in Fig. 2. This chapter analyzes the force characteristics of the motor in Fig. 2 based on the method described in [12]. Since two-four-phase electrostatic motor has six phases in total, it can be represented by a six-terminal capacitance network. The six-terminal capacitance network model of the motor is shown in Fig. 3. In the model, all the six terminals are connected by capacitors. Those capacitances can be mathematically represented using a 6\u00d76 capacitance coefficient matrix. In the matrix, element in i-th row and jth column expresses the relationship between i-th terminal and j-th terminal",
            " In the two-fourphase motor, considering the geometrical symmetry among electrodes, the capacitance matrix can be written as: C= \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 Cst \u2212Cta \u2212Ctb \u2212Cta \u2212Cta Cst \u2212Cta \u2212Ctb \u2212Ctb \u2212Cta Cst \u2212Cta \u2212Cta \u2212Ctb \u2212Cta Cst Cm(\u03b8x) Cm(\u03b8x\u2212\u03c0/2) Cm(\u03b8x\u2212\u03c0) Cm(\u03b8x+\u03c0/2) Cm(\u03b8x\u2212\u03c0) Cm(\u03b8x+\u03c0/2) Cm(\u03b8x) Cm(\u03b8x\u2212\u03c0/2) Cm(\u03b8x) Cm(\u03b8x\u2212\u03c0) Cm(\u03b8x\u2212\u03c0/2) Cm(\u03b8x+\u03c0/2) Cm(\u03b8x\u2212\u03c0) Cm(\u03b8x) Cm(\u03b8x+\u03c0/2) Cm(\u03b8x\u2212\u03c0/2) Csl \u2212Cl \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (1) Cm(\u03b8x) = \u2212Cm0 \u2212 Cm1 cos(\u03b8x) (2) \u03b8x = \u03c0x/(2p) (3) where Cst,Csl,Cta,Ctb,Cl,Cm0 and Cm1 are positive coefficients, x is the position of the slider electrodes, \u03b8x is another representation of the position x in electric angle, which one cycle (2\u03c0) is equal to 4p. The coefficients of the matrix are determined by geometric relations among electrodes, and in practice, they can be measured using a LCR meter [12]. Assuming charge and voltage vectors, the capacitance coefficient matrix satisfies the following condition. q = CV (4) where q and V are 6 \u00d7 1 vectors that represent the charges and voltages on the six terminals respectively. In the case of Fig. 2, V is expressed as follows: V= { Vt sin \u03c9tt, \u2212Vt cos\u03c9tt, \u2212Vt sin\u03c9tt, Vt cos\u03c9tt Vl sin \u03c9lt, \u2212Vl sin\u03c9lt } (5) where Vt, Vl, \u03c9t, \u03c9l are voltage amplitudes and angular frequencies of stator and slider voltages. Using the coefficient matrix and the voltage vector, thrust force can be obtained as fx = 1 2 VT \u2202C \u2202x V (6) Substituting for (1) and (5), (6) is rewritten as fx= \u03c0Cm1 p VlVt{sin(\u03c9lt+\u03c9tt\u2212\u03b8x)+sin(\u03c9lt\u2212\u03c9tt+\u03b8x)} (7) This formula suggests that the thrust force contains components of the sum of frequencies and the difference of frequencies"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002954_1128888.1128914-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002954_1128888.1128914-Figure6-1.png",
        "caption": "Figure 6: The \u2018hammer\u2019 example: (a) When the \u2018hammer\u2019 is at time t=0, it collides with the \u2018notch\u2019. (b) The collision-free placement of the \u2018hammer\u2019 for scenario (a). We use our containment optimization algorithm to get this free configuration, which realizes the UB1(PDg). (c) The \u2018hammer\u2019 at time t=0.5. (d) The collision-free placement is computed for scenario to get the UB1(PDg)",
        "texts": [
            " We can cull some of the separators by making use of the currently known upper bound on PDg during any stage of the algorithm. If the separator is farther away from the object A than the current upper bound, we can discard this separator. We use the PDt between the two convex hulls of input models as an initial upper bound of PDg. We have implemented our lower and upper bound computation algorithms for generalized PD computation between non-convex polyhedra. We have tested our algorithms for PDg on a set of benchmarks, including \u2018hammer\u2019 (Fig. 6), \u2018hammer in narrow notch\u2019 (Fig. 9), \u2018spoon in cup\u2019 (Fig. 8) and \u2018pawn\u2019 (Fig. 10) examples. All the timings reported in this section were taken on a 2.8GHz Pentium IV PC with 2 GB of memory. Lower bound on PDg. In our implementation, the convex covering is performed as a preprocessing step. Currently, we use the surface decomposition algorithm proposed by [Ehmann and Lin 2001], which can be regarded as a special case of convex covering problem. In order to compute the PDt between two convex polytopes, we use the implementation available as part of SOLID [van den Bergen 2001]",
            " UB1(PDg): The upper bound on PDg computed by containment optimization. 3. UB2(PDg). The upper bound on PDg based on the translational PDt computation between their convex hull. 1http://www2.isye.gatech.edu/\u02dcwcook/qsopt/ In order to get accurate timing profiling, we run our PD algorithms for each configuration with a batch number b. The average time for each bound computation is the total running time on all samples over the product of the number of samples and the batch number b. \u2019Hammer\u2019 example. Fig. 6, and Tab. 1 and Fig. 7 show the results and timings for the \u2018hammer\u2019 example. In this case, the \u2018hammer\u2019 model has 1,692 triangles, which is decomposed into 214 convex pieces. The \u2018notch\u2019 model has 28 triangles, which is decomposed into 3 convex pieces and there is a notch (i.e. convex separator) in the center of the \u2018notch\u2019 model. Initially (at t=0), the \u2018hammer\u2019 intersects with the \u2018notch\u2019 as shown in Fig. 6(a). Fig. 6(b) shows a collision-free placement of the \u2018hammer\u2019, which corresponds to the position after moving by UB1(PDg). According to Fig. 7, the value is UB1(PDg) = 4.577083, which is greater than LB(PDg) (0.744020) and less than UB2(PDg) (6.601070). For this example, we generate 101 samples for the \u2018hammer\u2019 when it is rotated around the Z axis. The rotation motion is linearly interpolated from the configuration (0,0,0)T to (0,0,\u03c0)T . Fig. 6(c) shows the placement of the \u2018hammer\u2019 at t = 0.5. Fig. 6(d) is the corresponding collision-free placement, which realizes the UB1(PDg). We also compare the lower and upper bounds on PDg over all the configurations. In Fig. 7, the solid green curve highlights the value of UB1(PDg) between the \u2018hammer\u2019 and the \u2018notch\u2019 over all interpolated configurations. The dashed red curve, which corresponds to UB1(PDg), always lies between LB(PDg) and UB2(PDg). In this example, UB1(PDg) is less than UB2(PDg). The timing for this example is shown in Tab. 1. We run the PDg algorithm 5 times (b=5) for all the configurations (n=101)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000683_890127-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000683_890127-Figure2-1.png",
        "caption": "Fig. 2 - Measuring function",
        "texts": [
            " PREDICTION OF PISTON SLAP NOISE Using the result of the simulation of the piston transverse motion, as the piston impacted the cylinder liner, lateral acceleration of reciprocating parts from the piston, the piston pin, the connecting rod, was calculated from Eq. (11): Yg(T) = Y(T) + Xg * A(T) Xg ; X coordinate gravity of parts - (11) of the center of reciprocating at rated operating condition are shown in Fig. 11. The contribution of piston slap noise to total engine noise in the high-frequency range is higher than in the low-frequency range. Then, the piston slap impacted force Fh(T) was transfered from time domain to frequency domain using Fourier transformation. Using the slap noise transfer function measured by the devices as shown in Fig. 2, 3 and Fh(f), the piston slap-induced noise Ns(f) was simulated from Eq. (13): Fh(T) = Mt * Yg(T) - TOTAL .- - SLAP .., ~I J-WLrw ~ '\"'-- l! .. \u2022~ ~ 'r...!~. AL5k 10k Hz 50 100 500 Ik FREQUENCY 80 ~ 70 90- (12) mass of the reciprocating part crank angle within the limits of the piston were impacted to the cylinder liner Mt T Ns(f) = ITh(f) I * Fh(f) (13) EXPERIMENTAL AND ANALYTICAL RESULT Fig. 11 - Measured noise in original engine RADIATED NOISE IN THE ORIGINAL ENGINE The radiated noise in the original engine was measured at the rated operating condition",
            " The contribution of slap noise was 82 dB(A), to total engine noise of 86 dB(A). Piston slap noise is a major conributor, as is combustion noise, against total engine noise. To reduce total engine noise, piston slap noise must be reduced. Total engine noise and piston slap noise measured at the piston thrust side CALCULATION OF PISTON LATERAL MOTION - Measured and simulated piston lateral motion are shown in Fig. 12. In Fig. 12, the solid line represents data measured by the link device as shown in Fig. 2 ; the dotted line represents simulated data considered with piston deformation; the remaining line represents simulated data for the piston as a rigid body. When measured data and simulated data are considered ~ithout piston deformation, the moved distance of the simulated value is 25% smaller than that of the measured data near firing top dead center. This is because the limits of piston lateral movement were expanded by piston deformation. When measured data and simulated data are compared considering piston deformation, the 890127 7 calculated values and measured data show good agreement, at each crank angle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000570_095440802760075021-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000570_095440802760075021-Figure4-1.png",
        "caption": "Fig. 4 Family of skew axes gears",
        "texts": [
            " A condition of special orientation of the helices of the synthesized tooth surfaces is not obligatory or is not possible. 3. Speci c technological requirements should be satis ed, e.g. the use of one tool for the manufacture of gear pairs regarding different angular velocity ratios, manufacture of gear pairs with different angular velocity ratios based on the same gear blank dimensions and gear pair mounting dimensions. Among progressive combinations of spatial gears, Spiroid and Helicon* gears occupy one essential place. Figure 4 illustrates the position of Spiroid gears among the skew axes gears: 1, worm gear; 2, Spiroid gear; 3, hypoid gear; 4, bevel gear; 5, mesh region of Spiroid gear pair \u203011; 12\u0160. This set is characterized by the following geometrical and technological features: 1. The mesh region of the two gears is displaced with respect to the offset line O1O2 along the axes of both gears. The shape of every additional surface that bounds the gears teeth is conical. Those features are typical of a hypoid gear geometry"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000525_sibgrapi.2001.963055-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000525_sibgrapi.2001.963055-Figure6-1.png",
        "caption": "Figure 6: Cat hindlimb.",
        "texts": [
            " i ( T i ( { U } \u2019 ) - T i ( { U } ) ) (17) where {U}\u2019 is obtained by changing the j th entry of the current vector { U } from uj to uj + h, h being a small number The system of linear equations to be solved at each ( h = 0.001). step can be expressed in matrix form as: [ J ] { A u } = - 1 . 1 (18) The current displacement vector is updated to {U} + {Au}, and the procedure is repeated until the norm of the residual vector { T } is lower than a pre-specified admissible error. 5 Skeletal Muscle Deformation The computational model was used to simulate muscle contraction of two ankle extensor skeletal muscles of the cat hindlimb (Figure 6). These muscles are the cat soleus (SOL), a nearly parallel-fibred muscle, and the cat medial gastrocnemius (MG), a perfect unipennate-fibred muscle [12] . In the computational model, we can specify whether an external support is fixed, partially fixed or free, and whether it is displacement controlled (the goal for the position of the support is specified) or force controlled (the goal for the loads of the support is specified). For the purpose of illustration, we adopted the values E = 25OMpu, E = 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002835_1.3092885-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002835_1.3092885-Figure1-1.png",
        "caption": "Fig. 1. Artist\u2019s illustration of the European ERICA advanced tiltrotor concept.",
        "texts": [
            " \u03b81s lateral cyclic swashplate input \u03b80 collective swashplate input \u00b5 advance ratio, forward speed/blade tip speed \u03c1 parameter governing state estimator dynamics (LQG) \u03c6 phase angle \u03d5 wing degree of freedom (deflection angle) \u00c4 rotor rotation speed \u03c9 angular velocity ( )b value related to wing beamwise bending ( )c value related to wing chordwise bending ( )d all pass ( )G plant related ( )H controller related ( )hp high pass ( )lp low pass ( )t value related to wing torsion ( )cri t critical quantity (flutter point) Tiltrotor aircraft have been the subject of research and development since well before the 1950s when the first flight of the Transcendental 1G took place. Considerable experience in tiltrotor design was acquired with the research aircraft XV-3 and XV-15 that followed, but the first tiltrotor to enter service in the near future will be the military V-22 Osprey and the smaller BA-609 for the civil market. The most recent European tiltrotor concept ERICA is shown in Fig. 1. Tiltrotor aircraft provide unique features, combining some of the advantages of helicopters, notably vertical take off, landing and hover capabilities, with the high cruise speed and range of turboprop airplanes. 244 The tiltrotor concept is subject to an instability called whirl flutter, which occurs in high speed flight in the airplane configuration, and which constitutes an important factor in tiltrotor design because it can lead to very high dynamic loads. It is therefore necessary to guarantee adequate stability margins throughout the flight envelope"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002939_ip-cta:20050161-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002939_ip-cta:20050161-Figure6-1.png",
        "caption": "Fig. 6 Quarter car forces and torques v is the longitudinal speed at which the car travels, v is the angular speed of the wheel, Fz is the vertical force, Fx is tyre friction force and Tb is brake torque",
        "texts": [],
        "surrounding_texts": [
            "Low-frequency noise, that is, model uncertainties are suppressed by adaptation, whereas high-frequency noise is suppressed by low-pass filtering techniques. Given the filter as stated in Theorem 3, the behaviour of uest(t) will evolve in a straight line between uest(0) and u. If the system is subjected to noise, the behaviour of uest(t) will not be fully straight. Instead, the straight line behaviour is degenerated to nearly straight, superimposed by noise. But this may be further suppressed by means of the grid coarseness of reset candidates. Increasing the distance between reset candidates will reduce the risk of erroneous resetting because of noise. This is illustrated in the example in the next section."
        ]
    },
    {
        "image_filename": "designv11_28_0002294_013-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002294_013-Figure1-1.png",
        "caption": "Figure 1. Schematic preparation of a CSWM: (a) layer sequence of the MBE grown sample. (b) Preparation of an array of GaAs wires. (c) Definition of the strained mesa. (d ) Preparation of two starting edges with tines. (e) The strained bilayer starts rolling up when released from the substrate by selective etching. ( f ) Due to the interlocking mechanism of the tines the opposite edges of the bilayer are aligned. Therefore further etching leads to a CSWM.",
        "texts": [
            " They have for example been demonstrated to be useful as hinges of moving parts in micro-origami [6, 7], nanopipettes which might act as light emitting sources on a substrate surface [8], needles for ink jet printing [9], metal coated cantilevers [10, 11] or for basic research applications like the investigation of strain in quantum wells [12] or magneto transport in curved two-dimensional electron systems [13]. However, due to their rolled-carpet-like shape, effects correlated to closed pathways around the rolling axis, e.g. like Aharonov\u2013Bohm-oscillations in carbon nanotubes or optical modes in ring resonators, have neither been expected nor measured in this kind of rolled-up semiconductor layer. In this paper we present an approach towards such experiments by developing a method to realize closed singlewalled InGaAs/GaAs microtubes (CSWM). Figure 1(a) shows a typical layer sequence of our samples grown by molecular beam epitaxy (MBE). On top of the GaAs substrate we grow 400 nm of GaAs (substrate temperature 590 \u25e6C, growth rate 0.8 ML s\u22121) as a buffer layer and 400 nm AlAs (590 \u25e6C, 0.4 ML s\u22121) as a sacrificial layer. The following two layers, i.e. 20 nm In0.2Ga0.8As (500 \u25e6C, 0.975 ML s\u22121) and 300 nm GaAs (590 \u25e6C, 0.4 ML s\u22121), form the strained film that rolls up after being released from the substrate by a selective etching process. This layer sequence can be used for the fabrication of either rolled-carpet-like scrolls or CSWMs",
            " As a result we get scrolls with length and revolution number predefined by the shape of the strained rolling mesa and with a diameter depending on the strain stored in the InGaAs/GaAs bilayer. In order to realize closed tubes instead of scrolls we modify the preparation process as follows. Before the actual rolling process we use three different steps of optical lithography and chemical wet etching with a solution of H3PO4:H2O2:H2O in the ratio of 1:10:500. Figures 1(b)\u2013( f ) show the preparation process schematically. First an array of wires is processed into the top GaAs layer (figure 1(b)). The interspaces of this array have to be larger than the widths of the wires to get a properly working interlocking system later 0268-1242/05/050402+04$30.00 \u00a9 2005 IOP Publishing Ltd Printed in the UK 402 on. In the second step we define the shallow strained rolling mesa (figure 1(c)). Similar to the case of semiconductor scroll preparation we remove the complete GaAs top layer and leave a thin layer of In0.2Ga0.8As surrounding the etch protected strained mesa. This layer will protect the AlAs sacrificial layer against the hydrofluoric acid during the final selective etching step. At this point the difference to the standard scroll preparation is made by the wires which protrude over the protected strained mesa into the etched area with a reduced GaAs top layer thickness. In the third step two starting edges are defined (figure 1(d )). Note that the length l2 of the mesa is reduced in comparison with the length l1 of the mesa in figure 1(c). The length l2 is chosen to correspond to the predefined circumference of the tube. Both starting edges are provided with tines consisting of a thin In0.2Ga0.8As layer. This is accomplished by etching down the unprotected area until the tines are reduced to a thin In0.2Ga0.8As layer and the AlAs is reached everywhere else. The length of these tines is determined by the difference between l1 and l2. Finally, the sample is put into hydrofluoric acid for the selective etching step. Figures 1(e) and ( f ) illustrate the rolling process",
            " The HF (diluted, 5%) begins etching along the starting edge and the thickness-modulated mesa bends up with an average radius which is approximately given by r = (rwbw + ribi)/(bw + bi). In this formula rw is the bending radius of a bilayer composed like the wires, in an analogous manner ri belongs to the interspaces; bw and bi are the widths of the wires and the interspaces, respectively. Importantly, due to the fact that there is no GaAs top layer on the tines, i.e. no strain left, the bending radius of the tines is infinite. This ensures that the tines interdigitate in a regular manner as shown in figure 1( f ) and do not get stuck before the rolling process is finished and the tube is completely closed. Figure 2 shows a scanning electron microscopy (SEM) picture of an exemplary CSWM. The bending radius of the CSWM is measured to 25 \u00b5m. The widths of the wires and the interspaces are bw = 3.3 \u00b5m and bi = 6.3 \u00b5m, respectively. The wires have the same bilayer composition and thickness as the unetched sample, whereas the interspaces have a reduced GaAs-layer thickness of 140 nm. Using the formula of Tsui and Clyne [3] which has been found to describe the dependence between bilayer composition and bending radius in good agreement [5, 6, 13], we calculate rw = 60 \u00b5m and ri = 11 \u00b5m",
            " A free-standing tine which is not bent down and which has taken its relaxed position with zero curvature is marked in figure 2 by an arrow. The centring of the tines within the opposite interspaces is supported by the profiled surface of the tube wall, which originates from the different bending diameters of the wires and the interspaces (ri < rw). Remarkably, we have found the interlocking mechanism to work very reliably. Note that in this configuration the strained rolling mesa has to be slightly twisted (figure 1( f )) to align tines and interspaces. Nevertheless, almost all fabricated objects resulted in interlocked tubes. The gap between the interlocked edges of the bilayer of these structures was measured to be between 500 nm and, see figure 3, smaller than the resolution of our SEM. We note that even in structures where a gap cannot be resolved by SEM, a proof of crystalline bonding cannot be given. Due to the solid interlocking mechanism it is not essential to use strained mesa with a length l2 corresponding exactly to the tube circumference expected from strain relaxation of the bilayer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001742_11539117_37-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001742_11539117_37-Figure1-1.png",
        "caption": "Fig. 1. Walking planning, in the sagittal plane, the robot\u2019s double support phase is the overlap of the two legs\u2019 swing phase. The four DOFs, which control the humanoid motion in the frontal plane, are assumed to be the same angle. The robot ZMP can be obtained from the transverse plane.",
        "texts": [
            " Humanoid walking is a periodic motion which alternates between the double-support phase and the single-support phase [14]. During the double-support phase, both of the humanoid robot feet are in contact with ground. During the single-support phase, only one foot is in contact with ground to support the humanoid, the other leg swings forward. For one leg, the walking process is composed of a stance phase and swing phase. We define the leg at robot\u2019s double support phase as leg\u2019s swing phase. The robot\u2019s double-support phase is the overlap period of two legs\u2019 swing phase. Fig. 1 gives a walking cycle starting from kth step, where Tc is one walking cycle period, Td is double support-phase time, and kTc+ Tm corresponds to the point when the foot of swing leg reaches its highest point, where the swing height is Hao, the length relative to the support foot is Lao, Ds is the step length. The motion in the transverse plane gives the desired robot ZMP trajectory. In order to control a humanoid robot\u2019s movement, it is necessary to generate the trajectories of all humanoid joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002074_tce.2004.1309454-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002074_tce.2004.1309454-Figure1-1.png",
        "caption": "Fig. 1. A typical pattern of the tracking error signal by radial runout.",
        "texts": [
            " Accurate focusing and tracking are achieved by closed-loop servos, which compensate for unpredictable positioning errors. Because the dynamics interaction between both loops is relatively low, each servo system can be analyzed independently. Owing to deficiencies in track geometry and eccentric rotation of the disk, disturbances acting on the track-following system contain a significant sinusoidal component appearing at the disk rotational frequency. The impact of the sinusoidal disturbance appears at the tracking error signal. Fig. 1 shows a typical pattern of the tracking error signal when only the focusing controller is activated. It clearly reveals how the tracking error can fluctuate due to the sinusoidal disturbance. The tracking error signal is periodic, with two distinct groups of error pulses per rotation. Each track creates one cycle of the tracking error signal as it passes outward the laser beam spot and again as it passes inward. At the upper and lower runout limits, the laser beam spot momentarily stops radial movement; so the error signal flattens out"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001246_isie.2001.931869-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001246_isie.2001.931869-Figure3-1.png",
        "caption": "Fig. 3. Vector diagram for flux-weakening region.",
        "texts": [
            " In this speed range, the back EMF increases rapidly proportional to speed so that the motor drive usually suffers from difficulty to achieve constant power operation. Recently, fluxweakening control has been developed to deal with this problem. By employing the field component of the stator current to weaken the air gap field produced by permanent magnets, this approach allow some BLDCM motor drives to achieve constant power operation. The principle of the proposed control scheme for flux weakening region is shown in Fig. 3. When the motor is operating above the base speed, the q-component of the back EMF increase from Eq-bose to Eql . In this constant power region, the qcomponent of the current should be controlled to the vector Iq l , because Edq = EqlIql = constant. This is equal to advancing the vectors Eql to Eq2 and Iq-hase to I,, by the phase advance angle $. 639 ISIE 2001, Pusan, KOREA Also this means that the magnet flux is weakened by Id2 and the back EMF can be maintained to by the negative vector Efw induced by Id2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001119_tei.1983.298633-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001119_tei.1983.298633-Figure1-1.png",
        "caption": "Fig. 1: Spherical eZectrode arrangement. (a) Unequal spheres using asymmetricaZZy appZied voltage.",
        "texts": [
            " Both symmetrically (+V/2 and-V/2) and asymmetrically (V and 0) applied voltages to the sphere electrodes are considered. The influence of the presence of the shanks, which serve the dual functions of electrical connections and physical supports to the electrodes, on the electric field and the potential values along the gap between the spheres is also investigated. The charge simulation method employing ring charges [6] is used. The accuracy of the computation is discussed. 2. ELECTRODE ARRANGEMENTS Fig. 1 shows the sphere electrodes used in the computation. Fig. la represents two spheres with unequal diameters and having asymmetrically applied voltage whereby -1=V is applied to sphere 1 and f2=0 to sphere 2. This asymmetric format of applying the voltage to the electrodes is the most widely used in HV engineering practice. However, in some specific applications the voltage may be applied symmetrically to both electrodes in the manner depicted in Fig. lb whereby -1=V/2 and \u00a22=-V/2 are the potentials of spheres 1 and 2, respectively",
            " (c) Unequal spheres with connecting shank and grounded plane using asymmetrically appZied voltage. 1, distance from the surface of top sphere. g, gap Length; (hi, h2, shanks hei/ghts T1i T2, thicknesses of the shanks) 3. COMPUTATIONAL METHOD The computational method used is the charge simulation technique which is based on the simulation of the actual electric field with a field formed by a finite number of fictitious charges. The values of the fictitious charges are determined from the boundary conditions at the contour points [6]. Since the electrode arrangements considered (Fig. 1) has a rotational symmetry, the charge simulation is carried out by employing ring charges to model the electrodes. The number of ring charges used is varied from 98 to 138. The higher number of ring charges is used when the ratio of r2/rl is high ('30). The assignment factor, defined as the ratio of the distance between two successive contour points and the distance between a contour point and the corresponding charge is kept throughout the computation between 0.92 to 1.5 [6,11]. Experience shows that an assignment factor in this range is required to obtain reliable field values [12,13]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002768_9780470116883.ch2-Figure2.3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002768_9780470116883.ch2-Figure2.3-1.png",
        "caption": "Figure 2.3 Two media configuration.",
        "texts": [
            " An electromagnetic field may occur in a material medium usually characterized by its constitutive parameters conductivity s, permeability m, and permittivity e. The material is linear if s, m, and e are independent of E and H, and nonlinear if otherwise. Similarly, the medium is homogeneous if s, m, and e are not space dependent and inhomogeneous otherwise. Finally, the medium is isotropic if s, m, and e are independent of direction or anisotropic otherwise. The boundary conditions at the interface separating two different media 1 and 2 with parameters s1, m1, e1 and s2, m2, and e2, respectively, as shown in Figure 2.3, can be easily derived from the Maxwell\u2019s equations in their integral form. A relation for the tangential components of the electric field may be found by taking a line integral along a closed path of length l on one side of the boundary and returning on the other side as it is indicated in Figure 2.2. The general conservative property of the electric field implies that any closed line of electrostatic field must be zero, that is,I c ~Ed~s \u00bc 0 \u00f02:93\u00de The sides normal to the boundary are assumed to be small enough that their contributions to the line integral vanish when compared with those of the sides parallel to the surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003765_09544070jauto969-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003765_09544070jauto969-Figure2-1.png",
        "caption": "Fig. 2 Engine drivetrain layout with fitted pulley torque transducers",
        "texts": [
            " The engine valve train friction torque measurement is carried out by using specially designed camshaft drive pulleys incorporating torque sensors fitted to both inlet and exhaust camshafts (see Fig. 1). The torque transducer is a two-part construction with instrumented central hub and toothed pulley gear. The transducers are designed to be insensitive to belt loading through the careful arrangement of strain gauges in the bridge. The calibration of the torque transducers indicated an error less than 0.03Nm for cyclic average drive torque, which is negligible. The engine drivetrain layout with the torque transducers in situ is shown in Fig. 2. The details of the torque transducer, calibration, and signal conditioning can be found in Mufti and Priest [2]. An optical encoder, having a resolution of 720 pulses per revolution, is fitted to the front end of the JAUTO969 Proc. IMechE Vol. 223 Part D: J. Automobile Engineering at Virginia Tech on March 13, 2015pid.sagepub.comDownloaded from engine crankshaft. The encoder is used to determine the cam/crank angle, not only for the camshaft friction measurement but also for bearing and piston assembly friction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000877_bf00384690-Figure3.2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000877_bf00384690-Figure3.2-1.png",
        "caption": "Fig. 3.2. One of the two families of steel wires. The number of fibres, measured per unit of length in a direction perpendicular to the wires, is n. The pitch angle (or thread angle) is called q~.",
        "texts": [
            " 3.1). The latter are considered as a two-dimensional continuum in common with the rubber sheet. The calculations are referred to a cylindrical coordinate system r, 0, z, as depicted in Fig. 3.1. The equation of the undeformed cylinder is r = r0. Its length is not relevant to our analysis. There are two families of wires. Ribbons of these are interlaced along helicoidal lines, the two families being symmetric. The uniform angle between the tangents to the wires and a cross-section is called ~0 (Fig. 3.2). We shall call q~ the pitch angle, and we note that the so-called helix angle is the complementary angle of ~o. It is assumed that the cylinder deforms axisymmetrically after exerting an axial load P and an internal pressure q to it. We denote the radial and axial displacement by u and w, respectively. These quantities, the first being constant and the latter a linear function of z, are assumed to be infinitesimally small. Accordingly, in this section we linearize our equations from the very beginning"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002754_3-540-26415-9_114-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002754_3-540-26415-9_114-Figure4-1.png",
        "caption": "Fig. 4. Future test bench",
        "texts": [
            " The interpretation of the effort is getting more complex, the measurement of the force interaction between the patient and the chair could be useful for a complete identification of the transfer. Theses previous interpretations do not allowed us to identify the posture of the patient during the transfer. Observations of the force interaction between the patient, the chair and also the floor added with measurement of motion of the body segment could give an interesting observation of the patient\u2019s posture (see Fig. 4). In order to compensate the fall during the transfer we design a criteria of stability, next section will present this criteria. Compensation of the fall during the transfer relay on a stability criteria, the AD have to produce the trajectory and force compensation helpful for the user in case of instability. In the following sub section we will introduce a stability criteria of the patient. This stability criteria is based on the establishment of the Zero Moment Point (ZMP) [13] on a simplified model of the patient"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003289_ac061910n-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003289_ac061910n-Figure1-1.png",
        "caption": "Figure 1. (a) Cell schematic and (b) cross sections through the electrochemical ESR flow cell: (i) inlet tube, (ii) outlet tube, (iii) counter electrode connection points, (iv) working/reference electrode connection points, (v) Pt foil secondary counter electrode, (vi) Au film primary counter electrode, (vii) inlet channel (1 mm wide, 250 \u00b5m deep), (viii) outlet channel, (ix) Au film working and pseudoreference electrodes, (x) glass base plate, (xi) polymer resin sealant, (xii) hole connecting inlet and outlet channels, and (xiii) standard 5 mm diameter NMR tube.",
        "texts": [
            " Furthermore, modern fabrication procedures should allow the positioning of electrodes and channels to be a highly accurate and reproducible process, allowing for the testing of multiple prototypes. In this work we present the design, fabrication, and characterization of a novel microfluidic channel flow cell suitable for variable temperature (233-293 K) electrochemical ESR. The cell consists of parallel inlet and outlet channels running back-to-back, connected at one end to form a U-tube configuration, as depicted in Figure 1. Working and quasi-reference electrodes are positioned in the inlet channel, and two large counter electrodes are located in the outlet channel. The cell is employed for the study of a range of stable and reactive halonitrobenzene systems in acetonitrile at room temperature and 233 K, and by employing low temperatures we report the spectrum of the reactive m-nitrobenzyl chloride radical anion, electrogenerated in acetonitrile, for the first time. The use of electrolysis at low temperatures is also shown to yield improvements in spectral resolution for the 1-chloroanthraquinone radical anion and the crystal violet radical"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003554_978-3-540-30301-5_4-Figure3.5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003554_978-3-540-30301-5_4-Figure3.5-1.png",
        "caption": "Fig. 3.5 The Salisbury three-fingered robot hand with its cable drive system",
        "texts": [],
        "surrounding_texts": [
            "Manipulator shape and size is determined by requirements on its workspace shape and layout, the precision of its movement, its acceleration and speed, and its construction. Cartesian manipulators (with or without revolute wrist axes) have the simplest transform and control equation solutions. Their prismatic (straight-line motion), perpendicular axes make motion planning and computation easy and relatively straightforward. Because their major motion axes do not couple dynamically (to a first order), their control equations are also simplified. Manipulators with all revolute joints are generally harder to control, but they feature a more compact and efficient structure for a given working volume. It is generally easier to design and build a good revolute joint than a long motion prismatic joint. The workspaces of revolute joint manipulators can easily overlap for coordinated multirobot installations, in contrast to gantry-style robots. Final selection of the robot configuration should capitalize on specific kinematic, structural or performance requirements. For example, a requirement for a very precise vertical straight-line motion may dictate the choice of a simple prismatic vertical axis rather than two or three revolute joints requiring coordinated control. Six degrees of freedom (DOFs) are the minimum required to place the end-effector or tool of a robotic manipulator at any arbitrary location (position and orientation) within its accessible workspace. Most simple or preplanned tasks can be performed with fewer than six DOFs. This is because they can be carefully set up to eliminate certain axis motions, or because the tool or task does not require full specification of location. An example of this is vertical assembly using a powered screwdriver, where all operations can be achieved with three degrees of freedom. Some applications require the use of manipulators with more than six DOFs, in particular when mobility or obstacle avoidance are necessary. For example, a pipe-crawling maintenance robot requires control of the robot\u2019s shape as well as precise positioning of its end-effector. Generally, adding degrees of freedom increases cycle time and reduces load capacity and accuracy for a given manipulator configuration and drive system."
        ]
    },
    {
        "image_filename": "designv11_28_0003935_s0263574709990506-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003935_s0263574709990506-Figure5-1.png",
        "caption": "Fig. 5. Position of the centre of mass of an actuator.",
        "texts": [
            " The gravitational components of the actuating forces can be easily obtained from the potential energy of the different rigid bodies that compose the system: \u03c4P (gra) = J\u2212T E \u00b7 \u2202PP ( BxP |B|E ) \u2202BxP |B|E , (55) \u03c4Ai (gra) = J\u2212T E \u00b7 \u2202PAi ( BxP |B|E ) \u2202BxP |B|E , (56) \u03c4Li (gra) = J\u2212T E \u00b7 \u2202PLi ( BxP |B|E ) \u2202BxP |B|E . (57) 3.4.1. Moving platform potential energy. Using the base frame, {B}, as a datum and assuming zB \u2261 \u2212g\u0302, the moving platform potential energy can be written as PP = mP \u00b7 g \u00b7 zP . (58) 3.4.2. Actuators potential energy. If all actuators are assumed to be equal and the centre of mass of each actuator cmA is placed at a fixed distance acm from its actuator to fixed-length link connecting point (Fig. 5), the position of the centre of mass relative to frame {B} is BpAi |B = bi + (li \u2212 acm) \u00b7 zB, (59) where BpAi |B is a vector expressed in {B}. Knowing the position of the centre of mass of each actuator relative to frame {B} (Fig. 5), its potential energy, PAi , can be written as PAi = mA \u00b7 g \u00b7 (li \u2212 acm) . (60) 3.4.3. Fixed-length links potential energy. In order to find the potential energy of each fixed-length link the position of its centre of mass relative to frame {B} (Fig. 4) must be known. Therefore, using Eq. (30) for each fixed-length link leads to PLi = mL \u00b7 g \u00b7 [( 1 \u2212 bcm L ) \u00b7 zP + ( 1 \u2212 bcm L ) \u00b7 P pi |Bz + bcm L \u00b7 li ] . (61) The RCID can be used working attached in series to a position controlled industrial robot: the latter one performs the large amplitude movements while the RCID is only used for the small and high bandwidth movements needed for force/impedance control (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000061_iecon.1993.339109-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000061_iecon.1993.339109-Figure2-1.png",
        "caption": "Figure 2 Mechanical Architecture",
        "texts": [
            " IMPLEMENTATION To demonstrate the research two mobile robots, Fred and Ginger shown in figure 1, have been developed based on the proprietary B 12 mobile platform from Real World Interfaces Inc. This is an omnidirectional platform which is controllable via an RS232 link and a simple command language. A superstructure has been added to the platform to provide additional sensing, computing and actuation. Mechanically, the superstructure consists of a series of levels constructed around a central core, as shown in figure 2. The core provides electrical connections to the layer above and below and can be considered analogous to a \"spinal vertebra\" since it distributes power and information to all levels of the mobile. Extra levels may be added if more board space is required providing a large expansion capability. Electronically, the hardware architecture is shown in figure 3. The computing system is based on Transputer parallel processing modules. Each transputer module contains its own processing, memory and communications"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002462_s00466-006-0120-3-Figure17-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002462_s00466-006-0120-3-Figure17-1.png",
        "caption": "Fig. 17 The basic unit in the beam element assembly",
        "texts": [
            " These correspond to the three degrees of freedom available at the centers of the elements. The beam elements form a two-dimensional network throughout the body. The strain energy stored in a general beam element oriented at an angle \u03b8 to the horizontal is given by U(\u03b8) = 2L2 \u23a7 \u23aa\u23a8 \u23aa\u23a9 Kneq [ c2 \u03b8\u03b5xx + s \u03b8 c \u03b8(\u03b5xy + \u03b5yx) + s2 \u03b8\u03b5yy ]2 + Kteq [ c2 \u03b8\u03b5yx + s \u03b8 c \u03b8(\u03b5yy \u2212 \u03b5xx) \u2212 s2 \u03b8\u03b5xy \u2212 \u03b22 ]2 \u23ab \u23aa\u23ac \u23aa\u23ad (33) where \u03b2 is the average rotation of the element [6]. Note that the notation c \u03b8 and s \u03b8 stands for cos \u03b8 and sin \u03b8 , respectively. Figure 17 shows the basic unit in the assembly of the beam elements, which is a square of side 2 \u221a 2L formed by four joints. The total strain energy associated with this volume of material is the summation of the strain energies associated with each of the four joints and is given by Utotal = U(\u03b8)+ U ( \u03b8 + \u03c0 2 ) +U(\u03b8 + \u03c0)+ U ( \u03b8 + 3\u03c0 2 ) (34) The strain energy per unit volume (strain energy density) of the material is then Uo = Utotal 8L2 (35) The orthogonal stresses \u03c3xx, \u03c3yy and \u03c4xy are related to the strain energy density by \u03c3xx = \u2202Uo \u2202\u03b5xx (36) \u03c3yy = \u2202Uo \u2202\u03b5yy (37) \u03c4xy = 1 2 ( \u2202Uo \u2202\u03b5xy + \u2202Uo \u2202\u03b5yx ) (38) From Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002027_1.2179460-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002027_1.2179460-Figure5-1.png",
        "caption": "Fig. 5 Planet worm-gear angular misalignment",
        "texts": [
            " The worm-gear center-distance offset is critical to the meshing process of a toroidal drive since the tooth profiles of the sun-worm and the stationary internal gear are formed by the enveloping movement of the meshing rollers. MAY 2006, Vol. 128 / 611 7 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F The sun-worm lateral misalignment w exists in assembly and dominates the meshing property and load capacity of a toroidal drive. Figure 4 illustrates the sun-worm lateral misalignment. The worm-gear angular misalignment occurs due to the manufacturing error of the planet worm-gear carrier and is reflected in the assembly as in Fig. 5. The ideal situation for four planet wormgears is that they are located symmetrically at a, b, c and d. While considering the angular misalignment , there are a number of possibilities in the assembly that the planet worm-gears are located away from their ideal locations. The latency errors impinge on meshing properties and load capacities of a toroidal drive. To study these errors, the coordinate frames between the planet worm-gear and the sun-worm is illustrated in Fig. 6. In the figure, a0 represents the theoretical center distance between the sun-worm and planet worm-gear, a is the center-distance offset, w the sun-worm lateral misalignment and the planet worm-gear angular misalignment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003340_bf00705581-Figure20-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003340_bf00705581-Figure20-1.png",
        "caption": "Fig. 20. Detail of the cycloidal pendulum showing the cheek arrangement and the rigid portion of the pendulum; Horologium Oscillatorium.",
        "texts": [],
        "surrounding_texts": [
            "already been studied by GALILEO and TORRICELLI. WILLIAM BROUNCKER (1620 ?- 1684), the first Charter President of the Royal Society, seems to have identified it, without proofs, as tautochronous. The correct curve is available. Now, the freely swinging pendulum gives HUYGENS the first clue. To bring the periods into agreement, the length of the pendulum in large oscillations must be shortened in proportion to the amplitude. This means that tile curvature of the correct curve is greater than that of a circle, the radius of which is equal to the length of the perpendicular pendulum. The next question is how to determine the cycloid of a particular pendulum, i.e., the proper curve of the cheeks. HUYGENS' method is the following: Now, to be able to determine the curvature of the cheeks (lamellarum formam), . . . i t is necessary first to have decided on the length of the pendulum from the law of the length . . . . Once that the length of the pendulum has been fixed ... the cycloidal line that will give the curvature of the cheeks T will be defined in the following manner: Let the ruler A B . . . be attached to a plane table. Then construct a cylinder CDE. . . of diameter equal to one half the length of the pendulum...120 (Fig. t9)"
        ]
    },
    {
        "image_filename": "designv11_28_0002984_icma.2006.257789-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002984_icma.2006.257789-Figure1-1.png",
        "caption": "Fig. 1 Locating the position and orientation",
        "texts": [
            "ndex Terms - Robot, Rotation Decomposition, Quaternion. I. INTRODUCTION A complete robot motion includes a 3D position transition and a 3D rotation. Because the position transition can be clearly represented by a transition vector, we are more concerned with the problems related to the rotation. Typically, a rotation is represented by a rotation matrix [1]. As shown in Fig. 1, a coordinate system {b}={XbYbZb} has been attached to the robot relative to the another coordinate system {a}={XaYaZa}. If we want to deal with the rotation only, we can assume {a} and {b} have the same origin, as shown in Fig. 2. Assume that a spatial point is represented in the coordinate vector aP with respect to the frame {a}, and Pb with respect to the frame {b}, then we have PRP ba , where R is the rotation matrix, a 3 by 3 matrix, which satisfies 1TT RRRR . The rotation matrix gives the general and resultant information of the robot rotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002307_1.2406105-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002307_1.2406105-Figure7-1.png",
        "caption": "Fig. 7 Orientation of rake-face of the precision gear hob",
        "texts": [
            "2 The DG/K Approach of Determining Orientation of he Rake Face. Figure 6 provides a clear understanding of geomtry of the precision involute gear hob with straight-line lateral utting edges. Understanding the features of the hob geometry see Subsec. 3.1 is very helpful for derivation of equations for omputation of major parameters of the gear hob of the design eveloped. 3.2.1 An Auxiliary Parameter R. Lateral tooth surfaces of the uxiliary rack R intersect each other along a straight line through oint A Fig. 7 . This straight line is at a distance R from the hob xis. For the distance R, Fig. 8 yields R = 0.5 \u00b7 dh + tc \u00b7 cot n 13 3.2.2 The Angle r Between the Lateral Cutting Edges of the ob Tooth. Prior to deriving the equation for computation of the ngle r that make the lateral cutting edges of the gear hob tooth, t is convenient to derive an equation for computation of projecion of the angle r onto the coordinate plane XhYh. The projections of the lateral cutting edges of the involute tooth nto the coordinate plane XhYh make an angle "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003549_156855308x294851-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003549_156855308x294851-Figure1-1.png",
        "caption": "Figure 1. Schematic diagram of the CMMS.",
        "texts": [
            "eywords Time optimal, specified path, limited actuators, cooperative manipulator, switching curve A cooperative multi-manipulator system (CMMS) is defined as a system of multiple robots handling a common object (Fig. 1). Application of multiple robots in an assembly line working on an object at a similar time or handling a big object with several manipulators could be considered as examples of such systems. * To whom correspondence should be addressed. E-mail: mh_ ghasemi@me.iut.ac.ir  Koninklijke Brill NV, Leiden and The Robotics Society of Japan, 2008 DOI:10.1163/156855308X294851 494 M. H. Ghasemi, M. J. Sadigh / Advanced Robotics 22 (2008) 493\u2013506 Many researchers studied the problem of minimum time tracking of a manipulator on a specified path",
            " Sadigh / Advanced Robotics 22 (2008) 493\u2013506 Step 3: From the lowest neighboring points on both side, (C6) repeat Step 2 until either the solution trajectories intersect line s = 0, s = 1 (b4) or it enters the NFR or it intersects with lines generated in previous steps (b3). Continue Step 3 for other points until either the generated path covers the whole domain of s from 0 to 1 or the solution trajectory ends up on the NFB. In the second case, one should search for critical points of the second category, s\u0308\u2212 s\u0307\u03ba \u2032 = 0, in the uncovered portion of the NFB and continue for calculated points with the same operation as mentioned in Step 3 (see Fig. 6). Figure 1 shows the schematic of a system composed of two planar manipulators handling a payload. The physical characteristics of the system are indicated in Table 1. Each manipulator has 3 d.o.f. It is assumed that the payload is rigidly grasped such that no slipping or rotation is possible at contact points. For this system n = 6,p = 3 and m = 6. The physical properties of the system are listed in Table 1. The system is assumed to move the payload on a prescribed path defined by (15), see Fig. 7. x(s) = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000839_s0168-874x(00)00072-x-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000839_s0168-874x(00)00072-x-Figure1-1.png",
        "caption": "Fig. 1. A rotor element with four degrees of freedom per node.",
        "texts": [
            " The sti!ness and damping coe$cients of the bearings can be directly used as input data, or obtained from the computer codes developed automatically based on the -\"lm theory when applicable. For marine propulsion systems, the program also includes the coe$cients for some commonly used special bearings, such as partial arc bearings or bearings with multiple axial grooves. These coe$cients have no closed form solutions and are calculated by solving higher dimensional #uid dynamic equations [16]. Fig. 1 shows the rotor element considered in this work. The element consists of two nodes, with four degrees of freedom at each node. The nodal element displacement vector can be described as [11] q \"[< = B < = B ] (1) The displacement vector within the element is interpolated as < = \"[N ] q , (2a) B \"[N ] q , (2b) where [N ]\" N 0 0 N N 0 0 N 0 N !N 0 0 N !N 0 , (3a) [N ]\" 0 !NM NM 0 0 !NM NM 0 NM 0 0 NM NM 0 0 NM . (3b) The shape functions shown in Eq. (3) are N \"1! 1 a(a #12g) (12gx#3ax !2x ), N \" 1 a(a #12g) [(a #6g)ax"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002584_robot.1987.1087740-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002584_robot.1987.1087740-Figure2-1.png",
        "caption": "Figure 2 : The pai-t assembled with two arms using great cooperation.",
        "texts": [],
        "surrounding_texts": [
            "ea ,b is i t s l a t h ' l i n e a n d ' b t h ' c o l u m n e l e m e n t ; * e=,b =1 i f t h ee x c h a n g e (Rob K,Frame a) t o (Rob L,Frame b) is p o s s i b l e ,\ne a,b =O otherwise.\nThe \"Exchange matr ix\" E i s a (nm x nm) boo lean ma t r ix composed of t h e l e m e n t a r y e x c h a n g e m a t r i c e s :\nF A , , -; - - - \u20ac v : 1 If E i , j i s t h e ' i t h ' l i n e and ' j t h '\nco lumn e lement o f E , it c o r r e s p o n d s to t h e exchange (Rob K,Frame a) To (Rob L,Frame b) w i t h : i = a + (K-l)xm (8)\nj = b + ( ~ - 1 ) x m\nIt is e a s y t o show t h a t t e p o s s i b i l i t y of t h e d i r e c t e x c h a n g e (Rob K,Frame a ) t o (Rob L,Frame b ) is possible i f E i , j = l a n d a nu d i r e c t e x c h a n g e is p o s s i b l e (it i s t o s a y by p i n t e r m e d i a t e c o n f i g u r a t i o n s ) i f we c a n f i n d p w i t h :\nP P E i , j =1 where E i , j is t h e ' i t h ' l i n e a n d\nj t h ' c o l u m n e l e m e n t o f t h e b o o l e a n p m u l t i p l i c a t i o n : p\nE =E X E X ... X E p times.\nThis l . eads t o t h e f o l l o w i n g a l g o r i t h m :\n* PHASE 1 : I n i t i a l i s a t i o n p=l\n* PHASE 2 : The m a t r i x E is P\ncomputed P\nI F E s , g = l (S ta r t and Goal c a n f i g u r a t i o n ) t h e e x c h a n g e s e q u e n c e e x i s t s . G O 3 ELSE GO 2 w i t h p = p + l\n* PHASE 3 : We choose an r which s a t i s f i e s p - 1\nE s , r l = E r l , g = l\na n d r e c u r s i v e l y an r l\nw i t h E s , r = ErTr 5 ~ 1 P-9\nRemark : we c a n e a s i l y f i n d cases i n w h i c h t h e e x c h a n g e s e q u e n c e d o e s n ' t e x i s t . T h e p r e v i o u s a l g o r i t h m f i n d s s u c h cases by c o m p a r i n g d u r i n g PHASE 2 t h e m a t r i c e s :\nP P-1 E and E ; I f w e have :\nP P-1 E = E we c a n show t h a t n o\ns e q u e n c e e x i s t s .\n111. PROGRAMMING ASPECTS, IMPLEMENTATION\nT h e s e m o d e l s a n d a l g o r i t h m s h a v e b e e n implemented for two k i n d s o f e x p e r i m e n t s . The f i r s t o n e c o n c e r n s s i m u l a t i o n o f p l a n a r robots and of s e q u e n c e s of exchanges and t h e s e c o n d o n e d e a l s w i t h a rea l a p p l i c a t i o n i n m u l t i - a r m s a s s e m b l i e s .\n- 1. Simula t ion\nThe f o l l o w i n g e x p e r i m e n t s h a v e been c a r r i e d o u t w i t h a M I N I 6 CII-HB computer i n FORTRAN.\na) k inemat i c mode l [5] F i g u r e 2 : The use of a r e l a t i v e k i n e m a t i c model for t h e a l i g n m e n t o f two 3 d e g r e e s of f r eedom robo t s .The j o i n t v a r i a b l e Y 1 is l o c k e d . F B 2 : C o o r d i n a t e d m o t i o n u s i n g t h e\no p t i m i z a t i o n term.Two robots ( 2 and 3 d e g r e e s o f f r e e d o m ) a re a l i g n e d ( t h e 2 t e r m i n a l d e v i c e s are j o i n e d ) , a n d move t o g e t h e r t r y i n g t o make t h e p o i n t 01=02 t o c o i n c i d e w i t h a p o i n t O f of t h e work area.\nF i g u r e 2\nF i g u r e 2",
            "b) Kequences 0-f exchanges [l!] For example : 2 robots, 4 grippinq frames The possible exchanges-betheen the two robots are described by the following exchanges list :\n(Rob 1, Frame 1) ---- (Rob 2,Frame 2) (1,l) ---- (213) (1,2) ---- (2,1) (1,2) ---- (2,4) (1,3) ---- (2,4) (1,3) e--- (2,2) (1,4) ---- (2,l) and the exchange matrix is :\nFrame 1 Frame 2 Frame 3 Frame 4 Frame 1 Frame 2 Frame 3 Frame 4\nLet suppose that the Initial Gripping Configuration is (Rob 1,Frame 1) and the Wanted Gripping Configuration is (Rob 1,Frame 2). The IGC corresponds to the line (start) of E and the WGC to the column \"gtl (goal) of E with : s = 1+ (1-1)x4=1 11 I t\ng = 2+(1-1)~4=2\nThe direct exchange is of course impossib_le which is confirmed by the equality:Es,g=O.This is also true for the next 2 matrices : 2 3\nE and E\nThe computation of E shows that Es,g=l ; it is to say that the exchange is possible through 3 intermediate configurations :\n4 4\nIGC (1,1)--(2,2)--(1,3)--(2,4)--(1,2) WGC\nOther examples have be n carried out.Because of the nature of exchanges matrices, this mgthod is very fast; it is also theoretically unlimited. For 5 robots and 5 gripping frames, exchanges matrices are (25 x 25) ; 7 exchanges (it is to say 7 multiplications of matrices (25 x 25) were computed in less than 2 seconds by a multi users computer.\n--- 2. On situ experiment\nThe aim of this experiment is to assemble a vice of 8 parts with two 6 rotative degrees of freedom manipulators (MA-23 Societe La Calhhe) (Figure 4). To build the vice, eight assemblies are needed : four of them are performed by a single arm , the four others require the use of both manipulators (part 1 on \"base',part 4 and part 5,part 3 and part 5,part 7 and part 8 ) ; in these last cases the kinematic model is used during relative motions and for the coordination of the robots when they are carrying a part together (Figure 5).\nBecause of inaccuracy of the robots, and lack of specialized assembly tools, the forces andtorques acting on the manipulators are m asured toc mpute correctinp;jvements making the assemblies possible The assembly parts, chosen in order to carry out various mechanical joinings (prismatic, cylindrical, multi-insertion, screwing , .. . ) , and the assembly strategies used to overcome the lack of precision of the manipulators (no possible precise position assemblies) During the grasping and carrying stages of the assembly parts, the two MA-23 have to move along large trajectories while avoiding any collision between themselves and with the work table. In these stages, the robot needs to be controlled by a safe trajectories algorithm which will be introduced in the experiment procedure.",
            "- IV . CON_CLUS ION The methods developed in this paper\ndon't deal with synchronization of robots but with real coordination. The mathematical difficulties are solved by using a kinematic model to carry out the task in a relative way.\nFuture complex exper iments will necessitate the uses of several robots in industry, working in high cooperative tasks. The studies summed up here are a necessary stage in the developments of these experiments. The next stage would be the us of Artificial Intelligence techniques to automaticaly dispaching the tasks between the concerned robots.\n-REFERENCES-\nM.Takahashi, M. Kohno. \"An assembly ,, robot system with twin arms and vision 6th Internat. Conf. on 1ndustr.Rob Technol. Paris 1982\nJ.B. Canner, \"TWO arms are better thar one\", 5th 1ntern.Symp.on 1ndustr.Rot Chicago 1975 S.Fuji, S. Kurono \"Co-ordinated computer control of a pair of manipulators.\",The Industr .Robot 1975 T.Ishida \"Force control in coordination of two arms\" 5th Int.Joint Conf. on Artificial Intelligence MIT 1917 P.Dauchez \"Etude de la commande de deux robots manipulateurs lors de tsches coordonn6es.I' These de 3O cycle Montpellier 1983 P.Dauchez, P.Coiffet, A.Fournier \"Cooperation of two manipulators in assembly tasks.\" Digital Systems for Industrial Automation, 1983\nA. Fournier \"GQnQr at ion de mouvements en robotique ; application des inverses g6n6ralis6es tdes pseudo-inverses. *I These d'ktat Montpellier 1980 R.Paul Ro bo t manipulators : Mathematics, -Programming and Control; The Computer Control of Robot Manipulators\" MIT Press 1982 T.L. Bouillon, P.L.Odel1 \"Generalized Inverses Matrices\" WILLEY-Interscience [lq S.M.Udupa \"Collision detection and avoidance in computer controlled manipulators\" 5th IJCAI Cambridge 1977 [ll] O.Khatib, JF Le Maitre, \"Dynamic control of manipulators operating in a comp1.e~ environment\" 3rd CISM-IFToMM Symp. on the Theory and Practice of Robots and Manipulators. Udine, Italia 1978 [12] T. Lozano-Perez \"Automatic Planning of manipulator transfer movements\" IEEE Trans. Vol.SMC-11 Oct.1981 [13] R.Zapata \"Le problsme de 1'6vitement des collisions dans la commande des robots manipulateurs\" These de 3O Cycle Montpellier 1983\n1141 P.H Winston \"Artificial Intelligence\" Add ison-Wesley 1971 [15] R.Zapata,P.Dauchez, P.Coiffet \"Cooperation of robots in gripping tasks: the exchange problem\" Robotica Volume\nk'q strategic d'assemblage automatique a B. Shar iat Tobargan \"Etude d un?\npartir de mesures dleefforts\" These de 3O cycle Montpellier 1984\n1, pp 73-77 1983"
        ]
    },
    {
        "image_filename": "designv11_28_0001241_robot.2002.1013564-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001241_robot.2002.1013564-Figure1-1.png",
        "caption": "Fig. 1. Coordinate system and Lariables At characterize the motion trajectories of the multi-legged robot",
        "texts": [
            " Section three formulates the optimizing indices and section four develops a set of experiments that reveal the influence of the system parameters in the periodic gaits, respectively. Finally, section five presents the main conclusions and directions towards future developments. 11. A MODEL FOR MULTI-LEGGED LOCOMOTION We consider a longitudinal walking system with n legs (n 2 2 and n even), with the legs equally distributed along both sides of the robot body, having each one two rotational joints (Fig. 1). Motion is described by means of a worid coordinate system. The kinematic model comprises: the cycle time T, the duty factor p, the transference time tT = (l-P)T, the support time ff = PT, the step length Ls, the stroke pitch Sp, the body height HB, the maximum foot clearance Fc, the r\"\" leg lengths L,, and Liz and the foot trajectory offset Oi (i=l, ..., n). Moreover, we consider a periodic trajectory for each foot, with body velocity VF= Ls /T . The algorithm for the forward motion planning accepts the body and ih feet Cartesian trajectories pp(t) = [xi&), y&lT as inputs and, by means of an inverse kinematics algorithm, generates the related joint trajectories O(t) = [Oil(t), selecting the solution corresponding to a forward knee"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001527_j.electacta.2004.07.053-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001527_j.electacta.2004.07.053-Figure2-1.png",
        "caption": "Fig. 2. A current\u2013voltage curve obtained with cyclic voltammetry of 0.2 mM terephthalaldehyde in aqueous buffer pH 2.0 containing 30% acetonitrile. \u03c5 = 1.0 V s\u22121, E0 = \u22120.25 V, Erev = \u22120.5 V.",
        "texts": [
            " This can be formed in the vicinity of the lectrode surface in a consecutive protonation (4) and (5), eiher from the unhydrated form (I) present in equilibrium, or from the monohydrate Ia by a dehydration [reverse reaction (1)] followed by consecutive protonations (4) and (5). The reduction of the diprotonated form (Ic) proceeds in wave i1 in a single, reversible two-electron step (6) (Scheme 1), in which a diradical-quinonemethide(IV) is formed [4]. The reversibility of reaction (6) has been proved by cyclic voltammetry (CV) (Fig. 2) and by rectangular voltage polarization in the commutator method by Kalousek [13,14]. In the latter method anodic waves of reduction products are r T a recorded curves are obtained under practically potentiostatic conditions, as the potential of each single drop varies (at t = 3 s and dE/dt = 200 mV min\u22121) by less than 15 mV. In CV, the potential applied to a constant electrode surface, is swept at 10\u20131000 mV s\u22121 and products formed at one potential can affect electrode processes at others. The peak currents obtained in CV also depend on the rate of the electrode process proper, whereas limiting currents, obtained by commutator, depend only on the transport of the electroactive material to the electrode surface by diffusion and chemical reactions. The reversibility of reaction (6) is supported by the small difference between the cathodic and anodic peak potentials (43 mV as compared to theoretical 57 mV/n), by comparable cathodic and anodic peak currents (Fig. 2), as well as by the presence of anodic waves of oxidation of the diradicalquinonemethide obtained by the commutator method. But the anodic currents obtained by these two techniques depend also on pH. The dependence of the anodic limiting current (obtained by the commutator method) on pH is bellshaped (Fig. 3, Ref. [4]) with a maximum at about pH 1.0. Any decrease in current indicates an increase in the rate of a reaction by which the oxidizable diradical-quinonemethide is converted into an anodically inactive species"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003740_1.2975154-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003740_1.2975154-Figure7-1.png",
        "caption": "FIG. 7. a Computation of n unit vector components along the axes X, Y, and Z for a right handed helicoidal magnet; b computation of M magnetization components along the axes X, Y, and Z for a right handed helicoidal magnet; c rotation S of M magnetization around the axis of the left handed helicoidal magnet; d rotation D of M magnetization around the axis of the right handed helicoidal magnet.",
        "texts": [
            " The only differences between the equations relative to right handed magnets that we can write and the previous ones are limited to certain signs. In fact, with reference to Figs. 6 and 7 a relative to a right handed helicoidal magnet, Eqs. 11 , 13 , and 18 must be substituted by the following: nx = \u2212 n cos , 33 nz = n sin cos \u2212 , 34 cos \u2212 = y y2 + z2 . 35 Therefore, in relation to the magnetization M of the right handed magnet, it is necessary to substitute Eqs. 14 and 16 with the correspondent see Fig. 7 b Mx = \u2212 M cos , 36 Mz = M sin cos \u2212 . 37 Substituting Eqs. 35 and 23 in Eq. 37 we find again Eq. 26 , that is, Mz is always the same one for both the right and the left magnets. Furthermore, since My is identical for the two magnets too, then Eqs. 28 and 29 are valid again. Finally, if we consider Mx, substituting Eq. 23 in Eq. 36 , we verify the validity of Eq. 27 . Then, Eq. 32 is valid for the right handed magnet too. [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation",
            "202 On: Thu, 18 Dec 2014 07:41:10 In this section we show that if the magnetization M of the magnet has still a helicoidal orientation, but is not the same as the normal n\u2212n that passes through the generic point P of the cylindrical helix , then the volume charge density M P is not equal to zero. As a starting point, let us consider the left handed helicoidal magnet characterized by a constant value of the magnetization magnitude M. As illustrated in the previous section, M is oriented along the normal n\u2212n. Now we rotate M so that it defines an angle S in the plane YZ with respect to n\u2212n. In Fig. 7 c , after the rotation S, M is denoted by the symbol M . The magnitude of M is M and is equal to M, M = M . 38 As illustrated in Fig. 7 c , the components My and Mz reported in Fig. 5 a become My and Mz , respectively. Moreover, observing Figs. 2 b and 7 c we see that the component Mx of M is equal to the component Mx of M. Then, an equation analogous to Eq. 14 is valid, Mx = M cos . 39 Substituting Eq. 23 in Eq. 39 , we can write the explicit expression of Mx , Mx = M cos arctan p 2 y2 + z2 . 40 Observing again Fig. 7 c , since the magnitudes of M and M are equal to M Eq. 38 , we can write the following equations: My = \u2212 M sin sin \u2212 + S , 41 Mz = \u2212 M sin cos \u2212 + S , 42 where sin \u2212 + S = sin \u2212 cos S + cos \u2212 sin S, 43 cos \u2212 + S = cos \u2212 cos S \u2212 sin \u2212 sin S. 44 Substituting Eqs. 20 , 21 , and 23 in Eqs. 43 and 44 , Eqs. 41 and 42 become My = \u2212 M sin arctan p 2 y2 + z2 z y2 + z2 cos S + y y2 + z2 sin S , 45 Mz = \u2212 M sin arctan p 2 y2 + z2 \u2212 y y2 + z2 cos S + z y2 + z2 sin S . 46 Computing the partial derivative Mx / x, where Mx is expressed by Eq",
            " 2 c , then the volume magnetic charge M P is always equal to zero. Consequently, in order to have M P =0, we have found that the M orientation along the normal n\u2212n is not necessary. As a matter of fact, in the above mentioned plane, the M orientation can be any, on condition that the magnitude of M does not depend on the coordinates x, y, and z of P, that is, the value of M must be a constant. In relation to a right handed cylindrical helicoidal magnet, we can substitute the angle S with D and define the components Mx , My , and Mz , as illustrated in Fig. 7 d . The same previous conclusions are valid also for this kind of magnet. VI. VOLUME CHARGE MAGNETIC DENSITY M FOR MAGNETS WITH CONCHOSPIRAL GEOMETRY AND MAGNETIZATION M The helicoidal permanent magnet of cylindrical kind can be considered as a particular case of a more general class of magnets characterized by a conchospiral geometry10 and magnetization. Therefore, in this section, we want to evaluate the volume magnetic charge M for the conchospiral magnets, on the usual assumption of a constant magnitude value M of M"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000460_robot.1992.219917-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000460_robot.1992.219917-Figure6-1.png",
        "caption": "Figure 6: A schematic and an actual view of the experimental setup.",
        "texts": [
            " 4 Experiments Once the synthesis algorithm in Section 3.6 computes the desired a arent impedance of each fin er, the rasp controller must be to control each finger such h a t it ex%ibits the desired apparent impedance. Presenting the results of two experiments where a finger exhibits a desired impedance is the aim of this section. The finger in our experiments is in fact a 2-link direct drive robot with a soft hemispherical (fingertip like) end effector [12]. A view of the finger and the schematic of the experimental setup are shown in Figure 6. The desired apparent impedance parameters in both experiments were I(d = Diag[250.0, 250.O]N/m, Bd = Dia [100.0 100.01N - s/m, M d = Diag[lO.O, 10.0 N - 8'/m. In bot! experiments, the fingertip was commanded tolbe at locations behind the wall. Aa can be seen from Figure 6, the wall is parallel to x-axis. The impedance control scheme used is a modified version of that described in [13. The details of the control scheme itself are not presented here due to space limitations. Experiment 1: Stiffness Regulation was initially in contact with the wall as shown in Figure 6. k was then commanded to move to and regulate its position at a point 0.105 m 105 mm) behind the wall (along y-sxls while maintaing its originA position on x-axis. The commandkd (desired) and the resulting actual) positions of the fingertip along y-axis are shown in Figure 4.. Since the desired position on y-axis is unreachable, the fin er applies a force along the direction of the desired but unachievagle motion in accordance with the specified impedance relation, Fingerti MdXe + BdXe + KdXe = Gctud, (16) where xe = (w - x), positions of the fingertip in Cartesian space"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001843_0020-7403(79)90015-8-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001843_0020-7403(79)90015-8-Figure2-1.png",
        "caption": "FIG. 2. Geometry of the caustic at points of discontinuities for an arbitrari ly distributed load applied along a part of a straight boundary.",
        "texts": [
            " (17a) corresponds to reflected-light rays from the rear and the front face of the specimen, respectively. It can be derived from the above relations that the geometry of the caustic and of its initial curve, is closely related to the jumps in the load Af = AN + i A T and in its slope Af' = AN' + iAT ' . For the determination of the components of the load jump and its slope AN, AN', AT, AT', from the above-mentioned equations, the coordinates of two characteristic points of the caustics will be used. As such points the points M and N were selected (Fig. 2), determined by the system of equations (13) and (14), for Oc = 0 and for Oc = - ~, respectively. We have for these points that: Intensity, slope and curvature discontinuities in loading distributions 343 (18) +AN\u2019ln\u201d(-\u201c)+AT\u2019r AT r,\u2018(- ?r) (19) (20) (21) where X&, Y&, Xt Y% are the coordinates corresponding to the coordinate system Oxy, where the origin 0 is coinciding with the jump point C without loss of generality and r&O) or rc(- a) represent the values of rc for gc = 0 or & = - P respectively (Fig. 2). In passing from relations (13) and (14) to relations (18) to (21) we have approximated the quantities In [rJO)/(a + c + r&O))] and In [rJ- w)/(a + c - rc(- rr))] by the quantities In [rc(O)/(a + c)] and In [rc(- ~)/(a + c)] respectively. This is justified by the fact that the value of rc is negligible in comparison with the length (a + c) (Fig. 1). From the system of linear equations (18) and (20) the unknown quantities AN, AN\u2019, AT and AT\u2019 can be expressed as functions of r=(O) and rc(- a), and after their introduction in relations (19) and (21) we can obtain the values r&O) and rc(- P) from the system of the resulting two non-linear equations",
            " Since in relation (24) we have neglected the function @i(z) in the exact expression of the @\u2018(z) (relation I l), an error occurs in the expression of the caustic (relation 24) formed at the discontinuity point of the load-intensity. An estimation of this error is possible by using the exact expression for 0\u2019(z), which is determined from equation (7). Then, the equations of the corresponding caustic take the form: where re. Sa (Fig. 1) are determined by the equations (IS). According to relations (26) and (24) the neglected quantity is given by: wz = _ g $ ei(r/2-B+4sl (27) 344 P . S . THEOCARIS and C. I. RAZEM which represents a caustic of negligible dimensions, coinciding with the image of the point C on the screen (Fig. 2). Also, for the pure shear loading (/3 = _+ \u00a2r/2) we can readily show that the caustic has its ex t reme points M and N (Fig. 2) on the corresponding image of the nondeformed boundary on the screen. For this purpose we introduce in the exact relations (26), the va lues /3 = +- ~r/2 and Oc = 0 or Oc = - w and we get: Im W~ = Y~- =- 0. (28) Following the approximate relations (24) and (23) (or (18)-(21)) the determinat ion of the loading discontinuity A / = IAII e ~ is also possible by the relations: g cos/3 I + g sin-------~ = tan a (29) D = [MN] = 2~/2rc(I + g sin/3),/2 (30) A\" - ~r)tsD2 I - i61cl( i ~ g sin/3) (31) where D is a diameter M N of the caustic (Fig. 2) and a is its angle with the image of the nondeformed boundary. It can be derived f rom relation (29) that the loci of the extremit ies M and N (Fig. 2) of the caustic formed at point C -= O where AT = 0 (/3 = 0), is a straight line making an angle a = -+45 with the image of the nondeformed boundary, and passing through the image of this point. In the last two cases, that is w h e n / 3 = 0 or /3 = -+ \u00a2r/2, the corresponding jumps in the intensity of the normal or tangential loads respectively may be determined by the simple approximate relation: [AN[ = \u00a2rD: for /3 = 0 (32) 16CA,, 7rD 2 [AT[ = 32CA,, for /3 = -+ ~r/2 (33) where D the diameter of the corresponding caustic, and C, Am are determined by relation (6). Also, following relations (26) and (15) the coordinates of the points M and N (Fig. 2) are determined by: W ~ = rc \u00f7 gA e \"~t2-~ (34) W ~ = - rc - gB e i(~12-0) (35) where (Fig. 2) rc A = ]MIM[ = r c ( I - a + c + r c ) (36) B = IN 'NI = rc ( I + a + c -rc rc)\" (37) It can be concluded f rom the geometric representat ion of W ~ and W~ (Fig. 2) that fo r /3 = 0 (i.e. for a normal loading) the line M N does not pass through the image of point C and makes an angle a =-+45 \u00b0 because A ~ B. Thus an error, which depends on the ratios rd (a + c + rc) and rel(a + c - rc), occurs in the practical evaluat ion of the angle a and of the diameter D = IMNI. The errors ea and en are given by = ( ( a - w14) lOr14) x I 0 0 = ~a(P) ~a (38) eD = ( (D - D45.)ID4s.) x I00 = ~:D(P) ~ where D45. is given by the relation (30) for /3 = 0, and a and D are the exact values obtained f rom relations (34) + (37), as follows: g cos /3 ) t a n a I - p Z + g sin/3 | / 2g ",
            " If A f = A N + i A T = 0, then it is valid that: Intensi ty, slope and curvature discontinuit ies in loading distr ibutions 345 and W~= X ~ + iY~= rc e'eC + glC*l e'('12-~'( ln a-~c - iOc) r~ = Ic*l = ~ ( A N ' : + AT'2) '~. (41) (42) We observe f rom relation (42) that the initial curve is a circle of radius re, which depends in the same way on the jumps in the derivative o f the normal (AN') and the tangential (AT') loading acting separately. Following a similar analysis as in the case of a discontinuity in the intensity of load, it can be derived f rom relation (41) and for Oc = 0 and Oc = - lr that the angle a and the diameter D = ]MNI (Fig. 2) of the caustic surrounding the discontinui ty point of the first derivative of load are expressed by: tan a gcr sin y (43) 2 + g~r cos y D = [MN[ = rc[(2 + gcr cos y)2 + g21r2 sin z y]u2. (44) Thus , the j ump Af' , expressed by: AI' = IM'I e\" (45) can be obtained from relations (43), (44) and (42) by measuring the diameter D of the caustic and its angle a, with the direction of non-deformed boundary. In the particular cases of a discontinuity in the derivative of either the normal (y = 0) or the tangential (y =-+ ~r12) load, (relation 16b), the jump may be obtained from relations (44) and (42) by the following simple formulas: IAN, I = . X . o 2C (2 + g~r) for y = 0, (46) (AT') = \u00a2r;t~ D 2C (4 + gZlr~)U2 for y = + 1r/2. (47) It can be derived f rom equat ion (43) that in the last two cases the caustic has as geometrical characterist ic the values of angle a (Fig. 2) given by: a = 0 for 3' = 0 and g = + I (48) and a = --+57.5 \u00b0 for y = -+It/2 and g = -+ I. (49) Therefore , in the case where y = 0 the caustic has its ext reme points M and N (Fig. 2) on a line parallel to the image of the nondeformed boundary and for y = -+ ~r/2, the diameter of the caustic makes an angle a = ---57.5 \u00b0 with the above ment ioned image. It should be noted that for a pure tangential loading, i.e. for fl = -+ \u00a2r/2 and y = -+ \u00a2d2, it can be derived f rom relation (13) that the coordinate YN of point N (Oc = - T r ) of the caustic is proportional to the discontinui ty in the first derivative o f this loading, and it does not depend on the intensity of loading itself at the discontinuity since it is valid that: Y~ = ~'g,[CTI = ~-CCg,IAT'I (50) where gm= g sign y, and y = -+ ~r12",
            " When a pure tangential loading is acting on the boundary of the half-plane and presents a discontinuity of order two (n = 0, I, relation 9), then the value of the discontinuity AT' in the first derivative of this loading may be determined by a simple formula which results from equation (50). All the above, properties of the geometrical shape of caustics were deduced under the assumption that for eO'(z) the non-singular terms Ore(z), relation (I I) were neglected and therefore an error is introduced by this a s sumpt ion in the evaluat ion of A N ' and AT' . To es t imate this error the exac t formula (7) will be used for the determinat ion of O'(z), and then the coordinates of points M and N (Fig. 2) can be derived as: _,,/2-,~ \u2022 rc(O)_ rc(O)'~ W ~ = X ~ + i Y ~ = r c ( O ) + [ C * [ c (m r--~ + I - ra(0)j for Pc = 0 (51) rB(O) = a + c + re(O) rc(O)[a + c + re(0)] 2 = 4fC*la 2 W~ = X~ + iY~ = - rc(- ~r)+ I C~[ e'\u00b0'12-v)(In rc(- It). I + ilr + rc:- ~ for ~c = - ,/r (52) 346 P . S . THEOCARIS and C. I. RAZEM rn( - Ir) = a + c - r c ( - Cr) r c ( - 7r)[a + c - r c ( - 7)12 = 4iC*la:. Relations (52).give the exact values for YN in the case of pure shear loading, i.e. /3 = 3' = -+ ir]2. This value of YN coincides with the one obtained from the approximate relation (50)",
            " It is well known[12], the initial curve (I) of the caustic is the generatrix curve of the caustic on the specimens which does not appear on the specimen or screen, while the caustic itself and the pseudocaustics are formed on the screen as bright continuous curves which separate the field of view on the screen in an illuminated part and a dark part as it can be seen in Figs. 10 and 11. Figs. 4(a) and 4(b) show the evolution of the shape and the dimensions of the caustics in the case of a discontinuity either in the intensity of the normal AN or of the tangential AT loading, respectively. For a discontinuity in the intensity of load the caustic has its diameter D = IMNI (Fig. 2) proportional to the square root of the load intensity IANI or [ATI (relations 32 and 33), as they can be seen in Figs. 4(a) and 4(b) respectively. Another geometrical characteristic of this caustic is the angle a subtended by the diameter connecting the extremities of the caustic and the image of the deformed boundary. This angle takes the values a = -+45 \u00b0 (Fig. 4a) or a = 0 \u00b0 (Fig. 4b) for a discontinuity in the intensity of the normal or of the tangential loading, respectively. Specimen I i \"--< I I [ 0",
            " The shape and the dimensions of the caustics take a particular form in the case when a discontinuity only in the first derivative of load distribution Af' acts on the boundary. This particular form is characterized by the diameter D (relations 46 and 47) which is proportional to IAN'[ or [AT'[ and by the angle a, which takes the corresponding values a = 0 \u00b0 or a = -+57 \u00b0 (relations 48 and 49) as it is shown in Figs. 5(a) and 5(b) and 6(a) and 6(b) respectively. We can remark from relations (18)--(21) that the values of the angle a (a = 0 \u00b0, -+45 \u00b0, -+57 \u00b0) and the length of the diameter D (Fig. 2) remain unchanged, if a continuously varying load P ( t ) = N ( t ) + i T ( t ) is superposed on the discontinuities Af = A N + t A T and/or Af' = A N ' + tAT ' which act on the boundary. This is illustrated by measuring the angle a and the diameter D in Fig. 7(a) where, with the exception of the discontinuities AN and AN' a tangential and a normal continuous load act simultaneously on the boundary, and in Fig. 7(b), where only the same discontinuities AN and AN' are operative. The small differences between the corresponding values of a and D in the two figures 7(a) and 7(b) are due to the fact that the caustic were drawn by using the exact expression for O(z) (relation 7), which differs from the approximate one (relation 13) by the neglected term ~dz ) (relation 7). If a pure tangential load has a double discontinuity, in its intensity AT and in its first derivative AT', then the coordinate YN (Fig. 2) is proportional (relation 50) only to the discontinuity of the first derivative AT' and does not depend on the value of the discontinuity AT, as it is shown in Figs. 8(a)-(c). The discontinuity in the intensity AT is determined by the system of equations (18)-(21). Finally, Figs. 9(a)--(c) show a series of pseudocaustics obtained from a normal or tangential distributed load having only a second order discontinuity AN\" or AT\" at the point t = 0. We can remark that the caustic reduces to a point C which represents a discontinuity point in the curvature of the two adjacent parts of the pseudoeaustic P"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002006_05698197708982834-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002006_05698197708982834-Figure4-1.png",
        "caption": "Fig. 4-Segment of a ring",
        "texts": [
            " Finally, fluid pressure acts in the radial and axial directions, but because these pressure distributions are uniform, they produce no face waviness and are not included. All of the loads shown in Fig. 3 and discussed above can produce waviness in some instances. Before specific cases are studied, general equations for deflection are derived. GENERAL DEFLECTION EQUATIONS FOR A CIRCULAR RING Since a typical seal ring cross section has comparable dimensions in both the axial and radial directions, de- of M'aviness in Mechanical Face Seals flections can be determined by assuming that the ring behaves like a curved beam. A segment of a circular ring is shown in Fig. 4. The ring is assumed to be loaded by distributed loads p, and p, acting through the shear center and pe acting through the centroid and by distributed moments m,, mu, m,. R is measured to the centroid of the cross section of the ring. Four displacement components are required to describe the displacement of the cross section. The displacements u, v, w correspond to the coordinate directions x,y, 8. Displacement C#I represents the angle of twist of the section. With reference to the ring segment shown in Fig. 4, assuming small displacements the equilibrium equations are ZF,= 0 = + No +p,R* [ l l XF, = 0 = VI + puR PI ZF, = o = N;, - V, +P,R 131 EM, = 0 = M, + Me - VuR + m,R PI E M , = o = M ; + RV, + mu^ [51 Z M , = 0 = M', - M, + NeesUt + m, R [6] In terms of moments and normal force only, the above equations can be reduced to the following: To find the appropriate stress resultant-displacement *Primes denote derivative with respect to 8. ?For the type of cross section considered herein e.,,/R << 1. It can be shown that the effect of this term is small and the term is neglected after this point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002698_6.2006-4931-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002698_6.2006-4931-Figure1-1.png",
        "caption": "Figure 1. Cut Away View of Finger Seal Assembly",
        "texts": [
            " Thus, the author offers a third generation two degree-of-freedom mass-spring-damper model that improves upon the previous models by incorporating variable fluid stiffness as a function of radial clearance between the rotor and the finger pad. III. The Finger Seal Geometry Proctor and Steinetz15, proposed a finger seal with aerodynamic selfacting lift pads added at the bottom of the low pressure fingers, illustrated in Figs. 1 and 2. The details of this geometry have been further clarified in Marie16. Fig. 1 presents a three-dimensional cut away view of the solid model containing the back- and front-plates and the low- and high-pressure finger laminates. The back-plate serves as an axial support against bending when the thin finger laminates are under pressure. This plate also contains a pressure equalization manifold that contributes to the mitigation of Coulomb friction between the plate and the low pressure laminate as the latter moves radially to follow the shaft orbit motion. The design configuration of the finger laminates, Fig",
            " As presented and discussed by Marie16, the introduction of the upper wedge/fillet combination has been essential in the reduction of the out-of-plane twisting of the finger pad in both the radial and axial directions. A working finger seal contains at least two finger laminates. This is so that one finger laminate can be oriented in such a way to the second finger laminate, specifically staggered, so as to cover the interstices between the individual fingers. Thus, when properly assembled, the high-pressure finger sticks are centered on the interstices between the low-pressure fingers, as can be seen in Fig. 1. In Dcc Rs Rs Do Db Di Df a Figure 3. Geometry and Notations for the Finger Seal Table 1. Geometric Values of the Basic Finger Finger Geometry Symbol Value (in) Seal Outside Diameter Do 9.666 Seal Inside Diameter Di 8.500 Finger Base Diameter Db 9.169 Stick Arc Radius Rs 4.511 Circle of Centers of Arcs Dcc 1.575 Foot Upper Diameter Df 8.600 Finger Repeat Angle a 4.444\u00b0 American Institute of Aeronautics and Astronautics 4 this regard, high pressure fingers\u2019 primary mission is to seal the axial leakage flow that otherwise would occur between the interstices of the low pressure fingers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001901_robot.2004.1308084-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001901_robot.2004.1308084-Figure2-1.png",
        "caption": "Fig. 2 Conceptual figure of the pmposed method for a hybrid mbot composed of hvo modules",
        "texts": [
            "00 82004 IEEE 1795 Note that the virtual joints are the same as the output , E of the lower module and the output velocity \u20184 of the hybrid robot is the velocity ,& of the upper module. By rearranging Fq. (I), (2), and (3), we can obtain the velocity equation of the hybrid robot as II. In this section, a hybrid robot structured by combination of a parallel 3 DOF 6-bar linkage and a serial type 3 DOF robot is employed as an illustrative example to explain the concept of the proposed dynamic formulation. Fig. 2 depicts the proposed model. In the proposeij method, it is assumed that the whole kinematic and dynamic-models of both the lower and upper modules are already given. To obtain the dynamic model of this hybrid robot, we need to derive the kinematic model ofthe robot first. A. Firsf-Order Kinematics The mobility of the given system is 6. Gus, the number of minimum joints required to position the system is 6, which are selected by any three joints of the 6-har~linkage and the three joints of the serial robot",
            " (1) where ,[G:-]E R\u201d\u2019 , ,A ;R3, and ?&E Ri . including the virtual joints is given as Similarly, the velocity \u2019 ,LE R\u2019 of the upper module where (3) ,in ER\u2019 and ER\u2019 denotes the velocity vector of the independent joints of upper module and that of the virtual joints, respectively and ,[G:]E R3\u201d\u201d6 . where and \u2018do - E R6 given by denotes the independent inputs of this hybrid system, and [O],,, and I,,, are a 3 x 3 null matrix and a 3 x 3 identity matrix, respectively. B. Dynamics The dynamic model of the lower module, shown in Fig. 2, can also be obtained by the open-lree structure model formed by cutting the ienter of the platform. The dynamic model with respect to the three independent joints of the lower module is obtained by applying the principle of virtual work between the Lagrangian coordinates and the minimum independent joints as [X, IO] ,L = ,rCI,ijO+ ,j: , [ C l , A . (7) Now, the dynamic model of the upper module including the virtual joints will be described. The dynamic equation can he described as where ,L ER^ denotes the dynamic load of the upper module itself"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001251_s00542-002-0260-0-Figure4-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001251_s00542-002-0260-0-Figure4-1.png",
        "caption": "Fig. 4a, b. Finite element models of a HDD spindle system for thermal analysis. a Stationary part. b Rotating part",
        "texts": [
            " Once the temperature changes, it has to be recalculated because the geometry of ball and race changes, too. 2.2 Determination of bearing displacement in double row ball bearings due to temperature variation Finite element analysis in thermal expansion and the force equilibrium equation between upper and lower bearings are used to determine the radial and axial displacements of inner and outer race due to temperature variation. In the finite element analysis, thermal expansion due to temperature variation is calculated for two parts, i.e. the stationary and rotating parts, separately. Figure 4 shows the finite element models developed using ANSYS. In Fig. 4, the stationary part consists of base, flange, shaft and inner race, and the rotating part consists of outer race and hub. The radial displacements of inner and outer races and the axial displacements of inner races of upper and lower ball bearings due to temperature variation (DrU I , DrU O, DrL I , DrL O, DhU I and DhL I ) can be easily determined by subtracting the initial positions of inner and outer races before temperature variation from the final positions after temperature variation, because a HDD spindle system has axisymmetric geometry with respect to the shaft",
            " It also makes the axial forces of the two bearings different, which moves the hub in the axial direction until the axial forces of upper and lower bearings are the same. Eq. (8) is the equilibrium equation of the axial forces between upper and lower ball bearings, and it is used to determine the axial movement of the hub.X F0A \u00bc n F0L sin a0L \u00fe n F0U sin a0U \u00bc 0 \u00f08\u00de Figure 5 shows the numerical procedures to determine the axial displacements of the outer races of upper and lower 245 ball bearings by using the Secant method. First, the finite element model of outer race and hub as shown in Fig. 4b is used to determine the axial displacements of the outer races of upper and lower ball bearings due to temperature variation only (DhU OT; DhL OT). Second, an initial guess of an axial hub movement is made, and the axial displacements of outer races of upper and lower ball bearings (DhU O; DhL O) are obtained by adding the axial movement of a hub. Third, the bearing contact forces of upper and lower bearings after temperature variation (F0U; F0L) are determined by applying the changed geometric parameters of ball and race after temperature variation to Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003554_978-3-540-30301-5_4-Figure3.8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003554_978-3-540-30301-5_4-Figure3.8-1.png",
        "caption": "Fig. 3.8 A single finger of the Salisbury hand is a serial chain robot",
        "texts": [
            "3 We have arranged this equation to introduce the forcetorque vector f = ( f , (Fp\u2212d) \u00d7 f ) at the reference point d. The equations (3.8) can be assembled into the matrix equation \u03c4 = J f , (3.9) where J is the Jacobian defined above in (3.5). For a chain with six joints this equation can be solved for the output force-torque vector f , f = (J )\u22121\u03c4 . (3.10) Thus, the matrix that defines the mechanical advantage for this system is the inverse of the matrix of speed ratios. A serial chain robot is a sequence of links and joints that begins at a base and ends with an end-effector (Fig. 3.8). The links and joints of a robot are often configured to provide separate translation and orientation structures. Usually, the first three joints are used to position a reference point in space and the last three form the wrist which orients the end-effector around this point [3.12, 13]. This reference point is called the wrist center. The volume of space in which the wrist center can be placed is called the reachable workspace of the robot. The rotations available at each of these points is called the dexterous workspace",
            " Small-diameter (low teeth count) pinions have poor contact ratios, resulting in vibration. Sliding involute tooth contact requires lubrication to minimize wear. These catalog stock drive components are often used on large gantry robots and track-mounted manipulators (Fig. 3.23). Other Drive Components Splined shafts, kinematic linkages (four-bar, slidercrank mechanisms, etc.) chains, cables, flex couplings, clutches, brakes, and limit stops are some examples of other mechanical components used in robot drive mechanisms (Fig. 3.8). The Yaskawa RobotWorld assembly and process automation robots are magnetically suspended, translate on air a planar (two-DOF) bearing, and are powered by a direct electromagnetic drive planar motor with no internal moving parts (Fig. 3.12). Industrial robot performance is often specified in terms of functional operations and cycle time. For assembly robots the specification is often the number of typical pick-and-place cycles per minute. Arc-welding robots are specified with a slow weld pattern and weave speed as well as by a fast repositioning speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002372_1.2167651-Figure11-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002372_1.2167651-Figure11-1.png",
        "caption": "Fig. 11 The employed coordinates for deriving the couplercurve equation",
        "texts": [
            " 18 is that this equation is valid rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/201 for all cases of type 2. Equation 18 is more appropriate than Eqs. 5 and 8 in the applications. 4.1 The Parametric Equation. Let again consider the spheri- cal SBL depicted in Fig. 1 b . Point C lies on the geodesic arc AB , so as the mechanism moves, the location of point C is changed on the surface of the sphere. To derive the parametric equation of the coupler curve for point C, according to Fig. 11, axis x1 passing through O should coincide with axis x6 passing through C. Let us assume the coordinate system x1y1z1 such that axis x1 will coin- cide with QO and axis y1 will coincide with the plane of QO and QB . Axis x1 can be transformed to the axis x3 when the coordinate system x1y1z1 transforms under the Eulerian orthogonal transformations as a rotation about x1 through and obtaining x2y2z2 and b rotation about z2 through 1 and obtaining x3y3z3. Matrixes T12 and T23 denote these transformations: T12 = 1 0 0 0 cos sin 0 \u2212 sin cos , T23 = cos 1 \u2212 sin 1 0 sin 1 cos 1 0 0 0 1 19 To find the final transformation we need x4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001667_robot.2004.1307171-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001667_robot.2004.1307171-Figure2-1.png",
        "caption": "Fig. 2 Concave eomer model",
        "texts": [
            " Modeling Comers Many authors have mentioned the idea of using comers as placement points, but only a few have implemented it [ 5 ] . Including corners in grasp planning is crucial since some objects cannot be grasped without using comers for finger placement. Even though both concave and convex comers may be involved in possible grasps, only the former are considered here hecause they lead to more stable grasping. Concave corners are modeled as zero length lines with the normal aligned with the bisector b of the incident lines' normals n, and n2 (see Fig. 2). The corner is offset along -b to take into account the fingertip width. The force applied at a corner may lie in the ffiction cones of the incident edges or in the region separating them [I]. Therefore, the pseudo Giction coefficient associated with a corner is: (1) /I = t a d (za, + za, + p) E. Discarding Non-accessible Lines Not all regions of the object profile are suitable for placing a contact point. Some are not reachable due to the hand kinematics, as for example, when a hole is too small for the finger to get into"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002110_2005-01-1927-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002110_2005-01-1927-Figure7-1.png",
        "caption": "Figure 7. Full vehicle model (ADAMS)",
        "texts": [
            " This will inform about the level of non-steady state(or transient) situation of every driving condition of the vehicle. The more transient the situation will be the sooner and the more aggressive the system will act on the suspension. Figure 6 shows the control logic flow of the AGCS system. Figure 6. Control logic flow In this section, in order to verify the effectiveness of AGCS the step steer input simulation is performed using full vehicle ADAMS model. The vehicle model comprises double wishbone front suspension and multi-link rear suspension. (Figure 7) The AGCS ADAMS model consists of assist link, control lever and actuator. Control lever is connected to the assist link with the bushing and also connected to the subframe by the revolute joint. The connecting part between the actuator and the control lever is modeled with a contact element of ADAMS. As the actuator generates translational motion, the control lever will rotate about the revolute joint, and assist link mounting point moves downward. Step steer input maneuver is simulated to investigate the transient response in AGCS OFF and ON condition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000246_bf00312219-Figure8-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000246_bf00312219-Figure8-1.png",
        "caption": "Fig. 8 a-c. Functional model of the pleural wing joint (pwj) with its gearbox (gl-a); seen a from above, b frorn behind and c from the side. ir Insertion region of the first subunit of the tergo-pleural muscle; positions 3 and 5: the nob (n) on the pulling wire (pw), which acts as a marker on a ruler (ru), is in 3 when the mechanical pulling spring (raps) is relaxed, i.e. the first subunit of the tergo-pleural muscle is not active. When the nob is in 5, it is under tension, i.e. the first subunit of the tergo-pteural muscle is active, a Anterior, d downward, p posterior, u upward movement",
        "texts": [
            " 7 b 1 + 2) or back by the antagonistic contraction of pterale III muscle I (Fig. 7 III 1) around the vertical axis of pterale II (Fig. 7 pt II). The positions A, B and C are adjusted by the relative strength of the contraction of basal muscles 1 and 2 and antagonistic pterale III muscle 1. During the first half of downstroke the groove of the tooth connects with one of the peaks of the pleural wing joint. Diagrams of the functional movements of the gearbox are shown in Figs. 8-10. The operational parts of the wing joint and thoracic structures are shown in Fig. 8. In Fig. 9 the first subunit of the tergo-pleural muscle is not contracted. In Fig. 10 the first subunit is active and the tooth has been moved so that its groove connects with one of the peaks. The first and second subunit of the tergo-pleural muscle act as a tension muscle, supporting pleuro-sternal muscle 1. The two subunits put the pleural wall under additional tension (cf. Heide 1971) when the gears are in action. Contraction of the first subunit pulls its kidney-shaped insertion region (Fig. 8 ir) inwards; the nob (n) on the pulling wire (pw) is puUed from position 3 (Fig. 8 3) to position 5 (Fig. 8 5) on a ruler (ru). The angle between the pleural wall (PO and this insertion region (ir) increases [see Figs. 9 a (wing up), b, c (wing down); 10a, b, c, arrow (wing down)]. This inward movement of the insertion region also turns the V-shaped stem of the pleural wing joint with the gearbox (Fig. 8 g l -3) outwards (Figs. 9, 10, d, e, f, > 1). Figure 9 g-i shows the two possible ways of interaction of the tooth if the gears are not activated: (1) during flight the tooth moves into the anterior groove described above (Fig. 9h); (2) it lies behind the gearbox of the pleural wing joint (Fig. 9i). This position is used when the indirect flight muscles are active and the wings are not coupled to the wing-base-driving sclerites (Nachtigall 1968) or when the wing lies in the resting position (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000460_robot.1992.219917-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000460_robot.1992.219917-Figure3-1.png",
        "caption": "Figure 3: ith soft fin er in contact with a grasped object. Shown in this i! ure are the four components of forces that can possibfy be applied by the finger on to the object.",
        "texts": [
            " The current approach is to generate these equations and to solve them for positive finger ti impedances. While solving, first priority is given to achieve an kknittance center, though not it be the desired, 80 that atleast the asp be stable. Then, to acquire the desired admittance center so g a t the gras will have the desired dynamic behavior on each object degree otfreedom. This process involves transformin the grasp synthesis problem to that ofsolving a set of constrained enear equations. 2.2 Finger Impedance Matrices The i*\" soft finger in contact with the grasped object is shown in Figure 3. Each finger has an ability to exhibit iteelf as a six dimensional s p r i n g - d a m p e r system. However, the grasped object can sense only a subset of these impedance elements a t each contact location. Such a subset will be referred to in this paper as each fin er's contact degrees of freedom, denoted by t . In a soft tip,+%, er, Fi re 4, only 4 of the 6 components are sensed by the ob ectj7J. Trese are exactly the ones present alon and or about t i e forces perceived by the object. Explicitly s t a td , the linear impedances (sprin mass, dampers) related to x, y,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000581_amc.1996.509331-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000581_amc.1996.509331-Figure3-1.png",
        "caption": "Fig. 3: Three axis robot model",
        "texts": [
            " The total electrical input energy to be consumed by the manipulator can be precisely calculated by (19). Thus the total consumed energy is compared with and without subperformance index for #1, #2 and #3 trajectories in Fig. 9, 10, and 11 respectively. The consumed energy was reduced between 20 and 40% than in case without subperformance index. 4.1 A s s u m p t i o n s and test t ra jec tor ies The described method is applied to a three-axis manipulator with redundant degree-of-freedom as shown in Fig. 3. 4.3 E x p e r i m e n t a l R e s u l t s and Discussion The parameters are listed in the table I. w h e r e : L , r , M , J , and D are the length of arm, the center of mass of arm, the mass of arm, the inertia moment, and the friction constant, respectivelly. R a , K e , and K t are a resistance, EMF constant, and torque constant of the motor. U, zu, Ea, T are the voltage, current, EMF and torque of the motor, respectivelly. Kg is the gear ratio To examine the proposed method. three kind of test trajectory references are selected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003580_0-387-33015-1_6-Figure6.6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003580_0-387-33015-1_6-Figure6.6-1.png",
        "caption": "Figure 6.6. Electrostatic \"sponge\" encapsulation scheme employing charged matrix in polyelectrolyte shell.",
        "texts": [
            "\u0302 '\u0302\u0302 ^ The diffusion-loaded capsules and emulsion-based systems have advantages in stability and ease of use, but are limited in concentrations that can be achieved. This may be a more critical limitation for enzyme-based systems, in which high enzyme concentrations are required to maintain diffusion-limited behavior and extend operating lifetimes when enzymatic activity is lost with time. Another possibility that has been studied is the use of charged matrix within a polyelectrolyte capsule, where the matrix serves to electrostatically adsorb high concentrations of oppositely-charged molecules from the surrounding solution. This is illustrated in (Figure 6.6), and demonstrated for anionic alginate matrix for attraction of cationic dextran (amino-dextran) in (Figure 6.7). The nature of the effect is clearly seen in the uptake of significant dextran-amino (SOOkDa), while smaller anionic dextran (77kDa) was excluded from the same particles. These examples constitute only a limited view of many possibilities for microcapsule-based sensor construction; they show promise for building stable systems with entrapped glucose-sensing chemistry and therefore provide sufficient basis for discussion of the different sensing systems that can be achieved using them"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002950_6.2006-4369-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002950_6.2006-4369-Figure5-1.png",
        "caption": "Figure 5. Simplified description of Vulcain 2 NE, FRP NE and Sandwich demo Vulcain 2+ NE.",
        "texts": [],
        "surrounding_texts": [
            "Based on the trade study and the continued design and manufacturing work a concept has been selected and consolidated, see Figure 4. The concept is designed to fit on a Vulcain 2 NE thrust chamber, using similar operation points and cooling media parameters. As the cooling media now is used to cool a NE surface that is more than 3.5 times as large as the dump cooled part of Vulcain 2NE, the main design challenge is the hot wall. The channel wall structure is thus optimized regarding material choice and channel design to give as low hot wall temperature as possible. The design is without TBC, but for a possible future flight application TBC may be added for extra margin. The nozzle wall consists of one upper and one lower laser welded sandwich wall. The Inlet manifold is designed to optimize the dump mass flow distribution between channels in order to minimize the flow variations. Reinforcement jacket and stiffeners are designed to ensure the axial and radial stability of the NE, and also optimized for minimum impact on the NE contour during flight. The jacket is manufactured by applying LMD. The outlet manifold is a more cost effective version of the current Vulcain NE outlet manifold, but is also expected to make a contribution to the overall NE performance in flight. \u2212 Simplified function as compared to spiraling tubular nozzle o Smooth hot gas wall \u2013 increased performance and no roll moment o Symmetric channel stratification"
        ]
    },
    {
        "image_filename": "designv11_28_0000040_robot.2001.933027-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000040_robot.2001.933027-Figure9-1.png",
        "caption": "Fig 9 Rotation about hand frame",
        "texts": [
            " P-axis is considered so that the rotation angle of X-axis is not generated and the operator can move it easily to the desired position. However, finally we consider to control all 6 degree-of-freedom position and posture in 3-D space. Then, X-axis is impedance controlled and we can control actively to remain the desired posture, if the rotation about X-axis coincides with the rotation about Y - and Z- axes. This method is used only with impedance control in each axis of the robot hand coordinate (Fig.9). The impedance parameter of each rotational axis is set to a small value and the robot can rotate the object around the grasping position like a free joint. As each axis in the robot hand coordinate are always kept the relative angle after the rotation in 3-D space, controllability in 3-D space is maintained (Fig. IO). z Fig.10 If &e posture of the object is changed, the orthogonality of the rotation axes is kept. method. The operator holds the object at H : (x,,,y,,,z,) . The position and posture of the robot hand is R : (x,,y,,~~,8,,8~,8~)",
            " It is possible to control the position ( x , , y , , z , ) and posture (8,,8,) of the object only by treating the translational velocity of the operator's hand. Finally, the rotation about X-axis ( 8, ) is controllable, because it is controlled directly by the . . + i(sin 0, sin 8, cos 8, - cos 8, sin ex) = 0 impedance control according to the operator's torque about X - axis (2,). (2) 4. Experiments 5. Conclusions Now, we explain the robot controller to implement the proposed method to the robot arm. The robot has a force sensor at the wrist. We consider the frame of robot hand in Fig.9 and use the impedance control for each axis of the following impedance characteristic. f,, = mxXr + bxXr fyr = m y c + b,c fa = mzz , + b,Z, 2, = Lye, + cyey Z, = izez + czez Z, = ixBx + cXOx (9) In this paper, we proposed a method for the human-robot cooperative transportation in 3-D space. In this method, we applied a virtual nonholonomic constraint like a unicycle to the robot hand. The constraint is achieved by anisotropic impedance control in the robot hand coordinate. The operator can transport an arbitrary position and posture in 3-D space by similar skill using a wheelbarrow"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000652_0470867906-Figure6.1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000652_0470867906-Figure6.1-1.png",
        "caption": "Figure 6.1 Multibody system with four bodies, springs, dampers, suspensions, joints, and inertial and body-related frames of reference",
        "texts": [
            " In the following we will consider how it is possible to obtain equations of motion for multibody systems, see for example, Dankert and Dankert [79], Greenwood [125], Hiller [144] or Nikravesh [299] for the basic principles shown. Multibody systems typically include the following components: \u2022 Particles with translational inertia. \u2022 Rigid bodies with translational and rotational inertia. \u2022 Suspensions and joints that limit the movement of individual particles and bodies in relation to one another. \u2022 Coupling elements, e.g. springs, dampers, servo motors, etc. In the consideration of the structure of a multibody system, an abstracted description such as that given in Figure 6.1 is generally sufficient. Decisive factors are the topography of the system and the parameters of the individual elements, such as mass, centre of gravity, moments of inertia with respect to the main axes or the point of application of forces. For the consideration of point-shaped masses we start from Newton\u2019s second law, which identifies the product of mass m and acceleration in the x, y, and z direction ax, ay, az of a particle with the forces Fx, Fy, Fz acting upon it: Fx = max, Fy = may, Fz = maz (6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002986_fuzzy.2006.1681916-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002986_fuzzy.2006.1681916-Figure2-1.png",
        "caption": "Figure 2.",
        "texts": [
            " The introduction of the dynamics of the main and tail rotors requires considering local angle of attack, dynamic pressure, blade geometry\u2026 The construction of a complete dynamic model of this highly non linear system requires taking into account a lot of physical considerations and leads to very complex models with many parameters [6, 7]. Obtaining control laws for automatic helicopter flight, starting from this type of model is a difficult problem. Moreover, the low computational power of the embedded system does not allow us to implement sophisticated, time consuming control algorithms. A representation of the helicopter behavior can be obtained on the basis of the following simplifying assumption \u2013 we consider a rigid body in 3D to which four independent forces are applied (Figure 2). This model is considered in many scientific papers which deal with the problem of helicopter automatic flight [9, 10]. The simplest model of the helicopter can be described as (1). (1) It is obvious that this model does not take into account all the physical phenomena which govern helicopter behaviour. Nonetheless, obtaining control laws based on this model according to the approaches of the nonlinear control theory remains a difficult problem. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )                       \u2212=                    \u2212           \u2212 \u2212 \u2212 =                               \u2212 +\u2212 \u2212+ \u2212           =           r q p ul ul ul pqii rpii qrii ri qi pi u u u M gz y x t h h yyxx xxzz zzyy zz yy xx \u03b8\u03c6\u03b8\u03c6 \u03c6\u03c6 \u03b8\u03c6\u03b8\u03c6 \u03c8 \u03b8 \u03c6 \u03c6\u03b8\u03b8\u03c6\u03b8 \u03c6\u03c8\u03c6\u03b8\u03c8\u03b8\u03c8\u03c6\u03c8\u03c6\u03b8\u03c8 \u03c6\u03c8\u03c6\u03b8\u03c8\u03b8\u03c8\u03c6\u03c8\u03c6\u03b8\u03c8 cos /coscos /sin0 sincos0 tancostansin1 sincossincoscos coscossinsinsincossinsincoscossinsin cossinsinsincoscoscossinsincossincos 10 0 4 2 3 3 2 1 B"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001749_icarcv.2002.1238554-Figure12-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001749_icarcv.2002.1238554-Figure12-1.png",
        "caption": "Fig. 12: Padcn-I<aha.ii Subproblaii 2",
        "texts": [],
        "surrounding_texts": [
            "detection of fortmrd siiigularitics is very hiiportaiit shicc at thcsc poses the end-effector gains extra. dcgrcc(s:) of frccdoiii and hence, tlic iiia.nipulator b c coiiics uiicontrollablc. It. is also difficult to obtain ai aiialytica.1 expression of thc dctcriiiinant of iiiatrix -4. in tcriiis of cartcsian coordiiiatcs of tlic platfonii to dctcriiiiiic tlic poses at which the iiia.iiipida.tor becoiiics uiic.oiitrollablc.\nA iiuiicrical method is followed by n-hichi the wholc workspacc is scanned for this kind of siiigularitics. IIcrc the parallcl manipulator consiilcrcd is a tlircc-legged. G-DOF parallel manipulator, saiiic as t1ia.t disciwed in scctioii 2.2. Syiiibolic. expression of thc iiiatrix of 1 of Eqii.3 of such kind of iiimipulators is givcii in [I'Z] (short cxprcssioiis axe givcii hi thic al)pcii&). can be found out in tcniis of ca.rtcsiai coorduiatcs ushig Padcii The tcriiis of this .Jaeobiaii arc fuiictioii of Iiik lengths and joint angles. A nota.blc feature of thicsc paxa.lle1 iiianipula.tors is t1ia.t tiicrc arc iiiidtiplc iiivcrsc solutions wid in th$ case thcrc arc U solutiois Therefore. it bcroiiics a. very difficult task to dcricc! ai a.iia1ytical expression of tlic singula.rity conditions. So a nuiiicrieal method is followcl for singularit?; rcprcsciitation. First, ai oriciitatioii and hcight of the of the ciitl-effector fraiiic is dioscii at. \\?vhich the singularity is to be reprcscntcd. Tlicn tlic a-orkspa.cc. as found out using thic proecdurc discitqscd in scctioii 3 of this paper. is seaxchccl for ca.di of the G4 iiiwrsc solutions [ 131. 5.1 Rcsults Tlic sa.iiic parallel iiiaiipula,tor, as discussed hi scetion 4 (Fig >:I, is considered. Oriciitstioii a id height of the aid-effector fraiic is choscii as an identity iiiatris and 4.55 iiuii rrspcc.tiwly. -4t this height and at this oriciitatioii. thc hie joining tlic sphicricitt joiiit aiid passive johit of cadi leg fa& 011 the plaw of thc cud-cffcctor a id all tlicdc liiics (each pcrta,ii~ig to cadi lcgj intersect a.t oiic point. The singularity curvcs for this robot is shown iii Fig 10. In this figure. the hatched a.rca.s rcprcsciit the closcd arcay of singularity. Froin tlLs figurc. it ca.11 be established that the siiigxikixity cunc5 a.re highly noillincar aJid tlicrc arc closcd a.rcas of shigxilaritics meaning a.ii?;\npoint in tliosc a.rea,s is a singular point. It is a.lso fouiid that tllcrc arc ccrtajli heights with identity oriciitatioii where thcrc is 110 shigxdarihy.\nTiicb coiiiplctc dgorithiii nhcii riui 011 a. PeiitiuiiD. 233klIIz PC to dctcriiiiiic tlic workspacc. its volume. voids and singu1a.rit.y points iiisidc take 12GGG sec.\n6 Conclusion hi this paper. a. iiuiicrical algorithm is prcseiitcd to dcteriniiic and analyze rcadiablc! workspacc of tluccIcggcd parallel maiiipulators based 011 it.s a.iia1yt.icnl backgrouiid. First of all? at a. particular Lei& ancl orientation. a.ii cstima.tcd iiiaxi~iiuii boiuidar!- is fouiid out. Tlib space is then cliscrctizcd into equal area. radial sectors. Ea.eh sector is represented by a diaractcristic point iiisidc it. This sector rcinahis iiisiclc the workspacc if the inverse hiciliaties exists a.t its clinractcrktic point. Dy searching like tlus. all tlic voids arc identified accurately niid its position and stretch inside tlic workspace is also found out. The voluiiic of tlic workspa,cc is fomid out in a iiunicrieal \"a.?;. In case of voids. a. parallclcpipcd is circumscribed a.rouiid it aid the voluiic of the yoid is rcprcsciitcd as t1ia.t of t h s paraUelcpipcd. Thcii followhig a iiuiiicrica.1 procedure, the singularity curves arc also showii inside tlic workspacc. For the csaiiplc purpose. it thrcc-legged modular pamllcl iiimipuilator is c.oiisidcrcd aiid thic abow mentioned issues arc addressed. The algorithiii gives a very rlcar picture of the total workspacc with voids iiisidc it aiid a dc.tailed iiifoniia.tioii regarding ttic voids. Detclmhiation of csthiiatcd ninsiiiimii worhpncc boundary cffcctivdy reduces the scarch effort. Thus cvalua.tioii of the voliiiiie of the rca.eliablc workspacc is pcrforiiicd at a rcasoiia.blc cost and, iiiorcovcr, thc algorithm is fouiid to be suitable for iiiultiproccssor a.pplicatioii by nlicli tlic ca.lcula.tion time mi be sigiuficaiitly rcduccd which can be very helpful froiii dcsigii aad opthilization point of view. :xLso characterization of voids and siiigulasit>- iiisidc the worlispacc will be very uscfd for trajectory pla.iming of paallcl manipulators. 'I\\hough tlic algorithm Ls a.pplicd to a tllrwlggcd pmdlcl iiiitnipula.tor. it is gciicra.1 cnough to be applied to a.iiy kind of paraJlcl iiia.nipula.tors.",
            "Acknowledgment This work is supported by Mhiistrv of Education (Singapore) and Gintic Institute of Jlaiiiifacturin;: Tcchiolop-. Smgaporc, under the Acadciiiic Rcscarcrch fuid RG 29/99 and t l c Upstream project L--9i-.4OOG\nSubproblem 2 Rotation about two subsequent axes Le1 .j., and 8 2 be lwo zero-pilclr, uni l magniludc screws wilh inler.wcling ams and p ! q C X4.':l be lwo poinls. Find 81 and 02 Such hCbl\n1' = Q c S I ~ I ~ $ ? f i 2\nSubproblem 3 Rotation to a given distance Le1 S 6e 18 zero-pilclr. uni l magmilude screw; p.q C 324'1 lwo poinls: nn,d 6 D real number p a l e r lhan 0. Find 6 such lhal\nllq - eS0gll = 6\n[13] .4nj<an Kuni;u Dnsh. I-Ming (Ihcn. Song IIuat Yco, 'and Guilin \\-a$. Instantaneous kincnmtics and singularity analysis or ~lircclcg& parallcl nianipulati,rs. In Procecdings o j IEEl$/RSJ Inlcmal iond Conference on Inlelligenl Rohuls and Syslems, pagcs 12'X+lBO. Maui. t34, so\\- 2001.\nDecomposable closed-form inverse kincmolics for wconfigurable robls wing producl-oJ-exponenlial formula. PhD thesis, Sanyang Tcchdogic.al Cnivctsilq-: Singapore, 2000.\n[13] G. Yan."
        ]
    },
    {
        "image_filename": "designv11_28_0000817_s0007-8506(07)60577-0-Figure3-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000817_s0007-8506(07)60577-0-Figure3-1.png",
        "caption": "Figure 3: Localization of the maximum contact pressure on the die",
        "texts": [],
        "surrounding_texts": [
            "Traditional metal stamping processes involve relevant ms ts linked to the equipments to be utilized and to the required set-up times. The industrial application of traditional metal stamping tech- is therefore e m c a l t y suitable only for large scale produdion (mass produdion). where the m s t s linked to die manufadure and set-up are distributed over a very large n u m e r of starrped parts. On the other hand in the last few decades new relevant and irrpellent needs have arisen such as the produdion of small batches of sheet metal m r q m e n t s . the inaeasing demand of process Rexibillty and finally the necesslty to reduce the time to market of the produds. The m e n t h e d needs are inmsistent Mh the traditional metal stamping processes. As a msequence two major adions are followed: first of all new forming processes Mich do not require expansive mventional equipments and time m s u m n g set-up operations have been recently proposed [MI; f u r t h e m e rapld tooling techniques have been recently introduced mainly to reduce the time to market of new produds [66]. It should be observed that the -em layer manufaduring technokgies saentmmlty support the mncept of \u2018Rapld Produd Development\u2019. The former applications of rapld tooling for plastic parts manufaduring have been successful and the efforts are ongang irproving materials productrvlty and quallty. On the other hand. when rapd tooling is aimed to the produdion of tools for sheet metal stamping no rapld t d i n g first choice technokgy is evident. T w approaches can be r e q n k e d : thredimensional printing m or seledive laser sintering [KIO] optrons. Layer CNC mt ro l l ed 9 D printing machines are in development for medium and big sized parts. Small sized parts may be mt effedivety produced using other rapld tooling options such as Seledive Laser Sintering. The research here addressed a i m to explore the use of SLS (Seledive Laser Sintering) tech- for this applimtion a m d i n g to the adual state of the art and identny M u r e research diredions."
        ]
    },
    {
        "image_filename": "designv11_28_0000525_sibgrapi.2001.963055-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000525_sibgrapi.2001.963055-Figure7-1.png",
        "caption": "Figure 7: SOL skeletal muscle architecture (a) relaxed state and (b) activated state; SOL polygonal surface (c) activated state.",
        "texts": [
            "49 for all materials, a value which represents volume preserving materials. In order to model other non-linear soft tissues with different material properties, we can simply change the values E and v, equation (12). Figures 7(a) and 8(a) show the initial geometry in the relaxed state that was used as input. Thus, we impose a 2mm displacement at the tendon with the muscle fully activated. The result of the displacement controlled simulations are shown in Figures 7(b)(c) and 8(b)(c). SOL contraction causes a bulging, Figure 7(b)(c), and, MG contraction causes a parallel sliding of the top aponeurosis relative to the bottom one, Figure 8(b)(c). As a result of the simulation, we can measure fibre lengths, angles of pinnation (angles between the muscle line-of-action and the direction of the muscle fibres), internally developed forces by the muscle fibres and the external force of the whole muscle. For the case of the SOL model (Figure 7), fibre length at maximal isometric force and muscle length, including the tendon, were assumed to be, respectively, 38.5rnrn and 80rnrr i (derived from Herzog et al. [12]). And, the maximal tendon force developed for SOL was 25N. For the case of the MG (Figure 8), we used the same initial muscle architecture as specified in our previous work [13]. Fibre lengths at maximal isometric force and muscle length, including the tendon, were assumed to be, respectively, 24.5rnrn and 1207nrn (derived from Carvalho et al",
            " However, for computer animation purposes or for structure-function relationship explanation purposes, we fully activated only the left side of the muscle. As a result, we obtained a strange deformation. SOL contraction causes a bulging in only half of the muscle, Figure 9(a)(b), and, MG contraction causes torsion and sliding of the top aponeurosis relative to the bottom one, Figure 9(c)(d). 6 Discussion The model can be applied to different classes of skeletal muscles according to shape such as parallel-fibred muscles (Figure 7) and pennate-fibred muscles (Figure 8), and may be applied to other non-linear soft tissues with different material properties. We can experiment with the model in order to discover what happens to it in particular conditions such as to fully activate only the left side of muscle during the muscle contraction (Figure 9). And, the model can be used to investigate how forces influences muscle deformation and how deformation affects the contractile properties of muscle. This investigation is done by taking into account the initial geometry of a particular skeletal muscle architecture, experimental data about the behaviour of the materials involved, and initial conditions about the muscle attachments and tendon insertions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001943_0954406042690407-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001943_0954406042690407-Figure1-1.png",
        "caption": "Fig. 1 (a) Model of a flexible rotor supported by two gas film journal bearings and (b) cross-section of a gas film journal bearing",
        "texts": [
            " Thus, there will be three unknowns (three points I , I 1, I \u00fe 1) in the y direction at every incremental time interval. The other two unknowns \u00f0 J \u00fe 1, J 1\u00de in the Z direction are substituted for the last iterative values. Lastly, all the equations may be substituted into C07704 # IMechE 2004 Proc. Instn Mech. Engrs Vol. 218 Part C: J. Mechanical Engineering Science at Harvard Libraries on June 30, 2015pic.sagepub.comDownloaded from a tridiagonal matrix and solved by using Gauss elimination. In Fig. 1, the pressure distribution, P\u00f0y, Z\u00de, of the gas film in the gap between the shaft and the bushing enables the estimation of the components of the force acting between the shaft and the bushing to be given as the integrals fgx \u00bc PaR 2 \u00f0L=R 0 \u00f02p 0 P\u00f0y, Z\u00de cos y dZ dy \u00f04\u00de fgy \u00bc PaR 2 \u00f0L=R 0 \u00f02p 0 P\u00f0y, Z\u00de sin y dZ dy \u00f05\u00de Proc. Instn Mech. Engrs Vol. 218 Part C: J. Mechanical Engineering Science C07704 # IMechE 2004 at Harvard Libraries on June 30, 2015pic.sagepub.comDownloaded from where L is the length of the bearing and R is the radius of the bearing. The analysis presented in this paper considers a rotor\u2013 bearing system comprised of a perfectly balanced, flexible rotor of mass mr supported symmetrically on two identical gas film journal bearings, which, in turn, are mounted on rigid pedestals. With these idealizations, it is possible to consider one bearing in isolation in which a rotating rotor of mass mr has two degrees of translatory oscillation in the transverse plane. The idealized rotor\u2013bearing model is shown in Fig. 1. Here, O1 is the geometric bearing centre, O2 is the geometric rotor centre, O3 is the geometric journal centre, r is the mass eccentricity of the rotor, Kp is the shaft stiffness and o is the rotational speed of the shaft. In the transient state, the equations of motion of O2 (rotor centre) in Cartesian coordinates may be written as mr d2x2 dt2 \u00fe Kp\u00f0x2 x3\u00de \u00bc mrro2 cosot \u00f06\u00de mr d2y2 dt2 \u00fe Kp\u00f0y2 y3\u00de \u00bc mrro2 sinot \u00f07\u00de Considering the journal centre O3, the resulting forces in the horizontal and vertical directions are shown in Fig. 1. From the equilibrium of forces, the forces applied to the journal centre O3 may be expressed as fgx \u00bc Kp x2 x3 2 \u00f08\u00de fgy \u00bc Kp y2 y3 2 \u00f09\u00de Let the transformation X2 \u00bc x2 Cr , X3 \u00bc x3 Cr , Y2 \u00bc y2 Cr , Y3 \u00bc y3 Cr t \u00bc ot, d dt \u00bc o d dt \u00f010\u00de be introduced and the non-dimensional groups be defined as Fgx \u00bc fgx PaRL , Fgy \u00bc fgy PaRL , Mr \u00bc mro2 Kp x \u00bc mrro2 KpCr If equations (10) and the above-introduced non-dimensional groups are substituted into equations (6) to (9), equations (6) to (9) become Fgx \u00bc KpCr 2PaRL \u00f0X2 X3\u00de \u00f011\u00de Fgy \u00bc KpCr 2PaRL \u00f0Y2 Y3\u00de \u00f012\u00de Mr d2X2 dt2 \u00fe \u00f0X2 X3\u00de \u00bc x cos t \u00f013\u00de Mr d2Y2 dt2 \u00fe \u00f0Y2 Y3\u00de \u00bc x sin t \u00f014\u00de Computationof the rotormotion is an iterative procedure that first determines the acceleration, then the velocities and finally the displacement, step by step over time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001813_146441904323074558-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001813_146441904323074558-Figure9-1.png",
        "caption": "Fig. 9 Machining spindle with optimized bearing design",
        "texts": [
            "7 mm, the determination of L is dependent on the ridge clearance C. A ridge clearance at zero eccentricity C \u02c6 10 mm yields a compressibility number L \u02c6 30 for o \u02c6 150 000 r/min. The dimensionless rotor mass \u00b7M is de ned by \u00b7M \u02c6 Mpa 2Lm2 C R 5\u0301 The corresponding dimensionless rotor mass \u00b7M from Fig. 6 {L \u02c6 30 (design value), H \u02c6 2 [H \u02c6 (hg/hr)0 \u02c6 hg/C]} is 0.498 so that the critical mass per bearing M at 151400 r/min becomes M \u02c6 2 \u00b7MLm2 (C/R)5pa M \u02c6 0:705 kg/bearing The spindle is supported by two journal bearings (Fig. 9). Therefore, a rotor mass of 1.41 would put this bearing on the threshold of instability. The actual bearing spindle has a weight of 0.600kg. Assuming that the bearings are equally loaded, the resulting load per bearing is 0.300 kg. Therefore, the designed bearing will be in the stable region. K01903 # IMechE 2004 Proc. Instn Mech. Engrs Vol. 218 Part K: J. Multi-body Dynamics at HOWARD UNIV UNDERGRAD LIBRARY on March 10, 2015pik.sagepub.comDownloaded from The bearing stiffness is de ned by Stiffness \u02c6 W Ce \u02c6 1 C paLD \u00b7W The corresponding dimensionless load from Fig",
            "89, so that the bearing stiffness at 150 000 r/min becomes Stiffness \u02c6 W Ce \u02c6 1 C paLD(3:89) \u02c6 52:072N/mm The dimensionless mass owrate in the concentric position is de ned by Fleming [5] m0 \u02c6 4 z0R T p 1 \u2021 d2 p Na2pa The lubricant ow per unit length is z0 \u02c6 Na2pam0 4R T p 1 \u2021 d2 p The corresponding dimensionless mass owrate from Fig. 5 {L \u02c6 30 (design value), H \u02c6 2 [H \u02c6 (hg/hr)0 \u02c6 hg/C]} is \u00a11.574 z0 \u02c6 \u00a13:567 \u00a3 10\u00a14 kg/ms The purpose of the experimental work was to verify the computer model. To do this, a standard aerostatic spindle was modi ed (Fig. 9). The modi cations were grooves machined into the shaft, with pressure sensors built into one bearing journal. These modi cations enable bearing stiffness and pressure to be measured as a function of speed, albeit at low compressibility numbers. The spindle was driven by an integral high-frequency motor located mid-way between the two journal bearings. Axial location was provided by a doubleacting thrust bearing positioned at the rear of the shaft. The spindle was instrumented to enable bearing pressure, shaft error motion and spindle stiffness to be measured over a range of speeds"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002852_iros.2006.281799-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002852_iros.2006.281799-Figure5-1.png",
        "caption": "Fig. 5 Spatial 4R coordinating manipulators",
        "texts": [
            " In comparison with the sudden change in joint velocity, the reduced manipulability takes priority in a fault tolerant operation. It is worth pointing out that the sudden change in velocity depends on both the joint velocities of the original manipulator and that of the reduced manipulator. Therefore, the maximum sudden change in velocity does not certainly occur at the configuration given by minimum singular value of iJk. 0 (a) First rotatii IV. SIMULATION EXAMPLES The concept presented in previous section will be illustrated for a coordinating system with two 4R manipulators shown in Fig. 5, where the two manipulators are identical and their D-H parameters are listed in Table 1. First, some assumptions are given as follows (1) The task is end-effector positioning only, and with this perspective, each manipulator has one redundancy. (2) There is a hard point contact between the end-effector and the grasped object (only forces are transmitted from the end-effector to the object). (3) The fault tolerant manipulations relative to joint 2 are considered only, that is, only the joint 2 of each manipulator is possible to fail"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001297_iros.1991.174423-Figure7-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001297_iros.1991.174423-Figure7-1.png",
        "caption": "Fig. 7: Departure motions of a triangular prism",
        "texts": [
            " the constraints on a triangular prism on a table. In the figure, tains the contact c a n be represented by a nonnegative linear combination of them. Three of them are shown in Fig.6. 0 _,_.'. ,. : .._ -.. ..... contact with a hole. Figure 5 shows an example of the contact between the vertices and between a vert,ex and an edge. At least one of four conditions must hold a t the contact point between the vertices, and a t least one of two ones must hold at t h e point between the vertex and the edge. Though such a Figure 7 shows three differential motions of the triangular prism that correspond t o V I E l , VIE, , VIE , in the equation (17) respectively. A n arbitrary motion that breaks the con- tact can be represented by a nonnegahe linear combination of them. Figure 8 illustrates three differential motions of the rectangular parallelepiped shown in Fig.4. They corresponds to V1E1. VxEa, VIES respectively, and there is no motion that does not change the contact state in this example. 5 Conclusion The results are summarized as follows: Acknowledgement The authors would like t o thank Dr"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003740_1.2975154-Figure10-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003740_1.2975154-Figure10-1.png",
        "caption": "FIG. 10. Plane tangent to the surface of the circular cone whose generatrix is gc\u2212gc.",
        "texts": [
            " Now, to identify the position of P for successively computing the volume magnetic charge M, it can be useful to consider a spherical coordinate system. The origin of this coordinate system is the vertex O, that corresponds to the origin of the orthogonal Cartesian system previously defined. Therefore, the position of P is defined by the following spherical coordinates: the length g straight line from P to O measured on the generatrix gc\u2212gc, the angle , and the angle of inclination of gc\u2212gc with respect to the axis X. The coordinate g is reported in Fig. 10. Furthermore, in relation to the point P of , it is possible to consider a tangent straight line to in P and the correspondent normal belonging to the plane . This plane is tangent to the surface of the circular cone whose generatrix is gc\u2212gc. Consequently, by the procedure of geometrical identification just described, for each point P of the conchospiral helicoid we can define a tangent and a normal, that is, a unit normal vector n. Figure 10 shows the plane and the unit vector n above quoted. Then, n belongs to and is sloped with respect to gc\u2212gc by the conchospiral inclination angle c. For each point P of , c always has the same value, that is, it does not depend on . Now we compute the expressions of the components ng, n , and n of the unit vector n versus the spherical coordinates g, , and previously defined. Observing Figs. 9 a and 10 we have ng = \u2212 n cos c, 59 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation",
            " 68 Here also represents the rotation of the whole conchospiral helicoid characterized by a finite rectangular section with sides re\u2212ri and b. Finally, by Eq. 68 , the components ng, n , and n of the unit vector n can be explicitly expressed versus the spherical coordinates g, , and , ng = \u2212 n cos arctan \u2212 sin ln g cos h , 69 n = n sin arctan \u2212 sin ln g cos h , 70 n = 0. 71 Now, let us fix the magnetization M of the magnet illustrated in Fig. 8. We choose direction and orientation of M equal to those of the unit vector n represented in Fig. 10. Then, we obtain a conchospiral magnetization whose magnitude is constant and equal to M in each point of the magnet. Substituting in Eqs. 69 and 70 the magnitude n of n with M, we get the components Mg, M , and M of M versus the spherical coordinates g, , and , Mg = \u2212 M cos arctan \u2212 sin ln g cos h , 72 M = M sin arctan \u2212 sin ln g cos h , 73 M = 0. 74 From Eq. 74 , in relation to the fixed orientation of M, we note that the component M is always zero. Moreover, since the volume magnetic charge M P in the generic point P of the magnet is defined as the divergence of M with the changed sign see Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002671_tsmcb.2006.870636-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002671_tsmcb.2006.870636-Figure5-1.png",
        "caption": "Fig. 5. Geometry between point Pc(xc, yc, zc) \u2208 R3 and point Pimg(u1, u2) \u2208 R2 on the image plane.",
        "texts": [
            " The relation between the base frame {B} and the camera frame {C} is depicted in Fig. 4, where the Yc axis is defined parallel with the Yb axis. Thus, point Pc(xc, yc, zc)with respect to {C} can be transformed into point Pb(xb, yb, zb) \u2208 R3 with respect to {B} as follows:   xb yb zb 1   =   cos \u03b8bc 0 sin \u03b8bc \u2206xbc 0 1 0 0 \u2212 sin \u03b8bc 0 cos \u03b8bc \u2206zbc 0 0 0 1     xc yc zc 1   (5) where \u2206xbc and \u2206zbc are the translational distances between origins of {B} and {C} about the Xb and Zb axes, respec- tively, and \u03b8bc is the angle between {B} and {C} about the Yb axis. In Fig. 5, point Pc(xc, yc, zc) \u2208 R3 on the laser line is obtained from point Pimg(u1, u2) \u2208 R2 on the image plane by comparing the similar triangles \u2206PcMC and \u2206PimgM \u2032C as follows: [xc yc zc] = b\u2032 f cot \u03b8lp + u2 [f u1 u2] (6) where f is the focal length of the camera, \u03b8lp is the projection angle of the laser line on the image plane, and b\u2032 is the distance between the center C of the camera lens and the intersection L\u2032 of the Zc axis and the laser beam. According to the Sines Law, the distance b\u2032 in triangle \u2206LCL\u2032 can be obtained as follows: b\u2032 = b sin(\u03b8lp \u2212 \u03b8bc) sin(180\u25e6 \u2212 \u03b8lp) (7) where b is the baseline distance between the center of the laserline generator L and the camera center C"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002741_cca.2006.286027-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002741_cca.2006.286027-Figure1-1.png",
        "caption": "Fig. 1. Picture of the \u03bc-LDV. The schematic of A-A\u2032 section is shown in Fig. 3.",
        "texts": [
            " Thus, few-millimeter-sized embeddable LDVs that can measure scattering surfaces are strongly desired for practical use. In this research, we successfully used our highly integrated \u03bc-LDV to measure the velocity of various scattering surfaces (aluminum, cardboard, and plastic) directly, without any attachment like a grating scale, by applying fast Fourier transform (FFT) analysis to the output of the device, and processing the resulting power spectra from the FFT analysis. We also confirmed characteristics of the measurement distance and tilt installation error corresponded to its allowable alignment error. Fig. 1 shows a picture of the \u03bc-LDV. It consists of two elements, a pyrex glass substrate (Fig. 2(a)) and a Si substrate (Fig. 2(b)). Electrodes are formed on the back surface of the Pyrex glass substrate by depositing Au, and the InGaAs PIN PD (size: 280 \u00d7 460 \u00d7 150 \u03bcm; active diameter: 70 \u03bcm) is bonded onto the electrode. The electrode pad and light-receiving area of the PD are formed on the back surface. Micro aspherical lenses for collimating the laser can be formed by inductively coupled plasma (ICP) etching with a gray-scale-patterned photoresist structure [25], [26]",
            " Both substrates also can be bonded to become airtight by a bonding method using an Au pattern for substrate bonding (Fig. 2(a) and (b)). The electrodes on the Pyrex glass substrate are connected to electrodes on the Si substrate, and all electrodes are connected by through-hole electrodes from the sensor bottom to outside the sensor. This design enables the sensor to be fabricated with wafer-level packaging and to have an extremely small size (2.8 \u00d7 2.8 mm \u00d7 1.0 mm). Fig. 3 shows a schematic of the A\u2013A\u2032 cross-section shown in Fig. 1. Two laser beams are simultaneously emitted from the LD, reflected by the Au mirrors, collimated by the refractive micro aspherical lenses, and impact the moving object. The moving object moves along a line orthogonal to the bisector of the two intersecting laser beams at velocity V . The two laser beams, which come from the left and right sides, are scattered by the moving object, and their frequencies are Doppler-shifted by fL and fR respectively: f L = \u2212 V \u03bb cos\u03b8 (1) and f R = V \u03bb cos\u03b8, (2) where \u03b8 (= 66\u00b0) is the angle between the direction of the laser beam and the direction of the object\u2019s motion, and \u03bb is the wavelength of the laser"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002140_bf03546352-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002140_bf03546352-Figure2-1.png",
        "caption": "FIG. 2. Geometry of the Observation Axis when ()i = 'Y, ()j = 'Y + 180\u00b0, cPi = cPimax, cPj = cPjmino",
        "texts": [
            " In the primary [X Y Z] axes, the unit vector along the desired ob servation axis can be written as l1d = cos 'Y cos ai + sin 'Y cos aj + sin ok (44) As the system consists of independent tethers, the task of the control system is to vary Oi and 4Ji in a way such that all tethers are rotating in the same plane of ro tation whose normal vector matches up with l1d. The normal vector to the ith tether's plane of rotation can be written in terms of the tether rotation angle as l1i = - cos Oi cos 4Jii - sin Oi cos 4Jij + sin 4Jik The required commands are (45) Oid(t) = Oi(O) + Odt (46) 4Jitlt) = I; + (; - a ) eos[ 'Y - Oiit)]I, 4Jid = 7T - 4Jid if 4Jid > 7T (47) with Od being the desired in-plane angular velocity relative to the [X Y Z] axes. An illustration of how the tether rotation angles relate to the direction of the optical axis can be seen in Fig. 2. Equations (46) and (47) can be applied to a system with an arbitrary number of tethers, as long as the tethers are properly separated. It is assumed that control accelerations are applied to the parent mass along the i, j, and k directions and those mounted on two end masses are along the y and z axes in the body frame. Since the masses are assumed to be point masses, the effect of these control thrusts on the attitude of the three bodies is not considered in this paper. While it is desirable for optical axis to point exactly as intended, this is not prac ticable in reality"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002835_1.3092885-Figure5-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002835_1.3092885-Figure5-1.png",
        "caption": "Fig. 5. Schematic of the SISO control principle. The response \u03d5s/p acts 180\u25e6 out of phase to the perturbation \u03d5 that is to be attenuated.",
        "texts": [
            " A unique set of ARX coefficients can then be calculated by solving these equations in a least-squares sense. More information about the ARX model can be found in Refs. 11 and 16. A classic approach to control vibration is the direct feedback of a measured quantity, like displacement or acceleration, to one of the control actuators. The principle of the control algorithm of this study is to calculate a command that generates a system response that is 180\u25e6 outof-phase with the perturbation that is to be attenuated. Phase shift and amplification are depicted in the complex plane in Fig. 5, where \u03b8 is the swashplate input and \u03d5 the plant response or output. The phase angle of this transfer function \u03c6G corresponds to the angle between the two arrows. To obtain a system response \u03d5s/p which acts in opposition to a measured perturbation, the controller has to account for this phase shift. Thus, the necessary phase angle \u03c6H of the controller is \u03c6H = \u2212180\u25e6 \u2212 \u03c6G (2) The mathematical formulation of the control law consists of a bandpass H1, an all-pass H2 and a proportional gain g. The band-pass filter reduces the disturbance of aircraft dynamics and handling characteristics by filtering out the dynamics that are not associated with the critical mode: H1 = s2 s2 + 2\u03b6H\u03c9hps + \u03c92 hp\ufe38 \ufe37\ufe37 \ufe38 high pass \u00b7 \u03c92 lp s2 + 2\u03b6H\u03c9lps + \u03c92 lp\ufe38 \ufe37\ufe37 \ufe38 low pass (3) The cut-off frequencies \u03c9hp and \u03c9lp are chosen in the vicinity of the natural frequency of the critical mode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0001283_robot.2000.846401-Figure2-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0001283_robot.2000.846401-Figure2-1.png",
        "caption": "Figure 2: Notation",
        "texts": [
            "1 Previous Work We know of no previous work on time-optimal control of the bounded velocity diff drive robot, but the techniques employed here draw extensively on the techniques devel- oped for steered vehicles [6, 2, 5, 41. Interested readers should see our companion paper [ I ] for a broader discussion. 2 Assumptions, definitions, notation The state of the robot is q = (x,y,8), where the robot reference point (z , y) is centered between the wheels, and the robot direction 8 is 0 when the robot is facing along the z-axis, and increases in the counterclockwise direction (Figure 2). The robot\u2019s velocity in the forward direction is .U and its angular velocity is w. The robot\u2019s width is 2b. The wheel angular velocities are wl and w7.. With a suitable choice of units we obtain 0-7803-5886-4/00/$1 O.OO@ 2000 IEEE 2479 and w1 = U - b w (3) WT = u+bw (4) The robot is a system with control input w(t) = (w l ( t ) , wT( t ) ) and output q( t ) . Admissible controls are bounded Lebesgue measurable functions from time interval 10,571 to the closed box W = [-1,1] x [-1,1], where T is the time at which the robot reaches the goal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002050_iros.1992.594257-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002050_iros.1992.594257-Figure1-1.png",
        "caption": "Fig. 1. A snake is a sequence of links serially connected by joints.",
        "texts": [
            " 2To exemplify the difference further, imagine a path inside a building of someone who comes routinely to his own office (planning with complete information), as compared to the path of someone else who tries t o find the same office for the first time (planning with incomplete information); each task has its own context and rational, although the second path may look absurdly long to the first man. 0-7803-0737-2/92$03.00 199201EEE lowing questions are being asked: olute j o in t s . We consider a very simple planar snake, Figure 1, composed of n links, Zi, i = 1, ..., n; each link is a line segment; all links are of equal length L. Link Ii is connected by a joint ji-, to the previous link, l i -1 , and by joint ji to the next link, li+l. The relative motion between two connected links li and li+l is produced in joint j ; and is measured by the angle B i ; it can change indefinitely: The two end points of the snake are distinct in their function: one end point, designated as the head, is responsible for initiating and generating motion along the desired p a t h and along obstacle boundaries; the other end point is the snake\u2019s tail ",
            " To write this in terms of finite displacements, denote 61 to be the segment, and its length, of the straight line ST traversed by the head j1 between points P and P\u2019, and 6, the segment, and its length, along the tractrix generated by the tail j, between the corresponding points 0 and 0\u2019. The differential property above implies that 6, 5 bl for all possible starting positions of the link relative to the line ST, Figure 2. Note that the motion of the tail j, along the tractrix is executed \u201cautomatically1\u2019 - it is simply being pulled by the head. In the robotics context, such motion can be actuated solely a t j,. Consider now a snake with n links, Figure 1, and consider a straight-line motion of the snake head along the line ST. As before, joint j,-l moves along the tractrix. \u2018This motion will pull link I n - l l which will make joint j,-Z move along what can be called the second-order tractriz, .which will make joint j,-3 to move along what can be called the t h i r d - o d e r tractr iz , a t d so on. The described pattern is called the t rac t r i z mo t ion . For link l,, denote 6, to be the displacement within one step of the head motion along the line ST"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000534_itcc.2001.918874-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000534_itcc.2001.918874-Figure1-1.png",
        "caption": "Figure 1: Scanning direction of: (a) the first strip, (b) the second strip, and (c) the third strip in Strip approach.",
        "texts": [
            " These sources are a few inches wide and they shoot methane gas in the air. 668 0-7695-1062-0/01 $ 0.00 0 2001 IEEE 2.1. Strip Approach In this approach, two robots move at a constant distance of d from each other and scan the area that is between the two. This area is referred to as a strip, which has a length equal to m and a width equal to d. The width d is the maximum distance under which the communication between the two robots does not fail. Since we deal with a tight scanning approach, the right side of one strip is overlaid on the left side of next strip, Figure 1. I .I Figure 2: Scanning Directions: Starting of (a) scanning process, (b) the second round of scanning, and (c) the third round of scanning in the Tube approach. The scanned area by the two robots is given by A, = mnd, where n is the number of strips scanned by the two robots. The total vertical (V) and horizontal (H) distances traveled by one robot is: Total = V + H = (mn) + (n-1)d. Thus, for two robots, the traveled distance D, = 2mn + 2(n-l)d. The quality ofperjiormance for this approach can be described by a factor Q, = A, / D, = mnd I [2mn +2(nl)d], which gives the ratio of the area scanned to the total distance the two robots travel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0000569_robot.2001.932950-Figure6-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0000569_robot.2001.932950-Figure6-1.png",
        "caption": "Figure 6: Four-fingered 3D power grasp",
        "texts": [
            "977 (33) ft is also written as f t = z t + Hix\u2019 where Hi = HtP-\u2019 = 0 -1 0 0 0 -1 (34) -0.3086 -0.0706 -0.2578 . (35) i -0.3273 0.0999 0.3645 P = ( 0.0000 -0.4822 0.1322 Since the matrix Hi is sparse, it is not difficult to use Theorem 1 directly. Then f is NGF if -0.8473 < x i < 0.8473 -2.2071 < xi < 2.2071 -1.5669 < x; < 1.5669. These define a rectangular solid with eight vertices. The vertices transformed by 5s = P-lz\u2019 are identical to those in Eq. (33). 4.2 Three dimensional power grasp Consider the four fingered power grasp in Fig. 6. Each finger has three links and placed at every 90 degrees. The distal and middbs links of each finger are in contact with the grasped object (not shown). The number of contact points is b!i = 8 and the number of joints are L = 12. The dimensions of the matrices W , J , etc. are 1 , A E R18x24 w E ~ 6 x 2 4 J E ~ 2 4 x 1 2 H E ~ 2 4 x 6 , ~ E ~ : ! 4 x l ( i , Ht E R\u20196xG. There are 2688 combinations of linearly independent six rows in Ht among I ( ~ C ~ = 8008 possible combinations. Givenw,,t = ( 0 0 -1[N] 0 0 0 ) T 711 = 721 = 7:jl = 741 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002062_tasc.2005.849620-Figure1-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002062_tasc.2005.849620-Figure1-1.png",
        "caption": "Fig. 1. A magnetically levitated superconducting conveyer composed of four hybrid magnetic bearings.",
        "texts": [
            " Thus, noncontact conveyer systems are very beneficial to semiconductor manufacturing industry because the systems don\u2019t produce dust in vacuum chambers or clean rooms [3], [4]. If silicon wafers are carried by magnetically levitated conveyers in vacuum chambers or clean rooms, some processes are completed without any dust. Thus, our group has developed a prototype of a magnetically levitated conveyer that uses superconducting levitation technique for these clean environments. To realize a magnetically levitated conveyer, a displacement sensor using a Hall sensor is applied to the system. Fig. 1 shows a conveyer which is composed of a magnetically levitated stage and a conveying stage. The levitated stage is supposed to be in a clean room or a vacuum chamber. The levitated Manuscript received October 5, 2004. M. Komori is with the Department of Applied Science for Integrated System Engineering, Graduate School of Engineering, Kyushu Institute of Technology, Fukuoka 804-8550, Japan (e-mail: komori@ele.kyutech.ac.jp). G. Kamogawa was with Kyushu Institute of Technology, Fukuoka 840-8502, Japan",
            " Each Hall sensor is put on each superconductor to detect magnetic field. The permanent magnets (PMs) of the levitated stage are used to produce magnetic field. In the system, field cooling process for the superconductors is carried out to make a stable magnetic levitation of the levitated stage. Thus, the levitated stage is basically supported by the conveying stage, and the vibrations of the levitated stage are suppressed by the four coils. In order to simulate the dynamics for the hybrid magnetic bearing shown in Fig. 1, a simple dynamic model is assumed as shown in Fig. 2 [1]. The dynamic model for the hybrid magnetic bearing is composed of a superconductor (SC), a permanent magnet (PM), and a coil. Since the permanent magnet is supported by the superconductor due to its pinning force, a spring 1051-8223/$20.00 \u00a9 2005 IEEE with stiffness (72.8 N/m) and a damper with damping coefficient (0.043 Ns/m) are introduced. The dynamic model for the levitation system is written as (1) where is the displacement of the permanent magnet from the initial position, is the mass of the permanent magnet, is the control force, and is the disturbance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0003590_978-3-540-79486-8_34-Figure9-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0003590_978-3-540-79486-8_34-Figure9-1.png",
        "caption": "Fig. 9. Flight simulation Platform Mechanism",
        "texts": [
            " Reflecting on Aristotle\u2019s Politics and the analysis of what could be a robot body on the theatre stage, The Colonies [10] are a series of performances and installations where the robot shapes are solely derived from an assemblage of pre-existing mechanism found in assembly lines and industrial manipulators/robots. The initial intents of these robots shapes are purely functional and furthermore, these structures are mostly unknown to the average audience. Thus, the sign-design of the machine is not directly conveying nor commenting on any anthropomorphic entities. The perceived behaviors of these shapes are then primarily rooted in the sign-actions rather than the sign-design of their morphologies or representations (again as opposed to the Androids of the mid 18th century). Figure 9 shows the patent drawings of a simulation platform used as part of the body of the robotic performers of Le Proc\u00e8s (Fig. 1). Utilizing existing mechanisms to construct life-like objects brings us back to the paradox of the quasi-living objects of the robot history (see section 2). The theatrical play of signs can happen owing to a \u201cdouble\u201d quality of the space - that is physical (theatrical) stage and (dramatic) scene at the same time. Every-thing and everybody that is brought on this double-space room is transformed into its double-existence"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_28_0002768_9780470116883.ch2-Figure2.16-1.png",
        "original_path": "designv11-28/openalex_figure/designv11_28_0002768_9780470116883.ch2-Figure2.16-1.png",
        "caption": "Figure 2.16 (a) The propagation of a plane wave. (b) The electric and magnetic field of an x-directed planewave.",
        "texts": [
            "311) represents a transmission-line type of wave that propagates in the x-direction. Ey component is one of the field component that acts in a direction perpendicular to the direction of propagation of the wave. There is no variation of the field quantities in the plane perpendicular to the pro- pagation direction, therefore, the wave is simply called a plane wave. The expression for the forward wave from (2.311) can be written in the form Ey \u00bc E0e jkx \u00f02:312\u00de where E0 is the magnitude of the electric field. The corresponding plane wave is shown in Figure 2.16. Until now the time-harmonic variation ejot has been assumed but omitted. The complete solution for the forward wave is thus given by Ey \u00bc E0ej\u00f0ot kx\u00de \u00f02:313\u00de and the associated magnetic field is then Hz \u00bc H0ej\u00f0ot kx\u00de \u00bc E0 Z0 ej\u00f0ot kx\u00de \u00f02:314\u00de where Z0 \u00bc E0 H0 \u00bc ffiffiffi m e r \u00f02:315\u00de is the wave impedance of the medium. For free space, it is approximately Z0 \u00bc 120 p. Radiation of electromagnetic energy is an undesired leakage phenomenon or a desired process for exciting waves in space. If one deals with desired radiation, the goal is to excite electromagnetic waves from the given source in the required direction as efficiently as possible"
        ],
        "surrounding_texts": []
    }
]